From fd6fbb3ce09c46abb2d4f4304c7c17bcd7675c0f Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 11 Oct 2020 21:40:39 -0400
Subject: [PATCH 01/57] Text update and docstring fix.

---
 andes/system.py          |  9 ++++++---
 docs/source/modeling.rst |  2 +-
 docs/source/tutorial.rst | 10 +++++-----
 3 files changed, 12 insertions(+), 9 deletions(-)

diff --git a/andes/system.py b/andes/system.py
index d0f84766d..b00a3171e 100644
--- a/andes/system.py
+++ b/andes/system.py
@@ -989,9 +989,9 @@ def find_models(self, flag: Optional[Union[str, Tuple]], skip_zero: bool = True)
 
     def dill(self):
         """
-        Serialize generated numerical functions in `System.calls` with package `dill`.
+        Serialize generated numerical functions in ``System.calls`` with package ``dill``.
 
-        The serialized file will be stored to ``~/andes/calls.pkl``, where `~` is the home directory path.
+        The serialized file will be stored to ``~/.andes/calls.pkl``, where `~` is the home directory path.
 
         Notes
         -----
@@ -1008,6 +1008,9 @@ def dill(self):
 
     @staticmethod
     def _load_pkl():
+        """
+        Helper function to open and load dill-pickled functions.
+        """
         import dill
         dill.settings['recurse'] = True
         pkl_path = get_pkl_path()
@@ -1027,7 +1030,7 @@ def _load_pkl():
 
     def undill(self):
         """
-        Deserialize the function calls from ``~/andes.calls.pkl`` with dill.
+        Deserialize the function calls from ``~/.andes/calls.pkl`` with ``dill``.
 
         If no change is made to models, future calls to ``prepare()`` can be replaced with ``undill()`` for
         acceleration.
diff --git a/docs/source/modeling.rst b/docs/source/modeling.rst
index 6a058bef5..3ac7ad67b 100644
--- a/docs/source/modeling.rst
+++ b/docs/source/modeling.rst
@@ -48,7 +48,7 @@ It takes several seconds up to a minute to finish the generation.
 .. warning::
     When models are modified (such as adding new models or changing equation strings), code generation needs
     to be executed again for consistency. It can be more conveniently triggered from command line with
-    ``andes prepare -qi``.
+    ``andes prepare -i``.
 
 .. autofunction:: andes.system.System.prepare
     :noindex:
diff --git a/docs/source/tutorial.rst b/docs/source/tutorial.rst
index 85a658fd3..b195711b2 100644
--- a/docs/source/tutorial.rst
+++ b/docs/source/tutorial.rst
@@ -94,14 +94,14 @@ Generated code are stored in the folder ``.andes/calls.pkl`` in your home direct
 In addition, ``andes selftest`` implicitly calls the code generation.
 If you are using ANDES as a package in the user mode, you won't need to call it again.
 
-For developers, ``andes prepare`` needs to be called immediately following any model equation
-modification. Otherwise, simulation results will not reflect the new equations and will likely lead to an error.
-
 Option ``-q`` or ``--quick`` (enabled by default) can be used to speed up the code generation.
 It skips the generation of :math:`\LaTeX`-formatted equations, which are only used in documentation and the interactive
 mode.
 
-Option ``-i`` or ``--incremental`` can be used to further speed up the code generation during model development.
+For developers, ``andes prepare`` needs to be called immediately following any model equation
+modification. Otherwise, simulation results will not reflect the new equations and will likely lead to an error.
+Option ``-i`` or ``--incremental``, instead of ``-q``, can be used to further speed up the code generation
+during model development.
 ``andes prepare -i`` only generates code for models with modified equations.
 
 andes run
@@ -247,7 +247,7 @@ For example, to convert ``case5.m`` into the ``xlsx`` format, run
 
     andes run case5.m --convert xlsx
 
-The output messages will look like
+The output messages will look like ::
 
     Parsing input file </Users/user/repos/andes/cases/matpower/case5.m>
     CASE5  Power flow data for modified 5 bus, 5 gen case based on PJM 5-bus system

From fcf8db8d2e4de955ffac7121cb5c86af712e9466 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 11 Oct 2020 21:42:03 -0400
Subject: [PATCH 02/57] Moved dill import to top level.

---
 andes/system.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/andes/system.py b/andes/system.py
index b00a3171e..8fc653993 100644
--- a/andes/system.py
+++ b/andes/system.py
@@ -18,6 +18,7 @@
 import os
 import sys
 import inspect
+import dill
 from collections import OrderedDict
 from typing import List, Dict, Tuple, Union, Optional
 
@@ -308,7 +309,6 @@ def _prepare_mp(self, quick=False):
         Function is not working. Serialization failed for `conj`.
         """
         from andes.shared import Pool
-        import dill
         dill.settings['recurse'] = True
 
         # consistency check for group parameters and variables
@@ -999,7 +999,6 @@ def dill(self):
 
         """
         logger.debug("Dumping calls to calls.pkl with dill")
-        import dill
         dill.settings['recurse'] = True
 
         pkl_path = get_pkl_path()
@@ -1011,7 +1010,6 @@ def _load_pkl():
         """
         Helper function to open and load dill-pickled functions.
         """
-        import dill
         dill.settings['recurse'] = True
         pkl_path = get_pkl_path()
 

From c6660be6934612654c3628746cf52ad137cb2439 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 11 Oct 2020 21:42:58 -0400
Subject: [PATCH 03/57] Removed unneeded model jit code.

---
 andes/system.py | 8 --------
 1 file changed, 8 deletions(-)

diff --git a/andes/system.py b/andes/system.py
index 8fc653993..2aeec09e9 100644
--- a/andes/system.py
+++ b/andes/system.py
@@ -1223,7 +1223,6 @@ def import_models(self):
 
         ``system.models['Bus']`` points the same instance as ``system.Bus``.
         """
-        # non-JIT models
         for file, cls_list in file_classes.items():
             for model_name in cls_list:
                 the_module = importlib.import_module('andes.models.' + file)
@@ -1236,13 +1235,6 @@ def import_models(self):
                 group_name = self.__dict__[model_name].group
                 self.__dict__[group_name].add_model(model_name, self.__dict__[model_name])
 
-        # *** JIT import code ***
-        # import JIT models
-        # for file, pair in jits.items():
-        #     for cls, name in pair.items():
-        #         self.__dict__[name] = JIT(self, file, cls, name)
-        # ***********************
-
     def import_routines(self):
         """
         Import routines as defined in ``routines/__init__.py``.

From cfcb09ec62a2af233e60baa64da06ded18513fbd Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 11 Oct 2020 21:44:31 -0400
Subject: [PATCH 04/57] Added docs.

---
 andes/system.py | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/andes/system.py b/andes/system.py
index 2aeec09e9..80ca6fa11 100644
--- a/andes/system.py
+++ b/andes/system.py
@@ -1358,6 +1358,10 @@ def _store_calls(self):
             self.calls[name] = mdl.calls
 
     def _list2array(self):
+        """
+        Helper function to call models' ``list2array`` method, which
+        usually performs memory preallocation.
+        """
         self.call_models('list2array', self.models)
 
     def set_config(self, config=None):

From 1d76564c8198c8e241c82108c4ca7a620da9e98e Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 12 Oct 2020 11:19:25 -0400
Subject: [PATCH 05/57] Patch numba jit issue on generated pycode.

---
 andes/core/model.py     | 23 ++++++++++++++---------
 andes/routines/pflow.py |  2 +-
 2 files changed, 15 insertions(+), 10 deletions(-)

diff --git a/andes/core/model.py b/andes/core/model.py
index 147ebd6d7..154171081 100644
--- a/andes/core/model.py
+++ b/andes/core/model.py
@@ -14,7 +14,7 @@
 import os
 import logging
 from collections import OrderedDict, defaultdict
-from typing import Iterable, Sized
+from typing import Iterable, Sized, Callable, Union
 
 from andes.core.common import ModelFlags, JacTriplet, Config
 from andes.core.discrete import Discrete
@@ -1621,22 +1621,27 @@ def numba_jitify(self, parallel=False, cache=False):
         if self.system.config.numba != 1:
             return
 
-        try:
-            import numba
-        except ImportError:
-            return
-
         if self.flags.jited is True:
             return
 
-        self.calls.f = numba.jit(self.calls.f, parallel=parallel, cache=cache)
-        self.calls.g = numba.jit(self.calls.g, parallel=parallel, cache=cache)
+        self.calls.f = self._jitify_func_only(self.calls.f, parallel=parallel, cache=cache)
+        self.calls.g = self._jitify_func_only(self.calls.g, parallel=parallel, cache=cache)
 
         for jname in self.calls.j:
-            self.calls.j[jname] = numba.jit(self.calls.j[jname], parallel=parallel, cache=cache)
+            self.calls.j[jname] = self._jitify_func_only(self.calls.j[jname],
+                                                         parallel=parallel, cache=cache)
 
         self.flags.jited = True
 
+    def _jitify_func_only(self, func: Union[Callable, None], parallel=False, cache=False):
+        try:
+            import numba
+        except ImportError:
+            return
+
+        if func is not None:
+            return numba.jit(func, parallel=parallel, cache=cache)
+
 
 class SymProcessor:
     """
diff --git a/andes/routines/pflow.py b/andes/routines/pflow.py
index 064256ce8..6b02cc8b5 100644
--- a/andes/routines/pflow.py
+++ b/andes/routines/pflow.py
@@ -64,6 +64,7 @@ def init(self):
         self.y_sol = None
 
         self.system.init(self.models, routine='pflow')
+        logger.info('Power flow initialized.')
 
         # force precompile if numba is on - improves timing accuracy
         if self.system.config.numba:
@@ -71,7 +72,6 @@ def init(self):
             self.system.g_update(self.models)
             self.system.j_update(models=self.models)
 
-        logger.info('Power flow initialized.')
         return self.system.dae.xy
 
     def nr_step(self):

From 46edc1e80c61593381d06e5e7a25f54840cf51d7 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 12 Oct 2020 11:31:52 -0400
Subject: [PATCH 06/57] Style fixes following pylint.

---
 andes/routines/pflow.py | 20 ++++++++++++--------
 1 file changed, 12 insertions(+), 8 deletions(-)

diff --git a/andes/routines/pflow.py b/andes/routines/pflow.py
index 6b02cc8b5..0cc523522 100644
--- a/andes/routines/pflow.py
+++ b/andes/routines/pflow.py
@@ -1,3 +1,8 @@
+"""
+Module for power flow calculation.
+"""
+
+import logging
 from collections import OrderedDict
 
 from andes.utils.misc import elapsed
@@ -5,7 +10,6 @@
 from andes.variables.report import Report
 from andes.shared import np, matrix, sparse, newton_krylov, IP_ADD
 
-import logging
 logger = logging.getLogger(__name__)
 
 
@@ -162,18 +166,18 @@ def run(self, **kwargs):
         self.niter = 0
         while True:
             mis = self.nr_step()
-            logger.info(f'{self.niter}: |F(x)| = {mis:<10g}')
+            logger.info('%d: |F(x)| = %.10g', self.niter, mis)
 
             if mis < self.config.tol:
                 self.converged = True
                 break
-            elif self.niter > self.config.max_iter:
+            if self.niter > self.config.max_iter:
                 break
-            elif np.isnan(mis).any():
+            if np.isnan(mis).any():
                 logger.error('NaN found in solution. Convergence not likely')
                 self.niter = self.config.max_iter + 1
                 break
-            elif mis > 1e4 * self.mis[0]:
+            if mis > 1e4 * self.mis[0]:
                 logger.error('Mismatch increased too fast. Convergence not likely.')
                 break
             self.niter += 1
@@ -185,12 +189,12 @@ def run(self, **kwargs):
                 max_idx = np.argmax(np.abs(system.dae.xy))
                 name = system.dae.xy_name[max_idx]
                 logger.error('Mismatch is not correctable possibly due to large load-generation imbalance.')
-                logger.error(f'Largest mismatch on equation associated with <{name}>')
+                logger.error('Largest mismatch on equation associated with <%s>', name)
             else:
-                logger.error(f'Power flow failed after {self.niter + 1} iterations for {system.files.case}.')
+                logger.error('Power flow failed after %d iterations for "%s".', self.niter + 1, system.files.case)
 
         else:
-            logger.info(f'Converged in {self.niter+1} iterations in {s1}.')
+            logger.info('Converged in %d iterations in %s.', self.niter + 1, s1)
 
             # make a copy of power flow solutions
             self.x_sol = system.dae.x.copy()

From b0b83114d61b62d6ba41fa1ee4a84c2c716ff37c Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 12 Oct 2020 11:47:21 -0400
Subject: [PATCH 07/57] Style fix.

---
 andes/routines/base.py |  4 +--
 andes/routines/eig.py  | 59 +++++++++++++++++++++---------------------
 2 files changed, 31 insertions(+), 32 deletions(-)

diff --git a/andes/routines/base.py b/andes/routines/base.py
index 15a682aa6..935087edb 100644
--- a/andes/routines/base.py
+++ b/andes/routines/base.py
@@ -43,8 +43,8 @@ def init(self):
     def run(self, **kwargs):
         raise NotImplementedError
 
-    def summary(self):
+    def summary(self, **kwargs):
         raise NotImplementedError
 
-    def report(self):
+    def report(self, **kwargs):
         raise NotImplementedError
diff --git a/andes/routines/eig.py b/andes/routines/eig.py
index bb78384d1..87c327c35 100644
--- a/andes/routines/eig.py
+++ b/andes/routines/eig.py
@@ -1,13 +1,18 @@
-import logging
-import scipy.io
+"""
+Module for eigenvalue analysis.
+"""
 
+import logging
 from math import ceil, pi
+
+import scipy.io
 from cvxopt import mul, div, spdiag
 from cvxopt.lapack import gesv
 
 from andes.io.txt import dump_data
 from andes.utils.misc import elapsed
 from andes.routines.base import BaseRoutine
+from andes.variables.report import report_info
 from andes.shared import np, matrix, spmatrix, plt, mpl
 from andes.plot import set_latex
 
@@ -142,10 +147,10 @@ def run(self, **kwargs):
         if system.PFlow.converged is False:
             logger.warning('Power flow not solved. Eig analysis will not continue.')
             return succeed
-        else:
-            if system.TDS.initialized is False:
-                system.TDS.init()
-                system.TDS._itm_step()
+
+        if system.TDS.initialized is False:
+            system.TDS.init()
+            system.TDS._itm_step()
 
         if system.dae.n == 0:
             logger.error('No dynamic model. Eig analysis will not continue.')
@@ -153,7 +158,7 @@ def run(self, **kwargs):
         else:
             if sum(system.dae.Tf != 0) != len(system.dae.Tf):
                 self.singular_idx = np.argwhere(np.equal(system.dae.Tf, 0.0)).ravel().astype(int)
-                logger.info(f"System contains {len(self.singular_idx)} zero time constants. ")
+                logger.info("System contains %d zero time constants. ", len(self.singular_idx))
                 logger.debug([system.dae.x_name[i] for i in self.singular_idx])
 
             self.x_name = np.array(system.dae.x_name)
@@ -183,6 +188,9 @@ def run(self, **kwargs):
 
     def plot(self, mu=None, fig=None, ax=None, left=-6, right=0.5, ymin=-8, ymax=8, damping=0.05,
              line_width=0.5, dpi=150, show=True, latex=True):
+        """
+        Plot utility for eigenvalues in the S domain.
+        """
         mpl.rc('font', family='Times New Roman', size=12)
 
         if mu is None:
@@ -206,11 +214,10 @@ def plot(self, mu=None, fig=None, ax=None, left=-6, right=0.5, ymin=-8, ymax=8,
 
         if len(p_mu_real) > 0:
             logger.warning(
-                'System is not stable due to {} positive eigenvalues.'.format(
-                    len(p_mu_real)))
+                'System is not stable due to %d positive eigenvalues.', len(p_mu_real))
         else:
             logger.info(
-                'System is small-signal stable in the initial neighbourhood.')
+                'System is small-signal stable in the initial neighborhood.')
 
         set_latex(latex)
 
@@ -257,33 +264,25 @@ def export_state_matrix(self):
                'x_tex_name': np.array(system.dae.x_tex_name, dtype=np.object),
                }
         scipy.io.savemat(system.files.mat, mdict=out)
-        logger.info(f'State matrix saved to "{system.files.mat}".')
+        logger.info('State matrix saved to "%s"', system.files.mat)
         return True
 
-    def report(self, x_name=None):
+    def report(self, x_name=None, **kwargs):
         """
-        Save eigenvalue analysis reports
+        Save eigenvalue analysis reports.
 
         Returns
         -------
         None
         """
-        from andes.variables.report import report_info
-
-        system = self.system
-        mu = self.mu
-        part_fact = self.part_fact
         if x_name is None:
             x_name = self.x_name
 
-        text = []
-        header = []
-        rowname = []
-        data = []
+        text, header, rowname, data = list(), list(), list(), list()
 
-        neig = len(mu)
-        mu_real = mu.real()
-        mu_imag = mu.imag()
+        neig = len(self.mu)
+        mu_real = self.mu.real()
+        mu_imag = self.mu.imag()
         n_positive = sum(1 for x in mu_real if x > 0)
         n_zeros = sum(1 for x in mu_real if x == 0)
         n_negative = sum(1 for x in mu_real if x < 0)
@@ -302,7 +301,7 @@ def report(self, x_name=None):
         freq = [0] * neig
         ufreq = [0] * neig
         damping = [0] * neig
-        for idx, item in enumerate(mu):
+        for idx, item in enumerate(self.mu):
             if item.imag == 0:
                 freq[idx] = 0
                 ufreq[idx] = 0
@@ -315,7 +314,7 @@ def report(self, x_name=None):
         # obtain most associated variables
         var_assoc = []
         for prow in range(neig):
-            temp_row = part_fact[prow, :]
+            temp_row = self.part_fact[prow, :]
             name_idx = list(temp_row).index(max(temp_row))
             var_assoc.append(x_name[name_idx])
 
@@ -323,7 +322,7 @@ def report(self, x_name=None):
         for prow in range(neig):
             temp_row = []
             for pcol in range(neig):
-                temp_row.append(round(part_fact[prow, pcol], 5))
+                temp_row.append(round(self.part_fact[prow, pcol], 5))
             pf.append(temp_row)
 
         # opening info section
@@ -372,5 +371,5 @@ def report(self, x_name=None):
                 rowname.append(x_name)
                 data.append(pf[start:end])
 
-        dump_data(text, header, rowname, data, system.files.eig)
-        logger.info(f'Report saved to "{system.files.eig}".')
+        dump_data(text, header, rowname, data, self.system.files.eig)
+        logger.info('Report saved to "%s".', self.system.files.eig)

From c6abed77f34633c82abfb398b4664aa581bf56c7 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 12 Oct 2020 12:07:58 -0400
Subject: [PATCH 08/57] Some style fixes.

---
 andes/routines/tds.py | 114 +++++++++++++++++++++++-------------------
 1 file changed, 63 insertions(+), 51 deletions(-)

diff --git a/andes/routines/tds.py b/andes/routines/tds.py
index cbb2f2f63..4ce403c55 100644
--- a/andes/routines/tds.py
+++ b/andes/routines/tds.py
@@ -1,7 +1,12 @@
+"""
+ANDES module for time-domain simulation.
+"""
+
 import sys
 import os
 import time
 import importlib
+import logging
 from collections import OrderedDict
 
 from andes.routines.base import BaseRoutine
@@ -10,7 +15,6 @@
 from andes.shared import tqdm, np, pd
 from andes.shared import matrix, sparse, spdiag
 
-import logging
 logger = logging.getLogger(__name__)
 
 
@@ -102,6 +106,13 @@ def __init__(self, system=None, config=None):
         self.qrt_start = None
         self.headroom = 0.0
 
+        # internal storage for iterations
+        self.x0 = None
+        self.y0 = None
+        self.f0 = None
+        self.Ac = None
+        self.inc = None
+
     def init(self):
         """
         Initialize the status, storage and values for TDS.
@@ -170,9 +181,9 @@ def init(self):
         _, s1 = elapsed(t0)
 
         if self.initialized is True:
-            logger.info(f"Initialization for dynamics was successful in {s1}.")
+            logger.info("Initialization for dynamics was successful in %s.", s1)
         else:
-            logger.error(f"Initialization for dynamics failed in {s1}.")
+            logger.error("Initialization for dynamics failed in %s.", s1)
 
         if system.dae.n == 0:
             tqdm.write('No dynamic component loaded.')
@@ -300,7 +311,7 @@ def run(self, no_pbar=False, no_summary=False, **kwargs):
 
                     # if the ending time has passed
                     if time.time() - rt_end > 0:
-                        logger.debug(f'Simulation over-run at t={dae.t:4.4g} s.')
+                        logger.debug('Simulation over-run at t=%4.4g s.', dae.t)
                     else:
                         self.headroom += (rt_end - time.time())
 
@@ -320,7 +331,7 @@ def run(self, no_pbar=False, no_summary=False, **kwargs):
 
         if self.busted:
             logger.error(self.err_msg)
-            logger.error(f"Simulation terminated at t={system.dae.t:.4f}.")
+            logger.error("Simulation terminated at t=%.4f s.", system.dae.t)
             system.exit_code += 1
         elif system.dae.t == self.config.tf:
             succeed = True   # success flag
@@ -329,10 +340,10 @@ def run(self, no_pbar=False, no_summary=False, **kwargs):
             system.exit_code += 1
 
         _, s1 = elapsed(t0)
-        logger.info(f'Simulation completed in {s1}.')
+        logger.info('Simulation completed in %s.', s1)
 
         if config.qrt:
-            logger.debug(f'QRT headroom time: {self.headroom} s.')
+            logger.debug('QRT headroom time: %.4g s.', self.headroom)
 
         system.TDS.save_output()
 
@@ -648,26 +659,27 @@ def test_init(self):
         if np.max(np.abs(system.dae.fg)) < self.config.tol:
             logger.debug('Initialization tests passed.')
             return True
-        else:
 
-            fail_idx = np.where(abs(system.dae.fg) >= self.config.tol)
-            fail_names = [system.dae.xy_name[int(i)] for i in np.ravel(fail_idx)]
+        # otherwise, show suspect initialization error
+        fail_idx = np.where(abs(system.dae.fg) >= self.config.tol)
+        fail_names = [system.dae.xy_name[int(i)] for i in np.ravel(fail_idx)]
 
-            title = 'Suspect initialization issue! Simulation may crash!'
-            err_data = {'Name': fail_names,
-                        'Var. Value': system.dae.xy[fail_idx],
-                        'Eqn. Mismatch': system.dae.fg[fail_idx],
-                        }
-            tab = Tab(title=title,
-                      header=err_data.keys(),
-                      data=list(map(list, zip(*err_data.values()))))
+        title = 'Suspect initialization issue! Simulation may crash!'
+        err_data = {'Name': fail_names,
+                    'Var. Value': system.dae.xy[fail_idx],
+                    'Eqn. Mismatch': system.dae.fg[fail_idx],
+                    }
+        tab = Tab(title=title,
+                  header=err_data.keys(),
+                  data=list(map(list, zip(*err_data.values()))),
+                  )
 
-            logger.error(tab.draw())
+        logger.error(tab.draw())
 
-            if system.options.get('verbose') == 1:
-                breakpoint()
-            system.exit_code += 1
-            return False
+        if system.options.get('verbose') == 1:
+            breakpoint()
+        system.exit_code += 1
+        return False
 
     def save_output(self, npz=True):
         """
@@ -685,19 +697,18 @@ def save_output(self, npz=True):
         """
         if self.system.files.no_output:
             return False
-        else:
-            t0, _ = elapsed()
 
-            self.system.dae.write_lst(self.system.files.lst)
+        t0, _ = elapsed()
 
-            if npz is True:
-                self.system.dae.write_npz(self.system.files.npz)
-            else:
-                self.system.dae.write_npy(self.system.files.npy)
+        self.system.dae.write_lst(self.system.files.lst)
+        if npz is True:
+            self.system.dae.write_npz(self.system.files.npz)
+        else:
+            self.system.dae.write_npy(self.system.files.npy)
 
-            _, s1 = elapsed(t0)
-            logger.info(f'TDS outputs saved in {s1}.')
-            return True
+        _, s1 = elapsed(t0)
+        logger.info('TDS outputs saved in %s.', s1)
+        return True
 
     def do_switch(self):
         """
@@ -782,19 +793,21 @@ def _load_pert(self):
         Load perturbation files to ``self.callpert``.
         """
         system = self.system
-        if system.files.pert:
-            if not os.path.isfile(system.files.pert):
-                logger.warning(f'Pert file not found at "{system.files.pert}".')
-                return False
-
-            sys.path.append(system.files.case_path)
-            _, full_name = os.path.split(system.files.pert)
-            name, ext = os.path.splitext(full_name)
-
-            module = importlib.import_module(name)
-            self.callpert = getattr(module, 'pert')
-            logger.info(f'Perturbation file "{system.files.pert}" loaded.')
-            return True
+        if not system.files.pert:
+            return False
+
+        if not os.path.isfile(system.files.pert):
+            logger.warning('Pert file not found at "%s".', system.files.pert)
+            return False
+
+        sys.path.append(system.files.case_path)
+        _, full_name = os.path.split(system.files.pert)
+        name, _ = os.path.splitext(full_name)
+
+        module = importlib.import_module(name)
+        self.callpert = getattr(module, 'pert')
+        logger.info('Perturbation file "%s" loaded.', system.files.pert)
+        return True
 
     def _load_csv(self, csv_file):
         """
@@ -811,7 +824,7 @@ def _load_csv(self, csv_file):
         data = df.to_numpy()
 
         if data.ndim != 2:
-            raise ValueError("Data from CSV is not 2-dimentional (time versus variable)")
+            raise ValueError("Data from CSV is not 2-dimensional (time versus variable)")
         if data.shape[0] < 2:
             logger.warning("CSV data does not contain more than one time step.")
 
@@ -831,7 +844,8 @@ def _debug_g(self, y_idx):
             Index of the equation into the `g` array. Diff. eqns. are not counted in.
         """
         y_idx = y_idx.tolist()
-        logger.debug(f'Max. algebraic mismatch associated with {self.system.dae.y_name[y_idx]} [y_idx={y_idx}]')
+        logger.debug('Max. algebraic mismatch associated with <%s> [y_idx=%d]',
+                     self.system.dae.y_name[y_idx], y_idx)
         assoc_vars = self.system.dae.gy[y_idx, :]
         vars_idx = np.where(np.ravel(matrix(assoc_vars)))[0]
 
@@ -839,9 +853,7 @@ def _debug_g(self, y_idx):
         logger.debug(f'{"y_index":<10} {"Variable":<20} {"Derivative":<20}')
         for v in vars_idx:
             v = v.tolist()
-            logger.debug(f'{v:<10} {self.system.dae.y_name[v]:<20} {assoc_vars[v]:<20g}')
-
-        pass
+            logger.debug('%10d %20s %20g', v, self.system.dae.y_name[v], assoc_vars[v])
 
     def _debug_ac(self, xy_idx):
         """

From 41813765c8f223fe46428b3e2d9c24edfbd4fbe4 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 12 Oct 2020 12:49:17 -0400
Subject: [PATCH 09/57] Style fixes for links.

---
 andes/cases/GBnetwork/README.md | 2 +-
 andes/cases/ieee14/README.md    | 2 +-
 andes/cases/nordic44/README.md  | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/andes/cases/GBnetwork/README.md b/andes/cases/GBnetwork/README.md
index ac10babbd..c24e2574f 100644
--- a/andes/cases/GBnetwork/README.md
+++ b/andes/cases/GBnetwork/README.md
@@ -1,4 +1,4 @@
 GBnetwork power flow case downloaded from
-https://www.maths.ed.ac.uk/optenergy/NetworkData/fullGB/
+<https://www.maths.ed.ac.uk/optenergy/NetworkData/fullGB/>
 
 Dynamic data is randomly generated and does not represent the actual system.
diff --git a/andes/cases/ieee14/README.md b/andes/cases/ieee14/README.md
index ff1fba78b..859425af2 100644
--- a/andes/cases/ieee14/README.md
+++ b/andes/cases/ieee14/README.md
@@ -2,7 +2,7 @@ IEEE 14-Bus System
 
 Power flow data is created by J. Conto.
 
-Data is available at https://drive.google.com/drive/folders/0B7uS9L2Woq_7YzYzcGhXT2VQYXc
+Data is available at <https://drive.google.com/drive/folders/0B7uS9L2Woq_7YzYzcGhXT2VQYXc>
 
 Dynamic data is created by H. Cui for ANDES.
 
diff --git a/andes/cases/nordic44/README.md b/andes/cases/nordic44/README.md
index 97b1b1f2b..68d43081c 100644
--- a/andes/cases/nordic44/README.md
+++ b/andes/cases/nordic44/README.md
@@ -1,5 +1,5 @@
 Nordic 44-Bus System
 
-Source: https://github.com/ALSETLab/Nordic44-Nordpool/tree/master/nordic44/models
+Source: <https://github.com/ALSETLab/Nordic44-Nordpool/tree/master/nordic44/models>
 
 Most dynamic models in this system have not been supported.

From 6eecf2504a3771988357bda843b85ad3bcf68dc8 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 12 Oct 2020 12:57:54 -0400
Subject: [PATCH 10/57] Style fixes.

---
 andes/core/service.py | 11 +++++++++++
 andes/io/psse.py      |  2 +-
 andes/plot.py         |  2 +-
 andes/utils/func.py   |  4 ++--
 4 files changed, 15 insertions(+), 4 deletions(-)

diff --git a/andes/core/service.py b/andes/core/service.py
index 254011601..026426cda 100644
--- a/andes/core/service.py
+++ b/andes/core/service.py
@@ -173,6 +173,9 @@ def __init__(self,
         self.u = dummify(u)
 
     def check(self, **kwargs):
+        """
+        Check status and set event flags.
+        """
         if not np.all(self.v == self.u.v):
             self.owner.system.TDS.custom_event = True
             logger.debug(f"Event flag set at t={self.owner.system.dae.t:.6f} sec.")
@@ -255,6 +258,9 @@ def __init__(self,
         self.n_ext = 0  # number of extended events
 
     def assign_memory(self, n):
+        """
+        Assign memory for internal data.
+        """
         VarService.assign_memory(self, n)
         self.t_final = np.zeros_like(self.v)
         self.v_event = np.zeros_like(self.v)
@@ -265,6 +271,11 @@ def assign_memory(self, n):
             self.t_ext.v = np.ones_like(self.u.v) * self.t_ext.v
 
     def check(self, **kwargs):
+        """
+        Check if an extended event is in place.
+
+        Supplied as a ``v_numeric`` to ``VarService``.
+        """
         dae_t = self.owner.system.dae.t
 
         if dae_t == 0.0:
diff --git a/andes/io/psse.py b/andes/io/psse.py
index 6181e6628..d32abb215 100644
--- a/andes/io/psse.py
+++ b/andes/io/psse.py
@@ -153,7 +153,7 @@ def _read_dyr_dict(file):
     # concatenate multi-line device data
     input_concat_dict = defaultdict(list)
     multi_line = list()
-    for i, line in enumerate(input_list):
+    for line in input_list:
         if line == '':
             continue
         if '/' not in line:
diff --git a/andes/plot.py b/andes/plot.py
index dc0e16a12..33f143890 100644
--- a/andes/plot.py
+++ b/andes/plot.py
@@ -416,7 +416,7 @@ def guess_event_time(self):
     def bqplot_data(self, xdata, ydata, *, xheader=None, yheader=None, xlabel=None, ylabel=None,
                     left=None, right=None, ymin=None, ymax=None, legend=True, grid=False, fig=None,
                     latex=True, dpi=150, line_width=1.0, greyscale=False, savefig=None, save_format=None,
-                    show=True, title=None,
+                    title=None,
                     **kwargs):
         """
         Plot with ``bqplot``. Experimental and incomplete.
diff --git a/andes/utils/func.py b/andes/utils/func.py
index 173d39dde..f2f36a94b 100644
--- a/andes/utils/func.py
+++ b/andes/utils/func.py
@@ -10,8 +10,8 @@ def list_flatten(input_list):
     """
     if len(input_list) > 0 and isinstance(input_list[0], (list, np.ndarray)):
         return functools.reduce(operator.iconcat, input_list, [])
-    else:
-        return input_list
+
+    return input_list
 
 
 def interp_n2(t, x, y):

From 0638961e1206f7373a518687aefb45dd19e06fcc Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 15 Oct 2020 11:50:34 -0400
Subject: [PATCH 11/57] Minor debug msg edit.

---
 andes/routines/tds.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/andes/routines/tds.py b/andes/routines/tds.py
index 4ce403c55..ca7b16c90 100644
--- a/andes/routines/tds.py
+++ b/andes/routines/tds.py
@@ -872,8 +872,8 @@ def _debug_ac(self, xy_idx):
         eqns_idx = np.where(np.ravel(matrix(assoc_eqns)))[0]
         vars_idx = np.where(np.ravel(matrix(assoc_vars)))[0]
 
-        logger.debug(f'Max. correction is for variable {self.system.dae.xy_name[xy_idx]} [{xy_idx}]')
-        logger.debug(f'Associated equation value is {self.system.dae.fg[xy_idx]:<20g}')
+        logger.debug('Max. correction is for variable %s [%d]', self.system.dae.xy_name[xy_idx], xy_idx)
+        logger.debug('Associated equation value is %20g', self.system.dae.fg[xy_idx])
         logger.debug('')
 
         logger.debug(f'{"xy_index":<10} {"Equation":<20} {"Derivative":<20} {"Eq. Mismatch":<20}')

From 0162269277a1c29e6c5deedaac47da58daddcedb Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Fri, 16 Oct 2020 23:28:34 -0400
Subject: [PATCH 12/57] Changes `_itm_step` to `itm_step`.

---
 andes/routines/eig.py       |  2 +-
 andes/routines/tds.py       | 23 ++++++++++++++---------
 examples/5. profiling.ipynb |  4 ++--
 3 files changed, 17 insertions(+), 12 deletions(-)

diff --git a/andes/routines/eig.py b/andes/routines/eig.py
index 87c327c35..ec3d5eba9 100644
--- a/andes/routines/eig.py
+++ b/andes/routines/eig.py
@@ -150,7 +150,7 @@ def run(self, **kwargs):
 
         if system.TDS.initialized is False:
             system.TDS.init()
-            system.TDS._itm_step()
+            system.TDS.itm_step()
 
         if system.dae.n == 0:
             logger.error('No dynamic model. Eig analysis will not continue.')
diff --git a/andes/routines/tds.py b/andes/routines/tds.py
index ca7b16c90..9250ef02d 100644
--- a/andes/routines/tds.py
+++ b/andes/routines/tds.py
@@ -178,6 +178,11 @@ def init(self):
         # if `dae.n == 1`, `calc_h_first` depends on new `dae.gy`
         self.calc_h()
 
+        # allocate for internal variables
+        self.x0 = np.zeros_like(system.dae.x)
+        self.y0 = np.zeros_like(system.dae.y)
+        self.f0 = np.zeros_like(system.dae.f)
+
         _, s1 = elapsed(t0)
 
         if self.initialized is True:
@@ -281,7 +286,7 @@ def run(self, no_pbar=False, no_summary=False, **kwargs):
             step_status = False
             # call the stepping method of the integration method (or data replay)
             if self.data_csv is None:
-                step_status = self._itm_step()  # compute for the current step
+                step_status = self.itm_step()  # compute for the current step
             else:
                 step_status = self._csv_step()
 
@@ -357,7 +362,7 @@ def run(self, no_pbar=False, no_summary=False, **kwargs):
 
         return succeed
 
-    def _itm_step(self):
+    def itm_step(self):
         """
         Integrate with Implicit Trapezoidal Method (ITM) to the current time.
 
@@ -377,12 +382,12 @@ def _itm_step(self):
         self.niter = 0
         self.converged = False
 
-        self.x0 = np.array(dae.x)
-        self.y0 = np.array(dae.y)
-        self.f0 = np.array(dae.f)
+        self.x0[:] = dae.x
+        self.y0[:] = dae.y
+        self.f0[:] = dae.f
 
         while True:
-            self._fg_update(models=system.exist.pflow_tds)
+            self.fg_update(models=system.exist.pflow_tds)
 
             # lazy Jacobian update
 
@@ -647,7 +652,7 @@ def test_init(self):
         Update f and g to see if initialization is successful.
         """
         system = self.system
-        self._fg_update(system.exist.pflow_tds)
+        self.fg_update(system.exist.pflow_tds)
         system.j_update(models=system.exist.pflow_tds)
 
         # warn if variables are initialized at limits
@@ -751,7 +756,7 @@ def do_switch(self):
 
         return ret
 
-    def _fg_update(self, models):
+    def fg_update(self, models):
         """
         Update `f` and `g` equations.
         """
@@ -784,7 +789,7 @@ def _fg_wrapper(self, xy):
         system.dae.y[:] = xy[system.dae.n:]
         system.vars_to_models()
 
-        self._fg_update(system.exist.pflow_tds)
+        self.fg_update(system.exist.pflow_tds)
 
         return system.dae.fg
 
diff --git a/examples/5. profiling.ipynb b/examples/5. profiling.ipynb
index eec9ec03c..0322067b5 100644
--- a/examples/5. profiling.ipynb	
+++ b/examples/5. profiling.ipynb	
@@ -101,7 +101,7 @@
       "\n",
       "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
       "        1    0.007    0.007    1.597    1.597 /Users/hcui7/repos/andes/andes/routines/tds.py:160(run)\n",
-      "      602    0.104    0.000    1.533    0.003 /Users/hcui7/repos/andes/andes/routines/tds.py:251(_itm_step)\n",
+      "      602    0.104    0.000    1.533    0.003 /Users/hcui7/repos/andes/andes/routines/tds.py:251(itm_step)\n",
       "     2318    0.010    0.000    1.141    0.000 /Users/hcui7/repos/andes/andes/routines/tds.py:590(_fg_update)\n",
       "    11649    0.092    0.000    1.085    0.000 /Users/hcui7/repos/andes/andes/system.py:1014(call_models)\n",
       "     2323    0.002    0.000    0.596    0.000 /Users/hcui7/repos/andes/andes/system.py:700(g_update)\n",
@@ -375,7 +375,7 @@
     }
    ],
    "source": [
-    "%lprun -f ss.TDS._itm_step ss.TDS.run()"
+    "%lprun -f ss.TDS.itm_step ss.TDS.run()"
    ]
   },
   {

From 0c3045e3fa2baa4b43120af23686bfd93a6cc90d Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Fri, 16 Oct 2020 23:29:25 -0400
Subject: [PATCH 13/57] Added notes.

---
 docs/source/release-notes.rst | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/docs/source/release-notes.rst b/docs/source/release-notes.rst
index 463ef25ff..9866607bc 100644
--- a/docs/source/release-notes.rst
+++ b/docs/source/release-notes.rst
@@ -8,6 +8,9 @@ The APIs before v3.0.0 are in beta and may change without prior notice.
 
 v1.2 Notes
 ----------
+v1.2.2
+```````````````````
+- Renamed `TDS._itm_step` to `TDS.itm_step` as a public API.
 
 v1.2.1 (2020-10-11)
 ```````````````````

From 07e43cdaa11c14af647231f100df1b3191b46913 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 18 Oct 2020 16:41:07 -0400
Subject: [PATCH 14/57] Patch an issue for pert path.

---
 andes/routines/tds.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/andes/routines/tds.py b/andes/routines/tds.py
index 9250ef02d..59635bcdf 100644
--- a/andes/routines/tds.py
+++ b/andes/routines/tds.py
@@ -805,8 +805,10 @@ def _load_pert(self):
             logger.warning('Pert file not found at "%s".', system.files.pert)
             return False
 
-        sys.path.append(system.files.case_path)
-        _, full_name = os.path.split(system.files.pert)
+        pert_path, full_name = os.path.split(system.files.pert)
+        logger.debug('Pert file "%s" located at path %s', full_name, pert_path)
+
+        sys.path.append(pert_path)
         name, _ = os.path.splitext(full_name)
 
         module = importlib.import_module(name)

From 4ba92b2c5aa2ed7a6b94ac2372505a21017e3117 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 18 Oct 2020 17:57:31 -0400
Subject: [PATCH 15/57] Added tests for pert path.

---
 andes/cases/ieee14/pert.py |  7 +++++++
 tests/test_paths.py        | 28 ++++++++++++++++++++++++----
 2 files changed, 31 insertions(+), 4 deletions(-)
 create mode 100644 andes/cases/ieee14/pert.py

diff --git a/andes/cases/ieee14/pert.py b/andes/cases/ieee14/pert.py
new file mode 100644
index 000000000..ae10577b5
--- /dev/null
+++ b/andes/cases/ieee14/pert.py
@@ -0,0 +1,7 @@
+"""
+Empty pert file
+"""
+
+
+def pert(t, system):
+    pass
diff --git a/tests/test_paths.py b/tests/test_paths.py
index ee0b67a8c..8761529c6 100644
--- a/tests/test_paths.py
+++ b/tests/test_paths.py
@@ -8,16 +8,36 @@ class TestPaths(unittest.TestCase):
     def setUp(self) -> None:
         self.kundur = 'kundur/'
         self.matpower = 'matpower/'
+        self.ieee14 = andes.get_case("ieee14/ieee14.raw")
 
     def test_tree(self):
         list_cases(self.kundur, no_print=True)
         list_cases(self.matpower, no_print=True)
 
     def test_addfile_path(self):
-        ieee14 = andes.get_case("ieee14/ieee14.raw")
-        path, case = os.path.split(ieee14)
-        andes.load('ieee14.raw', addfile='ieee14.dyr', input_path=path, default_config=True)
+        path, case = os.path.split(self.ieee14)
+        andes.load('ieee14.raw', addfile='ieee14.dyr',
+                   input_path=path, default_config=True,
+                   )
 
-        andes.run('ieee14.raw', addfile='ieee14.dyr', input_path=path,
+        andes.run('ieee14.raw', addfile='ieee14.dyr',
+                  input_path=path,
                   no_output=True, default_config=True,
                   )
+
+    def test_pert_file(self):
+        path, case = os.path.split(self.ieee14)
+
+        # --- with pert file ---
+        ss = andes.run('ieee14.raw', pert='pert.py',
+                       input_path=path, no_output=True, default_config=True,
+                       )
+        ss.TDS.init()
+        self.assertIsNotNone(ss.TDS.callpert)
+
+        # --- without pert file ---
+        ss = andes.run('ieee14.raw',
+                       input_path=path, no_output=True, default_config=True,
+                       )
+        ss.TDS.init()
+        self.assertIsNone(ss.TDS.callpert)

From 67d033f2500959b0ac90726e6bdbb5d9eafae47c Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 19 Oct 2020 15:48:17 -0400
Subject: [PATCH 16/57] Moved PVD1 to distributed.py

---
 andes/models/__init__.py    |   5 +-
 andes/models/distributed.py | 221 ++++++++++++++++++++++++++++++++++++
 andes/models/renewable.py   | 170 ---------------------------
 3 files changed, 224 insertions(+), 172 deletions(-)
 create mode 100644 andes/models/distributed.py

diff --git a/andes/models/__init__.py b/andes/models/__init__.py
index 6becf2429..b2cb57a40 100644
--- a/andes/models/__init__.py
+++ b/andes/models/__init__.py
@@ -1,4 +1,4 @@
-from collections import OrderedDict  # NOQA
+from collections import OrderedDict
 
 
 # Notes:
@@ -22,6 +22,7 @@
     ('coi', ['COI', ]),
     ('dcbase', ['Node', 'Ground', 'R', 'L', 'C', 'RCp', 'RCs', 'RLs', 'RLCs', 'RLCp']),
     ('vsc', ['VSCShunt']),
-    ('renewable', ['REGCA1', 'REECA1', 'REPCA1', 'WTDTA1', 'WTDS', 'WTARA1', 'WTPTA1', 'WTTQA1', 'PVD1']),
+    ('renewable', ['REGCA1', 'REECA1', 'REPCA1', 'WTDTA1', 'WTDS', 'WTARA1', 'WTPTA1', 'WTTQA1']),
+    ('distributed', ['PVD1']),
     ('experimental', ['PI2', 'TestDB1', 'TestPI', 'TestLagAWFreeze']),
 ])
diff --git a/andes/models/distributed.py b/andes/models/distributed.py
new file mode 100644
index 000000000..55267be05
--- /dev/null
+++ b/andes/models/distributed.py
@@ -0,0 +1,221 @@
+"""
+Distributed energy resource models.
+"""
+
+from andes.core.model import Model, ModelData
+from andes.core.param import NumParam, IdxParam
+from andes.core.block import Lag, GainLimiter, DeadBand1  # NOQA
+from andes.core.var import ExtAlgeb, ExtState, Algeb, State  # NOQA
+
+from andes.core.service import ConstService, ExtService, FlagValue, DataSelect, DeviceFinder  # NOQA
+from andes.core.service import VarService, Replace  # NOQA
+from andes.core.service import NumSelect  # NOQA
+from andes.core.discrete import Switcher, Limiter  # NOQA
+
+
+class PVD1Data(ModelData):
+    """
+    Data for distributed PV.
+    """
+    def __init__(self):
+        ModelData.__init__(self)
+
+        self.bus = IdxParam(model='Bus',
+                            info="interface bus id",
+                            mandatory=True,
+                            )
+
+        self.gen = IdxParam(info="static generator index",
+                            mandatory=True,
+                            )
+
+        self.Sn = NumParam(default=100.0, tex_name='S_n',
+                           info='Model MVA base',
+                           unit='MVA',
+                           )
+
+        self.busf = IdxParam(info='Optional BusFreq idx',
+                             model='BusFreq',
+                             default=None,
+                             )
+
+        self.xc = NumParam(default=0.0, tex_name='x_c',
+                           info='coupling reactance',
+                           unit='p.u.',
+                           z=True,
+                           )
+
+        # --- parameters found from ESIG.energy ---
+        self.igreg = IdxParam(model='Bus',
+                              info='Remote bus idx for droop response, None for local',
+                              )
+
+        self.qmx = NumParam(default=0.33, tex_name='q_{mx}',
+                            info='Max. reactive power command',
+                            power=True,
+                            )
+
+        self.qmn = NumParam(default=-0.33, tex_name='q_{mn}',
+                            info='Min. reactive power command',
+                            power=True,
+                            )
+
+        self.v0 = NumParam(default=0.0, tex_name='v_0',
+                           info='Lower limit of deadband for Vdroop response',
+                           unit='pu',
+                           )
+        self.v1 = NumParam(default=0.0, tex_name='v_1',
+                           info='Upper limit of deadband for Vdroop response',
+                           unit='pu',
+                           )
+
+        self.dqdv = NumParam(default=0.0, tex_name='dq/dv',
+                             info='Q-V droop characteristics',
+                             power=True,
+                             )
+
+        self.fdbd = NumParam(default=-0.01, tex_name='f_{dbd}',
+                             info='frequency deviation deadband',
+                             )
+
+        self.ddn = NumParam(default=0.0, tex_name='D_{dn}',
+                            info='Gain after f deadband',
+                            )
+
+        self.ialim = NumParam(default=1.3, tex_name='I_{alim}',
+                              info='Apparent power limit',
+                              current=True,
+                              )
+
+        self.vt0 = NumParam(default=0.88, tex_name='V_{t0}',
+                            info='Voltage tripping response curve point 0',
+                            )
+
+        self.vt1 = NumParam(default=0.90, tex_name='V_{t1}',
+                            info='Voltage tripping response curve point 1',
+                            )
+
+        self.vt2 = NumParam(default=1.1, tex_name='V_{t2}',
+                            info='Voltage tripping response curve point 2',
+                            )
+
+        self.vt3 = NumParam(default=1.2, tex_name='V_{t3}',
+                            info='Voltage tripping response curve point 3',
+                            )
+
+        self.vrflag = NumParam(default=0.0, tex_name='z_{VR}',
+                               info='Voltage tripping is latching (0) or partially self-resetting (0-1)',
+                               )
+
+        self.ft0 = NumParam(default=59.5, tex_name='f_{t0}',
+                            info='Frequency tripping response curve point 0',
+                            )
+
+        self.ft1 = NumParam(default=59.7, tex_name='f_{t1}',
+                            info='Frequency tripping response curve point 1',
+                            )
+
+        self.ft2 = NumParam(default=60.3, tex_name='f_{t2}',
+                            info='Frequency tripping response curve point 2',
+                            )
+
+        self.ft3 = NumParam(default=60.5, tex_name='f_{t3}',
+                            info='Frequency tripping response curve point 3',
+                            )
+
+        self.frflag = NumParam(default=0.0, tex_name='z_{FR}',
+                               info='Frequency tripping is latching (0) or partially self-resetting (0-1)',
+                               )
+
+        self.tip = NumParam(default=0.02, tex_name='T_{ip}',
+                            info='Inverter active current lag time constant',
+                            unit='s',
+                            )
+
+        self.tiq = NumParam(default=0.02, tex_name='T_{iq}',
+                            info='Inverter reactive current lag time constant',
+                            unit='s',
+                            )
+
+
+class PVD1Model(Model):
+    """
+    Model implementation of PVD1.
+    """
+    def __init__(self, system, config):
+        Model.__init__(self, system, config)
+
+        self.flags.tds = True
+        self.group = 'DG'
+
+        self.buss = DataSelect(self.igreg, self.bus,
+                               info='selected bus (bus or igreg)',
+                               )
+
+        self.busfreq = DeviceFinder(self.busf, link=self.buss, idx_name='bus')
+
+        # initial voltages from selected bus
+        self.v = ExtAlgeb(model='Bus', src='v', indexer=self.buss, tex_name='V',
+                          info='bus (or igreg) terminal voltage',
+                          unit='p.u.',
+                          )
+
+        self.a = ExtAlgeb(model='Bus', src='a', indexer=self.buss, tex_name=r'\theta',
+                          info='bus (or igreg) phase angle',
+                          unit='rad.',
+                          )
+
+        self.p0 = ExtService(model='StaticGen',
+                             src='p',
+                             indexer=self.gen,
+                             tex_name='P_0',
+                             )
+        self.q0 = ExtService(model='StaticGen',
+                             src='q',
+                             indexer=self.gen,
+                             tex_name='Q_0',
+                             )
+        # frequency measurement variable `f`
+        self.f = ExtAlgeb(model='FreqMeasurement', src='f', indexer=self.busfreq, export=False,
+                          info='Bus frequency', unit='p.u.',
+                          )
+
+        # --- frequency branch ---
+        self.FL1 = Limiter(u=self.f, lower=self.ft0, upper=self.ft1,
+                           info='Under frequency comparer',
+                           )
+        self.FL2 = Limiter(u=self.f, lower=self.ft2, upper=self.ft3,
+                           info='Over frequency comparer',
+                           )
+
+        self.Kft01 = ConstService(v_str='1/(ft1 - ft0)', tex_name='K_{ft01}')
+
+        self.Ffl = Algeb(info='Coeff. for under frequency',
+                         v_str='FL1_zi * Kft01 * (f - ft0) + FL1_zu',
+                         e_str='FL1_zi * Kft01 * (f - ft0) + FL1_zu - Ffl',
+                         tex_name='F_{fl}',
+                         discrete=self.FL1,
+                         )
+
+        self.Kft23 = ConstService(v_str='-1/(ft2 - ft3)', tex_name='K_{ft23}')
+
+        self.Ffh = Algeb(info='Coeff. for over frequency',
+                         v_str='FL2_zl + FL2_zi * (1 + Kft23 * (ft2 - f))',
+                         e_str='FL2_zl + FL2_zi * (1 + Kft23 * (ft2 - f)) - Ffh',
+                         tex_name='F_{fh}',
+                         discrete=self.FL2,
+                         )
+
+
+class PVD1(PVD1Data, PVD1Model):
+    """
+    Distributed PV model. (TODO: work in progress)
+
+    Power rating specified in `Sn`.
+
+    Reference: ESIG, WECC Distributed and Small PV Plants Generic Model (PVD1), [Online],
+    Available: https://www.esig.energy/wiki-main-page/wecc-distributed-and-small-pv-plants-generic-model-pvd1/
+    """
+    def __init__(self, system, config):
+        PVD1Data.__init__(self)
+        PVD1Model.__init__(self, system, config)
diff --git a/andes/models/renewable.py b/andes/models/renewable.py
index d37a796a5..b073f74fc 100644
--- a/andes/models/renewable.py
+++ b/andes/models/renewable.py
@@ -2102,173 +2102,3 @@ class WTTQA1(WTTQA1Data, WTTQA1Model):
     def __init__(self, config, system):
         WTTQA1Data.__init__(self)
         WTTQA1Model.__init__(self, system, config)
-
-
-class PVD1Data(ModelData):
-    """
-    Data for distributed PV.
-    """
-    def __init__(self):
-        ModelData.__init__(self)
-
-        self.bus = IdxParam(model='Bus',
-                            info="interface bus id",
-                            mandatory=True,
-                            )
-
-        self.gen = IdxParam(info="static generator index",
-                            mandatory=True,
-                            )
-
-        self.Sn = NumParam(default=100.0, tex_name='S_n',
-                           info='Model MVA base',
-                           unit='MVA',
-                           )
-
-        self.xc = NumParam(default=0.0, tex_name='x_c',
-                           info='coupling reactance',
-                           unit='p.u.',
-                           z=True,
-                           )
-
-        self.igreg = IdxParam(model='Bus',
-                              info='Remote bus idx for droop response, None for local',
-                              )
-
-        self.qmx = NumParam(default=0.33, tex_name='q_{mx}',
-                            info='Max. reactive power command',
-                            power=True,
-                            )
-
-        self.qmn = NumParam(default=-0.33, tex_name='q_{mn}',
-                            info='Min. reactive power command',
-                            power=True,
-                            )
-
-        self.v0 = NumParam(default=0.0, tex_name='v_0',
-                           info='Lower limit of deadband for Vdroop response',
-                           unit='pu',
-                           )
-        self.v1 = NumParam(default=0.0, tex_name='v_1',
-                           info='Upper limit of deadband for Vdroop response',
-                           unit='pu',
-                           )
-
-        self.dqdv = NumParam(default=0.0, tex_name='dq/dv',
-                             info='Q-V droop characteristics',
-                             power=True,
-                             )
-
-        self.fdbd = NumParam(default=-0.01, tex_name='f_{dbd}',
-                             info='frequency deviation deadband',
-                             )
-
-        self.ddn = NumParam(default=0.0, tex_name='D_{dn}',
-                            info='Gain after f deadband',
-                            )
-
-        self.ialim = NumParam(default=1.3, tex_name='I_{alim}',
-                              info='Apparent power limit',
-                              current=True,
-                              )
-
-        self.vt0 = NumParam(default=0.88, tex_name='V_{t0}',
-                            info='Voltage tripping response curve point 0',
-                            )
-
-        self.vt1 = NumParam(default=0.90, tex_name='V_{t1}',
-                            info='Voltage tripping response curve point 1',
-                            )
-
-        self.vt2 = NumParam(default=1.1, tex_name='V_{t2}',
-                            info='Voltage tripping response curve point 2',
-                            )
-
-        self.vt3 = NumParam(default=1.2, tex_name='V_{t3}',
-                            info='Voltage tripping response curve point 3',
-                            )
-
-        self.vrflag = NumParam(default=0.0, tex_name='z_{VR}',
-                               info='Voltage tripping is latching (0) or partially self-resetting (0-1)',
-                               )
-
-        self.ft0 = NumParam(default=59.5, tex_name='f_{t0}',
-                            info='Frequency tripping response curve point 0',
-                            )
-
-        self.ft1 = NumParam(default=59.7, tex_name='f_{t1}',
-                            info='Frequency tripping response curve point 1',
-                            )
-
-        self.ft2 = NumParam(default=60.3, tex_name='f_{t2}',
-                            info='Frequency tripping response curve point 2',
-                            )
-
-        self.ft3 = NumParam(default=60.5, tex_name='f_{t3}',
-                            info='Frequency tripping response curve point 3',
-                            )
-
-        self.frflag = NumParam(default=0.0, tex_name='z_{FR}',
-                               info='Frequency tripping is latching (0) or partially self-resetting (0-1)',
-                               )
-
-        self.tip = NumParam(default=0.02, tex_name='T_{ip}',
-                            info='Inverter active current lag time constant',
-                            unit='s',
-                            )
-
-        self.tiq = NumParam(default=0.02, tex_name='T_{iq}',
-                            info='Inverter reactive current lag time constant',
-                            unit='s',
-                            )
-
-
-class PVD1Model(Model):
-    """
-    Model implementation of PVD1.
-    """
-    def __init__(self, system, config):
-        Model.__init__(self, system, config)
-
-        self.flags.tds = True
-        self.group = 'DG'
-
-        self.buss = DataSelect(self.igreg, self.bus,
-                               info='selected bus (bus or igreg)',
-                               )
-
-        # initial voltages from selected bus
-        self.v = ExtAlgeb(model='Bus', src='v', indexer=self.buss, tex_name='V',
-                          info='bus (or igreg) terminal voltage',
-                          unit='p.u.',
-                          )
-
-        self.a = ExtAlgeb(model='Bus', src='a', indexer=self.buss, tex_name=r'\theta',
-                          info='bus (or igreg) phase angle',
-                          unit='rad.',
-                          )
-
-        self.p0 = ExtService(model='StaticGen',
-                             src='p',
-                             indexer=self.gen,
-                             tex_name='P_0',
-                             )
-        self.q0 = ExtService(model='StaticGen',
-                             src='q',
-                             indexer=self.gen,
-                             tex_name='Q_0',
-                             )
-
-
-class PVD1(PVD1Data, PVD1Model):
-    """
-    Distributed PV model. (TODO: work in progress)
-
-    Power rating specified in `Sn`.
-
-    Reference: ESIG, WECC Distributed and Small PV Plants Generic Model (PVD1), [Online],
-    Available: https://www.esig.energy/wiki-main-page/wecc-distributed-and-small-pv-plants-generic-model-pvd1/
-    """
-    def __init__(self, system, config):
-        PVD1Data.__init__(self)
-        PVD1Model.__init__(self, system, config)

From 369dd7ea87789379c6c0eadf0626c82a494307f5 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 19 Oct 2020 16:33:05 -0400
Subject: [PATCH 17/57] PVD1 implements frequency droop.

---
 andes/models/distributed.py | 36 ++++++++++++++++++++++++++++++------
 1 file changed, 30 insertions(+), 6 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 55267be05..ca1f3f11e 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -34,6 +34,11 @@ def __init__(self):
                            unit='MVA',
                            )
 
+        self.fn = NumParam(default=60.0, tex_name='f_n',
+                           info='nominal frequency',
+                           unit='Hz',
+                           )
+
         self.busf = IdxParam(info='Optional BusFreq idx',
                              model='BusFreq',
                              default=None,
@@ -180,19 +185,26 @@ def __init__(self, system, config):
                           info='Bus frequency', unit='p.u.',
                           )
 
+        self.fHz = Algeb(info='frequency in Hz',
+                         v_str='fn * f', e_str='fn * f - fHz',
+                         unit='Hz',
+                         )
+
         # --- frequency branch ---
-        self.FL1 = Limiter(u=self.f, lower=self.ft0, upper=self.ft1,
+        self.FL1 = Limiter(u=self.fHz, lower=self.ft0, upper=self.ft1,
                            info='Under frequency comparer',
                            )
-        self.FL2 = Limiter(u=self.f, lower=self.ft2, upper=self.ft3,
+        self.FL2 = Limiter(u=self.fHz, lower=self.ft2, upper=self.ft3,
                            info='Over frequency comparer',
                            )
+        self.FL1.no_warn = True
+        self.FL2.no_warn = True
 
         self.Kft01 = ConstService(v_str='1/(ft1 - ft0)', tex_name='K_{ft01}')
 
         self.Ffl = Algeb(info='Coeff. for under frequency',
-                         v_str='FL1_zi * Kft01 * (f - ft0) + FL1_zu',
-                         e_str='FL1_zi * Kft01 * (f - ft0) + FL1_zu - Ffl',
+                         v_str='FL1_zi * Kft01 * (fHz - ft0) + FL1_zu',
+                         e_str='FL1_zi * Kft01 * (fHz - ft0) + FL1_zu - Ffl',
                          tex_name='F_{fl}',
                          discrete=self.FL1,
                          )
@@ -200,11 +212,23 @@ def __init__(self, system, config):
         self.Kft23 = ConstService(v_str='-1/(ft2 - ft3)', tex_name='K_{ft23}')
 
         self.Ffh = Algeb(info='Coeff. for over frequency',
-                         v_str='FL2_zl + FL2_zi * (1 + Kft23 * (ft2 - f))',
-                         e_str='FL2_zl + FL2_zi * (1 + Kft23 * (ft2 - f)) - Ffh',
+                         v_str='FL2_zl + FL2_zi * (1 + Kft23 * (ft2 - fHz))',
+                         e_str='FL2_zl + FL2_zi * (1 + Kft23 * (ft2 - fHz)) - Ffh',
                          tex_name='F_{fh}',
                          discrete=self.FL2,
                          )
+        self.Fdev = Algeb(info='Frequency deviation',
+                          v_str='fn - fHz', e_str='fn - fHz - Fdev',
+                          unit='Hz', tex_name='f_{dev}',
+                          )
+
+        self.Dfdbd = ConstService(v_str='fdbd * ddn', info='Deadband lower limit after gain',
+                                  tex_name='D_{fdbd}',
+                                  )
+        self.DB = DeadBand1(u=self.Fdev, center=0.0, lower=self.Dfdbd, upper=0.0,
+                            info='frequency deviation deadband with gain',
+                            )  # outputs   `Pdrp`
+        self.DB.db.no_warn = True
 
 
 class PVD1(PVD1Data, PVD1Model):

From 94a27971ad4c2140da3de94dba8b94133585fdb1 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 19 Oct 2020 17:39:45 -0400
Subject: [PATCH 18/57] Added `no_warn` for Limiter.

---
 andes/core/discrete.py | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/andes/core/discrete.py b/andes/core/discrete.py
index 86d8cf592..33c0dbca6 100644
--- a/andes/core/discrete.py
+++ b/andes/core/discrete.py
@@ -203,8 +203,10 @@ class Limiter(Discrete):
         True to only use the upper limit
     no_upper : bool
         True to only use the lower limit
-    equal: bool
+    equal : bool
         True to include equal signs in comparison (>= or <=).
+    no_warn : bool
+        Disable initial limit warnings
     zu : 0 or 1
         Default value for `zu` if not enabled
     zl : 0 or 1
@@ -224,7 +226,8 @@ class Limiter(Discrete):
     """
 
     def __init__(self, u, lower, upper, enable=True, name=None, tex_name=None, info=None,
-                 no_upper=False, no_lower=False, equal=True, zu=0.0, zl=0.0, zi=1.0):
+                 no_upper=False, no_lower=False, equal=True, no_warn=False,
+                 zu=0.0, zl=0.0, zi=1.0):
         Discrete.__init__(self, name=name, tex_name=tex_name, info=info)
         self.u = u
         self.lower = dummify(lower)
@@ -233,6 +236,7 @@ def __init__(self, u, lower, upper, enable=True, name=None, tex_name=None, info=
         self.no_upper = no_upper
         self.no_lower = no_lower
         self.equal = equal
+        self.no_warn = no_warn
 
         self.zu = np.array([zu])
         self.zl = np.array([zl])

From 75d7e694d6784b35f30039c4164ea7dbb93eea2f Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 19 Oct 2020 17:52:33 -0400
Subject: [PATCH 19/57] Added voltage flags for PVD1

---
 andes/models/distributed.py | 33 ++++++++++++++++++++++++++++-----
 1 file changed, 28 insertions(+), 5 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index ca1f3f11e..1ca7d1148 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -192,13 +192,11 @@ def __init__(self, system, config):
 
         # --- frequency branch ---
         self.FL1 = Limiter(u=self.fHz, lower=self.ft0, upper=self.ft1,
-                           info='Under frequency comparer',
+                           info='Under frequency comparer', no_warn=True,
                            )
         self.FL2 = Limiter(u=self.fHz, lower=self.ft2, upper=self.ft3,
-                           info='Over frequency comparer',
+                           info='Over frequency comparer', no_warn=True,
                            )
-        self.FL1.no_warn = True
-        self.FL2.no_warn = True
 
         self.Kft01 = ConstService(v_str='1/(ft1 - ft0)', tex_name='K_{ft01}')
 
@@ -209,7 +207,7 @@ def __init__(self, system, config):
                          discrete=self.FL1,
                          )
 
-        self.Kft23 = ConstService(v_str='-1/(ft2 - ft3)', tex_name='K_{ft23}')
+        self.Kft23 = ConstService(v_str='1/(ft3 - ft2)', tex_name='K_{ft23}')
 
         self.Ffh = Algeb(info='Coeff. for over frequency',
                          v_str='FL2_zl + FL2_zi * (1 + Kft23 * (ft2 - fHz))',
@@ -230,6 +228,31 @@ def __init__(self, system, config):
                             )  # outputs   `Pdrp`
         self.DB.db.no_warn = True
 
+        # --- Voltage flags ---
+        self.VL1 = Limiter(u=self.v, lower=self.vt0, upper=self.vt1,
+                           info='Under voltage comparer', no_warn=True,
+                           )
+        self.VL2 = Limiter(u=self.v, lower=self.vt2, upper=self.vt3,
+                           info='Over voltage comparer', no_warn=True,
+                           )
+
+        self.Kvt01 = ConstService(v_str='1/(vt1 - vt0)', tex_name='K_{vt01}')
+
+        self.Fvl = Algeb(info='Coeff. for under voltage',
+                         v_str='VL1_zi * Kvt01 * (v - vt0) + VL1_zu',
+                         e_str='VL1_zi * Kvt01 * (v - vt0) + VL1_zu - Fvl',
+                         tex_name='F_{vl}',
+                         discrete=self.VL1,
+                         )
+
+        self.Kvt23 = ConstService(v_str='1/(vt3 - vt2)', tex_name='K_{vt23}')
+
+        self.Fvh = Algeb(info='Coeff. for over voltage',
+                         v_str='VL2_zl + VL2_zi * (1 + Kvt23 * (vt2 - v))',
+                         e_str='VL2_zl + VL2_zi * (1 + Kvt23 * (vt2 - v)) - Fvh',
+                         tex_name='F_{vh}',
+                         discrete=self.VL2,
+                         )
 
 class PVD1(PVD1Data, PVD1Model):
     """

From de3ff1347f8951a58877d95f9bbd99299bc86e4c Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Mon, 19 Oct 2020 18:22:57 -0400
Subject: [PATCH 20/57] Added variables for power ref.

---
 andes/models/distributed.py | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 1ca7d1148..3f85133f6 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -253,6 +253,32 @@ def __init__(self, system, config):
                          tex_name='F_{vh}',
                          discrete=self.VL2,
                          )
+        # --- sensed voltage with lower limit of 0.01 ---
+
+        self.VLo = Limiter(u=self.v, lower=0.01, upper=999, no_upper=True,
+                           info='Voltage lower limit (0.01) flag',
+                           )
+        self.vp = Algeb(tex_name='V_p',
+                        info='Sensed positive voltage',
+                        v_str='v * VLo_zi + 0.01 * VLo_zl',
+                        e_str='v * VLo_zi + 0.01 * VLo_zl - vp',
+                        )
+
+        self.Pext = Algeb(tex_name='P_{ext}',
+                          info='External power signal',
+                          v_str='0',
+                          e_str='0 - Pext'
+                          )
+
+        self.Psum = Algeb(tex_name='P_{tot}',
+                          info='Sum of P signals',
+                          v_str='Pext + p0 + DB_y',
+                          e_str='Pext + p0 + DB_y - Psum',
+                          )  # `p0` is the initial `Pref`, and `DB_y` is `Pdrp` (f droop)
+
+        # TODO: retrieve line and calculate current It
+        # TODO: implement the voltage droop on reactive power
+
 
 class PVD1(PVD1Data, PVD1Model):
     """

From 7fd7441ec4be2079556aabf2241b1685a705cefe Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Tue, 27 Oct 2020 14:09:01 -0400
Subject: [PATCH 21/57] Use mass-matrix formulation for dc components.

---
 andes/models/dcbase.py | 27 ++++++++++++++++++---------
 1 file changed, 18 insertions(+), 9 deletions(-)

diff --git a/andes/models/dcbase.py b/andes/models/dcbase.py
index 6e2402df6..c432daf28 100644
--- a/andes/models/dcbase.py
+++ b/andes/models/dcbase.py
@@ -272,7 +272,8 @@ def __init__(self, system, config):
                         info='Inductance current',
                         unit='p.u.',
                         v_str='0',
-                        e_str='-u * (v1 - v2) / L',
+                        e_str='-u * (v1 - v2)',
+                        t_const=self.L,
                         )
         self.v1.e_str = '-IL'
         self.v2.e_str = '+IL'
@@ -297,7 +298,8 @@ def __init__(self, system, config):
                         info='Capacitor current',
                         unit='p.u.',
                         v_str='0',
-                        e_str='-u * Idc / C',
+                        e_str='-u * Idc',
+                        t_const=self.C
                         )
         self.Idc = Algeb(tex_name='I_{dc}',
                          info='Current from node 2 to 1',
@@ -334,8 +336,9 @@ def __init__(self, system, config):
         self.IL = State(tex_name='I_L',
                         info='Inductance current',
                         unit='p.u.',
-                        e_str='u * (v1 - v2 - R * IL) / L',
+                        e_str='u * (v1 - v2 - R * IL)',
                         v_str='(v1 - v2) / R',
+                        t_const=self.L,
                         )
         self.Idc = Algeb(tex_name='I_{dc}',
                          info='Current from node 2 to 1',
@@ -370,8 +373,9 @@ def __init__(self, system, config):
         self.vC = State(tex_name='v_C',
                         info='Capacitor current',
                         unit='p.u.',
-                        e_str='-u * (Idc - vC/R) / C',
+                        e_str='-u * (Idc - vC/R)',
                         v_str='v1 - v2',
+                        t_const=self.C,
                         )
         self.Idc = Algeb(tex_name='I_{dc}',
                          info='Current from node 2 to 1',
@@ -416,13 +420,15 @@ def __init__(self, system, config):
                         info='Inductance current',
                         unit='p.u.',
                         v_str='0',
-                        e_str='u * vC / L',
+                        e_str='u * vC',
+                        t_const=self.L,
                         )
         self.vC = State(tex_name='v_C',
                         info='Capacitor current',
                         unit='p.u.',
-                        e_str='-u * (Idc - vC/R - IL) / C',
+                        e_str='-u * (Idc - vC/R - IL)',
                         v_str='v1 - v2',
+                        t_const=self.C,
                         )
         self.Idc = Algeb(tex_name='I_{dc}',
                          info='Current from node 2 to 1',
@@ -459,8 +465,9 @@ def __init__(self, system, config):
         self.vC = State(tex_name='v_C',
                         info='Capacitor current',
                         unit='p.u.',
-                        e_str='-u * Idc / C',
+                        e_str='-u * Idc',
                         v_str='v1 - v2',
+                        t_const=self.C,
                         )
         self.Idc = Algeb(tex_name='I_{dc}',
                          info='Current from node 2 to 1',
@@ -504,14 +511,16 @@ def __init__(self, system, config):
         self.IL = State(tex_name='I_L',
                         info='Inductance current',
                         unit='p.u.',
-                        e_str='u * (v1 - v2 - R * IL - vC) / L',
+                        e_str='u * (v1 - v2 - R * IL - vC)',
                         v_str='0',
+                        t_const=self.L,
                         )
         self.vC = State(tex_name='v_C',
                         info='Capacitor current',
                         unit='p.u.',
-                        e_str='u * IL / C',
+                        e_str='u * IL',
                         v_str='v1 - v2',
+                        t_const=self.C,
                         )
         self.Idc = Algeb(tex_name='I_{dc}',
                          info='Current from node 2 to 1',

From 7141d48c01d5991ea736cfeb2a3f376c5588ceef Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Wed, 28 Oct 2020 14:10:24 -0400
Subject: [PATCH 22/57] Refactored logger info with lazy eval.

---
 andes/io/__init__.py | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/andes/io/__init__.py b/andes/io/__init__.py
index 683c00b71..1a8c86cda 100644
--- a/andes/io/__init__.py
+++ b/andes/io/__init__.py
@@ -73,7 +73,7 @@ def guess(system):
             if testlines(fid):
                 true_format = item
                 files.input_format = true_format
-                logger.debug(f'Input format guessed as {true_format}.')
+                logger.debug('Input format guessed as %s.', true_format)
                 break
 
     if not true_format:
@@ -85,7 +85,7 @@ def guess(system):
         for key, val in input_formats.items():
             if add_ext[1:] in val:
                 files.add_format = key
-                logger.debug(f'Addfile format guessed as {key}.')
+                logger.debug('Addfile format guessed as %s.', key)
                 break
 
     return true_format
@@ -106,32 +106,32 @@ def parse(system):
     # exit when no input format is given
     if not system.files.input_format:
         if not guess(system):
-            logger.error('Input format is not specified and cannot be inferred.')
+            logger.error('Input format unknown for file "%s".', system.files.case)
             return False
 
     # try parsing the base case file
-    logger.info(f'Parsing input file "{system.files.case}"')
+    logger.info('Parsing input file "%s"...', system.files.case)
     input_format = system.files.input_format
     parser = importlib.import_module('.' + input_format, __name__)
     if not parser.read(system, system.files.case):
-        logger.error(f'Error parsing case file {system.files.fullname} with {input_format} format parser.')
+        logger.error('Error parsing file "%s" with <%s> parser.', system.files.fullname, input_format)
         return False
 
     _, s = elapsed(t)
-    logger.info(f'Input file parsed in {s}.')
+    logger.info('Input file parsed in %s.', s)
 
     # Try parsing the addfile
     t, _ = elapsed()
 
     if system.files.addfile:
-        logger.info(f'Parsing additional file "{system.files.addfile}"')
+        logger.info('Parsing additional file "%s"...', system.files.addfile)
         add_format = system.files.add_format
         add_parser = importlib.import_module('.' + add_format, __name__)
         if not add_parser.read_add(system, system.files.addfile):
-            logger.error(f'Error parsing addfile {system.files.addfile} with {input_format} parser.')
+            logger.error('Error parsing addfile "%s" with %s parser.', system.files.addfile, input_format)
             return False
         _, s = elapsed(t)
-        logger.info(f'Addfile parsed in {s}.')
+        logger.info('Addfile parsed in %s.', s)
 
     return True
 
@@ -175,7 +175,7 @@ def dump(system, output_format, full_path=None, overwrite=False, **kwargs):
     ret = writer.write(system, system.files.dump, overwrite=overwrite, **kwargs)
     _, s = elapsed(t)
     if ret:
-        logger.info(f'Format conversion completed in {s}.')
+        logger.info('Format conversion completed in %s.', s)
         return True
     else:
         logger.error('Format conversion failed.')

From 03979a6de6d7fdf3a5c0fac2b896e1279918b531 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Wed, 28 Oct 2020 14:48:03 -0400
Subject: [PATCH 23/57] Patch pycode import for Jacobians.

---
 andes/system.py | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/andes/system.py b/andes/system.py
index 80ca6fa11..5ed458880 100644
--- a/andes/system.py
+++ b/andes/system.py
@@ -813,11 +813,10 @@ def j_update(self, models: OrderedDict, info=None):
                                      f'j_size={j_size}')
                         raise e
 
-        msg = f"Jacobian updated at t={self.dae.t}"
         if info:
-            msg += f' due to {info}'
-
-        logger.debug(msg)
+            logger.debug("Jacobian updated at t=%.6f due to %s.", self.dae.t, info)
+        else:
+            logger.debug("Jacobian updated at t=%.6f.", self.dae.t)
 
     def store_sparse_pattern(self, models: OrderedDict):
         """
@@ -1056,11 +1055,13 @@ def undill(self):
         # try to replace equations and jacobian calls with saved code
         if pycode is not None and self.config.use_pycode:
             for model in self.models.values():
-                model.calls.f = pycode.__dict__[model.class_name].__dict__.get("f_update")
-                model.calls.g = pycode.__dict__[model.class_name].__dict__.get("g_update")
+                pycode_model = pycode.__dict__[model.class_name]
+
+                model.calls.f = pycode_model.__dict__.get("f_update")
+                model.calls.g = pycode_model.__dict__.get("g_update")
 
                 for jname in model.calls.j:
-                    model.calls.j[jname] = pycode.__dict__[model.class_name].__dict__[f'{jname}_update']
+                    model.calls.j[jname] = pycode_model.__dict__.get(f'{jname}_update')
             logger.info("Using generated Python code for equations and Jacobians.")
         else:
             logger.debug("Using undilled lambda functions.")

From b92e1c1b0504367e6e953bca25534b8a2b29ef25 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 15:49:10 -0400
Subject: [PATCH 24/57] Support kvxopt library (mostly for Windows).

---
 andes/shared.py | 39 ++++++++++++++++++++++++++-------------
 1 file changed, 26 insertions(+), 13 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index 22d392874..f0e5176a8 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -12,28 +12,41 @@
 from andes.utils.lazyimport import LazyImport
 
 import math
-import coloredlogs      # NOQA
-import numpy as np      # NOQA
-from tqdm import tqdm   # NOQA
-
-import cvxopt           # NOQA
-from cvxopt import umfpack                           # NOQA
-from cvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
-from numpy import ndarray                            # NOQA
-
-from andes.utils.texttable import Texttable          # NOQA
-from andes.utils.paths import get_dot_andes_path     # NOQA
+import coloredlogs         # NOQA
+import numpy as np         # NOQA
+from numpy import ndarray  # NOQA
+from tqdm import tqdm      # NOQA
 
 try:
-    from cvxoptklu import klu
+    import kvxopt       # NOQA
 except ImportError:
-    klu = None
+    kvxopt = None
 
+from cvxopt import spmatrix
 if hasattr(spmatrix, 'ipadd'):
     IP_ADD = True
 else:
     IP_ADD = False
 
+if IP_ADD or (kvxopt is None):
+    from cvxopt import umfpack                           # NOQA
+    from cvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
+    from cvxopt import mul, div                          # NOQA
+    from cvxopt.lapack import gesv                       # NOQA
+    try:
+        from cvxoptklu import klu  # NOQA
+    except ImportError:
+        klu = None
+else:
+    from kvxopt import umfpack, klu                      # NOQA
+    from kvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
+    from kvxopt import mul, div                          # NOQA
+    from kvxopt.lapack import gesv                       # NOQA
+
+
+from andes.utils.texttable import Texttable          # NOQA
+from andes.utils.paths import get_dot_andes_path     # NOQA
+
 # --- constants ---
 
 deg2rad = math.pi/180

From 5df8cafec8c0cdd42a02fdb102912c790ffde1ba Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 15:52:07 -0400
Subject: [PATCH 25/57] Format change.

---
 andes/shared.py | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index f0e5176a8..e0350d1e6 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -62,12 +62,14 @@
 
 pd = LazyImport('import pandas')
 cupy = LazyImport('import cupy')
-plt = LazyImport('from matplotlib import pyplot')
 mpl = LazyImport('import matplotlib')
-Pool = LazyImport('from pathos.multiprocessing import Pool')
-Process = LazyImport('from multiprocess import Process')
 unittest = LazyImport('import unittest')
 yaml = LazyImport('import yaml')
+
+plt = LazyImport('from matplotlib import pyplot')
+Pool = LazyImport('from pathos.multiprocessing import Pool')
+Process = LazyImport('from multiprocess import Process')
+
 newton_krylov = LazyImport('from scipy.optimize import newton_krylov')
 fsolve = LazyImport('from scipy.optimize import fsolve')
 solve_ivp = LazyImport('from scipy.integrate import solve_ivp')

From 91b808009617481b312f7b17d1cf686a56224899 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 16:21:20 -0400
Subject: [PATCH 26/57] Import from andes share.

---
 andes/routines/eig.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/andes/routines/eig.py b/andes/routines/eig.py
index ec3d5eba9..558b79a15 100644
--- a/andes/routines/eig.py
+++ b/andes/routines/eig.py
@@ -6,8 +6,7 @@
 from math import ceil, pi
 
 import scipy.io
-from cvxopt import mul, div, spdiag
-from cvxopt.lapack import gesv
+from andes.shared import mul, div, spdiag, gesv
 
 from andes.io.txt import dump_data
 from andes.utils.misc import elapsed

From 3c27f76d909f0c6e159de0004c5ae41066bc3605 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 16:22:16 -0400
Subject: [PATCH 27/57] Added reactive power droop arm [wip]

---
 andes/models/distributed.py | 75 +++++++++++++++++++++++++++++++++----
 1 file changed, 67 insertions(+), 8 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 3f85133f6..8e2790b5b 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -65,18 +65,18 @@ def __init__(self):
                             power=True,
                             )
 
-        self.v0 = NumParam(default=0.0, tex_name='v_0',
+        self.v0 = NumParam(default=0.8, tex_name='v_0',
                            info='Lower limit of deadband for Vdroop response',
-                           unit='pu',
+                           unit='pu', non_zero=True,
                            )
-        self.v1 = NumParam(default=0.0, tex_name='v_1',
+        self.v1 = NumParam(default=1.1, tex_name='v_1',
                            info='Upper limit of deadband for Vdroop response',
-                           unit='pu',
+                           unit='pu', non_zero=True,
                            )
 
-        self.dqdv = NumParam(default=0.0, tex_name='dq/dv',
-                             info='Q-V droop characteristics',
-                             power=True,
+        self.dqdv = NumParam(default=-1.0, tex_name='dq/dv',
+                             info='Q-V droop characteristics (negative)',
+                             power=True, non_zero=True
                              )
 
         self.fdbd = NumParam(default=-0.01, tex_name='f_{dbd}',
@@ -258,6 +258,7 @@ def __init__(self, system, config):
         self.VLo = Limiter(u=self.v, lower=0.01, upper=999, no_upper=True,
                            info='Voltage lower limit (0.01) flag',
                            )
+
         self.vp = Algeb(tex_name='V_p',
                         info='Sensed positive voltage',
                         v_str='v * VLo_zi + 0.01 * VLo_zl',
@@ -276,13 +277,71 @@ def __init__(self, system, config):
                           e_str='Pext + p0 + DB_y - Psum',
                           )  # `p0` is the initial `Pref`, and `DB_y` is `Pdrp` (f droop)
 
+        # self.Vcomp = VarService(v_str='abs(v*exp(1j*a) + (1j * Xc) * (Id + 1j * Iq))',
+        #                         info='Voltage before Xc compensation',
+        #                         tex_name='V_{comp}'
+        #                         )
+
+        self.Vcomp = VarService(v_str='abs(v*exp(1j*a) + (1j * xc) * 1)',
+                                info='Voltage before Xc compensation',
+                                tex_name='V_{comp}'
+                                )
+
+        self.Vqu = ConstService(v_str='v1 - (q0 - qmn) / dqdv',
+                                info='Upper voltage bound => qmx',
+                                tex_name='V_{qu}',
+                                )
+
+        self.Vql = ConstService(v_str='v0 + (qmx - q0) / dqdv',
+                                info='Lower voltage bound => qmn',
+                                tex_name='V_{ql}',
+                                )
+
+        self.VQ1 = Limiter(u=self.Vcomp, lower=self.Vql, upper=self.v0,
+                           info='Under voltage comparer for Q droop',
+                           no_warn=True,
+                           )
+
+        self.VQ2 = Limiter(u=self.Vcomp, lower=self.v1, upper=self.Vqu,
+                           info='Over voltage comparer for Q droop',
+                           no_warn=True,
+                           )
+
+        Qsum = 'VQ1_zl * qmx + VQ2_zu * qmn + ' \
+               'VQ1_zi * (qmx + dqdv *(Vqu - Vcomp)) + ' \
+               'VQ2_zi * (q0 + dqdv * (v1 - Vcomp)) + ' \
+               'VQ1_zu * VQ2_zl * p0 + p0'
+
+        self.Qsum = Algeb(info='Total Q (droop + initial)',
+                          v_str=Qsum,
+                          e_str=f'{Qsum} - Qsum',
+                          tex_name='Q_{sum}',
+                          discrete=(self.VQ1, self.VQ2),
+                          )
+
+        self.Ipul = Algeb(info='Ipcmd before hard limit',
+                          v_str='Psum / vp',
+                          e_str='Psum / vp - Ipul',
+                          tex_name='I_{p,ul}',
+                          )
+
+        self.Iqul = Algeb(info='Iqcmd before hard limit',
+                          v_str='Qsum / vp',
+                          e_str='Qsum / vp - Iqul',
+                          tex_name='I_{q,ul}',
+                          )
+
+        self.Fcoef = VarService(v_str='Ffh * Ffh * Fvl * Fvh',
+                                tex_name='F_{coef}',
+                                )
+
         # TODO: retrieve line and calculate current It
         # TODO: implement the voltage droop on reactive power
 
 
 class PVD1(PVD1Data, PVD1Model):
     """
-    Distributed PV model. (TODO: work in progress)
+    WECC Distributed PV model. (TODO: work in progress)
 
     Power rating specified in `Sn`.
 

From b3ac38f54a245c695379ea572bde37acb01d67ed Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 17:54:12 -0400
Subject: [PATCH 28/57] Added LimiterGain block.

---
 andes/core/block.py | 64 ++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 63 insertions(+), 1 deletion(-)

diff --git a/andes/core/block.py b/andes/core/block.py
index b2b5cf101..1fe436029 100644
--- a/andes/core/block.py
+++ b/andes/core/block.py
@@ -1467,6 +1467,8 @@ class GainLimiter(Block):
              │     │ _____/
              └─────┘ lower
 
+    TODO: Add an extra gain block "R" for y.
+
     Parameters
     ----------
     u : str, BaseVar
@@ -1474,7 +1476,7 @@ class GainLimiter(Block):
 
     """
 
-    def __init__(self, u, K, upper, lower, no_upper=False, no_lower=False,
+    def __init__(self, u, K, lower, upper, no_lower=False, no_upper=False,
                  name=None, tex_name=None, info=None):
         Block.__init__(self, name=name, tex_name=tex_name, info=info)
         self.u = dummify(u)
@@ -1518,6 +1520,66 @@ def define(self):
         self.y.e_str += f' - {self.name}_y'
 
 
+class LimiterGain(Block):
+    """
+    Limiter followed by a gain.
+
+    Exports the limited output `y`, unlimited output `x`, and HardLimiter `lim`. ::
+
+                   upper ┌─────┐
+                  /¯¯¯¯¯ │     │
+        u  ->    /   ->  │  K  │ -> y
+           _____/        │     │
+           lower         └─────┘
+
+    The intermediate variable before the gain is not saved.
+
+    Parameters
+    ----------
+    u : str, BaseVar
+        Input variable, or an equation string for constructing an anonymous variable
+
+    """
+
+    def __init__(self, u, K, lower, upper, no_lower=False, no_upper=False,
+                 name=None, tex_name=None, info=None):
+        Block.__init__(self, name=name, tex_name=tex_name, info=info)
+        self.u = u
+        self.K = dummify(K)
+        self.upper = dummify(upper)
+        self.lower = dummify(lower)
+
+        if (no_upper and no_lower) is True:
+            raise ValueError("no_upper or no_lower cannot both be True")
+
+        self.no_lower = no_lower
+        self.no_upper = no_upper
+
+        self.lim = HardLimiter(u=self.u, lower=self.lower, upper=self.upper,
+                               no_upper=no_upper, no_lower=no_lower,
+                               tex_name='lim')
+
+        self.y = Algeb(info='Gain output after limiter', tex_name='y', discrete=self.lim)
+
+        self.vars = {'lim': self.lim, 'y': self.y}
+
+    def define(self):
+        """
+        TODO: write docstring
+        """
+        self.y.e_str = f'{self.K.name} * {self.u.name} * {self.name}_lim_zi'
+        self.y.v_str = f'{self.K.name} * {self.u.name} * {self.name}_lim_zi'
+
+        if not self.no_upper:
+            self.y.e_str += f' + {self.K.name} * {self.name}_lim_zu*{self.upper.name}'
+            self.y.v_str += f' + {self.K.name} * {self.name}_lim_zu*{self.upper.name}'
+        if not self.no_lower:
+            self.y.e_str += f' + {self.K.name} * {self.name}_lim_zl*{self.lower.name}'
+            self.y.v_str += f' + {self.K.name} * {self.name}_lim_zl*{self.lower.name}'
+
+        self.y.e_str += f' - {self.name}_y'
+
+
 class Piecewise(Block):
     """
     Piecewise block. Outputs an algebraic variable `y`.

From c0450f0f4a2ce7119d8f44e34f16fb2a28b7994c Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 17:54:20 -0400
Subject: [PATCH 29/57] Added current limits.

---
 andes/models/distributed.py | 54 ++++++++++++++++++++++++++++++++-----
 1 file changed, 47 insertions(+), 7 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 8e2790b5b..48957ff93 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -4,7 +4,7 @@
 
 from andes.core.model import Model, ModelData
 from andes.core.param import NumParam, IdxParam
-from andes.core.block import Lag, GainLimiter, DeadBand1  # NOQA
+from andes.core.block import Lag, DeadBand1, LimiterGain  # NOQA
 from andes.core.var import ExtAlgeb, ExtState, Algeb, State  # NOQA
 
 from andes.core.service import ConstService, ExtService, FlagValue, DataSelect, DeviceFinder  # NOQA
@@ -50,6 +50,11 @@ def __init__(self):
                            z=True,
                            )
 
+        self.pqflag = NumParam(info='P/Q priority for I limit; 0-Q priority, 1-P priority',
+                               mandatory=True,
+                               unit='bool',
+                               )
+
         # --- parameters found from ESIG.energy ---
         self.igreg = IdxParam(model='Bus',
                               info='Remote bus idx for droop response, None for local',
@@ -215,6 +220,7 @@ def __init__(self, system, config):
                          tex_name='F_{fh}',
                          discrete=self.FL2,
                          )
+
         self.Fdev = Algeb(info='Frequency deviation',
                           v_str='fn - fHz', e_str='fn - fHz - Fdev',
                           unit='Hz', tex_name='f_{dev}',
@@ -310,7 +316,7 @@ def __init__(self, system, config):
         Qsum = 'VQ1_zl * qmx + VQ2_zu * qmn + ' \
                'VQ1_zi * (qmx + dqdv *(Vqu - Vcomp)) + ' \
                'VQ2_zi * (q0 + dqdv * (v1 - Vcomp)) + ' \
-               'VQ1_zu * VQ2_zl * p0 + p0'
+               'q0'
 
         self.Qsum = Algeb(info='Total Q (droop + initial)',
                           v_str=Qsum,
@@ -331,12 +337,46 @@ def __init__(self, system, config):
                           tex_name='I_{q,ul}',
                           )
 
-        self.Fcoef = VarService(v_str='Ffh * Ffh * Fvl * Fvh',
-                                tex_name='F_{coef}',
-                                )
+        # --- Ipmax, Iqmax and Iqmin ---
+        Ipmaxsq = "(Piecewise((0, Le(ialim**2 - Iqcmd_y**2, 0)), ((ialim**2 - Iqcmd_y ** 2), True)))"
+        Ipmaxsq0 = "(Piecewise((0, Le(ialim**2 - (q0 / v)**2, 0)), ((ialim**2 - (q0 / v) ** 2), True)))"
+        self.Ipmaxsq = VarService(v_str=Ipmaxsq)
+        self.Ipmaxsq0 = ConstService(v_str=Ipmaxsq0)
+
+        self.Ipmax = Algeb(v_str='SWPQ_s1 * ialim + SWPQ_s0 * sqrt(Ipmaxsq0)',
+                           e_str='SWPQ_s1 * ialim + SWPQ_s0 * sqrt(Ipmaxsq) - Ipmax',
+                           tex_name='I_{pmax}',
+                           )
+
+        Iqmaxsq = "(Piecewise((0, Le(ialim**2 - Ipcmd_y**2, 0)), ((ialim**2 - Ipcmd_y ** 2), True)))"
+        Iqmaxsq0 = "(Piecewise((0, Le(ialim**2 - (p0 / v)**2, 0)), ((ialim**2 - (p0 / v) ** 2), True)))"
+        self.Iqmaxsq = VarService(v_str=Iqmaxsq)
+        self.Iqmaxsq0 = ConstService(v_str=Iqmaxsq0)
+
+        self.Iqmax = Algeb(v_str='SWPQ_s0 * ialim + SWPQ_s1 * sqrt(Iqmaxsq0)',
+                           e_str='SWPQ_s0 * ialim + SWPQ_s1 * sqrt(Iqmaxsq) - Iqmax',
+                           tex_name='I_{qmax}',
+                           )
+
+        self.Iqmin = VarService(v_str='-Iqmax')
+
+        # --- Ipcmd, Iqcmd ---
+
+        self.Ipcmd = LimiterGain(u=self.Ipul, K='Fvl * Fvh * Ffl * Ffh',
+                                 lower=0.0, upper=self.Ipmax,
+                                 info='Ip with limiter and coeff.',
+                                 )
+
+        self.Iqcmd = LimiterGain(u=self.Iqul, K='Fvl * Fvh * Ffl * Ffh',
+                                 lower=self.Iqmin, upper=self.Iqmax,
+                                 info='Iq with limiter and coeff.',
+                                 )
+
+        self.Ipout = Lag(u=self.Ipcmd_y, T=self.tip, K=1.0)
+
+        self.Iqout = Lag(u=self.Iqcmd_y, T=self.tiq, K=1.0)
 
-        # TODO: retrieve line and calculate current It
-        # TODO: implement the voltage droop on reactive power
+        self.SWPQ = Switcher(u=self.pqflag, options=(0, 1), tex_name='SW_{PQ}', cache=True)
 
 
 class PVD1(PVD1Data, PVD1Model):

From 4747d22cd46e4a8d2593c0892ee1d4f33d9ceb20 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 20:00:56 -0400
Subject: [PATCH 30/57] Prototype of PVD1 model.

---
 andes/models/distributed.py | 18 ++++++++++--------
 1 file changed, 10 insertions(+), 8 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 48957ff93..48e808fb7 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -154,10 +154,11 @@ class PVD1Model(Model):
     """
     def __init__(self, system, config):
         Model.__init__(self, system, config)
-
         self.flags.tds = True
         self.group = 'DG'
 
+        self.SWPQ = Switcher(u=self.pqflag, options=(0, 1), tex_name='SW_{PQ}', cache=True)
+
         self.buss = DataSelect(self.igreg, self.bus,
                                info='selected bus (bus or igreg)',
                                )
@@ -168,11 +169,13 @@ def __init__(self, system, config):
         self.v = ExtAlgeb(model='Bus', src='v', indexer=self.buss, tex_name='V',
                           info='bus (or igreg) terminal voltage',
                           unit='p.u.',
+                          e_str='-Iqout_y * v',
                           )
 
         self.a = ExtAlgeb(model='Bus', src='a', indexer=self.buss, tex_name=r'\theta',
                           info='bus (or igreg) phase angle',
                           unit='rad.',
+                          e_str='-Ipout_y * v',
                           )
 
         self.p0 = ExtService(model='StaticGen',
@@ -283,12 +286,7 @@ def __init__(self, system, config):
                           e_str='Pext + p0 + DB_y - Psum',
                           )  # `p0` is the initial `Pref`, and `DB_y` is `Pdrp` (f droop)
 
-        # self.Vcomp = VarService(v_str='abs(v*exp(1j*a) + (1j * Xc) * (Id + 1j * Iq))',
-        #                         info='Voltage before Xc compensation',
-        #                         tex_name='V_{comp}'
-        #                         )
-
-        self.Vcomp = VarService(v_str='abs(v*exp(1j*a) + (1j * xc) * 1)',
+        self.Vcomp = VarService(v_str='abs(v*exp(1j*a) + (1j * xc) * (Ipout_y + 1j * Iqout_y))',
                                 info='Voltage before Xc compensation',
                                 tex_name='V_{comp}'
                                 )
@@ -376,7 +374,11 @@ def __init__(self, system, config):
 
         self.Iqout = Lag(u=self.Iqcmd_y, T=self.tiq, K=1.0)
 
-        self.SWPQ = Switcher(u=self.pqflag, options=(0, 1), tex_name='SW_{PQ}', cache=True)
+    def v_numeric(self, **kwargs):
+        """
+        Disable the corresponding `StaticGen`s.
+        """
+        self.system.groups['StaticGen'].set(src='u', idx=self.gen.v, attr='v', value=0)
 
 
 class PVD1(PVD1Data, PVD1Model):

From a1e7c76116a73abf13ca27e7101cb791470bdb73 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 20:05:46 -0400
Subject: [PATCH 31/57] Updated PVD1 test case.

---
 andes/cases/ieee14/ieee14_pvd1.xlsx | Bin 0 -> 25947 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 andes/cases/ieee14/ieee14_pvd1.xlsx

diff --git a/andes/cases/ieee14/ieee14_pvd1.xlsx b/andes/cases/ieee14/ieee14_pvd1.xlsx
new file mode 100644
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HcmV?d00001


From 062e32a324c99f8a8750eacd325c8a47a9965be3 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 20:57:37 -0400
Subject: [PATCH 32/57] Update docs.

---
 andes/models/distributed.py | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 48e808fb7..39eab989b 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -370,9 +370,13 @@ def __init__(self, system, config):
                                  info='Iq with limiter and coeff.',
                                  )
 
-        self.Ipout = Lag(u=self.Ipcmd_y, T=self.tip, K=1.0)
+        self.Ipout = Lag(u=self.Ipcmd_y, T=self.tip, K=1.0,
+                         info='Output Ip filter',
+                         )
 
-        self.Iqout = Lag(u=self.Iqcmd_y, T=self.tiq, K=1.0)
+        self.Iqout = Lag(u=self.Iqcmd_y, T=self.tiq, K=1.0,
+                         info='Output Iq filter',
+                         )
 
     def v_numeric(self, **kwargs):
         """
@@ -383,11 +387,12 @@ def v_numeric(self, **kwargs):
 
 class PVD1(PVD1Data, PVD1Model):
     """
-    WECC Distributed PV model. (TODO: work in progress)
+    WECC Distributed PV model.
 
     Power rating specified in `Sn`.
 
-    Reference: ESIG, WECC Distributed and Small PV Plants Generic Model (PVD1), [Online],
+    Reference:
+    [1] ESIG, WECC Distributed and Small PV Plants Generic Model (PVD1), [Online],
     Available: https://www.esig.energy/wiki-main-page/wecc-distributed-and-small-pv-plants-generic-model-pvd1/
     """
     def __init__(self, system, config):

From dbaa0e43e6b1087ebea5a57f94dde7f1f0e2a6e9 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 21:30:58 -0400
Subject: [PATCH 33/57] Updated tex names.

---
 andes/models/distributed.py | 15 +++++++++------
 1 file changed, 9 insertions(+), 6 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 39eab989b..31f021a46 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -157,7 +157,7 @@ def __init__(self, system, config):
         self.flags.tds = True
         self.group = 'DG'
 
-        self.SWPQ = Switcher(u=self.pqflag, options=(0, 1), tex_name='SW_{PQ}', cache=True)
+        self.SWPQ = Switcher(u=self.pqflag, options=(0, 1), tex_name='SW^{PQ}', cache=True)
 
         self.buss = DataSelect(self.igreg, self.bus,
                                info='selected bus (bus or igreg)',
@@ -196,6 +196,7 @@ def __init__(self, system, config):
         self.fHz = Algeb(info='frequency in Hz',
                          v_str='fn * f', e_str='fn * f - fHz',
                          unit='Hz',
+                         tex_name='f_{Hz}',
                          )
 
         # --- frequency branch ---
@@ -338,8 +339,8 @@ def __init__(self, system, config):
         # --- Ipmax, Iqmax and Iqmin ---
         Ipmaxsq = "(Piecewise((0, Le(ialim**2 - Iqcmd_y**2, 0)), ((ialim**2 - Iqcmd_y ** 2), True)))"
         Ipmaxsq0 = "(Piecewise((0, Le(ialim**2 - (q0 / v)**2, 0)), ((ialim**2 - (q0 / v) ** 2), True)))"
-        self.Ipmaxsq = VarService(v_str=Ipmaxsq)
-        self.Ipmaxsq0 = ConstService(v_str=Ipmaxsq0)
+        self.Ipmaxsq = VarService(v_str=Ipmaxsq, tex_name='I_{pmax}^2')
+        self.Ipmaxsq0 = ConstService(v_str=Ipmaxsq0, tex_name='I_{pmax0}^2')
 
         self.Ipmax = Algeb(v_str='SWPQ_s1 * ialim + SWPQ_s0 * sqrt(Ipmaxsq0)',
                            e_str='SWPQ_s1 * ialim + SWPQ_s0 * sqrt(Ipmaxsq) - Ipmax',
@@ -348,26 +349,28 @@ def __init__(self, system, config):
 
         Iqmaxsq = "(Piecewise((0, Le(ialim**2 - Ipcmd_y**2, 0)), ((ialim**2 - Ipcmd_y ** 2), True)))"
         Iqmaxsq0 = "(Piecewise((0, Le(ialim**2 - (p0 / v)**2, 0)), ((ialim**2 - (p0 / v) ** 2), True)))"
-        self.Iqmaxsq = VarService(v_str=Iqmaxsq)
-        self.Iqmaxsq0 = ConstService(v_str=Iqmaxsq0)
+        self.Iqmaxsq = VarService(v_str=Iqmaxsq, tex_name='I_{qmax}^2')
+        self.Iqmaxsq0 = ConstService(v_str=Iqmaxsq0, tex_name='I_{qmax0}^2')
 
         self.Iqmax = Algeb(v_str='SWPQ_s0 * ialim + SWPQ_s1 * sqrt(Iqmaxsq0)',
                            e_str='SWPQ_s0 * ialim + SWPQ_s1 * sqrt(Iqmaxsq) - Iqmax',
                            tex_name='I_{qmax}',
                            )
 
-        self.Iqmin = VarService(v_str='-Iqmax')
+        self.Iqmin = VarService(v_str='-Iqmax', tex_name='I_{qmin}')
 
         # --- Ipcmd, Iqcmd ---
 
         self.Ipcmd = LimiterGain(u=self.Ipul, K='Fvl * Fvh * Ffl * Ffh',
                                  lower=0.0, upper=self.Ipmax,
                                  info='Ip with limiter and coeff.',
+                                 tex_name='I^{pcmd}',
                                  )
 
         self.Iqcmd = LimiterGain(u=self.Iqul, K='Fvl * Fvh * Ffl * Ffh',
                                  lower=self.Iqmin, upper=self.Iqmax,
                                  info='Iq with limiter and coeff.',
+                                 tex_name='I^{qcmd}',
                                  )
 
         self.Ipout = Lag(u=self.Ipcmd_y, T=self.tip, K=1.0,

From 26c913df1f1c2375b06b876e0499992277d1de58 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Thu, 29 Oct 2020 21:37:15 -0400
Subject: [PATCH 34/57] Patch for a codegen error

---
 andes/models/distributed.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 31f021a46..9e6a8228e 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -157,7 +157,7 @@ def __init__(self, system, config):
         self.flags.tds = True
         self.group = 'DG'
 
-        self.SWPQ = Switcher(u=self.pqflag, options=(0, 1), tex_name='SW^{PQ}', cache=True)
+        self.SWPQ = Switcher(u=self.pqflag, options=(0, 1), tex_name='SW_{PQ}', cache=True)
 
         self.buss = DataSelect(self.igreg, self.bus,
                                info='selected bus (bus or igreg)',

From 27fa9635821d3284761024e660f4776610395123 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Fri, 30 Oct 2020 12:07:52 -0400
Subject: [PATCH 35/57] Added `gammap` and `gammaq` power ratios.

---
 andes/models/distributed.py | 47 ++++++++++++++++++++++++++++---------
 1 file changed, 36 insertions(+), 11 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 9e6a8228e..9632b80fa 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -147,6 +147,16 @@ def __init__(self):
                             unit='s',
                             )
 
+        self.gammap = NumParam(default=1.0, tex_name=r'\gamma_p',
+                               info='Ratio of P from PVD1 w.r.t to that from PV generator',
+                               unit='(0, 1]',
+                               )
+
+        self.gammaq = NumParam(default=1.0, tex_name=r'\gamma_q',
+                               info='Ratio of Q from PVD1 w.r.t to that from PV generator',
+                               unit='(0, 1]',
+                               )
+
 
 class PVD1Model(Model):
     """
@@ -165,7 +175,12 @@ def __init__(self, system, config):
 
         self.busfreq = DeviceFinder(self.busf, link=self.buss, idx_name='bus')
 
-        # initial voltages from selected bus
+        # --- initial values from power flow ---
+        # v : bus voltage magnitude
+        # a : bus voltage angle
+        # p0s : active power from connected static PV generator
+        # q0s : reactive power from connected static PV generator
+
         self.v = ExtAlgeb(model='Bus', src='v', indexer=self.buss, tex_name='V',
                           info='bus (or igreg) terminal voltage',
                           unit='p.u.',
@@ -178,16 +193,26 @@ def __init__(self, system, config):
                           e_str='-Ipout_y * v',
                           )
 
-        self.p0 = ExtService(model='StaticGen',
-                             src='p',
-                             indexer=self.gen,
-                             tex_name='P_0',
-                             )
-        self.q0 = ExtService(model='StaticGen',
-                             src='q',
-                             indexer=self.gen,
-                             tex_name='Q_0',
-                             )
+        self.p0s = ExtService(model='StaticGen',
+                              src='p',
+                              indexer=self.gen,
+                              tex_name='P_{0s}',
+                              info='Initial P from static gen',
+                              )
+        self.q0s = ExtService(model='StaticGen',
+                              src='q',
+                              indexer=self.gen,
+                              tex_name='Q_{0s}',
+                              info='Initial Q from static gen',
+                              )
+        # --- calculate the initial P and Q for this distributed device ---
+        self.p0 = ConstService(v_str='gammap * p0s', tex_name='P_0',
+                               info='Initial P for the PVD1 device',
+                               )
+        self.q0 = ConstService(v_str='gammaq * q0s', tex_name='Q_0',
+                               info='Initial Q for the PVD1 device',
+                               )
+
         # frequency measurement variable `f`
         self.f = ExtAlgeb(model='FreqMeasurement', src='f', indexer=self.busfreq, export=False,
                           info='Bus frequency', unit='p.u.',

From 19e79a1cd47220c742af01bcaa8af87c926a4ad8 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Fri, 30 Oct 2020 12:08:14 -0400
Subject: [PATCH 36/57] Added multiple PVD1s on the same bus.

---
 andes/cases/ieee14/ieee14_pvd1.xlsx | Bin 25947 -> 27291 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/andes/cases/ieee14/ieee14_pvd1.xlsx b/andes/cases/ieee14/ieee14_pvd1.xlsx
index 688242ef18a4f4a80adeb020f009b06b7d0982b0..93e834b5edfbcd16e57277149c1a101f8971695e 100644
GIT binary patch
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From 2006f75a3c902c9257aa017bd0766c0df86e640b Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Fri, 30 Oct 2020 12:34:42 -0400
Subject: [PATCH 37/57] Minor edits

---
 andes/models/distributed.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 9632b80fa..2fcf930c5 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -149,12 +149,12 @@ def __init__(self):
 
         self.gammap = NumParam(default=1.0, tex_name=r'\gamma_p',
                                info='Ratio of P from PVD1 w.r.t to that from PV generator',
-                               unit='(0, 1]',
+                               vrange='(0, 1]',
                                )
 
         self.gammaq = NumParam(default=1.0, tex_name=r'\gamma_q',
                                info='Ratio of Q from PVD1 w.r.t to that from PV generator',
-                               unit='(0, 1]',
+                               vrange='(0, 1]',
                                )
 
 

From d02c07c34584c3ea9fa92a67544a7406fc9c51f5 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Fri, 30 Oct 2020 12:39:17 -0400
Subject: [PATCH 38/57] Added a note.

---
 andes/models/distributed.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 2fcf930c5..9c58e61f7 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -418,6 +418,7 @@ class PVD1(PVD1Data, PVD1Model):
     WECC Distributed PV model.
 
     Power rating specified in `Sn`.
+    Frequency and voltage recovery latching has not been implemented.
 
     Reference:
     [1] ESIG, WECC Distributed and Small PV Plants Generic Model (PVD1), [Online],

From cf320d5b820b5b28e755a83e0d415b432ca52cd3 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Fri, 30 Oct 2020 12:46:30 -0400
Subject: [PATCH 39/57] Add connection status to interface equations.

---
 andes/models/distributed.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index 9c58e61f7..fbff22799 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -184,13 +184,13 @@ def __init__(self, system, config):
         self.v = ExtAlgeb(model='Bus', src='v', indexer=self.buss, tex_name='V',
                           info='bus (or igreg) terminal voltage',
                           unit='p.u.',
-                          e_str='-Iqout_y * v',
+                          e_str='-Iqout_y * v * u',
                           )
 
         self.a = ExtAlgeb(model='Bus', src='a', indexer=self.buss, tex_name=r'\theta',
                           info='bus (or igreg) phase angle',
                           unit='rad.',
-                          e_str='-Ipout_y * v',
+                          e_str='-Ipout_y * v * u',
                           )
 
         self.p0s = ExtService(model='StaticGen',

From 3fe5ee6f60b2d32bca8dbc2b12853185736f178d Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:09:49 -0500
Subject: [PATCH 40/57] Added continuous ACE model `ACEc`.

---
 andes/models/__init__.py |  2 +-
 andes/models/area.py     | 52 ++++++++++++++++++++++++++++------------
 2 files changed, 38 insertions(+), 16 deletions(-)

diff --git a/andes/models/__init__.py b/andes/models/__init__.py
index b2cb57a40..d5b86546e 100644
--- a/andes/models/__init__.py
+++ b/andes/models/__init__.py
@@ -12,7 +12,7 @@
     ('pv', ['PV', 'Slack']),
     ('shunt', ['Shunt']),
     ('line', ['Line']),
-    ('area', ['Area', 'ACE']),
+    ('area', ['Area', 'ACE', 'ACEc']),
     ('synchronous', ['GENCLS', 'GENROU']),
     ('governor', ['TG2', 'TGOV1', 'TGOV1DB', 'IEEEG1']),
     ('exciter', ['EXDC2', 'IEEEX1', 'ESDC2A', 'EXST1', 'ESST3A', 'SEXS']),
diff --git a/andes/models/area.py b/andes/models/area.py
index 524c9f9ec..4fa8414c7 100644
--- a/andes/models/area.py
+++ b/andes/models/area.py
@@ -65,13 +65,13 @@ def __init__(self):
         self.bias = NumParam(default=1.0, info='bias parameter', tex_name=r'\beta',
                              unit='MW/0.1Hz', power=True)
 
-        self.busf = IdxParam(info='Optional BusFreq idx', model='BusFreq',
+        self.busf = IdxParam(info='Optional BusFreq device idx', model='BusFreq',
                              default=None)
 
 
-class ACE(ACEData, Model):
+class ACEc(ACEData, Model):
     """
-    Area Control Error model.
+    Area Control Error model. Continuous frequency sampling.
 
     Note: area idx is automatically retrieved from `bus`.
     """
@@ -84,13 +84,10 @@ def __init__(self, system, config):
         self.group = 'Calculation'
 
         self.config.add(OrderedDict([('freq_model', 'BusFreq'),
-                                     ('interval', 4.0),
-                                     ('offset', 0.0),
                                      ]))
-        self.config.add_extra('_help', {'freq_model': 'default freq. measurement model',
-                                        'interval': 'sampling time interval',
-                                        'offset': 'sampling time offset'})
-
+        self.config.add_extra('_help',
+                              {'freq_model': 'default freq. measurement model',
+                               })
         self.config.add_extra('_alt', {'freq_model': ('BusFreq',)})
 
         self.area = ExtParam(model='Bus', src='area', indexer=self.bus, export=False)
@@ -98,9 +95,37 @@ def __init__(self, system, config):
         self.busf.model = self.config.freq_model
         self.busfreq = DeviceFinder(self.busf, link=self.bus, idx_name='bus')
 
-        self.f = ExtAlgeb(model='FreqMeasurement', src='f', indexer=self.busfreq,
-                          export=False, info='Bus frequency',
+        self.f = ExtAlgeb(model='FreqMeasurement',
+                          src='f',
+                          indexer=self.busfreq,
+                          export=False,
+                          info='Bus frequency',
                           )
+        self.ace = Algeb(info='area control error', unit='MW (p.u.)',
+                         tex_name='ace',
+                         e_str='10 * bias * (f - 1) - ace',
+                         )
+
+
+class ACE(ACEc):
+    """
+    Area Control Error model. Discrete frequency sampling.
+
+    Frequency sampling period (in seconds) can be specified in
+    ``ACE.config.interval``. The sampling start time (in seconds)
+    can be specified in ``ACE.config.offset``.
+
+    Note: area idx is automatically retrieved from `bus`.
+    """
+
+    def __init__(self, system, config):
+        ACEc.__init__(self, system, config)
+
+        self.config.add(OrderedDict([('interval', 4.0),
+                                     ('offset', 0.0),
+                                     ]))
+        self.config.add_extra('_help', {'interval': 'sampling time interval',
+                                        'offset': 'sampling time offset'})
 
         self.fs = Sampling(self.f,
                            interval=self.config.interval,
@@ -109,7 +134,4 @@ def __init__(self, system, config):
                            info='Sampled freq.',
                            )
 
-        self.ace = Algeb(info='area control error', unit='MW (p.u.)',
-                         tex_name='ace',
-                         e_str='10 * bias * (fs_v - 1) - ace',
-                         )
+        self.ace.e_str = '10 * bias * (fs_v - 1) - ace'

From 01f409041de99c4de8a87253439e39380bf309a7 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:16:26 -0500
Subject: [PATCH 41/57] Allow `sys_f` for system frequency in equations.

---
 andes/core/model.py | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/andes/core/model.py b/andes/core/model.py
index 154171081..f07de476f 100644
--- a/andes/core/model.py
+++ b/andes/core/model.py
@@ -504,7 +504,8 @@ def __init__(self, system, config):
 
     where the `e_str` attribute is the equation string attribute. `u` is the connectivity status.
     Any parameter, config, service or variables can be used in equation strings.
-    An addition variable `dae_t` for the current simulation time can be used if the model has flag `tds`.
+    The addition variable `dae_t` for the current simulation time can be used if the model has flag `tds`.
+    The additional variable `sys_f` is for system frequency (from ``system.config.freq``).
 
     The above example is overly simplified. Our `PQ` model wants a feature to switch itself to
     a constant impedance if the voltage is out of the range `(vmin, vmax)`.
@@ -572,7 +573,9 @@ def __init__(self, system=None, config=None):
         self.services_ext = OrderedDict()  # external services (to be retrieved)
         self.services_ops = OrderedDict()  # operational services (for special usages)
 
-        self.tex_names = OrderedDict((('dae_t', 't_{dae}'),))
+        self.tex_names = OrderedDict((('dae_t', 't_{dae}'),
+                                      ('sys_f', 'f_{sys}'),
+                                      ))
 
         # Model behavior flags
         self.flags = ModelFlags()
@@ -877,8 +880,9 @@ def refresh_inputs(self):
         for key, val in self.config.as_dict(refresh=True).items():
             self._input[key] = np.array(val)
 
-        # update`dae_t`
+        # update`dae_t` and `sys_f`
         self._input['dae_t'] = self.system.dae.t
+        self._input['sys_f'] = self.system.config.freq
 
     def refresh_inputs_arg(self):
         """
@@ -1678,7 +1682,7 @@ def __init__(self, parent):
 
         self.parent = parent
         # symbols that are input to lambda functions
-        # including parameters, variables, services, configs and "dae_t"
+        # including parameters, variables, services, configs, and scalars (dae_t, sys_f)
         self.inputs_dict = OrderedDict()
         self.vars_dict = OrderedDict()
         self.iters_dict = OrderedDict()
@@ -1803,6 +1807,7 @@ def generate_symbols(self):
                 self.tex_names[Symbol(var)] = Symbol(self.parent.__dict__[var].tex_name)
 
         self.inputs_dict['dae_t'] = Symbol('dae_t')
+        self.inputs_dict['sys_f'] = Symbol('sys_f')
 
         # build ``non_vars_dict`` by removing ``vars_dict`` keys from a copy of ``inputs``
         self.non_vars_dict = OrderedDict(self.inputs_dict)

From b3d00dda973e6855b077ab18f8077459396c8ee7 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:24:16 -0500
Subject: [PATCH 42/57] Fix ACE/ACEc model equation (sys_f)

---
 andes/models/area.py | 18 +++++++++++++-----
 1 file changed, 13 insertions(+), 5 deletions(-)

diff --git a/andes/models/area.py b/andes/models/area.py
index 4fa8414c7..bd6d05d6c 100644
--- a/andes/models/area.py
+++ b/andes/models/area.py
@@ -71,7 +71,10 @@ def __init__(self):
 
 class ACEc(ACEData, Model):
     """
-    Area Control Error model. Continuous frequency sampling.
+    Area Control Error model.
+
+    Continuous frequency sampling.
+    System base frequency from ``system.config.freq`` is used.
 
     Note: area idx is automatically retrieved from `bus`.
     """
@@ -100,16 +103,21 @@ def __init__(self, system, config):
                           indexer=self.busfreq,
                           export=False,
                           info='Bus frequency',
+                          unit='p.u. (Hz)'
                           )
-        self.ace = Algeb(info='area control error', unit='MW (p.u.)',
+        self.ace = Algeb(info='area control error',
+                         unit='p.u. (MW)',
                          tex_name='ace',
-                         e_str='10 * bias * (f - 1) - ace',
+                         e_str='10 * bias * sys_f * (f - 1) - ace',
                          )
 
 
 class ACE(ACEc):
     """
-    Area Control Error model. Discrete frequency sampling.
+    Area Control Error model.
+
+    Discrete frequency sampling.
+    System base frequency from ``system.config.freq`` is used.
 
     Frequency sampling period (in seconds) can be specified in
     ``ACE.config.interval``. The sampling start time (in seconds)
@@ -134,4 +142,4 @@ def __init__(self, system, config):
                            info='Sampled freq.',
                            )
 
-        self.ace.e_str = '10 * bias * (fs_v - 1) - ace'
+        self.ace.e_str = '10 * bias * sys_f * (fs_v - 1) - ace'

From 7c8519e67e75802aa626c9226de82ed9cff59a34 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:25:38 -0500
Subject: [PATCH 43/57] Use KVXOPT.spmatrix inplace functions if available

---
 andes/shared.py | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index e0350d1e6..09542845e 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -19,18 +19,19 @@
 
 try:
     import kvxopt       # NOQA
+    from kvxopt import spmatrix
 except ImportError:
     kvxopt = None
+    from cvxopt import spmatrix
 
-from cvxopt import spmatrix
 if hasattr(spmatrix, 'ipadd'):
     IP_ADD = True
 else:
     IP_ADD = False
 
-if IP_ADD or (kvxopt is None):
+if kvxopt is None:
     from cvxopt import umfpack                           # NOQA
-    from cvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
+    from cvxopt import matrix, sparse, spdiag  # NOQA
     from cvxopt import mul, div                          # NOQA
     from cvxopt.lapack import gesv                       # NOQA
     try:
@@ -39,7 +40,7 @@
         klu = None
 else:
     from kvxopt import umfpack, klu                      # NOQA
-    from kvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
+    from kvxopt import matrix, sparse, spdiag  # NOQA
     from kvxopt import mul, div                          # NOQA
     from kvxopt.lapack import gesv                       # NOQA
 

From d993eff80165dcef867eea47e73c2cb01ecced11 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:38:59 -0500
Subject: [PATCH 44/57] Test case for VSCShunt in power flow.

---
 andes/cases/kundur/kundur_vsc.xlsx | Bin 0 -> 17537 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 andes/cases/kundur/kundur_vsc.xlsx

diff --git a/andes/cases/kundur/kundur_vsc.xlsx b/andes/cases/kundur/kundur_vsc.xlsx
new file mode 100644
index 0000000000000000000000000000000000000000..bd4a351a9df386a7551ed53b97469ab9e8fd6863
GIT binary patch
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From 52522383088da2d4164635329d51acdc64d3e3a1 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:40:39 -0500
Subject: [PATCH 45/57] WECC test cases in xlsx format.

---
 andes/cases/wecc/wecc_full.xlsx   | Bin 0 -> 70809 bytes
 andes/cases/wecc/wecc_gencls.xlsx | Bin 0 -> 68485 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 andes/cases/wecc/wecc_full.xlsx
 create mode 100644 andes/cases/wecc/wecc_gencls.xlsx

diff --git a/andes/cases/wecc/wecc_full.xlsx b/andes/cases/wecc/wecc_full.xlsx
new file mode 100644
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HcmV?d00001


From 3d2589854912fa32da473c6a0793b215cccdd30b Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:54:42 -0500
Subject: [PATCH 46/57] Fix logic for kvxopt.

---
 andes/shared.py | 31 ++++++++++++++++---------------
 1 file changed, 16 insertions(+), 15 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index 09542845e..5a709e075 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -1,13 +1,10 @@
 """
 Shared constants and delayed imports.
 """
-
-#
 # Known issues of LazyImport ::
 #
 #     1) High overhead when called hundreds of thousands times.
 #     For example, NumPy must not be imported with LazyImport.
-#
 
 from andes.utils.lazyimport import LazyImport
 
@@ -17,36 +14,40 @@
 from numpy import ndarray  # NOQA
 from tqdm import tqdm      # NOQA
 
+# import `kvxopt` and test for `ipadd`
+# only use `kvxopt` when `ipadd` is available
 try:
-    import kvxopt       # NOQA
-    from kvxopt import spmatrix
+    from kvxopt import spmatrix as kspmatrix
+    if not hasattr(kspmatrix, 'ipadd'):
+        kvxopt = None
+        IP_ADD = False
+    else:
+        IP_ADD = True
 except ImportError:
     kvxopt = None
-    from cvxopt import spmatrix
-
-if hasattr(spmatrix, 'ipadd'):
-    IP_ADD = True
-else:
-    IP_ADD = False
 
 if kvxopt is None:
     from cvxopt import umfpack                           # NOQA
-    from cvxopt import matrix, sparse, spdiag  # NOQA
+    from cvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
     from cvxopt import mul, div                          # NOQA
     from cvxopt.lapack import gesv                       # NOQA
     try:
         from cvxoptklu import klu  # NOQA
     except ImportError:
         klu = None
+    if hasattr(spmatrix, 'ipadd'):
+        IP_ADD = True
+    else:
+        IP_ADD = False
 else:
     from kvxopt import umfpack, klu                      # NOQA
-    from kvxopt import matrix, sparse, spdiag  # NOQA
+    from kvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
     from kvxopt import mul, div                          # NOQA
     from kvxopt.lapack import gesv                       # NOQA
 
 
-from andes.utils.texttable import Texttable          # NOQA
-from andes.utils.paths import get_dot_andes_path     # NOQA
+from andes.utils.texttable import Texttable              # NOQA
+from andes.utils.paths import get_dot_andes_path         # NOQA
 
 # --- constants ---
 

From 3ee9e0b803debaa799bd56717e387541f4319adc Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 16:57:57 -0500
Subject: [PATCH 47/57] Patch kvxopt logic again.

---
 andes/shared.py | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index 5a709e075..5f8124128 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -14,19 +14,19 @@
 from numpy import ndarray  # NOQA
 from tqdm import tqdm      # NOQA
 
-# import `kvxopt` and test for `ipadd`
-# only use `kvxopt` when `ipadd` is available
 try:
+    import kvxopt
     from kvxopt import spmatrix as kspmatrix
-    if not hasattr(kspmatrix, 'ipadd'):
-        kvxopt = None
-        IP_ADD = False
-    else:
-        IP_ADD = True
 except ImportError:
     kvxopt = None
 
-if kvxopt is None:
+# only use `kvxopt` when `ipadd` is available
+if kvxopt and not hasattr(kspmatrix, 'ipadd'):
+    IP_ADD = False
+else:
+    IP_ADD = True
+
+if IP_ADD is False:
     from cvxopt import umfpack                           # NOQA
     from cvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
     from cvxopt import mul, div                          # NOQA

From fdb2c844e49dac5c776cd910364340d55cb3c906 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:03:21 -0500
Subject: [PATCH 48/57] Show ipadd module name.

---
 andes/routines/pflow.py | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/andes/routines/pflow.py b/andes/routines/pflow.py
index 0cc523522..d18ba2076 100644
--- a/andes/routines/pflow.py
+++ b/andes/routines/pflow.py
@@ -130,9 +130,15 @@ def summary(self):
         Output a summary for the PFlow routine.
         """
         ipadd_status = 'CVXOPT normal (ipadd not available)'
+
+        # extract package name, `cvxopt` or `kvxopt`
+        sp_module = sparse.__module__
+        if '.' in sp_module:
+            sp_module = sp_module.split('.')[0]
+
         if IP_ADD:
             if self.system.config.ipadd:
-                ipadd_status = 'Fast in-place'
+                ipadd_status = f'Fast in-place ({sp_module})'
             else:
                 ipadd_status = 'CVXOPT normal (ipadd disabled in config)'
 

From fc751a180f4b1c5e36742d16b05be7e224ca72c7 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:17:40 -0500
Subject: [PATCH 49/57] Patch kvxopt import

---
 andes/shared.py | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index 5f8124128..c7f80fec6 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -19,12 +19,13 @@
     from kvxopt import spmatrix as kspmatrix
 except ImportError:
     kvxopt = None
+    kspmatrix = None
 
 # only use `kvxopt` when `ipadd` is available
-if kvxopt and not hasattr(kspmatrix, 'ipadd'):
-    IP_ADD = False
-else:
-    IP_ADD = True
+IP_ADD = False
+if kvxopt:
+    if hasattr(kspmatrix, 'ipadd'):
+        IP_ADD = True
 
 if IP_ADD is False:
     from cvxopt import umfpack                           # NOQA

From 12f8de98b16612441742c9a95427b0450120b298 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:30:08 -0500
Subject: [PATCH 50/57] Updated library import preference.

---
 andes/shared.py | 38 ++++++++++++++++++++++----------------
 1 file changed, 22 insertions(+), 16 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index c7f80fec6..53fdddc7a 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -14,20 +14,35 @@
 from numpy import ndarray  # NOQA
 from tqdm import tqdm      # NOQA
 
+# Library preference:
+# KVXOPT + ipadd > CVXOPT + ipadd > KXVOPT > CVXOPT (+ KLU or not)
+
 try:
     import kvxopt
     from kvxopt import spmatrix as kspmatrix
+    KIP_ADD = False
+    if hasattr(kspmatrix, 'ipadd'):
+        KIP_ADD = True
 except ImportError:
     kvxopt = None
     kspmatrix = None
+    KIP_ADD = False
+
+
+from cvxopt import spmatrix as cspmatrix
+if hasattr(cspmatrix, 'ipadd'):
+    CIP_ADD = True
+else:
+    CIP_ADD = False
 
-# only use `kvxopt` when `ipadd` is available
-IP_ADD = False
-if kvxopt:
-    if hasattr(kspmatrix, 'ipadd'):
-        IP_ADD = True
 
-if IP_ADD is False:
+if KIP_ADD is True:
+    from kvxopt import umfpack, klu                      # NOQA
+    from kvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
+    from kvxopt import mul, div                          # NOQA
+    from kvxopt.lapack import gesv                       # NOQA
+    IP_ADD = KIP_ADD
+elif CIP_ADD is True:
     from cvxopt import umfpack                           # NOQA
     from cvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
     from cvxopt import mul, div                          # NOQA
@@ -36,16 +51,7 @@
         from cvxoptklu import klu  # NOQA
     except ImportError:
         klu = None
-    if hasattr(spmatrix, 'ipadd'):
-        IP_ADD = True
-    else:
-        IP_ADD = False
-else:
-    from kvxopt import umfpack, klu                      # NOQA
-    from kvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
-    from kvxopt import mul, div                          # NOQA
-    from kvxopt.lapack import gesv                       # NOQA
-
+    IP_ADD = CIP_ADD
 
 from andes.utils.texttable import Texttable              # NOQA
 from andes.utils.paths import get_dot_andes_path         # NOQA

From 5f416bdc09efbe6a3f27053569c18118a5e9d2af Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:33:57 -0500
Subject: [PATCH 51/57] import logic fix.

---
 andes/shared.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/andes/shared.py b/andes/shared.py
index 53fdddc7a..4a66722b7 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -36,13 +36,7 @@
     CIP_ADD = False
 
 
-if KIP_ADD is True:
-    from kvxopt import umfpack, klu                      # NOQA
-    from kvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
-    from kvxopt import mul, div                          # NOQA
-    from kvxopt.lapack import gesv                       # NOQA
-    IP_ADD = KIP_ADD
-elif CIP_ADD is True:
+if kvxopt is None or (KIP_ADD is False and CIP_ADD is True):
     from cvxopt import umfpack                           # NOQA
     from cvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
     from cvxopt import mul, div                          # NOQA
@@ -52,6 +46,12 @@
     except ImportError:
         klu = None
     IP_ADD = CIP_ADD
+else:
+    from kvxopt import umfpack, klu                      # NOQA
+    from kvxopt import spmatrix, matrix, sparse, spdiag  # NOQA
+    from kvxopt import mul, div                          # NOQA
+    from kvxopt.lapack import gesv                       # NOQA
+    IP_ADD = KIP_ADD
 
 from andes.utils.texttable import Texttable              # NOQA
 from andes.utils.paths import get_dot_andes_path         # NOQA

From 86bd84fe790e37269aa8253e80655b4e2fa48610 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:39:41 -0500
Subject: [PATCH 52/57] Added kvxopt as a dependency.

---
 docs/source/install.rst       | 37 +++++++++++++----------------------
 docs/source/release-notes.rst | 16 ++++++++++++++-
 requirements.txt              |  1 +
 3 files changed, 30 insertions(+), 24 deletions(-)

diff --git a/docs/source/install.rst b/docs/source/install.rst
index d7686f5a6..a4e5cbb17 100644
--- a/docs/source/install.rst
+++ b/docs/source/install.rst
@@ -165,46 +165,37 @@ Change directory to the ANDES source code folder that contains ``setup.py`` and
 
 Performance Packages (Advanced)
 ===============================
-The following two forks of ``cvxopt``, ``cvxoptklu``, ``cvxopt`` with ``spmatrix.ipadd``
+The following two forks of ``cvxopt``: ``kvxopt`` and ``cvxopt`` with ``spmatrix.ipadd``
 are optional but can significantly boost the performance of ANDES.
-**Installation requires a C compiler**, ``openblas`` and ``SuiteSparse`` libraries.
 
 .. note::
 
     Performance packages can be safely skipped and will not affect the
     functionality of ANDES.
 
-.. warning::
-
-    We have not tried to compile either package on Windows.
-    Refer to the CVXOPT installation instructions for Windows at
-    http://cvxopt.org/install/index.html#windows
-
-cxvoptklu
----------
-``cvxoptklu`` is a fork of the CVXOPT with KLU by Uriel Sandoval (@sanurielf).
-In addition to UMFPACK, ``cvxoptklu`` interfaces ``cvxopt`` to KLU, which is
+KVXOPT
+------
+``KVXOPT`` is a fork of the CVXOPT with KLU by Uriel Sandoval (@sanurielf).
+In addition to UMFPACK, ``KVXOPT`` interfaces ``cvxopt`` to KLU, which is
 roughly 20% faster than UMFPACK for circuit simulation based on our testing.
 
-To install ``cvxoptklu``, on Debian GNU/Linux, one can do
+To install ``KVXOPT`` run
 
 .. code:: bash
 
-      sudo apt install libopenblas-dev libsuitesparse-dev
-      pip install cvxoptklu
+      python -m pip install kvxopt
 
-On macOS, one can install with homebrew using
+CVXOPT with ipadd
+-----------------
 
-.. code:: bash
+**Installation requires a C compiler**, ``openblas`` and ``SuiteSparse`` libraries.
 
-    brew install openblas suitesparse
-    pip install cvxoptklu
+.. warning::
 
-To install from source code, use the repository at
-https://github.com/cuihantao/cvxoptklu.
+    We have not tried to compile CVXOPT on Windows.
+    Refer to the CVXOPT installation instructions for Windows at
+    http://cvxopt.org/install/index.html#windows
 
-CVXOPT with ipadd
------------------
 To install our fork of ``cvxopt`` with ``spmatrix.ipadd``, one need to clone the
 repository and compile from source.
 
diff --git a/docs/source/release-notes.rst b/docs/source/release-notes.rst
index 9866607bc..6037b5354 100644
--- a/docs/source/release-notes.rst
+++ b/docs/source/release-notes.rst
@@ -8,9 +8,23 @@ The APIs before v3.0.0 are in beta and may change without prior notice.
 
 v1.2 Notes
 ----------
-v1.2.2
+v1.2.2 (2020-11-01)
 ```````````````````
+New Models:
+
+- ``PVD1`` model, WECC distributed PV model.
+  Supports multiple PVD1 devices on the same bus.
+- Added ``ACEc`` model, ACE calculation with continuous freq.
+
+Changes and fixes:
+
 - Renamed `TDS._itm_step` to `TDS.itm_step` as a public API.
+- Allow variable `sys_f` (system frequency) in equation strings.
+- Fixed ACE equation.
+  measurement.
+- Support ``kvxopt`` as a drop-in replacement for ``cvxopt``
+  to bring KLU to Windows (and other platforms).
+- Added ``kvxopt`` as a dependency for PyPI installation.
 
 v1.2.1 (2020-10-11)
 ```````````````````
diff --git a/requirements.txt b/requirements.txt
index f42b79606..67815b9ca 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,4 +1,5 @@
 cvxopt>=1.2.3
+kvxopt
 numpy
 scipy
 sympy==1.5.1

From 9211d194929ee6b207bfed65433228f6b6072fe8 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:50:28 -0500
Subject: [PATCH 53/57] Skip kvxopt if shared libs are not available.

---
 andes/shared.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/andes/shared.py b/andes/shared.py
index 4a66722b7..45548500e 100644
--- a/andes/shared.py
+++ b/andes/shared.py
@@ -19,6 +19,7 @@
 
 try:
     import kvxopt
+    from kvxopt import umfpack   # test if shared libs can be found
     from kvxopt import spmatrix as kspmatrix
     KIP_ADD = False
     if hasattr(kspmatrix, 'ipadd'):

From 747fe28337149f24be21a542fe776bf24dac1a04 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:54:11 -0500
Subject: [PATCH 54/57] Reverted kvxopt dependency.

---
 requirements.txt | 1 -
 1 file changed, 1 deletion(-)

diff --git a/requirements.txt b/requirements.txt
index 67815b9ca..f42b79606 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,5 +1,4 @@
 cvxopt>=1.2.3
-kvxopt
 numpy
 scipy
 sympy==1.5.1

From 9750d557c4ec5d0f272efc55f4c58ebaaaec2a64 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:55:37 -0500
Subject: [PATCH 55/57] Updated docs.

---
 andes/cases/ieee14/pert.py | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/andes/cases/ieee14/pert.py b/andes/cases/ieee14/pert.py
index ae10577b5..151dd266c 100644
--- a/andes/cases/ieee14/pert.py
+++ b/andes/cases/ieee14/pert.py
@@ -1,7 +1,14 @@
 """
-Empty pert file
+An empty pert file.
 """
 
 
 def pert(t, system):
+    """
+    Perturbation function called at each step.
+
+    The function is named "pert" and takes two arguments:
+    ``t`` for simulation time, and ``system`` for the system object.
+
+    """
     pass

From b8c07af6b17995610baac57e3d1a2969a4ac1f61 Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:57:51 -0500
Subject: [PATCH 56/57] Removed unused imports.

---
 andes/models/distributed.py | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/andes/models/distributed.py b/andes/models/distributed.py
index fbff22799..b7e38d672 100644
--- a/andes/models/distributed.py
+++ b/andes/models/distributed.py
@@ -4,13 +4,12 @@
 
 from andes.core.model import Model, ModelData
 from andes.core.param import NumParam, IdxParam
-from andes.core.block import Lag, DeadBand1, LimiterGain  # NOQA
-from andes.core.var import ExtAlgeb, ExtState, Algeb, State  # NOQA
+from andes.core.block import Lag, DeadBand1, LimiterGain
+from andes.core.var import ExtAlgeb, Algeb
 
-from andes.core.service import ConstService, ExtService, FlagValue, DataSelect, DeviceFinder  # NOQA
-from andes.core.service import VarService, Replace  # NOQA
-from andes.core.service import NumSelect  # NOQA
-from andes.core.discrete import Switcher, Limiter  # NOQA
+from andes.core.service import ConstService, ExtService, VarService
+from andes.core.service import DataSelect, DeviceFinder
+from andes.core.discrete import Switcher, Limiter
 
 
 class PVD1Data(ModelData):

From 194bdac840c0b917de974321f3ebb3b1f2b01dcd Mon Sep 17 00:00:00 2001
From: Hantao Cui <cuihantao@gmail.com>
Date: Sun, 1 Nov 2020 17:58:04 -0500
Subject: [PATCH 57/57] Added docs.

---
 tests/test_paths.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/tests/test_paths.py b/tests/test_paths.py
index 8761529c6..a4d64659d 100644
--- a/tests/test_paths.py
+++ b/tests/test_paths.py
@@ -26,6 +26,7 @@ def test_addfile_path(self):
                   )
 
     def test_pert_file(self):
+        """Test path of pert file"""
         path, case = os.path.split(self.ieee14)
 
         # --- with pert file ---