04AssemblingCircuits.ipynb

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    "# [Weather data and solar radiation](01WeatherData.ipynb)\n",
    "\n",
    "# [Thermal circuit and state-space representation for a thermal circuit with capacities in every node: simple wall](02SimpleWall.ipynb)\n",
    "\n",
    "# [Thermal circuit and state-space representation for a thermal circuit with capacities in some nodes: cubic building](03CubicBuilding.ipynb)\n",
    "\n",
    "# Thermal circuits assembling\n",
    "\n",
    "**Objectives:**\n",
    "- Obtain the thermal model by assembling thermal circuits.\n",
    "- Convert thermal circuit to state-space representation.\n",
    "- Simulate the assembled circuits."
   ]
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import dm4bem\n",
    "import tuto"
   ]
  },
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   "source": [
    "*Note*: The module `tuto.py` contains the implementation of the model as presented in this notebook. If the model in this notebook is changed, the same changes need to be done in `tuto.py`.  "
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    "## Defining the problem of circuit assembling\n",
    "\n",
    "The problem of assembling thermal circuits can be stated as:\n",
    "\n",
    "> Given a number of disassembled thermal circuits, $TCd_0$, $TCd_1$, ... , $TCd_n$, and knowing that some of their nodes are common, find the assembled thermal circuit $TC$ (see Figure 1).\n",
    "\n",
    "To exemplify the procedure, we will use the same model as in tutorial [Thermal circuit and state-space representation for a thermal circuit with capacities in some nodes: cubic building](03CubicBuilding.ipynb)\n",
    " representing a room with an insulated concrete wall and a glass wall. The room is ventilated and the indoor air temperature is controlled by a P-controller. This [toy model](https://en.m.wikipedia.org/wiki/Toy_model) is used to explain the assembling procedure, not for the correctness of the modelling.\n",
    "\n",
    "![assembling](./figures/04_assembling.svg)\n",
    "> Figure 1. Example of the problem of assembling thermal circuits: given four circuits, TCd0, ..., TCd3, assemble them knowing that the following nodes are common to two or more circuits:\n",
    "> - Node 4 of circuit TCd0 (in red) is in common with node 0 of circuit TCd1 (in blue).\n",
    "> - Node 1 of circuit TCd1 (in blue) is in common with node 1 of circuit TCd2 (in green).\n",
    "> - Node 2 of circuit TCd1 (in blue) is in common with node 0 of circuit TCd3 (in violet).\n",
    "\n",
    "![circuit](./figures/04_circuit.svg)\n",
    "> Figure 2. Thermal circuit obtained by assembling elementary circuits TCd0, ..., TCd3. The heat-flow sources and the capacities in a node are the sum of those of each circuit. The numbers in black correspond to the global indexing and the numbers in colors (red, blue, green and violet) correspond to the local indexing.\n",
    "\n",
    "![matrices](./figures/04_matrices.svg)\n",
    "> Figure 3. Algebraic representation of the thermal circuit: \n",
    "> - a) assembly-connectivity matrix; \n",
    "> - b) elementary thermal circuits, TCd0, ..., TCd3, characterized by the matrices $A, G, C$ and the vectors $b, f$ and $y$.\n",
    "\n",
    "From the conservation of energy, it results that if there is a flow source in the common node of the assembled circuit, it needs to be the sum of the sources from the corresponding node of each elementary circuit. For example, the source in node 4 of the assembled circuit is the sum of the sources from node 4 of TCd0 and node 0 of TCd1 (Figure 2). From the conservation of mass, it results that if there is a common capacity in the node of the assembled circuit, it needs to be the sum of the capacities present in the corresonding node of each elemendaty circuit. For example, the capacity in node 6 of the assembled circuit is the sum of the capacities of node 2 of TCd1 and of node 0 of TCd3. \n",
    "\n",
    "We would like to construct separate models for the disassembled thermal circuits (e.g., for concrete wall TCD0, room air TCd1, glass wall TCd2, ventilation and HVAC system TCd2) and to assemble them into a single thermal circuit."
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    "## Numbering the circuits\n",
    "\n",
    "### Numbering elementary circuits\n",
    "\n",
    "In principle, the numbering of the nodes and the branches can be done arbitrarily. The connections are indicated by the oriented incidence matrix $A$. Since numbering becomes tedious for large circuits, the following rules may be adopted:\n",
    "- number the nodes in order (e.g. from left to right and from top to bottom);\n",
    "- number the branches in increasing order of nodes and direct them from the lower to the higher node number.\n",
    "\n",
    "### Numbering the assembled circuit\n",
    "When assembling the thermal circuits, some nodes are put in common. Therefore, the number of nodes in the assembled circuit will be smaller than the sum of the nodes of the elementary circuits. However, the number of branches will not change. The nodes and the branches of the assembled circuit will be in the order of assembling.\n",
    "\n",
    "\n",
    "\n",
    "> Table 1. Local and global indexing of nodes in circuits shown  Figure 2. Local nodes have the color of the circuit. Global nodes are in black.\n",
    "\n",
    "|Thermal circuit  |TCd0      |TCd1    |TCd2 |TCd3|\n",
    "|-----------------|:--------:|:------:|:---:|:--:|\n",
    "|Local node index |0 1 2 3 4 |0 1  2  |0  1 |0   |\n",
    "|Global node index|0 1 2 3 4 |4 5  6  |7  5 |6   |\n",
    "\n",
    "\n",
    "> Table 2. Local and global indexing of branches in circuits shown  Figure 2. Local branches have the color of the circuit. Global branches are in black.\n",
    "\n",
    "|Thermal circuit    |TCd0      |TCd1  |TCd3 |TCd3 |\n",
    "|-------------------|:--------:|:----:|:---:|:---:|\n",
    "|Local branch index |0 1 2 3 4 |0 1 2 |0 1  | 0  1|\n",
    "|Global branch index|0 1 2 3 4 |5 6 7 |8 9  |10 11|\n",
    "\n",
    "The assembling of the circuits is described by the assembling matrix. Each row of this matrix has four elements that indicate the two nodes that will be put together:\n",
    "1. index of the 1st circuit\n",
    "2. node of the 1st circuit\n",
    "3. index of the 2nd circuit \n",
    "4. node of the 2nd circuit\n",
    "\n",
    "For our example, the assembling matrix is (see Figure 1):\n",
    "\n",
    "$$A_{ss} =\\begin{bmatrix}\n",
    "0 & 4 & 1 & 0\\\\ \n",
    "1 & 1 & 2 & 1\\\\ \n",
    "1 & 2 & 3 & 0\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "meaning that:\n",
    "- circuit TCd0, node 4, identic with circuit TCd1, node 0;\n",
    "- circuit TCd1, node 1, identic with circuit TCd2, node 1;\n",
    "- circuit TCd1, node 2, identic with circuit TCd3, node 0.\n",
    "\n",
    "The description of the disassembled circuits, given by the [dictionary](https://docs.python.org/3/tutorial/datastructures.html#dictionaries) $TC_d = \\{TC_0,…, TC_i,…, TC_n\\}$ of [dictionaries](https://docs.python.org/3/tutorial/datastructures.html#dictionaries) $TC_i=\\{A_i,G_i,C_i,b_i,f_i,y_i\\}$, and the assembling matrix $A_{ss}$ contain all the necessary information for obtaining the assembled circuit. "
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   "source": [
    "## Conductances and capacities"
   ]
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   "source": [
    "Let's consider the same geometry and thermophysical properties as in [Tutorial 3](03CubicBuilding.ipynb)."
   ]
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    "# Dimensions and surface areas of the building\n",
    "l = 3               # m length of the cubic room\n",
    "Sg = l**2           # m² surface of the glass wall\n",
    "Sc = Si = 5 * Sg    # m² surface of concrete & insulation of the 5 walls\n",
    "Va = l**3           # m³ volume of air\n",
    "\n",
    "# Thermophysical properties of the air (in SI units) \n",
    "air = {'Density': 1.2,                      # kg/m³\n",
    "       'Specific heat': 1000}               # J/kg.K\n",
    "\n",
    "wall = {'Conductivity': [1.4, 0.027, 1.4],  # W/m.K\n",
    "        'Density': [2300, 55, 2500],        # kg/m³\n",
    "        'Specific heat': [880, 1210, 750],  # J/kg.K\n",
    "        'Width': [0.2, 0.08, 0.004],\n",
    "        'Surface': [5 * l**2, 5 * l**2, l**2],  # m²\n",
    "        'Meshes': [1, 1, 1]}                # number of meshes\n",
    "wall = pd.DataFrame(wall, index=['Concrete', 'Insulation', 'Glass'])\n",
    "\n",
    "# Radiative properties\n",
    "ε_wLW = 0.85    # long wave emmisivity wall concrete\n",
    "ε_gLW = 0.90    # long wave emmisivity glass pyrex\n",
    "α_wSW = 0.25    # short wave absortivity white smooth surface\n",
    "α_gSW = 0.38    # short wave absortivity reflective blue glass\n",
    "τ_gSW = 0.30    # short wave transmitance reflective blue glass\n",
    "\n",
    "# Stefan-Boltzmann constant\n",
    "σ = 5.67e-8     # W/m²⋅K⁴ Stefan-Bolzmann constant\n",
    "\n",
    "# View factor\n",
    "Fwg = 1 / 5     # view factor wall - glass\n",
    "\n",
    "Tm = 20 + 273   # mean temp for radiative exchange\n",
    "\n",
    "# Convection coeficients\n",
    "h = pd.DataFrame([{'in': 8., 'out': 25}], index=['h'])  # W/m²⋅K"
   ]
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    "The HVAC system can be modelled as a proportional controller with the gain $K_p$:\n",
    "* If $K_p \\rightarrow \\infty$, then the controller tends towards perfection, i.e., the indoor temperature tends towards its set-point.\n",
    "* If $K_p \\rightarrow  0$, then the controller is ineffective, i.e., the indoor temperature is in free-floating.\n",
    "\n",
    "Let's consider the case of free-floating."
   ]
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   "source": [
    "Kp = 1e-3       # no controller Kp -> 0"
   ]
  },
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   "source": [
    "The air infiltration rate is chatacterized by the number of air changes per hour."
   ]
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   "source": [
    "ACH = 1                     # air changes per hour\n",
    "Va_dot = ACH * Va / 3600    # m³/s air infiltration"
   ]
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   "source": [
    "This information allows us to calculate the conductances of:\n",
    "- insulated concrete wall,\n",
    "- glass wall,\n",
    "- long wave radiation exchange between the walls,\n",
    "- advection by ventilation,\n",
    "- proportional controller,\n",
    "\n",
    "and the capacities of the walls and of the air (Figures 1 and 2)."
   ]
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    "# Thermal conductances\n",
    "# Conduction\n",
    "G_cd = wall['Conductivity'] / wall['Width'] * wall['Surface']\n",
    "\n",
    "# Convection\n",
    "Gw = h * wall['Surface'][0]     # wall\n",
    "Gg = h * wall['Surface'][2]     # glass\n",
    "\n",
    "# Long-wave radiation exchnage\n",
    "GLW1 = ε_wLW / (1 - ε_wLW) * wall['Surface']['Insulation'] * 4 * σ * Tm**3\n",
    "GLW2 = Fwg * wall['Surface']['Insulation'] * 4 * σ * Tm**3\n",
    "GLW3 = ε_gLW / (1 - ε_gLW) * wall['Surface']['Glass'] * 4 * σ * Tm**3\n",
    "# long-wave exg. wall-glass\n",
    "GLW = 1 / (1 / GLW1 + 1 / GLW2 + 1 / GLW3)\n",
    "\n",
    "# ventilation & advection\n",
    "Gv = Va_dot * air['Density'] * air['Specific heat']\n",
    "\n",
    "# glass: convection outdoor & conduction\n",
    "Ggs = float(1 / (1 / Gg['out'] + 1 / (2 * G_cd['Glass'])))\n",
    "\n",
    "# Thermal capacities\n",
    "Capacity = wall['Density'] * wall['Specific heat'] *\\\n",
    "    wall['Surface'] * wall['Width']\n",
    "Capacity['Air'] = air['Density'] * air['Specific heat'] * Va"
   ]
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   "source": [
    "## Procedure for assembling"
   ]
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   "source": [
    "### Defining the elementary thermal circuits\n",
    "The elementary (or disassembled) thermal circuits TCd0, ... , TCd2  are described by the matrices and vectors $A, G, C, b, f, y$.\n",
    "\n",
    "#### Thermal circuit TCd0\n",
    "The thermal circuit TCd0 (in red in Figures 1 and 2) models convection on the outside surface of the wall and conduction in concrete and insulation. TCd0 has `nq` flow branches and `nθ` temperature nodes."
   ]
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   "source": [
    "# TCd0:  Concrete and insulation wall (in red)\n",
    "nq = 1 + 2 * (wall['Meshes']['Concrete'] + wall['Meshes']['Insulation'])\n",
    "nθ = 1 + 2 * (wall['Meshes']['Concrete'] + wall['Meshes']['Insulation'])"
   ]
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    "The incidence matrix $A$ is a difference operator for temperatures, $-A = \\Delta$:\n",
    "\n",
    "$$\\Delta \\theta = -A \\theta = \\begin{bmatrix}\n",
    "1 & 0 & 0 & 0 & 0\\\\ \n",
    "-1 &  1 & 0 & 0 & 0\\\\ \n",
    "0 & -1 & 1 & 0 & 0\\\\ \n",
    "0 & 0 & -1 & 1 & 0\\\\ \n",
    "0 & 0 & 0 & -1 & 1\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\theta_0\\\\ \n",
    "\\theta_1\\\\ \n",
    "\\theta_2\\\\ \n",
    "\\theta_3\\\\ \n",
    "\\theta_4\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "\\theta_0 - 0\\\\ \n",
    "\\theta_1 - \\theta_0\\\\ \n",
    "\\theta_2 - \\theta_1\\\\ \n",
    "\\theta_3 - \\theta_2\\\\ \n",
    "\\theta_4 - \\theta_3\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
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   "source": [
    "A = np.eye(nq + 1, nθ)\n",
    "A = -np.diff(A, 1, 0).T"
   ]
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   "source": [
    "The conductance matrix $G$ contains the conductances of the flow branches. The conductances of the concrete and the insulation are discretized in meshes. The conductances of the outdoor convection, conduction in concrete and conduction in insulation are stacked horizontally. Then, $G$ is obtained as a diagonal matrix."
   ]
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   "source": [
    "nc = wall['Meshes']['Concrete']\n",
    "ni = wall['Meshes']['Insulation']\n",
    "Gc = 2 * nc * [G_cd['Concrete']]    # creates 2 * nc values of G_cd\n",
    "Gc = 2 * nc * np.array(Gc)          # multiplies G_cd with 2 * nc\n",
    "Gi = 2 * ni * [G_cd['Insulation']]\n",
    "Gi = 2 * ni * np.array(Gi)\n",
    "G = np.hstack([Gw['out'], Gc, Gi])\n",
    "G = np.diag(G)"
   ]
  },
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   "source": [
    "The capacity matrix $C$ contains the capacities of the thermal nodes correspondig to concrete and insulation. These capacities are stacked horizontally and then the capacity matrix $C$ is obtained as a diagonal matrix. "
   ]
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   "source": [
    "Cc = Capacity['Concrete'] / nc * np.mod(range(0, 2 * nc), 2)\n",
    "Ci = Capacity['Insulation'] / ni * np.mod(range(0, 2 * ni), 2)\n",
    "C = np.hstack([Cc, Ci, 0])\n",
    "C = np.diag(C)"
   ]
  },
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   "id": "5a183103-a336-40b5-bec5-4eb8120043b2",
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   "source": [
    "The vector of temperature sources, $b$, has the size of the number of branches (of heat flow rates). There is only one branch with a temperature source: $b_0$."
   ]
  },
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   "source": [
    "b = np.zeros(nq)    # nq is the number of flow branches\n",
    "b[0] = 1            # node with temperature source"
   ]
  },
  {
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   "id": "044bfad4-da5a-4817-a754-7ed0a976f343",
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   "source": [
    "The vector of flow rate sources, $f$, has the size of the number of nodes (of temperatures). There are two nodes with a flow rate sources: the 1st node $f_0$ and the last node $f_{last}$."
   ]
  },
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   "source": [
    "f = np.zeros(nθ)    # nθ is the number of temperature nodes\n",
    "f[0] = f[-1] = 1    # nodes with flow sources"
   ]
  },
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   "id": "88bae330-e0f5-4847-9eff-54bb156a08d4",
   "metadata": {},
   "source": [
    "There is no temperature from circuit TCd0 in the output vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8fc8f40e-c444-427a-b8fc-e2d1d8caaec7",
   "metadata": {},
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   "source": [
    "y = np.zeros(nθ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b35d1e5a-9bab-4b1d-b0bb-78e7c15a3b45",
   "metadata": {},
   "source": [
    "The circuit TCd0 is characterized by the matrices and vectors $A, G, b, C, f, y$, collected into a [dictionary](https://docs.python.org/3/tutorial/datastructures.html#dictionaries)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c8521eeb-ba2d-4736-b430-e9e839a8d019",
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   "source": [
    "TCd0 = {'A': A,'G': G, 'b': b, 'C': C, 'f': f, 'y': y}"
   ]
  },
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   "source": [
    "#### Thermal circuits TCd1 ... TCd3\n",
    "\n",
    "The thermal circuits TCd1, TCd2 and TCd3are constructed similarly."
   ]
  },
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   "source": [
    "# TCd1: Indoor air (in blue)\n",
    "A = np.array([[-1, 1, 0],\n",
    "              [-1, 0, 1],\n",
    "              [0, -1, 1]])\n",
    "G = np.diag(np.hstack([GLW, Gw['in'], h['in'] * wall['Surface']['Glass']]))\n",
    "b = np.zeros(3)\n",
    "C = np.diag([0, 0, Capacity['Air'] / 2])\n",
    "f = np.array([1, 0, 1])\n",
    "y = np.array([0, 0, 1])\n",
    "TCd1 = {'A': A, 'G': G, 'b': b, 'C': C, 'f': f, 'y': y}\n",
    "\n",
    "# TCd2: Glass (in green)\n",
    "A = np.array([[1, 0],\n",
    "              [-1, 1]])\n",
    "Ggo = h['out'] * wall['Surface']['Glass']\n",
    "Ggs = 1 / (1 / Ggo + 1 / (2 * G_cd['Glass']))\n",
    "G = np.diag(np.hstack([Ggs, 2 * G_cd['Glass']]))\n",
    "b = np.array([1, 0])\n",
    "C = np.diag([Capacity['Glass'], 0])\n",
    "f = np.array([1, 0])\n",
    "y = np.array([0, 0])\n",
    "TCd2 = {'A': A, 'G': G, 'b': b, 'C': C, 'f': f, 'y': y}\n",
    "\n",
    "# TCd3: air infiltration and controller (in purple)\n",
    "A = np.array([[1],\n",
    "              [1]])\n",
    "G = np.diag(np.hstack([Gv, Kp]))\n",
    "b = np.array([1, 1])\n",
    "C = np.array([Capacity['Air'] / 2])\n",
    "f = 1\n",
    "y = 1\n",
    "TCd3 = {'A': A, 'G': G, 'b': b, 'C': C, 'f': f, 'y': y}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "202404fa-56a9-4db8-b07a-1d9521b842d6",
   "metadata": {},
   "source": [
    "### Assembling the elementary thermal circuits\n",
    "\n",
    "The *elementary* dissembled circuits, TCd0, ... , TCd3 are used to construct a dissembled thermal circuit TCd. Note that the *elementary* circuits may be used more than once in the dissembled thermal circuit TCd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3a04fbc8-31a0-4df9-9495-cc2e3ae09f2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "TCd = {'0': TCd0,\n",
    "       '1': TCd1,\n",
    "       '2': TCd2,\n",
    "       '3': TCd3}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "119efb7b-9489-4f7e-8ef0-34f2412ba9ca",
   "metadata": {
    "tags": []
   },
   "source": [
    "The assembly matrix\n",
    "\n",
    "$$A_{ss} =\\begin{bmatrix}\n",
    "0 & last & 1 & 0\\\\ \n",
    "1 & 1 & 2 & 1\\\\ \n",
    "1 & 2 & 3 & 0\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "indicates how the circuits are connected. For example, the 1st row of matrix $A_{ss}$ indicates that the `last` node (i.e. node number `nθ - 1`) of circuit TCd0 is merged with the 1st node (i.e. node number 0) of circuit TCd1; the 1st node (i.e., node number 0) of circuit TCd1 is deleted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b00c7b44-6ae4-475e-a01b-37d1588dd1c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ass = np.array([[0, nθ - 1, 1, 0],\n",
    "                [1, 1, 2, 1],\n",
    "                [1, 2, 3, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53d4e6f2-a93d-44fc-be14-b5193d738dc8",
   "metadata": {
    "tags": []
   },
   "source": [
    "Finally, the dissambled thermal circuit TCd is assembled according to the connexions indicated by the assembly matrix $A_{ss}$ by using the functionn `dm4bem.TCAss`. The result is an assembled thermal circuit with matrices and vectors $A, G, b, C, f, y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b0da3572-236e-4f90-bc5b-877331dda932",
   "metadata": {},
   "outputs": [],
   "source": [
    "TCa = dm4bem.TCAss(TCd, Ass)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abb6dc18-0df7-4405-a650-750014307740",
   "metadata": {
    "tags": []
   },
   "source": [
    "### State-space representation from DAE\n",
    "#### Model matrices\n",
    "The state-space representation is obtained from the thermal circuit `TCa`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "611198ff-db31-4424-ac90-ccf40d2b4df0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Thermal circuit -> state-space\n",
    "[As, Bs, Cs, Ds] = dm4bem.tc2ss(\n",
    "    TCa['A'], TCa['G'], TCa['C'], TCa['b'], TCa['f'], TCa['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15e41847-9134-47b4-afa2-7a23c5dd6db4",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Input vector\n",
    "The input vector $u$ of the state-space representation is obtained by stacking the vectors $b_T$ and $f_Q$ of the system of Differential Algebraic Equations (DAE):\n",
    "\n",
    "$$u = \\begin{bmatrix} b_T \\\\ f_Q\\end{bmatrix}$$\n",
    "\n",
    "where:\n",
    "- vector $b_T$ consists of the nonzero elements of vector $b$ of temperature sources; for the circuit presented in Figure 3, $b_T = [T_o, T_o, T_o, T_{i,sp}]^T$ corresponding to branches 0, 8, 10 and 11; \n",
    "- vector $f_Q$ is the nonzero elements of vector $f$ of flow sources; for the circuit presented in Figure 3, $f_Q = [\\Phi_o, \\Phi_i, \\dot{Q}_a, \\Phi_a]^T$ corresponding to nodes 0, 4, 6, and 7.\n",
    "\n",
    "The input vector, $u = [u_0, u_1, ... , u_{n-1}]^T$, becomes:\n",
    "\n",
    "$$u = \n",
    "\\begin{bmatrix}\n",
    "T_o\\\\ \n",
    "T_o\\\\ \n",
    "T_o\\\\ \n",
    "T_{i,sp}\\\\ \n",
    "\\Phi_o\\\\ \n",
    "\\Phi_i\\\\ \n",
    "\\dot{Q}_a\\\\ \n",
    "\\Phi_a\n",
    "\\end{bmatrix}\n",
    "= \\begin{bmatrix}\n",
    "T_{o(0)} & T_{o(1)}& ... & T_{o(n-1)}\\\\ \n",
    "T_{o(0)} & T_{o(1)}& ... & T_{o(n-1)}\\ \\\\ \n",
    "T_{o(0)} & T_{o(1)}& ... & T_{o(n-1)}\\ \\\\ \n",
    " T_{i,sp(0)} & T_{i,sp(1)}& ... & T_{i,sp(n-1)}\\ \\\\ \n",
    "\\Phi_{o,(0)} & \\Phi_{o,(1)} & ... & \\Phi_{o,(n-1)}\\\\\n",
    "\\Phi_{i,(0)} & \\Phi_{i,(1)} & ... & \\Phi_{i,(n-1)}\\\\ \n",
    " \\dot{Q}_{a(0)} & \\dot{Q}_{a(1)} & ... & \\dot{Q}_{a(n-1)}\\\\ \n",
    "\\Phi_{a,(0)} & \\Phi_{a,(1)} & ... & \\Phi_{a,(n-1)}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "where:\n",
    "- $T_o = [T_{o(0)}, T_{o(1)}, ..., T_{o(n-1)}]^T$ is the [time series](https://en.m.wikipedia.org/wiki/Time_series) of the oudoor temperature at [discrete time](https://en.m.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time) $t = [t_0, t_1, ... , t_{n-1}]^T$.\n",
    "- $T_{i, sp} = [T_{{i, sp}(0)}, T_{{i, sp}(1)}, ..., T_{{i, sp}(n-1)}]^T$ is the [time series](https://en.m.wikipedia.org/wiki/Time_series) of the setpoint indoor temperature at [discrete time](https://en.m.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time) $t = [t_0, t_1, ... , t_{n-1}]^T$.\n",
    "- $\\Phi_o = [\\Phi_{o(0)}, \\Phi_{o(1)}, ..., \\Phi_{o(n-1)}]^T$ is the [time series](https://en.m.wikipedia.org/wiki/Time_series) of the solar radiation absorbed by the outdoor surface of the wall at [discrete time](https://en.m.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time) $t = [t_0, t_1, ... , t_{n-1}]^T$.\n",
    "- $\\Phi_i = [\\Phi_{i(0)}, \\Phi_{i(1)}, ..., \\Phi_{i(n-1)}]^T$ is the [time series](https://en.m.wikipedia.org/wiki/Time_series) of the solar radiation absorbed by the indoor surface of the wall at [discrete time](https://en.m.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time) $t = [t_0, t_1, ... , t_{n-1}]^T$.\n",
    "- $\\dot{Q}_a = [\\dot{Q}_{a(0)}, \\dot{Q}_{a(1)}, ..., \\dot{Q}_{a(n-1)}]^T$ is the [time series](https://en.m.wikipedia.org/wiki/Time_series) of the auxiliary heat gains (i.e., occupants, electrical devices, etc.) at [discrete time](https://en.m.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time) $t = [t_0, t_1, ... , t_{n-1}]^T$.\n",
    "- $\\Phi_a = [\\Phi_{a(0)}, \\Phi_{a(1)}, ..., \\Phi_{a(n-1)}]^T$ is the [time series](https://en.m.wikipedia.org/wiki/Time_series) of the solar radiation absorbed by the glass at [discrete time](https://en.m.wikipedia.org/wiki/Discrete_time_and_continuous_time#Discrete_time) $t = [t_0, t_1, ... , t_{n-1}]^T$.\n",
    "\n",
    "Note the order of the elements of the input vector. There are two groups: the temperature sources are fist followed by the flow-rate sources. In each group, the sources are in the order of the numbering of the circuits (e.g. TCd0, TCd1, ..., TCd3). For each circuit, the sources are in the order of the numbering of the branches and of the nodes, for temperature and flow-rate sources, respectively. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d17b4e46-b1d3-4124-ab6f-ab215c2e89d3",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Simulation\n",
    "\n",
    "### Free-floating\n",
    "\n",
    "Let's consider that the P-controller is not effective, i.e. $K_p \\rightarrow 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec931190-fb99-4fab-a98d-f70e96131acc",
   "metadata": {
    "tags": []
   },
   "source": [
    "The maximum time step for [numerical stability](https://en.m.wikipedia.org/wiki/Euler_method#Numerical_stability) of [Euler explicit integration](https://en.m.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations#Euler_method) in time is given by the minimum eigenvalue $\\lambda$ of the state matrix $A_s$:\n",
    "\n",
    "$$ \\Delta t_{max} \\leq \\min -2 / \\lambda_i = \\min 2 T_i$$\n",
    "\n",
    "where $T_i$ are the [time constants](https://en.m.wikipedia.org/wiki/Time_constant), $T_i = - \\frac{1}{\\lambda_i} $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "115b6c00-6e4b-4a8d-b9c5-ed7eb5c66e1f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum time step: 289.22 s\n"
     ]
    }
   ],
   "source": [
    "# Maximum time-step\n",
    "dtmax = min(-2. / np.linalg.eig(As)[0])\n",
    "print(f'Maximum time step: {dtmax:.2f} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fba8d434-6aae-471b-b9c5-92cc39be1597",
   "metadata": {},
   "source": [
    "We will chose a time step for integration slighly smaller than the maximum time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "417165e6-86ca-48d4-833d-cce4f84952c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dt = 240 s\n"
     ]
    }
   ],
   "source": [
    "dt = 240  # [s] simulation time step\n",
    "print(f'dt = {dt} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7f3d730-89c0-4692-9bd6-1ca9e0505415",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Step response\n",
    "\n",
    "Let's obtain the dynamic response of the system to a [step input](https://en.m.wikipedia.org/wiki/Step_response).\n",
    "\n",
    "The duration of the simulation needs to be larger than the estimated [settling time](https://en.m.wikipedia.org/wiki/Settling_time). This requires a corresponding number of time steps in the time vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4e643343-3f2f-4611-84d4-b20c5641033a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Settling time: 175888 s = 2931.5 min = 48.86 h = 2.04 days\n"
     ]
    }
   ],
   "source": [
    "λ = np.linalg.eig(As)[0]    # eigenvalues of matrix As\n",
    "t_resp = 4 * max(-1 / λ)    # response time\n",
    "print(f'Settling time: {t_resp:.0f} s = {t_resp / 60:.1f} min \\\n",
    "= {t_resp / (3600):.2f} h = {t_resp / (3600 * 24):.2f} days')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ee85cf-b275-4bee-99e2-9eb14de1cabb",
   "metadata": {},
   "source": [
    "Let's choose the duration of the simulation equal to two days."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "27e3bbf9-d3c8-4c36-af76-e03914b3b571",
   "metadata": {},
   "outputs": [],
   "source": [
    "duration = 3600 * 24 * 2        # [s]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58ae0b14-e43e-45e9-8b8e-5a4d34d8f650",
   "metadata": {
    "tags": []
   },
   "source": [
    "The step response by using [explicit and implicit Euler](https://en.m.wikipedia.org/wiki/Explicit_and_implicit_methods) methods is obtained with `tuto.step_response()` function which reproduces the algorithm presented in tutorial `t03CubeFb.ipynb` in section on *step response*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "84c35537-3f0b-4860-b845-9db43f29419e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8WbdlFy//9qfU/PXnHJ9axkwL2BqfyGvTP8mEEz/OuMNOYmyenn8rIrI3lChyKJkO+P2f/kTr7xdxYsuTnGPN7IiN5a+HfJopcy+hdvocanX/goiMcEoUObB7TydPPfogtStu57SgnrTFebP2ffgplzFu1tnUxPW1i8j+Q1esYbSjtZMnf/1Tjnjl3/movUZTrJo3j/onpp71JQ6t0uBVEdk/KVEMg/Zkml89uoQpy/6Nj9sr7CgaT+OJ/8ak911GVZGerSYi+zclin30zMuvse3hf+EjqcdpiVez9eTrqJ33j6DhrCJygFCiGKLdbUkeuO8OPrz2O9RYCxuP+DSTL/g2lFYVOjQRkWGlRDEEK9ZuZtXdV/KZ9K/ZMupQUhc9wuQpxxU6LBGRnFCi2Eu/XPoC0578LH9nb7Bl5mWMv+AGKCotdFgiIjmjRDFI7s5Pfvko85Z9gZrYHprPv4vxs88vdFgiIjmnRDEI7s4dP3uQj628HC8qJ37p45TWzS50WCIieaFEMQh3P/gIf7fyctIl1VQveJxYzcGFDklEJG+UKAbw4FNPc+5L/0RQXMXof3wMG6MkISLRokSRxTMvv8axT8+nKBGjbP6vsTHTCh2SiEjeKVH0Y8POPfgD85ka20pw8S9I1B5a6JBERAoir/Nam9lZZvaqma02s6v72F9tZr80sz+b2Stmdlk+4+sSBM6j//WvnMYLNM39JiWHnlqIMERERoS8JQoziwO3AWcDM4GLzGxmr2JfAFa6+7HAPOD/mllxvmLscu+S3/DJ3YvYWHsKY9//pXx/vIjIiJLPGsUJwGp3f8PdO4H7gN43IjhQaWYGVAA7gFQeY2T1lmYmPX89Hi9i4qfuAD0vQkQiLp+JYjKwvsd6Q7itp1uBI4FG4GXgCncPeh/IzOabWb2Z1W/dunXYAgwCZ/E9d/N+W0bHiV/Gqg4atmOLiOyv8pko+vpp7r3WzwSWA5OA2cCtZvaOWfbcfZG7z3H3ObW1tcMW4OJn13LWjh/TVDye0aeryUlEBPKbKBqAKT3W68jUHHq6DHjQM1YDa4Ajch1YezLN7c+8wT2/fpJT469QdvJ80HMkRESA/A6PfR6YYWbTgQ3AJ4CLe5VZB3wAeMbMJgCHA2/kOrAjvvEYAFcmniVNjKI5n871R4qI7DfylijcPWVmlwOPA3HgTnd/xcwWhPsXAt8GFpvZy2Saqq5y9225jOuVxt3dy++L/RnqjoeK8bn8SBGR/Upeb7hz9yXAkl7bFvZYbgTOyGdM59yyFIAamphla4jN6F3JERGJtrzecDeSHR97lZg5HDKv0KGIiIwoShShGdaQWZjQ+x5AEZFoU6IIHRrbQFA1BYpHFToUEZERRYkiNMM2YONzPhJXRGS/o0QBxAh4lzVitYcXOhQRkRFHiQKYZNsptSSMO6zQoYiIjDhKFMAEdmQWqusKG4iIyAikRAFMsJ2ZhUpNAigi0psSBTCxO1FMLGwgIiIjkBIFMN52EsSKoWxMoUMRERlxlCiAMbSQLqvRQ4pERPqgRAGMthbSJaMLHYaIyIikRIEShYhINkoUQDWtxMprCh2GiMiIpEQBTCzaQ1nV2EKHISIyIilRAKO8BcpGFzoMEZERKdKJIgicBCmKgg4oqS50OCIiI1K0E4U75bRnVjS9uIhInyKdKK64bzmj6MisKFGIiPQp0oni1y9vpNzCGkVJRWGDEREZoSKdKAAqaMssFCtRiIj0JfKJotzU9CQikk3kE4VqFCIi2UU+Ubw16kmJQkSkL5FPFKO6m57KCxuIiMgIFflEUUpnZqGorLCBiIiMUJFPFCUkMwsJJQoRkb5EPlGUWlijSJQUNhARkREq8omihCTpWLGebici0g8lCjpJx1SbEBHpjxIFnaTjShQiIv3Ja6Iws7PM7FUzW21mV/dTZp6ZLTezV8zsf3IdU4klSalGISLSr0S+PsjM4sBtwAeBBuB5M3vE3Vf2KDMa+CFwlruvM7PxuY6rVE1PIiJZ5bNGcQKw2t3fcPdO4D7g/F5lLgYedPd1AO6+JddBlaAahYhINvlMFJOB9T3WG8JtPR0GjDGz35nZMjP7+74OZGbzzazezOq3bt26T0F1j3oSEZE+5TNR9DX+1HutJ4D3AOcAZwLfMLPD3vEm90XuPsfd59TW1u5TUKXWSVI1ChGRfuWtj4JMDWJKj/U6oLGPMtvcvRVoNbOngWOBv+YqKNUoRESyy2eN4nlghplNN7Ni4BPAI73K/AKYa2YJMysH3gusymVQJSRJmWoUIiL9yVuNwt1TZnY58DgQB+5091fMbEG4f6G7rzKzx4CXgAC43d1X5DKuIlIkrSiXHyEisl/LZ9MT7r4EWNJr28Je698Hvp+vmIotRbvl9WsQEdmvDHiFNLOaQRwncPdd+x5OflWXFVEUpJg0tqrQoYiIjFiD+SndGL6yzZoXB6YOS0R5dPjESso2B1RV6HnZIiL9GUyiWOXux2UrYGYvDlM8+eWQ8BTENepJRKQ/gxn1dNIwlRlxHA8ThTqzRUT6M5hEUWdmp/TeaGZzzexdAO7ePuyR5YE7JFCiEBHJZjCJ4maguY/tbeG+/ZZ5mhiBmp5ERLIYTKKY5u4v9d7o7vXAtGGPKI/iHj4vWzUKEZF+DSZRlGbZVzZcgRRC3FPhgmoUIiL9GUyieN7MPt97o5l9Flg2/CHljxKFiMjABjM89svAQ2Z2CW8lhjlAMXBBjuLKi+5EEdOd2SIi/RnwCunum4GTzex04Ohw86/d/b9zGlkeJLr7KFSjEBHpz6B+SoczuT7n7r/NcTx5lUBNTyIiAxnMXE9fInNDXWBmz7v7zTmPKk806klEZGCDqVF8mkyfhAH17Of3TvSUUGe2iMiABpMovgc8GC7fnLtQ8k81ChGRgQ2mM/unwE/zEEvevTU8VolCRKQ/+XwU6oij4bEiIgMbMFGY2QvDUWYkipEOF1SjEBHpz2B+Sh9pZu+Y66kHA6qHKZ68inuYKOKqUYiI9GcwV8gjBlEmva+BFMJbNQolChGR/gymM/vNfARSCN01CiUKEZF+RbwzO8gsKFGIiPQr0okihkY9iYgMZK+vkGb2LSAOLAeWu/trwx1UvsS6m57ihQ1ERGQEG8zw2Bt7rrv7N4FbyDwe9aNm9p85ii3n1JktIjKwwVwh3997Qzj1+GPha7+lG+5ERAYW6T6KOF2d2brhTkSkP4P5KX2sma0BXgZW9Pj7F/euWfX2T3H1UYiIDGgwNYqXgFOAW4HtwBnAfwHbzGxFDmPLOfVRiIgMbFBXSHdvBBqBJ7q2mZkBh+YorrzQDXciIgMbTI3itr42esZeDY01s7PM7FUzW21mV2cpd7yZpc3swr05/t5SjUJEZGADJgp3v304PsjM4mSSztnATOAiM5vZT7nvAo8Px+dmE0d9FCIiA8nnqKcTgNXu/oa7dwL3Aef3Ue6LwAPAllwHFPeANDEwy/VHiYjst/KZKCYD63usN4TbupnZZOACYGE+AoqTIjA1O4mIZJPPRNHXz3bvtX4zcJW7Z5223Mzmm1m9mdVv3bp1yAHFSROgZicRkWzy+XO6AZjSY72OzEiqnuYA92UGVDEO+JCZpdz94Z6F3H0RsAhgzpw5vZPNoMU8TdqUKEREsslnongemGFm04ENwCeAi3sWcPfpXctmthj4Ve8kMZzipAmUKEREsspbonD3lJldTmY0Uxy4091fMbMF4f689Ev0FPc0gUY8iYhkldeeXHdfAizpta3PBOHul+Y6njiB+ihERAYQ6UkBY2p6EhEZUKQTRaaPQsNjRUSyiXSiSHhKNQoRkQFEOlGoj0JEZGCRThQxAgKL9FcgIjKgSF8lYwS4EoWISFaRvkrGNIWHiMiAIp0o4q4ahYjIQCJ9lVTTk4jIwCJ9lYxp1JOIyIAinyhUoxARyS7SV0klChGRgUX6KhknwHVntohIVpFOFJk+ikh/BSIiA4r0VVIPLhIRGVi0E4Wr6UlEZCCRThQxAjzaX4GIyIAifZWMqTNbRGRAkU4UcQ2PFREZUKSvkppmXERkYJG+SqrpSURkYJFOFGp6EhEZWKSvkqpRiIgMLNKJIk6Aa/ZYEZGsIp0oNCmgiMjAIn2VVB+FiMjAIn2VVB+FiMjAIp0oVKMQERlYpK+SMXVmi4gMKNKJIkFAEFOiEBHJJrqJwp2YOVH+CkREBiOvV0kzO8vMXjWz1WZ2dR/7LzGzl8LXs2Z2bM6CCdKZP6pRiIhklbdEYWZx4DbgbGAmcJGZzexVbA3wPnefBXwbWJSreDxIZf6qj0JEJKt81ihOAFa7+xvu3gncB5zfs4C7P+vuO8PVPwJ1OYvGMzUKYmp6EhHJJp9XycnA+h7rDeG2/nwWeLSvHWY238zqzax+69atQwrG02HTk/ooRESyyudV0vrY5n0WNDudTKK4qq/97r7I3ee4+5za2tohBeNdNQrdcCciklUij5/VAEzpsV4HNPYuZGazgNuBs919e66C6apR6M5sEZHs8lmjeB6YYWbTzawY+ATwSM8CZjYVeBD4lLv/NZfBdNUodGe2iEh2eatRuHvKzC4HHgfiwJ3u/oqZLQj3LwS+CYwFfmhmACl3n5OTeNJKFCIig5HPpifcfQmwpNe2hT2WPwd8Lj+xZIbHovsoRESyiuzPaQ+CzF/dRyEiklVkE4WFd2a77qMQEckqsldJ70oUqlGIiGQV2UTRNdeT+ihERLKLbKLomusp0H0UIiJZRTZRdNcoNDxWRCSrvA6PHUneuuFONQqR4ZJMJmloaKC9vb3QoUiotLSUuro6ioqKhnyM6CaKsOlJcz2JDJ+GhgYqKyuZNm0a4U2zUkDuzvbt22loaGD69OlDPk5021267qNQ05PIsGlvb2fs2LFKEiOEmTF27Nh9ruFF9irZPTxWNQqRYaUkMbIMx79HZBMF3TfcKVGIiGQT+UQR5a9A5EAUj8eZPXt29+uGG27IWn7x4sVcfvnleYouu4qKCgAaGxu58MILs5b93Oc+x8qVKwG4/vrrcxpXhDuzdcOdyIGorKyM5cuX5+z4qVSKRCK3l85JkyZx//33Zy1z++23dy9ff/31fP3rX89ZPJFNFOh5FCI5dd0vX2FlY9OwHnPmpCqu+fBRQ3rvtGnTqK+vZ9y4cdTX1/PVr36V3/3ud28rs3XrVhYsWMC6desAuPnmmznllFO49tpraWxsZO3atYwbN4577733be/7/ve/z89+9jM6Ojq44IILuO6663jooYe47bbbePLJJ9m0aRPve9/7ePrpp3nsscd46KGH6OjoYM2aNVx88cVcc801bzve2rVrOffcc1mxYgXpdJqrrrqKxx9/HDPj85//PF/84heZN28eN954I/fffz9tbW3Mnj2bo446invuuWdI3082ShTqzBY5oHRdNLt87Wtf4+Mf//ig3nvFFVdw5ZVXcuqpp7Ju3TrOPPNMVq1aBcCyZctYunQpZWVlb3vPE088wWuvvcZzzz2Hu3Peeefx9NNPc8EFF/DAAw9w22238dhjj3HdddcxceJEAJ577jlWrFhBeXk5xx9/POeccw5z5vT96J1FixaxZs0aXnzxRRKJBDt27Hjb/htuuIFbb701p7WoyCaK7qYnJQqRnBjqL/99tS9NT0899VR3uz9AU1MTzc3NAJx33nnvSBKQSRRPPPEExx13HAAtLS289tprnHbaafzgBz/g6KOP5sQTT+Siiy7qfs8HP/hBxo4dC8BHPvIRli5d2m+ieOqpp1iwYEF3c1dNTc2Qzm1fRDZRvDUpoJqeRKIgkUgQhPdP9XdfQRAE/OEPf+gzIYwaNarP97g7X/va1/iHf/iHd+zbsGEDsViMzZs3EwQBsfB603vIarYhrO5e8CHHkb1K6j4KkWiZNm0ay5YtA+CBBx7os8wZZ5zBrbfe2r0+mJrJmWeeyZ133klLSwuQSQ5btmwhlUpx2WWXce+993LkkUdy0003db/nySefZMeOHbS1tfHwww9zyimn9Hv8M844g4ULF5JKZWaT6N30BFBUVEQymRww1qGKbKJQH4XIgamrj6LrdfXVVwNwzTXXcMUVVzB37lzi8b7/399yyy3U19cza9YsZs6cycKFC/ss19MZZ5zBxRdfzEknncQxxxzDhRdeSHNzM9dffz1z585l7ty53HTTTdx+++3d/R2nnnoqn/rUp5g9ezYf/ehH+212gsww2KlTpzJr1iyOPfbYd3SkA8yfP59Zs2ZxySWXDOYr2mvm7jk5cL7MmTPH6+vr9/p9u5+7l+ol/8gjp/6C8/5m3vAHJhJBq1at4sgjjyx0GCPa4sWLqa+vf1vNJdf6+ncxs2Xu3n+G6iG6NQrdmS0iMiiR7czuau/L9Y0zIiI9XXrppVx66aWFDmOvRLZG0ZUoivdhjnYRkSiIcKLIjBDYl4d5iIhEQXQTRTqsUajpSUQkq8gminTY9KQahYhIdtFNFGGNoqRYiULkQJLvacYHMyX4YPWMZeHChdx1112D+tzly5ezZMmSYYmhL5Ftd0mnMsNj1ZktcmDJ9zTjg5kSfCgWLFiQdX/Pz12+fDn19fV86EMfGvY4IMqJIp3pzFaiEMmRR6+GTS8P7zEnHgNnZ68h9CdX04z3nBJ88eLFPPzww6TTaVasWMFXvvIVOjs7ufvuuykpKWHJkiXU1NQwb948Zs+ezXPPPUdTUxN33nknJ5xwwttiufbaa6moqOCrX/0qq1evZsGCBWzdupV4PM7Pf/5z4vE45557Li+88ALf/OY3aWtrY+nSpXs1W+5gRTdRdNUoiiP7FYgckPI9zXhvK1as4MUXX6S9vZ1DDz2U7373u7z44otceeWV3HXXXXz5y18GoLW1lWeffZann36az3zmM6xYsaLfY15yySVcffXVXHDBBbS3txMEAVu2bAGguLiYb33rWzm92zuyV8nuPoqi4gJHInKAGuIv/32V72nGezv99NOprKyksrKS6upqPvzhDwNwzDHH8NJLL3WX65p2/LTTTqOpqYldu3b1ebzm5mY2bNjABRdcAEBpaemQzm1f5DVRmNlZwL8DceB2d7+h134L938I2ANc6u4v5CKWQJ3ZIpGSq2nGeyspKelejsVi3euxWKz7Rl8Y/FTjI2E+vryNejKzOHAbcDYwE7jIzGb2KnY2MCN8zQf+I1fxBOFcT6XqoxCJhFxNMz5UP/3pTwFYunQp1dXVVFdX91muqqqKuro6Hn74YQA6OjrYs2fP28pUVlZ213xyIZ/DY08AVrv7G+7eCdwHnN+rzPnAXZ7xR2C0mR2Ui2DS6RRpN4oSkR0hLHJAyvc040M1ZswYTj75ZBYsWMAdd9yRtezdd9/NLbfcwqxZszj55JPZtGnT2/affvrprFy5ktmzZ3cnoOGUt2nGzexC4Cx3/1y4/ingve5+eY8yvwJucPel4fpvgKvcvb7XseaTqXEwderU97z55pt7HU/9rxZhrz7Ke77y0FBPSUR60TTjgzNv3jxuvPHGrM+hGE770zTjfTXA9c5SgymDuy9y9znuPqe2tnZIwcw5d76ShIjIIOSzM7sBmNJjvQ5oHEIZEZH9Wu/7N0a6fNYongdmmNl0MysGPgE80qvMI8DfW8aJwG5335jHGEVkH42EUTryluH498hbjcLdU2Z2OfA4meGxd7r7K2a2INy/EFhCZmjsajLDYy/LV3wisu9KS0vZvn07Y8eO7Xe4p+SPu7N9+/Z9vvciss/MFpHhl0wmaWho6Pc+Bcm/0tJS6urq3jFT9t50Zkf2zmwRGX5FRUVMnz690GHIMNNNBCIikpUShYiIZKVEISIiWe33ndlmthXY+1uzM8YB24YxnP1NlM8/yucO0T7/KJ87vHX+B7v7oO5Y3u8Txb4ws/rB9vofiKJ8/lE+d4j2+Uf53GFo56+mJxERyUqJQkREsop6olhU6AAKLMrnH+Vzh2iff5TPHYZw/pHuoxARkYFFvUYhIiIDUKIQEZGsIpsozOwsM3vVzFab2dWFjieXzOxOM9tiZit6bKsxsyfN7LXw75hCxphLZjbFzH5rZqvM7BUzuyLcfsB/B2ZWambPmdmfw3O/Ltx+wJ97FzOLm9mL4RM0o3bua83sZTNbbmb14ba9Pv9IJgoziwO3AWcDM4GLzGxmYaPKqcXAWb22XQ38xt1nAL8J1w9UKeAr7n4kcCLwhfDfOwrfQQfwfnc/FpgNnBU+6yUK597lCmBVj/UonTvA6e4+u8e9E3t9/pFMFMAJwGp3f8PdO4H7gPMLHFPOuPvTwI5em88HfhQu/wj423zGlE/uvtHdXwiXm8lcNCYTge/AM1rC1aLw5UTg3AHMrA44B7i9x+ZInHsWe33+UU0Uk4H1PdYbwm1RMqHr6YHh3/EFjicvzGwacBzwJyLyHYRNL8uBLcCT7h6ZcwduBv43EPTYFpVzh8yPgifMbJmZzQ+37fX5R/V5FH09ekvjhA9wZlYBPAB82d2bovIENndPA7PNbDTwkJkdXeCQ8sLMzgW2uPsyM5tX4HAK5RR3bzSz8cCTZvaXoRwkqjWKBmBKj/U6oLFAsRTKZjM7CCD8u6XA8eSUmRWRSRL3uPuD4eZIfQfuvgv4HZn+qiic+ynAeWa2lkzz8vvN7MdE49wBcPfG8O8W4CEyze57ff5RTRTPAzPMbLqZFQOfAB4pcEz59gjw6XD508AvChhLTlmm6nAHsMrdb+qx64D/DsysNqxJYGZlwN8AfyEC5+7uX3P3OnefRub/+H+7+yeJwLkDmNkoM6vsWgbOAFYwhPOP7J3ZZvYhMu2XceBOd/9OYSPKHTP7CTCPzPTCm4FrgIeBnwFTgXXA37l77w7vA4KZnQo8A7zMW23VXyfTT3FAfwdmNotMh2WczA/Dn7n7t8xsLAf4ufcUNj191d3Pjcq5m9khZGoRkOlmuNfdvzOU849sohARkcGJatOTiIgMkhKFiIhkpUQhIiJZKVGIiEhWShQiIpKVEoWIiGSlRCECmNnYcCrm5Wa2ycw2hMstZvbDHHzeYjNbY2YLeqxf2Ee5d3XFMdwxiAxWVOd6Enkbd99OZhpuzOxaoMXdb8zxx/4vd79/gLheJzNPkxKFFIxqFCJZmNm8Hg+8udbMfmRmT4QPhPmImX0vfDDMY+F8UpjZe8zsf8IZOx/vmldnEE4zs2fN7I2+ahcihaJEIbJ33kXm+QbnAz8GfuvuxwBtwDlhsvgBcKG7vwe4Exjs9DAHAacC5wI3DHfgIkOlpieRvfOouyfN7GUy8yc9Fm5/GZgGHA4cTWZKZ8IyGwd57IfdPQBWmtmEYY1aZB8oUYjsnQ4Adw/MLOlvTZYWkPn/ZMAr7n7SUI8disbDMmS/oKYnkeH1KlBrZidB5jkYZnZUgWMS2SdKFCLDKHwG+4XAd83sz8By4OSCBiWyjzTNuEgBmNli4FcDDY/tUb7F3StyG5VI31SjECmM3cC3u26460/XDXdkHjglUhCqUYiISFaqUYiISFZKFCIikpUShYiIZKVEISIiWf1/BxAl69v8gr4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tuto.step_response(duration, dt, As, Bs, Cs, Ds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68a1b9a4-794a-44c6-922a-b2463cb2c284",
   "metadata": {},
   "source": [
    "> Figure 4. Step response to outdoor temperature by using Euler\n",
    "[implicit](https://en.m.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations#Backward_Euler_method)\n",
    "and\n",
    "[explicit](https://en.m.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations#Euler_method) integration."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2d29daa-7623-4fb0-b5c9-06672ca079f5",
   "metadata": {},
   "source": [
    "#### Simulation by using weather data\n",
    "\n",
    "For simulation with weather data, we need to indicate the weather data file name and the start and end date of the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "06c9d493-1e3e-4ea2-a8d5-4777ee179f73",
   "metadata": {},
   "outputs": [],
   "source": [
    "weather_file = './weather_data/FRA_Lyon.074810_IWEC.epw'\n",
    "start_date = '2000-01-03 12:00:00'\n",
    "end_date = '2000-03-04 18:00:00'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "207a8903-4595-4aec-b7c3-5f1769a7189c",
   "metadata": {
    "tags": []
   },
   "source": [
    "The simulation is done by using `tuto.P_control()` function with implicit values:\n",
    "- initial value for the indoor temperature is 20°C.\n",
    "- auxiliary heat rate flow (internal sources) is zero.\n",
    "- orientation of the wall:\n",
    "    - slope 90° (i.e. vertical),\n",
    "    - azimuth 0 (i.e. South), \n",
    "    - latitude 45°."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b4d59646-84a4-4291-a41f-f28b8ffabca3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Tisp = 20\n",
    "y, q_HVAC, data = tuto.P_control(\n",
    "    weather_file, start_date, end_date, dt,\n",
    "    As, Bs, Cs, Ds, Kp, Tisp)\n",
    "tuto.plot_results(y, q_HVAC, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43027c40-9ab4-43f4-a613-7784d84822bb",
   "metadata": {},
   "source": [
    "> Figure 5. Simulation in free-running with weather data using Euler explicit method of integration. a) Indoor and outdoor temperatures. b) Solar and HVAC heat flow rates.\n",
    "\n",
    "Figure 5 shows that, in free running, the indoor temperature follows the outdoor temperature and that the solar radiation influences the indoor temperature. The flow rate of the HVAC system is zero."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6b32fe3-2da5-4c8d-a802-a4e2a45b79c5",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Perfect controller\n",
    "\n",
    "Let's consider that the controller is perfect, i.e. $K_p \\rightarrow \\infty$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "81a4a073-d7e9-47a7-960c-25153b1f9e93",
   "metadata": {},
   "outputs": [],
   "source": [
    "Kp = 1e3    # P-controler gain, Kp -> ∞"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b683186b-2e11-4502-a6fb-a4c0bf304809",
   "metadata": {
    "tags": []
   },
   "source": [
    "The steps previously used in order to obtain the assembled circuit are done in the function `tuto.thermal_circuit(Kp)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1ab7159c-91b3-4f14-b077-3bce5acd1da7",
   "metadata": {},
   "outputs": [],
   "source": [
    "TCa = tuto.thermal_circuit(Kp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f0c5faf-2060-4436-b6b8-accd28b2d88e",
   "metadata": {},
   "source": [
    "The thermal circuit `TCa` is converted into state-space representation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e3f9fcb6-a8ce-4dcc-85ea-d56db5d94dc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "[As, Bs, Cs, Ds] = dm4bem.tc2ss(\n",
    "    TCa['A'], TCa['G'], TCa['C'], TCa['b'], TCa['f'], TCa['y'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c338b2b-ed71-45cc-87d9-de856f1297f8",
   "metadata": {
    "tags": []
   },
   "source": [
    "The maximum timestep in this case is:\n",
    "\n",
    "$$ \\Delta t_{max} \\leq \\min -2 / \\lambda_i$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "f0cc971a-5168-4ed8-860f-9a9b635cdc64",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum time step: 58.92 s\n"
     ]
    }
   ],
   "source": [
    "dtmax = min(-2. / np.linalg.eig(As)[0])\n",
    "dtmax = -2. / min(np.linalg.eig(As)[0])\n",
    "print(f'Maximum time step: {dtmax:.2f} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "893dcf83-318e-411a-8064-a048735187fe",
   "metadata": {
    "tags": []
   },
   "source": [
    "Let's choose a time step slightly smaller than the maximum time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "31e59357-23c6-44c1-9161-7807d61c54d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dt = 50 s\n"
     ]
    }
   ],
   "source": [
    "dt = 50   # [s] simulation time step\n",
    "print(f'dt = {dt} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b97029cd-a314-469a-a920-1ca12d0fa534",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y, q_HVAC, data = tuto.P_control(\n",
    "    weather_file, start_date, end_date, dt,\n",
    "    As, Bs, Cs, Ds, Kp, Tisp)\n",
    "tuto.plot_results(y, q_HVAC, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39bba721-2aa4-4015-9fff-47428d36555d",
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   "source": [
    "> Figure 6. Simulation with weather data using Euler explicit method of integration. a) Indoor and outdoor temperatures. b) Solar and HVAC heat flow rates.\n",
    "\n",
    "Figure 6 shows that, when the controller is *\"perfect\"*, the indoor temperature follows the setpoint of the indoor temperature and that the flow rate of the HVAC system has positive and negative values (i.e. it is a system that provides heating and cooling)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7bc0e9b-3ad4-442e-b12e-31fd5bbe0d6c",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1. C. Ghiaus (2013). Causality issue in the heat balance method for calculating the design heating and cooling load. *Energy* 50: 292-301\n",
    "[DOI 10.1016/j.energy.2012.10.024](http://dx.doi.org/10.1016/j.energy.2012.10.024), [HAL 03605823]( https://hal.archives-ouvertes.fr/hal-03605823/document)\n",
    "\n",
    "2. C. Ghiaus, N. Ahmad (2020). Thermal circuits assembling and state-space extraction for modelling heat transfer in buildings, *Energy*, 195:117019\n",
    "[DOI 10.1016/j.energy.2020.117019](https://doi.org/10.1016/j.energy.2020.117019), [HAL 03600778](https://hal.archives-ouvertes.fr/hal-03600778/document)\n",
    "\n",
    "3. C. Ghiaus (2021). Dynamic Models for Energy Control of Smart Homes, in *S. Ploix M. Amayri, N. Bouguila (eds.) Towards Energy Smart Homes*, Online ISBN: 978-3-030-76477-7, Print ISBN: 978-3-030-76476-0, Springer, pp. 163-198 (ref.)\n",
    "[DOI 10.1007/978-3-030-76477-7_5](https://doi.org/10.1007/978-3-030-76477-7_5), [HAL 03578578](https://hal.archives-ouvertes.fr/hal-03578578/document)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad817ba8-343b-4ab5-a232-3892155b9294",
   "metadata": {},
   "source": [
    "# [Switch between models: heating & cooling and free-running](05SwitchModels.ipynb)\n",
    "\n",
    "# [Control input: heating & cooling and free-running](06Control_Input.ipynb)\n",
    "\n",
    "# [Radiation coupled with convection](07Coupled_rad_convection.ipynb)\n",
    "\n",
    "# [Sensible thermal load in steady-state](08Thermal_load.ipynb)\n",
    "\n",
    "# [Air flow by ventilation](09Air_flow_ventilation.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b00842fa-8971-4e5c-ac0c-7390a47b679b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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