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kalman_filter_operation.py
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kalman_filter_operation.py
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# DESCRIPTION
# -----------
# This program uses a Kalman Filter to estimate the state of charge (SoC) of two Li-ion batteries in series.
#
# OCV Measurement Frequency: 600s
# I Measurement Frequency: 10s
# Estimate Variance: [[5.0, 0], [0, 5.0]]
# Observation Variance: [[0.2, 0], [0, 0.2]
#
# CONTACT
# -------
# For inquiries, contact jogrady@usc.edu
#
# Jack O'Grady
# © 2019
# IMPORTS
# -------
import numpy as np
import serial
import time
# FUNCTIONS
# ---------
# Reads data from Serial (from Arduino)
# Inputs: the serial connection
# Returns: the decoded serial data
def readSerialLine(ser):
line = ser.readline()
line = line.decode("utf-8")
dataLine = line
lineOutput = dataLine.strip()
return lineOutput
# Used to get the state of charge (SoC) from an open circuit voltage (OCV) reading,
# using a SoC(OCV) function calculated with an 8th order polynomial fit of the cell's quasi-OCV discharge at ~1/20C
# Inputs: the measured cell OCV from Arduino
# Returns: the state of charge SoC
def getSoCFromOCV(OCV):
coefficients = [268.4970355259198, -6879.270367122276, 76716.49575172913, -486365.6733759814, 1917287.1707991716,
-4812471.06572991, 7511312.300797121, -6665390.783393391, 2574719.229612701]
OCV_used = OCV
# ensures that only OCVs within the bounds of the polynomial fit are used
if OCV_used < 2.5:
OCV_used = 2.5093
if OCV_used > 4.057:
OCV_used = 4.057
# calculates the state of charge from the OCV
SoC = 0
i = 0
while 8 - i >= 0:
SoC += coefficients[i] * OCV_used ** (8 - i)
i += 1
# returns the state of charge as a function of measured open circuit voltage (OCV)
return SoC
# FUNCTIONS FOR KALMAN FILTER OPERATIONS
# --------------------------------------
# Initializes the state matrix for the Kalman Filter
# Inputs: the initial measured state of charge SoC and current I
# Returns: the state matrix to be used in the Kalman Filter
def initStateVariable(SoC, I):
return np.array([SoC], [I])
# Updates the Kalman Filter's transformation matrix with the appropriate time interval
# Inputs: the measured time interval between operations
# Returns: the correct transformation matrix to be used in Kalman Filter operations
def updateTransformationMatrix(deltaT):
totalCoulombs = 10800
return np.array([[1, -1 * (deltaT / totalCoulombs) * 100], [0, 1]])
# OVERVIEW OF MAIN
# ----------------
# 1. Initialize the Serial Port to communicate with the Arduino
# 2. Set up a CSV file for data recording
# 3. Get initial OCV and current measurement from Arduino sensors
# 4. Create the last state matrix and state estimate variance
# 5. Every 10s, measure the current and update the state estimate
# 6. Every 10min, measure the OCV and run an iteration of the Kalman Filter
# 7. Update the state estimate
# 8. Write the data to a CSV file
def main():
# Initialize serial port
serialPort = '/dev/cu.usbmodem14201'
baudRate = 9600
arduino = serial.Serial(serialPort, baudRate)
time.sleep(2)
# Set up CSV data output
write_to_file_path = "Kalman_Filter_Comparison_5column_extra_time2.csv"
output_file = open(write_to_file_path, "w+")
estimate1Name = "Coulomb Counting"
estimate2Name = "OCV"
estimate3Name = "KF I=10s P=0.5 R=0.25"
estimate4Name = "KF I=10s P=5.0 R=0.2"
estimate5Name = "KF I=30s P=5.0 R=0.2"
output_file.write("Time" + "," + estimate1Name + "," + estimate2Name + "," + estimate3Name + "," + estimate4Name +
"," + estimate5Name + "\n")
# Set codes for the arduino output
CURRENT_CODE = '1'
OCV_CODE = '2'
# INITIALIZE
# ----------
# Tell the Arduino to take the initial OCV measurement
arduino.write(str.encode(OCV_CODE))
while arduino.inWaiting() < 0:
time.sleep(0.1)
arduinoData = readSerialLine(arduino)
initialVoltage = float(arduinoData) / 2 # divide by 2 since SoC(OCV) function is for 1 cell's OCV
# calculate the initial SoC
initialSoC = getSoCFromOCV(initialVoltage)
# Tell the Arduino to take the initial current measurement
arduino.write(str.encode(CURRENT_CODE))
while arduino.inWaiting() < 0:
time.sleep(0.1)
arduinoData = readSerialLine(arduino)
initialCurrent = float(arduinoData)
# Display the initial SoC for the user
displaySoC = round(initialSoC, 2)
print("Battery Charge (" + estimate1Name + "): " + str(round(displaySoC, 2)) + "%")
print("Battery Charge (" + estimate2Name + "): " + str(round(displaySoC, 2)) + "%")
print("Battery Charge (" + estimate3Name + "): " + str(round(displaySoC, 2)) + "%")
print("Battery Charge (" + estimate4Name + "): " + str(round(displaySoC, 2)) + "%")
print("Battery Charge (" + estimate5Name + "): " + str(round(displaySoC, 2)) + "%")
print("------------------------------------------")
csvLine = "0.0" + "," + str(round(displaySoC, 2)) + "," + str(round(displaySoC, 2)) + "," + \
str(round(displaySoC, 2)) + "," + str(round(displaySoC, 2)) + "," + str(round(displaySoC, 2)) + "\n"
output_file.write(csvLine)
# Initialize the state variable with an initial SoC estimate
lastState1 = np.array([[initialSoC], [initialCurrent]])
lastState2 = np.array([[initialSoC], [initialCurrent]])
lastState3 = np.array([[initialSoC], [initialCurrent]])
lastState4 = np.array([[initialSoC], [initialCurrent]])
lastState5 = np.array([[initialSoC], [initialCurrent]])
# Initialize the variance matrix, using predetermined values
# This was originally 0.09, but I increased it to 0.5 to allow the Kalman Filter to automatically
# choose the correct value
lastVariance1 = np.array([[.5, 0], [0, .5]])
lastVariance2 = np.array([[.5, 0], [0, .5]])
lastVariance3 = np.array([[.5, 0], [0, .5]])
lastVariance4 = np.array([[5.0, 0], [0, 5.0]])
lastVariance5 = np.array([[5.0, 0], [0, 5.0]])
# Initialize the observation matrix
observationMatrix = np.array([[1, 0], [0, 1]])
# Initialize the observation noise matrix
observationNoise1 = np.array([[.25, 0], [0, .25]])
observationNoise2 = np.array([[.25, 0], [0, .25]])
observationNoise3 = np.array([[.25, 0], [0, .25]])
observationNoise4 = np.array([[.2, 0], [0, .2]])
observationNoise5 = np.array([[.2, 0], [0, .2]])
# Initialize the transformation matrix
totalCoulombs = 10800
# Updated by Arduino
deltaT = 0
transformationMatrix = np.array([[1, -1 * (deltaT / totalCoulombs)*100], [0, 1]])
# ESTIMATE
# --------
# Creates a non stop loop until the user stops data collection
operate = True
# Gets various initial times to control measurement frequencies
dataStartTime = time.time()
ocvStartTime = time.time()
longCurrentStartTime = time.time()
doLongCurrentUpdate = False
extraTimeReference = 0
extraTime = 0
# Operate the Kalman Filter until shut off
while operate:
# Get an initial time to determine when to measure current
startTime = time.time()
# Delay 10 seconds to avoid over-use of CPU and energy
time.sleep(10)
# Update the deltaT value in the transformation matrix for the current period
transformationMatrix = updateTransformationMatrix(time.time() - startTime + extraTime)
# Estimate the state
stateEstimate1 = np.matmul(transformationMatrix, lastState1)
stateEstimate2 = lastState2
stateEstimate3 = np.matmul(transformationMatrix, lastState3)
stateEstimate4 = np.matmul(transformationMatrix, lastState4)
# Only update estimate 5 if it has been 30 seconds
if time.time() - longCurrentStartTime > 30:
doLongCurrentUpdate = True
transformationMatrixLong = updateTransformationMatrix(time.time() - longCurrentStartTime + extraTime)
stateEstimate5 = np.matmul(transformationMatrixLong, lastState5)
else:
stateEstimate5 = lastState5
# Estimate the variance
varianceEstimate1 = np.matmul(np.matmul(transformationMatrix, lastVariance1), np.linalg.inv(transformationMatrix))
varianceEstimate3 = np.matmul(np.matmul(transformationMatrix, lastVariance3), np.linalg.inv(transformationMatrix))
varianceEstimate4 = np.matmul(np.matmul(transformationMatrix, lastVariance4), np.linalg.inv(transformationMatrix))
# Only update variance for estimate 5 if it has been 30 seconds
if doLongCurrentUpdate:
varianceEstimate5 = np.matmul(np.matmul(transformationMatrixLong, lastVariance5),
np.linalg.inv(transformationMatrixLong))
else:
varianceEstimate5 = lastVariance5
# Reset the extra time variable, which measures the unaccounted for processing delays as Python executes
extraTime = 0
extraTimeReference = time.time()
# Measure current to update the state estimate current
arduino.write(str.encode(CURRENT_CODE))
while arduino.inWaiting() < 0:
time.sleep(0.1)
arduinoData = readSerialLine(arduino)
stateCurrent = float(arduinoData)
# Update the current stored in the last state
stateEstimate1[1] = stateCurrent
stateEstimate3[1] = stateCurrent
stateEstimate4[1] = stateCurrent
if doLongCurrentUpdate:
stateEstimate5[1] = stateCurrent
# Update the last state to current state estimate
lastState1 = stateEstimate1
lastState3 = stateEstimate3
lastState4 = stateEstimate4
lastState5 = stateEstimate5
# Update the last variance to current variance estimate
lastVariance1 = varianceEstimate1
lastVariance3 = varianceEstimate3
lastVariance4 = varianceEstimate4
lastVariance5 = varianceEstimate5
# If 10 minutes has elapsed, get an OCV measurement and run the full KF
if time.time() - ocvStartTime > 600:
# MEASURE
# -------
# Measure the current OCV
arduino.write(str.encode(OCV_CODE))
while arduino.inWaiting() < 0:
time.sleep(0.1)
arduinoData = readSerialLine(arduino)
measuredVoltage = float(arduinoData) / 2 # divide by 2 since SoC(OCV) function is for 1 cell's OCV
# Calculate the measured SoC from OCV
measuredSoC = getSoCFromOCV(measuredVoltage)
# Use the measured current from most recent estimated state update
measuredCurrent = stateCurrent
# Create the state measurement matrix
stateMeasurement = np.array([[measuredSoC], [measuredCurrent]])
# CALCULATE
# ---------
# Calculate the measurement residual vector
measurementResidual3 = stateMeasurement - stateEstimate3
measurementResidual4 = stateMeasurement - stateEstimate4
measurementResidual5 = stateMeasurement - stateEstimate5
# Calculate the residual variance matrix
residualVariance3 = varianceEstimate3 + observationNoise3
residualVariance4 = varianceEstimate4 + observationNoise4
residualVariance5 = varianceEstimate5 + observationNoise5
# Calculate the Kalman gain
kalmanGain3 = np.matmul(varianceEstimate3, np.linalg.inv(residualVariance3))
kalmanGain4 = np.matmul(varianceEstimate4, np.linalg.inv(residualVariance4))
kalmanGain5 = np.matmul(varianceEstimate5, np.linalg.inv(residualVariance5))
# UPDATE
# ------
# Update the state
lastState2 = stateMeasurement
lastState3 = stateEstimate3 + np.matmul(kalmanGain3, measurementResidual3)
lastState4 = stateEstimate4 + np.matmul(kalmanGain4, measurementResidual4)
lastState5 = stateEstimate5 + np.matmul(kalmanGain5, measurementResidual5)
# Update the variance
lastVariance3 = np.matmul((np.identity(2) - kalmanGain3), varianceEstimate3)
lastVariance4 = np.matmul((np.identity(2) - kalmanGain4), varianceEstimate4)
lastVariance5 = np.matmul((np.identity(2) - kalmanGain5), varianceEstimate5)
# Reset the clock for periodic OCV measurement
ocvStartTime = time.time()
# Reset long current clock (for estimate5 which only updates every 30 seconds
if doLongCurrentUpdate:
longCurrentStartTime = time.time()
doLongCurrentUpdate = False
# Print the results for the user to follow in real time
displaySoC1 = float(lastState1[0])
print("Battery Charge (" + estimate1Name + "): " + str(round(displaySoC1, 2)) + "%")
displaySoC2 = float(lastState2[0])
print("Battery Charge (" + estimate2Name + "): " + str(round(displaySoC2, 2)) + "%")
displaySoC3 = float(lastState3[0])
print("Battery Charge (" + estimate3Name + "): " + str(round(displaySoC3, 2)) + "%")
displaySoC4 = float(lastState4[0])
print("Battery Charge (" + estimate4Name + "): " + str(round(displaySoC4, 2)) + "%")
displaySoC5 = float(lastState5[0])
print("Battery Charge (" + estimate5Name + "): " + str(round(displaySoC5, 2)) + "%")
print("------------------------------------------")
# Write the data to a .csv file
csvLine = str(round((time.time() - dataStartTime), 2)) + "," + str(round(displaySoC1, 2)) + "," + \
str(round(displaySoC2, 2)) + "," + str(round(displaySoC3, 2)) + "," + str(round(displaySoC4, 2)) \
+ "," + str(round(displaySoC5, 2)) + "\n"
output_file.write(csvLine)
# Calculate the time it took Python to run a Kalman Filter iteration after the transformation matrix was set
extraTime = time.time() - extraTimeReference
main()