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Copy pathutils.py
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326 lines (293 loc) · 15.5 KB
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import numpy as np
import matplotlib.pyplot as plt
## ------------ Clarke Park Tranformation ------------ ##
class ClarkePark:
def __init__(self):
return
@staticmethod
def abc_to_alphabeta0(a, b, c):
alpha = (2 / 3) * (a - b / 2 - c / 2)
beta = (2 / 3) * (np.sqrt(3) * (b - c) / 2)
z = (2 / 3) * ((a + b + c) / 2)
return alpha, beta, z
@staticmethod
def alphabeta0_to_abc(alpha, beta, z):
a = alpha + z
b = -alpha / 2 + beta * np.sqrt(3) / 2 + z
c = -alpha / 2 - beta * np.sqrt(3) / 2 + z
return a, b, c
@staticmethod
def abc_to_dq0_d(a, b, c, wt, delta=0):
d = (2 / 3) * (a * np.cos(wt + delta) + b * np.cos(wt + delta - (2 * np.pi / 3)) + c * np.cos(wt + delta + (2 * np.pi / 3)))
q = (2 / 3) * (-a * np.sin(wt + delta) - b * np.sin(wt + delta - (2 * np.pi / 3)) - c * np.sin(wt + delta + (2 * np.pi / 3)))
z = (2 / 3) * (a + b + c) / 2
return d, q, z
@staticmethod
def abc_to_dq0_q(a, b, c, wt, delta=0):
d = (2 / 3) * (a * np.sin(wt + delta) + b * np.sin(wt + delta - (2 * np.pi / 3)) + c * np.sin(wt + delta + (2 * np.pi / 3)))
q = (2 / 3) * (a * np.cos(wt + delta) + b * np.cos(wt + delta - (2 * np.pi / 3)) + c * np.cos(wt + delta + (2 * np.pi / 3)))
z = (2 / 3) * (a + b + c) / 2
return d, q, z
@staticmethod
def dq0_to_abc_d(d, q, z, wt, delta=0):
a = d * np.cos(wt + delta) - q * np.sin(wt + delta) + z
b = d * np.cos(wt - (2 * np.pi / 3) + delta) - q * np.sin(wt - (2 * np.pi / 3) + delta) + z
c = d * np.cos(wt + (2 * np.pi / 3) + delta) - q * np.sin(wt + (2 * np.pi / 3) + delta) + z
return a, b, c
@staticmethod
def dq0_to_abc_q(d, q, z, wt, delta=0):
a = d * np.sin(wt + delta) + q * np.cos(wt + delta) + z
b = d * np.sin(wt - (2 * np.pi / 3) + delta) + q * np.cos(wt - (2 * np.pi / 3) + delta) + z
c = d * np.sin(wt + (2 * np.pi / 3) + delta) + q * np.cos(wt + (2 * np.pi / 3) + delta) + z
return a, b, c
# def plot_results():
class SSAnalysis:
def __init__(self):
return
def continuous(self,a, b, w=None, plot_current=False):
if w is not None:
# dx/dt = a*x + b*u + w - a,b is state-space matrix, w is disturbance
# Steady-state
# 0 = a * x_ss + b * u_ss + w
# x_ss = - a^-1 * (b * u_ss + w)
x_ss = lambda vdq: -np.linalg.inv(a) @ (b @ vdq + np.kron(np.ones((vdq.shape[1], 1)), w).T) if vdq.shape == (
2, 1000) else -np.linalg.inv(a) @ (b @ vdq + w) #If vdq is a 2x1000 matrix, use the kron product to add w to each column
#Boundary conditions
x_ss1 = x_ss(np.array([0, self.vdq_max]))
x_ss2 = x_ss(np.array([self.vdq_max, 0]))
x_ss3 = x_ss(np.array([0, -self.vdq_max]))
x_ss4 = x_ss(np.array([-self.vdq_max, 0]))
x_ss5 = x_ss(np.array([self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss6 = x_ss(np.array([self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
x_ss7 = x_ss(np.array([-self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss8 = x_ss(np.array([-self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
# 0 = a * x_ss + b * u_ss + w
# u_ss = - b^-1 * (a * x_ss + w)
u_ss = lambda idq: -np.linalg.inv(b) @ (a @ idq + w)
u_ss1 = u_ss([0, self.i_max])
u_ss2 = u_ss([self.i_max, 0])
u_ss3 = u_ss([0, -self.i_max])
u_ss4 = u_ss([-self.i_max, 0])
u_ss5 = u_ss([self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss6 = u_ss([self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
u_ss7 = u_ss([-self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss8 = u_ss([-self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
if plot_current:
v_d = np.linspace(-1, 1, 1000)
v_q = np.sqrt(1 - np.power(v_d, 2))
vdq = self.vdq_max * np.array([v_d, v_q])
x_ss_data_pos = x_ss(vdq)
vdq = self.vdq_max * np.array([v_d, -v_q])
x_ss_data_neg = x_ss(vdq)
id = np.concatenate((x_ss_data_pos[0], x_ss_data_neg[0]), 0)
iq = np.concatenate((x_ss_data_pos[1], x_ss_data_neg[1]), 0)
plt.plot(id, iq, label="Current by voltage limitation")
id = np.linspace(-1, 1, 1000)
iq = np.sqrt(1 - np.power(id, 2))
id_circle = self.i_max * np.concatenate((id, id), 0)
iq_circle = self.i_max * np.concatenate((iq, -iq), 0)
plt.plot(id_circle, iq_circle, label="Maximum current circle")
plt.legend(loc='upper center', bbox_to_anchor=(0.5, -0.05),
fancybox=True, shadow=True, ncol=2)
plt.title("Continuous state-space model")
plt.show()
else:
# dx/dt = a*x + b*u
# Steady-state
# 0 = a * x_ss + b * u_ss
# x_ss = - a^-1 * (b * u_ss )
x_ss = lambda vdq: -np.linalg.inv(a) @ (b @ vdq)
x_ss1 = x_ss(np.array([0, self.vdq_max]))
x_ss2 = x_ss(np.array([self.vdq_max, 0]))
x_ss3 = x_ss(np.array([0, -self.vdq_max]))
x_ss4 = x_ss(np.array([-self.vdq_max, 0]))
x_ss5 = x_ss(np.array([self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss6 = x_ss(np.array([self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
x_ss7 = x_ss(np.array([-self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss8 = x_ss(np.array([-self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
# 0 = a * x_ss + b * u_ss
# u_ss = - b^-1 * (a * x_ss)
u_ss = lambda idq: -np.linalg.inv(b) @ (a @ idq)
u_ss1 = u_ss([0, self.i_max])
u_ss2 = u_ss([self.i_max, 0])
u_ss3 = u_ss([0, -self.i_max])
u_ss4 = u_ss([-self.i_max, 0])
u_ss5 = u_ss([self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss6 = u_ss([self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
u_ss7 = u_ss([-self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss8 = u_ss([-self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
if plot_current:
v_d = np.linspace(-1, 1, 1000)
v_q = np.sqrt(1 - np.power(v_d, 2))
vdq = self.vdq_max * np.array([v_d, v_q])
x_ss_data_pos = x_ss(vdq)
vdq = self.vdq_max * np.array([v_d, -v_q])
x_ss_data_neg = x_ss(vdq)
id = np.concatenate((x_ss_data_pos[0], x_ss_data_neg[0]), 0)
iq = np.concatenate((x_ss_data_pos[1], x_ss_data_neg[1]), 0)
plt.plot(id, iq, label="Current by voltage limitation")
id = np.linspace(-1, 1, 1000)
iq = np.sqrt(1 - np.power(id, 2))
id_circle = self.i_max * np.concatenate((id, id), 0)
iq_circle = self.i_max * np.concatenate((iq, -iq), 0)
plt.plot(id_circle, iq_circle, label="Maximum current circle")
plt.legend(loc='upper center', bbox_to_anchor=(0.5, -0.05),
fancybox=True, shadow=True, ncol=2)
plt.title("Continuous state-space model")
plt.show()
def discrete(self, ad, bd, wd=None, plot_current=False):
if wd is not None:
# x_k+1 = ad * x_k + bd * u_k + wd
# Steady-state
# x_ss = ad * x_ss + bd * u_ss + wd
# x_ss = (I - ad)^-1 * (bd * u_ss + wd)
x_ss = lambda vdq: -np.linalg.inv(np.eye(2) - ad) @ (
bd @ vdq + np.kron(np.ones((vdq.shape[1], 1)), wd).T) if vdq.shape == (
2, 1000) else -np.linalg.inv(ad) @ (bd @ vdq + wd)
x_ss1 = x_ss(np.array([0, self.vdq_max]))
x_ss2 = x_ss(np.array([self.vdq_max, 0]))
x_ss3 = x_ss(np.array([0, -self.vdq_max]))
x_ss4 = x_ss(np.array([-self.vdq_max, 0]))
x_ss5 = x_ss(np.array([self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss6 = x_ss(np.array([self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
x_ss7 = x_ss(np.array([-self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss8 = x_ss(np.array([-self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
# x_ss = ad * x_ss + bd * u_ss + wd
# u_ss = bd^-1 * ((I - ad) * x_ss - wd)
u_ss = lambda idq: -np.linalg.inv(bd) @ ((np.eye(2) - ad) @ idq - wd)
u_ss1 = u_ss([0, self.i_max])
u_ss2 = u_ss([self.i_max, 0])
u_ss3 = u_ss([0, -self.i_max])
u_ss4 = u_ss([-self.i_max, 0])
u_ss5 = u_ss([self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss6 = u_ss([self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
u_ss7 = u_ss([-self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss8 = u_ss([-self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
if plot_current:
v_d = np.linspace(-1, 1, 1000)
v_q = np.sqrt(1 - np.power(v_d, 2))
vdq = self.vdq_max * np.array([v_d, v_q])
x_ss_data_pos = x_ss(vdq)
vdq = self.vdq_max * np.array([v_d, -v_q])
x_ss_data_neg = x_ss(vdq)
id = np.concatenate((x_ss_data_pos[0], x_ss_data_neg[0]), 0)
iq = np.concatenate((x_ss_data_pos[1], x_ss_data_neg[1]), 0)
plt.plot(id, iq, label="Current by voltage limitation")
id = np.linspace(-1, 1, 1000)
iq = np.sqrt(1 - np.power(id, 2))
id_circle = self.i_max * np.concatenate((id, id), 0)
iq_circle = self.i_max * np.concatenate((iq, -iq), 0)
plt.plot(id_circle, iq_circle, label="Maximum current circle")
plt.legend(loc='upper center', bbox_to_anchor=(0.5, -0.05),
fancybox=True, shadow=True, ncol=2)
plt.title("Discrete state-space model")
plt.show()
else:
# x_k+1 = ad * x_k + bd * u_k
# Steady-state
# x_ss = ad * x_ss + bd * u_ss
# x_ss = (I - ad)^-1 * (bd * u_ss)
x_ss = lambda vdq: -np.linalg.inv(np.eye(2) - ad) @ (bd @ vdq)
x_ss1 = x_ss(np.array([0, self.vdq_max]))
x_ss2 = x_ss(np.array([self.vdq_max, 0]))
x_ss3 = x_ss(np.array([0, -self.vdq_max]))
x_ss4 = x_ss(np.array([-self.vdq_max, 0]))
x_ss5 = x_ss(np.array([self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss6 = x_ss(np.array([self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
x_ss7 = x_ss(np.array([-self.vdq_max / np.sqrt(2), self.vdq_max / np.sqrt(2)]))
x_ss8 = x_ss(np.array([-self.vdq_max / np.sqrt(2), -self.vdq_max / np.sqrt(2)]))
# x_ss = ad * x_ss + bd * u_ss
# u_ss = bd^-1 * ((I - ad) * x_ss)
u_ss = lambda idq: -np.linalg.inv(bd) @ ((np.eye(2) - ad) @ idq)
u_ss1 = u_ss([0, self.i_max])
u_ss2 = u_ss([self.i_max, 0])
u_ss3 = u_ss([0, -self.i_max])
u_ss4 = u_ss([-self.i_max, 0])
u_ss5 = u_ss([self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss6 = u_ss([self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
u_ss7 = u_ss([-self.i_max / np.sqrt(2), self.i_max / np.sqrt(2)])
u_ss8 = u_ss([-self.i_max / np.sqrt(2), -self.i_max / np.sqrt(2)])
if plot_current:
v_d = np.linspace(-1, 1, 1000)
v_q = np.sqrt(1 - np.power(v_d, 2))
vdq = self.vdq_max * np.array([v_d, v_q])
x_ss_data_pos = x_ss(vdq)
vdq = self.vdq_max * np.array([v_d, -v_q])
x_ss_data_neg = x_ss(vdq)
id = np.concatenate((x_ss_data_pos[0], x_ss_data_neg[0]), 0)
iq = np.concatenate((x_ss_data_pos[1], x_ss_data_neg[1]), 0)
plt.plot(id, iq, label="Current by voltage limitation")
id = np.linspace(-1, 1, 1000)
iq = np.sqrt(1 - np.power(id, 2))
id_circle = self.i_max * np.concatenate((id, id), 0)
iq_circle = self.i_max * np.concatenate((iq, -iq), 0)
plt.plot(id_circle, iq_circle, label="Maximum current circle")
plt.legend(loc='upper center', bbox_to_anchor=(0.5, -0.05),
fancybox=True, shadow=True, ncol=2)
plt.title("Discrete state-space model")
plt.show()
class PlotTest():
def __init__(self):
return
def plot_single_phase(self, idx, observations, actions, reward, env_name, reward_type):
plt.clf()
plt.suptitle(f"Reward: {reward_type}\n")
# Plot State
ax = plt.subplot(131)
ax.set_title("State vs step")
ax.plot(observations, label=['I', 'Iref'])
box = ax.get_position()
ax.set_position([box.x0, box.y0 + box.height * 0.1,
box.width, box.height * 0.9])
ax.legend(loc='lower center', bbox_to_anchor=(0.5, -0.25),
ncol=2, fancybox=True, shadow=True)
# Plot action
ax = plt.subplot(132)
ax.set_title("Action vs step")
ax.plot(actions, label=['V'])
box = ax.get_position()
ax.set_position([box.x0, box.y0 + box.height * 0.1,
box.width, box.height * 0.9])
ax.legend(loc='lower center', bbox_to_anchor=(0.5, -0.25),
ncol=2, fancybox=True, shadow=True)
# Plot reward
ax = plt.subplot(133)
ax.set_title("Reward vs step")
ax.plot(reward)
box = ax.get_position()
ax.set_position([box.x0, box.y0 + box.height * 0.1,
box.width, box.height * 0.9])
plt.savefig(f"plots/{env_name}_{idx}.pdf", bbox_inches='tight')
plt.pause(0.001) # pause a bit so that plots are updated
def plot_three_phase(self, idx, observations, actions, reward, env_name, reward_type, speed=None):
plt.clf()
if speed is not None:
plt.suptitle(f"Reward: {reward_type}\nSpeed = {speed} [rad/s]")
# Plot State
ax = plt.subplot(131)
ax.set_title("State vs step")
ax.plot(observations, label=['Id', 'Iq', 'Idref', 'Iqref'])
box = ax.get_position()
ax.set_position([box.x0, box.y0 + box.height * 0.1,
box.width, box.height * 0.9])
ax.legend(loc='lower center', bbox_to_anchor=(0.5, -0.25),
ncol=2, fancybox=True, shadow=True)
# Plot action
ax = plt.subplot(132)
ax.set_title("Action vs step")
ax.plot(actions, label=['Vd', 'Vq'])
box = ax.get_position()
ax.set_position([box.x0, box.y0 + box.height * 0.1,
box.width, box.height * 0.9])
ax.legend(loc='lower center', bbox_to_anchor=(0.5, -0.25),
ncol=2, fancybox=True, shadow=True)
# Plot reward
ax = plt.subplot(133)
ax.set_title("Reward vs step")
ax.plot(reward)
box = ax.get_position()
ax.set_position([box.x0, box.y0 + box.height * 0.1,
box.width, box.height * 0.9])
plt.savefig(f"plots/{env_name}_{idx}.pdf", bbox_inches='tight')
plt.pause(0.001) # pause a bit so that plots are updated
# plt.show()