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create_jacobian_facts.py
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create_jacobian_facts.py
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# -*- coding: utf-8 -*-
# Copyright (c) 2016-2024 by University of Kassel and Fraunhofer Institute for Energy Economics
# and Energy System Technology (IEE), Kassel. All rights reserved.
import numpy as np
from scipy.sparse import csr_matrix
from pandapower.pf.makeYbus_facts import calc_y_svc_pu
def create_J_modification_svc(J, svc_buses, pvpq, pq, pq_lookup, V, x_control, svc_x_l_pu, svc_x_cvar_pu,
nsvc, nsvc_controllable, svc_controllable):
J_m = np.zeros_like(J.toarray())
controllable = np.arange(nsvc)[svc_controllable]
in_pq = np.isin(svc_buses, pq)
y_svc = calc_y_svc_pu(x_control, svc_x_l_pu, svc_x_cvar_pu)
q_svc = np.abs(V[svc_buses]) ** 2 * y_svc
# J_C_Q_u
J_C_Q_u = np.zeros(shape=(len(pq), len(pq)), dtype=np.float64)
J_C_Q_u[pq_lookup[svc_buses[in_pq]], pq_lookup[svc_buses[in_pq]]] = 2 * q_svc[in_pq]
# count pvpq rows and pvpq columns from top left
J_m[len(pvpq):len(pvpq) + len(pq), len(pvpq):len(pvpq) + len(pq)] = J_C_Q_u
# J_C_Q_c
if np.any(svc_controllable):
J_C_Q_c = np.zeros(shape=(len(pq), nsvc), dtype=np.float64)
values = 2 * np.abs(V[svc_buses]) ** 2 * (np.cos(2 * x_control) - 1) / (np.pi * svc_x_l_pu)
J_C_Q_c[pq_lookup[svc_buses[in_pq & svc_controllable]], controllable] = values[in_pq & svc_controllable]
# count pvpq rows and pvpq columns from top left
J_m[len(pvpq):len(pvpq) + len(pq),
len(pvpq) + len(pq):len(pvpq) + len(pq) + nsvc_controllable] = J_C_Q_c[:, controllable]
# J_C_C_u
# d(Ui - Ui,set)/d(Ui) = dUi/dUi = 1
if np.any(svc_controllable):
J_C_C_u = np.zeros(shape=(nsvc, len(pq)), dtype=np.float64)
J_C_C_u[controllable, pq_lookup[svc_buses[in_pq & controllable]]] = 1
# count pvpq rows and pvpq columns from top left
J_m[len(pvpq) + len(pq):len(pvpq) + len(pq) + nsvc_controllable,
len(pvpq):len(pvpq) + len(pq)] = J_C_C_u[controllable, :]
J_m = csr_matrix(J_m)
return J_m
def create_J_modification_tcsc(V, Ybus_tcsc, x_control, svc_controllable, tcsc_controllable,
tcsc_x_l_pu, tcsc_x_cvar_pu, f, t, pvpq, pq, pvpq_lookup, pq_lookup, nsvc, ntcsc):
Y_TCSC = calc_y_svc_pu(x_control, tcsc_x_l_pu, tcsc_x_cvar_pu)
# S_tcsc_pu = V * (Ybus_tcsc.conj() @ V.conj())
dY_TCSC_dx = 2 * (np.cos(2 * x_control) - 1) / (np.pi * tcsc_x_l_pu)
Vf = V[f]
Vt = V[t]
Vmf = np.abs(Vf)
Vmt = np.abs(Vt)
S_Fii = Vf * np.conj(Ybus_tcsc.toarray()[f, f] * Vf)
S_Fkk = Vt * np.conj(Ybus_tcsc.toarray()[t, t] * Vt)
S_Fik = Vf * np.conj(Ybus_tcsc.toarray()[f, t] * Vt)
S_Fki = Vt * np.conj(Ybus_tcsc.toarray()[t, f] * Vf)
# seems like it is not used:
# S_ii = np.abs(V[f]) ** 2 * np.abs(Ybus[f, f]) * np.exp(1j * np.angle(Ybus[f, f].conj())) ####
# S_kk = np.abs(V[t]) ** 2 * np.abs(Ybus[t, t]) * np.exp(1j * np.angle(Ybus[t, t].conj())) ####
#
# S_ij = Sbus[f] - S_ii
# S_kj = Sbus[t] - S_kk
S_Fi_dx = dY_TCSC_dx / Y_TCSC * (S_Fii + S_Fik)
S_Fk_dx = dY_TCSC_dx / Y_TCSC * (S_Fkk + S_Fki)
f_in_pq = np.isin(f, pq)
t_in_pq = np.isin(t, pq)
f_in_pvpq = np.isin(f, pvpq)
t_in_pvpq = np.isin(t, pvpq)
# todo: use _sum_by_group what multiple elements start (or end) at the same bus?
J_C_P_d = np.zeros(shape=(len(pvpq), len(pvpq)), dtype=np.float64)
if np.any(f_in_pvpq):
J_C_P_d[pvpq_lookup[f[f_in_pvpq]], pvpq_lookup[f[f_in_pvpq]]] = -S_Fik.imag
if np.any(f_in_pvpq & t_in_pvpq):
J_C_P_d[pvpq_lookup[f[f_in_pvpq]], pvpq_lookup[t[t_in_pvpq]]] = S_Fik.imag
J_C_P_d[pvpq_lookup[t[t_in_pvpq]], pvpq_lookup[f[f_in_pvpq]]] = S_Fki.imag
if np.any(t_in_pvpq):
J_C_P_d[pvpq_lookup[t[t_in_pvpq]], pvpq_lookup[t[t_in_pvpq]]] = -S_Fki.imag
# J_C_P_d = np.array([[-S_Fik.imag, S_Fik.imag],
# [S_Fki.imag, -S_Fki.imag]]).reshape(2, 2) # todo: generalize shapes to work with many TCSC
# J_C_P_u = np.array([[S_Fik.real / Vm[f], S_Fik.real / Vm[t]],
# [S_Fki.real / Vm[f], S_Fki.real / Vm[t]]]).reshape(2, 2)
J_C_P_u = np.zeros(shape=(len(pvpq), len(pq)), dtype=np.float64)
if np.any(f_in_pvpq & f_in_pq):
J_C_P_u[pvpq_lookup[f[f_in_pvpq]], pq_lookup[f[f_in_pq]]] = S_Fik.real / Vmf
if np.any(f_in_pvpq & t_in_pq):
J_C_P_u[pvpq_lookup[f[f_in_pvpq]], pq_lookup[t[t_in_pq]]] = S_Fik.real / Vmt
if np.any(t_in_pvpq & f_in_pq):
J_C_P_u[pvpq_lookup[t[t_in_pvpq]], pq_lookup[f[f_in_pq]]] = S_Fki.real / Vmf
if np.any(t_in_pvpq & t_in_pq):
J_C_P_u[pvpq_lookup[t[t_in_pvpq]], pq_lookup[t[t_in_pq]]] = S_Fki.real / Vmt
J_C_Q_d = np.zeros(shape=(len(pq), len(pvpq)), dtype=np.float64)
if np.any(f_in_pvpq & f_in_pq):
J_C_Q_d[pq_lookup[f[f_in_pq]], pvpq_lookup[f[f_in_pvpq]]] = S_Fik.real
if np.any(f_in_pq & t_in_pvpq):
J_C_Q_d[pq_lookup[f[f_in_pq]], pvpq_lookup[t[t_in_pvpq]]] = -S_Fik.real
if np.any(t_in_pq & f_in_pvpq):
J_C_Q_d[pq_lookup[t[t_in_pq]], pvpq_lookup[f[f_in_pvpq]]] = -S_Fki.real
if np.any(t_in_pvpq & t_in_pq):
J_C_Q_d[pq_lookup[t[t_in_pq]], pvpq_lookup[t[t_in_pvpq]]] = S_Fki.real
# J_C_Q_d = np.array([[S_Fik.real, -S_Fik.real],
# [-S_Fki.real, S_Fki.real]]).reshape(2, 2)
J_C_Q_u = np.zeros(shape=(len(pq), len(pq)), dtype=np.float64)
if np.any(f_in_pq):
J_C_Q_u[pq_lookup[f[f_in_pq]], pq_lookup[f[f_in_pq]]] = (2 * S_Fii.imag + S_Fik.imag) / Vmf
if np.any(f_in_pq & t_in_pq):
J_C_Q_u[pq_lookup[f[f_in_pq]], pq_lookup[t[t_in_pq]]] = S_Fik.imag / Vmt
J_C_Q_u[pq_lookup[t[t_in_pq]], pq_lookup[f[f_in_pq]]] = S_Fki.imag / Vmf
if np.any(t_in_pq):
J_C_Q_u[pq_lookup[t[t_in_pq]], pq_lookup[t[t_in_pq]]] = (2 * S_Fkk.imag + S_Fki.imag) / Vmt
# J_C_Q_u = np.array([[(2 * S_Fii.imag + S_Fik.imag) / Vm[f], S_Fik.imag / Vm[f]],
# [S_Fki.imag / Vm[t], (2 * S_Fkk.imag + S_Fki.imag) / Vm[f]]]).reshape(2, 2)
J_C_P_c = np.zeros(shape=(len(pvpq), nsvc + ntcsc), dtype=np.float64)
if np.any(f_in_pvpq):
J_C_P_c[pvpq_lookup[f[f_in_pvpq]], (nsvc + np.arange(ntcsc))[f_in_pvpq]] = S_Fi_dx.real
if np.any(t_in_pvpq):
J_C_P_c[pvpq_lookup[t[t_in_pvpq]], (nsvc + np.arange(ntcsc))[t_in_pvpq]] = S_Fk_dx.real
# J_C_P_c = np.array([[S_Fi_dx.real], [S_Fk_dx.real]]).reshape(2, 1)
J_C_Q_c = np.zeros(shape=(len(pq), nsvc + ntcsc), dtype=np.float64)
if np.any(f_in_pq):
J_C_Q_c[pq_lookup[f[f_in_pq]], (nsvc + np.arange(ntcsc))[f_in_pq]] = S_Fi_dx.imag
if np.any(t_in_pq):
J_C_Q_c[pq_lookup[t[t_in_pq]], (nsvc + np.arange(ntcsc))[t_in_pq]] = S_Fk_dx.imag
# J_C_Q_c = np.array([[S_Fi_dx.imag], [S_Fk_dx.imag]]).reshape(2, 1)
# the signs are opposite here for J_C_C_d, J_C_C_u, J_C_C_c and I don't know why
# main mode of operation - set point for p_to_mw:
# J_C_C_d = np.zeros(shape=(len(pvpq), len(pvpq)))
J_C_C_d = np.zeros(shape=(nsvc + ntcsc, len(pvpq)), dtype=np.float64)
if np.any(f_in_pvpq):
J_C_C_d[(nsvc + np.arange(ntcsc))[f_in_pvpq], pvpq_lookup[f[f_in_pvpq]]] = S_Fik.imag
if np.any(t_in_pvpq):
J_C_C_d[(nsvc + np.arange(ntcsc))[t_in_pvpq], pvpq_lookup[t[t_in_pvpq]]] = -S_Fik.imag
J_C_C_u = np.zeros(shape=(nsvc + ntcsc, len(pq)), dtype=np.float64)
if np.any(f_in_pq):
J_C_C_u[(nsvc + np.arange(ntcsc))[f_in_pq], pq_lookup[f[f_in_pq]]] = S_Fik.real / Vmf
if np.any(t_in_pq):
J_C_C_u[(nsvc + np.arange(ntcsc))[t_in_pq], pq_lookup[t[t_in_pq]]] = S_Fik.real / Vmt
J_C_C_c = np.zeros(shape=(nsvc + ntcsc, nsvc + ntcsc), dtype=np.float64)
J_C_C_c[np.r_[nsvc:nsvc + ntcsc], np.r_[nsvc:nsvc + ntcsc]] = -S_Fi_dx.real # .flatten()?
# alternative mode of operation: for Vm at to bus (mismatch and setpoint also must be adjusted):
# J_C_C_d = np.zeros(shape=(len(x_control), len(pvpq)), dtype=np.float64)
# J_C_C_u = np.zeros(shape=(len(x_control), len(pq)), dtype=np.float64)
# J_C_C_u[np.arange(len(x_control)), pq_lookup[t]] = 1
# J_C_C_c = np.zeros((len(x_control), len(x_control)), dtype=np.float64)
if np.all(tcsc_controllable):
J_m = np.vstack([np.hstack([J_C_P_d, J_C_P_u, J_C_P_c]),
np.hstack([J_C_Q_d, J_C_Q_u, J_C_Q_c]),
np.hstack([J_C_C_d, J_C_C_u, J_C_C_c])])
elif np.any(tcsc_controllable) or np.any(svc_controllable):
relevant = np.r_[np.arange(nsvc), nsvc + np.arange(ntcsc)[tcsc_controllable]]
J_m = np.vstack([np.hstack([J_C_P_d, J_C_P_u, J_C_P_c[:, relevant]]),
np.hstack([J_C_Q_d, J_C_Q_u, J_C_Q_c[:, relevant]]),
np.hstack([J_C_C_d[relevant, :], J_C_C_u[relevant, :],
J_C_C_c[:, relevant][relevant, :]])])
else:
J_m = np.vstack([np.hstack([J_C_P_d, J_C_P_u]),
np.hstack([J_C_Q_d, J_C_Q_u])])
J_m = csr_matrix(J_m)
return J_m
def create_J_modification_ssc(J, V, Ybus_ssc, f, t, pvpq, pq, pvpq_lookup, pq_lookup):
"""
creates the modification Jacobian matrix for SSC (STATCOM)
Parameters
----------
V
array of np.complex128
Ybus_ssc
scipy.sparse.csr_matrix
f
array of np.int64
t
array of np.int64
pvpq
array of np.int64
pq
array of np.int64
pvpq_lookup
array of np.int64
pq_lookup
array of np.int64
Returns
-------
J_m
scipy.sparse.csr_matrix
"""
#
J_m = np.zeros_like(J.toarray())
Vf = V[f]
Vt = V[t]
Vmf = np.abs(Vf)
Vmt = np.abs(Vt)
S_Fii = Vf * np.conj(Ybus_ssc.toarray()[f, f] * Vf)
S_Fkk = Vt * np.conj(Ybus_ssc.toarray()[t, t] * Vt)
S_Fik = Vf * np.conj(Ybus_ssc.toarray()[f, t] * Vt)
S_Fki = Vt * np.conj(Ybus_ssc.toarray()[t, f] * Vf)
# seems like it is not used:
# S_ii = np.abs(V[f]) ** 2 * np.abs(Ybus[f, f]) * np.exp(1j * np.angle(Ybus[f, f].conj())) ####
# S_kk = np.abs(V[t]) ** 2 * np.abs(Ybus[t, t]) * np.exp(1j * np.angle(Ybus[t, t].conj())) ####
#
# S_ij = Sbus[f] - S_ii
# S_kj = Sbus[t] - S_kk
f_in_pq = np.isin(f, pq)
f_in_pvpq = np.isin(f, pvpq)
# todo: use _sum_by_group what multiple elements start (or end) at the same bus?
# J_C_P_d = np.zeros(shape=(len(pvpq) + len(x_control), len(pvpq) + len(x_control)), dtype=np.float64)
# J_C_P_d = np.zeros(shape=(len(pvpq), len(pvpq)), dtype=np.float64)
if np.any(f_in_pvpq):
# J_C_P_d[pvpq_lookup[f[f_in_pvpq]], pvpq_lookup[f[f_in_pvpq]]] = -S_Fik.imag
# # J_C_P_d[pvpq_lookup[f[f_in_pvpq]], pvpq_lookup[t[f_in_pvpq]]+ len(x_control)] = S_Fik.imag
# J_C_P_d[pvpq_lookup[f[f_in_pvpq]], pvpq_lookup[t[f_in_pvpq]]] = S_Fik.imag
#
# # J_C_P_d[pvpq_lookup[t[f_in_pvpq]] + len(x_control), pvpq_lookup[f[f_in_pvpq]]] = S_Fki.imag
# # J_C_P_d[pvpq_lookup[t[f_in_pvpq]] + len(x_control), pvpq_lookup[t[f_in_pvpq]]+ len(x_control)] = -S_Fki.imag
#
# J_C_P_d[pvpq_lookup[t[f_in_pvpq]] , pvpq_lookup[f[f_in_pvpq]]] = S_Fki.imag
# J_C_P_d[pvpq_lookup[t[f_in_pvpq]] , pvpq_lookup[t[f_in_pvpq]]] = -S_Fki.imag
J_m[pvpq_lookup[f[f_in_pvpq]], pvpq_lookup[f[f_in_pvpq]]] = -S_Fik.imag
J_m[pvpq_lookup[f[f_in_pvpq]], pvpq_lookup[t[f_in_pvpq]]] = S_Fik.imag
J_m[pvpq_lookup[t[f_in_pvpq]] , pvpq_lookup[f[f_in_pvpq]]] = S_Fki.imag
J_m[pvpq_lookup[t[f_in_pvpq]] , pvpq_lookup[t[f_in_pvpq]]] = -S_Fki.imag
# J_C_P_u = np.zeros(shape=(len(pvpq), len(pq)), dtype=np.float64)
# J_C_P_u = np.zeros(shape=(len(pvpq)+ len(x_control), len(pq)+ len(x_control)), dtype=np.float64)
if np.any(f_in_pvpq & f_in_pq): ## TODO check if this conditon includes all cases, and check trough tests
# J_C_P_u[pvpq_lookup[f[f_in_pvpq]], pq_lookup[f[f_in_pq]]] = (2 * S_Fii.real + S_Fik.real) / Vmf
# J_C_P_u[pvpq_lookup[f[f_in_pvpq]], pq_lookup[t[f_in_pq]] ] = S_Fik.real/Vmt
#
# J_C_P_u[pvpq_lookup[t[f_in_pvpq]], pq_lookup[f[f_in_pq]]] = S_Fki.real/Vmf
# J_C_P_u[pvpq_lookup[t[f_in_pvpq]], pq_lookup[t[f_in_pq]]] = (2 * S_Fkk.real + S_Fki.real) / Vmt
J_m[pvpq_lookup[f[f_in_pvpq]], len(pvpq)+pq_lookup[f[f_in_pq]]] = (2 * S_Fii.real + S_Fik.real) / Vmf
J_m[pvpq_lookup[f[f_in_pvpq]], len(pvpq)+pq_lookup[t[f_in_pq]] ] = S_Fik.real/Vmt
J_m[pvpq_lookup[t[f_in_pvpq]], len(pvpq)+pq_lookup[f[f_in_pq]]] = S_Fki.real/Vmf
J_m[pvpq_lookup[t[f_in_pvpq]], len(pvpq)+pq_lookup[t[f_in_pq]]] = (2 * S_Fkk.real + S_Fki.real) / Vmt
# J_C_Q_d = np.zeros(shape=(len(pq), len(pvpq)), dtype=np.float64)
# J_C_Q_d = np.zeros(shape=(len(pq)+ len(x_control), len(pvpq)+ len(x_control)), dtype=np.float64)
if np.any(f_in_pvpq & f_in_pq):
# J_C_Q_d[pq_lookup[f[f_in_pq]], pvpq_lookup[f[f_in_pvpq]]] = S_Fik.real
# J_C_Q_d[pq_lookup[f[f_in_pq]], pvpq_lookup[t[f_in_pvpq]]] = -S_Fik.real
#
# # J_C_Q_d[pq_lookup[t[f_in_pq]]+ len(x_control), pvpq_lookup[f[f_in_pvpq]]] = 0
# # J_C_Q_d[pq_lookup[t[f_in_pq]]+ len(x_control), pvpq_lookup[t[f_in_pvpq]]+ len(x_control)] = 0
J_m[len(pvpq) + pq_lookup[f[f_in_pq]], pvpq_lookup[f[f_in_pvpq]]] = S_Fik.real
J_m[len(pvpq) + pq_lookup[f[f_in_pq]], pvpq_lookup[t[f_in_pvpq]]] = -S_Fik.real
# J_C_Q_u = np.zeros(shape=(len(pq), len(pq)), dtype=np.float64)
# J_C_Q_u = np.zeros(shape=(len(pq)+ len(x_control), len(pq)+ len(x_control)), dtype=np.float64)
if np.any(f_in_pq):
# J_C_Q_u[pq_lookup[f[f_in_pq]], pq_lookup[f[f_in_pq]]] = (2 * S_Fii.imag + S_Fik.imag) / Vmf
# J_C_Q_u[pq_lookup[f[f_in_pq]], pq_lookup[t[f_in_pq]]] = S_Fik.imag/Vmt
#
# J_C_Q_u[pq_lookup[t[f_in_pq]], pq_lookup[f[f_in_pq]]] = 1
# J_C_Q_u[pq_lookup[t[f_in_pq]], pq_lookup[t[f_in_pq]]] = 0
J_m[len(pvpq)+pq_lookup[f[f_in_pq]], len(pvpq)+pq_lookup[f[f_in_pq]]] = (2 * S_Fii.imag + S_Fik.imag) / Vmf
J_m[len(pvpq)+pq_lookup[f[f_in_pq]], len(pvpq)+pq_lookup[t[f_in_pq]]] = S_Fik.imag/Vmt
J_m[len(pvpq)+pq_lookup[t[f_in_pq]], len(pvpq)+pq_lookup[f[f_in_pq]]] = 1
J_m[len(pvpq)+pq_lookup[t[f_in_pq]], len(pvpq)+pq_lookup[t[f_in_pq]]] = 0
#
# J_C_Q_u[pq_lookup[t[f_in_pq]]+ len(x_control), pq_lookup[f[f_in_pq]]] = 1
# J_C_Q_u[pq_lookup[t[f_in_pq]]+ len(x_control), pq_lookup[t[f_in_pq]]+ len(x_control)] = 0
# J_C_P_c = np.zeros(shape=(len(pvpq), nsvc + ntcsc), dtype=np.float64)
# J_C_Q_c = np.zeros(shape=(len(pq), nsvc + ntcsc + 2 * nssc), dtype=np.float64)
# J_C_C_d = np.zeros(shape=(nsvc + ntcsc + 2 * nssc, len(pvpq)), dtype=np.float64)
# J_C_C_u = np.zeros(shape=(nsvc + ntcsc + 2 * nssc, len(pq)), dtype=np.float64)
# J_C_C_c = np.zeros(shape=(nsvc + ntcsc + 2 *nssc, nsvc + ntcsc + 2 *nssc), dtype=np.float64)
# if np.any(tcsc_controllable) or np.any(svc_controllable): # todo
# relevant = np.r_[np.arange(nsvc), nsvc + np.arange(ntcsc)[tcsc_controllable]]
# J_m = np.vstack([np.hstack([J_C_P_d, J_C_P_u, J_C_P_c[:, relevant]]),
# np.hstack([J_C_Q_d, J_C_Q_u, J_C_Q_c[:, relevant]]),
# np.hstack([J_C_C_d[relevant, :], J_C_C_u[relevant, :],
# J_C_C_c[:, relevant][relevant, :]])])
# else:
# J_m = np.vstack([np.hstack([J_C_P_d, J_C_P_u]),
# np.hstack([J_C_Q_d, J_C_Q_u])])
J_m = csr_matrix(J_m)
return J_m