def dfdx(guess):
network.buses_t.v_ang.loc[now,sub_network.pvpqs] = guess[:len(sub_network.pvpqs)]
network.buses_t.v_mag_pu.loc[now,sub_network.pqs] = guess[len(sub_network.pvpqs):]
v_mag_pu = network.buses_t.v_mag_pu.loc[now,buses_o]
v_ang = network.buses_t.v_ang.loc[now,buses_o]
V = v_mag_pu*np.exp(1j*v_ang)
index = r_[:len(buses_o)]
#make sparse diagonal matrices
V_diag = csr_matrix((V,(index,index)))
V_norm_diag = csr_matrix((V/abs(V),(index,index)))
I_diag = csr_matrix((sub_network.Y*V,(index,index)))
dS_dVa = 1j*V_diag*np.conj(I_diag - sub_network.Y*V_diag)
dS_dVm = V_norm_diag*np.conj(I_diag) + V_diag * np.conj(sub_network.Y*V_norm_diag)
J00 = dS_dVa[1:,1:].real
J01 = dS_dVm[1:,1+len(sub_network.pvs):].real
J10 = dS_dVa[1+len(sub_network.pvs):,1:].imag
J11 = dS_dVm[1+len(sub_network.pvs):,1+len(sub_network.pvs):].imag
J = svstack([
shstack([J00, J01]),
shstack([J10, J11])
], format="csr")
return J
def dfdx(guess):
network.buses_t.v_ang.loc[now,sub_network.pvpqs] = guess[:len(sub_network.pvpqs)]
network.buses_t.v_mag_pu.loc[now,sub_network.pqs] = guess[len(sub_network.pvpqs):]
v_mag_pu = network.buses_t.v_mag_pu.loc[now,buses_o]
v_ang = network.buses_t.v_ang.loc[now,buses_o]
V = v_mag_pu*np.exp(1j*v_ang)
index = r_[:len(buses_o)]
#make sparse diagonal matrices
V_diag = csr_matrix((V,(index,index)))
V_norm_diag = csr_matrix((V/abs(V),(index,index)))
I_diag = csr_matrix((sub_network.Y*V,(index,index)))
dS_dVa = 1j*V_diag*np.conj(I_diag - sub_network.Y*V_diag)
dS_dVm = V_norm_diag*np.conj(I_diag) + V_diag * np.conj(sub_network.Y*V_norm_diag)
J00 = dS_dVa[1:,1:].real
J01 = dS_dVm[1:,1+len(sub_network.pvs):].real
J10 = dS_dVa[1+len(sub_network.pvs):,1:].imag
J11 = dS_dVm[1+len(sub_network.pvs):,1+len(sub_network.pvs):].imag
J = svstack([
shstack([J00, J01]),
shstack([J10, J11])
], format="csr")
return J
def dfdx(guess, distribute_slack=False, slack_weights=None):
last_pq = -1 if distribute_slack else None
network.buses_t.v_ang.loc[
now, sub_network.pvpqs] = guess[:len(sub_network.pvpqs)]
network.buses_t.v_mag_pu.loc[
now, sub_network.pqs] = guess[len(sub_network.pvpqs):last_pq]
v_mag_pu = network.buses_t.v_mag_pu.loc[now, buses_o]
v_ang = network.buses_t.v_ang.loc[now, buses_o]
V = v_mag_pu * np.exp(1j * v_ang)
index = r_[:len(buses_o)]
#make sparse diagonal matrices
V_diag = csr_matrix((V, (index, index)))
V_norm_diag = csr_matrix((V / abs(V), (index, index)))
I_diag = csr_matrix((sub_network.Y * V, (index, index)))
dS_dVa = 1j * V_diag * np.conj(I_diag - sub_network.Y * V_diag)
dS_dVm = V_norm_diag * np.conj(I_diag) + V_diag * np.conj(
sub_network.Y * V_norm_diag)
J10 = dS_dVa[1 + len(sub_network.pvs):, 1:].imag
J11 = dS_dVm[1 + len(sub_network.pvs):, 1 + len(sub_network.pvs):].imag
if distribute_slack:
J00 = dS_dVa[:, 1:].real
J01 = dS_dVm[:, 1 + len(sub_network.pvs):].real
J02 = csr_matrix(slack_weights, (1, 1 + len(sub_network.pvpqs))).T
J12 = csr_matrix((1, len(sub_network.pqs))).T
J_P_blocks = [J00, J01, J02]
J_Q_blocks = [J10, J11, J12]
else:
J00 = dS_dVa[1:, 1:].real
J01 = dS_dVm[1:, 1 + len(sub_network.pvs):].real
J_P_blocks = [J00, J01]
J_Q_blocks = [J10, J11]
J = svstack([shstack(J_P_blocks), shstack(J_Q_blocks)], format="csr")
return J
def _dfdx(guess, Y):
"""
Compute the Jacobian matrix.
Parameters
----------
guess : numpy.ndarray
The current v_guess for the roots of f(x), of size 2*(N-1), where elements
[0,...,N-2] are the nodal voltage angles \theta_i and [N-1,...,2(N-1)]
the nodal voltage magnitudes |V_i|. The slack bus variables are
excluded.
Y : scipy.sparse.csc_matrix
The nodal admittance matrix of shape (N, N) as a sparse matrix.
Returns
-------
J : scipy.sparse.csr_matrix
The Jacobian matrix as a sparse matrix.
"""
# Construct nodal voltage vector V, setting V_slack = 1+0j.
v = _construct_v_from_guess(guess)
index = np.array(range(len(v)))
# Construct sparse diagonal matrices.
v_diag = csr_matrix((v, (index, index)))
v_norm_diag = csr_matrix((v / abs(v), (index, index)))
i_diag = csr_matrix((Y * v, (index, index)))
# Construct the Jacobian matrix.
dS_dVa = 1j * v_diag * np.conj(i_diag - Y * v_diag) # dS / d \theta
dS_dVm = v_norm_diag * np.conj(i_diag) + v_diag * np.conj(
Y * v_norm_diag) # dS / d |V|
J00 = dS_dVa[1:, 1:].real
J01 = dS_dVm[1:, 1:].real
J10 = dS_dVa[1:, 1:].imag
J11 = dS_dVm[1:, 1:].imag
J = svstack([shstack([J00, J01]), shstack([J10, J11])], format='csr')
return J