def add_dc_nodal_power_balance(numerical_circuit, problem: pl.LpProblem, theta, P):
"""
Add the nodal power balance
:param numerical_circuit: NumericalCircuit instance
:param problem: LpProblem instance
:param theta: Voltage angles LpVars (n, nt)
:param P: Power injection at the buses LpVars (n, nt)
:return: Nothing, the restrictions are added to the problem
"""
# do the topological computation
calculation_inputs = numerical_circuit.split_into_islands()
nodal_restrictions = np.empty(numerical_circuit.nbus, dtype=object)
# simulate each island and merge the results
for i, calc_inpt in enumerate(calculation_inputs):
# if there is a slack it means that there is at least one generator,
# otherwise these equations do not make sense
if len(calc_inpt.vd) > 0:
# find the original indices
bus_original_idx = np.array(calc_inpt.original_bus_idx)
# re-pack the variables for the island and time interval
P_island = P[bus_original_idx] # the sizes already reflect the correct time span
theta_island = theta[bus_original_idx] # the sizes already reflect the correct time span
B_island = calc_inpt.Ybus.imag
pqpv = calc_inpt.pqpv
vd = calc_inpt.vd
# Add nodal power balance for the non slack nodes
idx = bus_original_idx[pqpv]
nodal_restrictions[idx] = pl.lpAddRestrictions2(problem=problem,
lhs=pl.lpDot(B_island[np.ix_(pqpv, pqpv)], theta_island[pqpv]),
rhs=P_island[pqpv],
name='Nodal_power_balance_pqpv_is' + str(i),
op='=')
# Add nodal power balance for the slack nodes
idx = bus_original_idx[vd]
nodal_restrictions[idx] = pl.lpAddRestrictions2(problem=problem,
lhs=pl.lpDot(B_island[vd, :], theta_island),
rhs=P_island[vd],
name='Nodal_power_balance_vd_is' + str(i),
op='=')
# slack angles equal to zero
pl.lpAddRestrictions2(problem=problem,
lhs=theta_island[vd],
rhs=np.zeros(len(vd)),
name='Theta_vd_zero_is' + str(i),
op='=')
return nodal_restrictions
def get_power_injections(C_bus_gen, Pg, C_bus_bat, Pb, C_bus_load, LSlack, Pl):
"""
Create the power injections per bus
:param C_bus_gen: Bus-Generators sparse connectivity matrix (n, ng)
:param Pg: generator LpVars (ng, nt)
:param C_bus_bat: Bus-Batteries sparse connectivity matrix (n, nb)
:param Pb: Batteries LpVars (nb, nt)
:param C_bus_load: Bus-Load sparse connectivity matrix (n, nl)
:param LSlack: Load slack LpVars (nl, nt)
:param Pl: Load values (nl, nt)
:return: Power injection at the buses (n, nt)
"""
return pl.lpDot(C_bus_gen, Pg) + pl.lpDot(C_bus_bat, Pb) - pl.lpDot(C_bus_load, Pl - LSlack)