def declare_eq_branch_power_btheta_approx(model, index_set, branches, approximation_type=ApproximationType.BTHETA): """ Create the equality constraints for power (from BTHETA approximation) in the branch """ m = model con_set = decl.declare_set("_con_eq_branch_power_btheta_approx_set", model, index_set) m.eq_pf_branch = pe.Constraint(con_set) for branch_name in con_set: branch = branches[branch_name] from_bus = branch['from_bus'] to_bus = branch['to_bus'] tau = 1.0 shift = 0.0 if branch['branch_type'] == 'transformer': tau = branch['transformer_tap_ratio'] shift = math.radians(branch['transformer_phase_shift']) if approximation_type == ApproximationType.BTHETA: x = branch['reactance'] b = -1/(tau*x) elif approximation_type == ApproximationType.BTHETA_LOSSES: b = tx_calc.calculate_susceptance(branch)/tau m.eq_pf_branch[branch_name] = \ m.pf[branch_name] == \ b * (m.va[from_bus] - m.va[to_bus] + shift)
def power_flow_through_branch(Vi, Vj, delta, branch, bus_type="from_bus", power_type="Reactive"): if not (power_type == "Active" or power_type == "Reactive"): raise ValueError( 'Power type must be "Active" (for p) or "Reactive" (for q)') if not (bus_type == "from_bus" or bus_type == "to_bus"): raise ValueError( 'Bus type must be "from_bus" (for f) or "to_bus" (for t)') g = tx_calc.calculate_conductance(branch) b = tx_calc.calculate_susceptance(branch) if power_type == "Active": if bus_type == "from_bus": return Vi**2 * g - Vi * Vj * g * pe.cos( delta) - Vi * Vj * b * pe.sin(delta) else: return Vj**2 * g - Vi * Vj * g * pe.cos( delta) - Vi * Vj * b * pe.sin(delta) else: if bus_type == "from_bus": return -Vi**2 * b + Vi * Vj * b * pe.cos( delta) - Vi * Vj * g * pe.sin(delta) else: return -Vj**2 * b + Vi * Vj * b * pe.cos( delta) - Vi * Vj * g * pe.sin(delta)
def declare_eq_branch_current(model, index_set, branches, coordinate_type=CoordinateType.RECTANGULAR): """ Create the equality constraints for the real and imaginary current in the branch """ assert (coordinate_type != CoordinateType.POLAR and "Branch current in polar coordinates not implemented.") m = model con_set = decl.declare_set("_con_eq_branch_current_set", model, index_set) m.eq_ifr_branch = pe.Constraint(con_set) m.eq_ifj_branch = pe.Constraint(con_set) m.eq_itr_branch = pe.Constraint(con_set) m.eq_itj_branch = pe.Constraint(con_set) for branch_name in con_set: branch = branches[branch_name] from_bus = branch['from_bus'] to_bus = branch['to_bus'] g = tx_calc.calculate_conductance(branch) b = tx_calc.calculate_susceptance(branch) bc = branch['charging_susceptance'] tau = 1.0 shift = 0.0 if branch['branch_type'] == 'transformer': tau = branch['transformer_tap_ratio'] shift = math.radians(branch['transformer_phase_shift']) g11 = g / tau**2 g12 = (g * math.cos(shift) - b * math.sin(shift)) / tau g21 = (g * math.cos(shift) + b * math.sin(shift)) / tau g22 = g b11 = (b + bc / 2) / tau**2 b12 = (b * math.cos(shift) + g * math.sin(shift)) / tau b21 = (b * math.cos(shift) - g * math.sin(shift)) / tau b22 = b + bc / 2 m.eq_ifr_branch[branch_name] = \ m.ifr[branch_name] == \ g11 * m.vr[from_bus] - g12 * m.vr[to_bus] - (b11 * m.vj[from_bus] - b12 * m.vj[to_bus]) m.eq_ifj_branch[branch_name] = \ m.ifj[branch_name] == \ g11 * m.vj[from_bus] - g12 * m.vj[to_bus] + (b11 * m.vr[from_bus] - b12 * m.vr[to_bus]) m.eq_itr_branch[branch_name] = \ m.itr[branch_name] == \ -(g21 * m.vr[from_bus] - g22 * m.vr[to_bus] - (b21 * m.vj[from_bus] - b22 * m.vj[to_bus])) m.eq_itj_branch[branch_name] = \ m.itj[branch_name] == \ -(g21 * m.vj[from_bus] - g22 * m.vj[to_bus] + (b21 * m.vr[from_bus] - b22 * m.vr[to_bus]))
def declare_eq_branch_power_ptdf_approx(model, index_set, branches, buses, bus_p_loads, gens_by_bus, bus_gs_fixed_shunts, ptdf_tol = 1e-10, approximation_type = ApproximationType.PTDF): """ Create the equality constraints for power (from PTDF approximation) in the branch """ m = model con_set = decl.declare_set("_con_eq_branch_power_ptdf_approx_set", model, index_set) m.eq_pf_branch = pe.Constraint(con_set) for branch_name in con_set: branch = branches[branch_name] expr = 0 tau = 1.0 shift = 0.0 if branch['branch_type'] == 'transformer': tau = branch['transformer_tap_ratio'] shift = math.radians(branch['transformer_phase_shift']) if approximation_type == ApproximationType.PTDF: ptdf = branch['ptdf'] if shift != 0.: b = -(1 / branch['reactance']) expr += b * (shift / tau) elif approximation_type == ApproximationType.PTDF_LOSSES: ptdf = branch['ptdf_r'] if shift != 0.: b = tx_calc.calculate_susceptance(branch) expr += b * (shift / tau) for bus_name, coef in ptdf.items(): if ptdf_tol and abs(coef) < ptdf_tol: continue bus = buses[bus_name] phi_from = bus['phi_from'] phi_to = bus['phi_to'] if bus_gs_fixed_shunts[bus_name] != 0.0: expr += coef * bus_gs_fixed_shunts[bus_name] if bus_p_loads[bus_name] != 0.0: expr += coef * m.pl[bus_name] for gen_name in gens_by_bus[bus_name]: expr -= coef * m.pg[gen_name] for _, phi in phi_from.items(): expr += coef * phi for _, phi in phi_to.items(): expr -= coef * phi m.eq_pf_branch[branch_name] = \ m.pf[branch_name] == expr
def pwl_active_from_ub_rule(model, branch_name, i): branch = branches[branch_name] from_bus = branch['from_bus'] to_bus = branch['to_bus'] g = tx_calc.calculate_conductance(branch) b = tx_calc.calculate_susceptance(branch) coeffs = branch_dict["Active_from_bus"][branch_name]['boxes']['coefficients'][i-1] #M = 10*(g+b) + 4*(coeffs[0]+coeffs[1]+coeffs[2]+coeffs[3]) M = 2*s_max[branch_name] + 10*(np.abs(coeffs[0])+np.abs(coeffs[1])+np.abs(coeffs[2])+np.abs(coeffs[3])) return -model.pf[branch_name] + coeffs[0]*model.vm[from_bus] + coeffs[1]*model.vm[to_bus] + coeffs[2]*model.dva_branch[branch_name, i, 0] + coeffs[3] <= M*(1-model.u_branch[branch_name, i, 0])
def _calculate_phase_shift(self): phase_shift_array = np.array([ tx_calc.calculate_susceptance(branch) * (radians(branch['transformer_phase_shift']) / branch['transformer_tap_ratio']) if (branch['branch_type'] == 'transformer') else 0. for branch in (self._branches[bn] for bn in self.branches_keys) ]) ## protect the array using numpy phase_shift_array.flags.writeable = False self.phase_shift_array = phase_shift_array
def declare_eq_branch_power(model, index_set, branches): """ Create the equality constraints for the real and reactive power in the branch """ m = model con_set = decl.declare_set("_con_eq_branch_power_set", model, index_set) m.eq_pf_branch = pe.Constraint(con_set) m.eq_pt_branch = pe.Constraint(con_set) m.eq_qf_branch = pe.Constraint(con_set) m.eq_qt_branch = pe.Constraint(con_set) for branch_name in con_set: branch = branches[branch_name] from_bus = branch['from_bus'] to_bus = branch['to_bus'] vmsq_from_bus = m.vmsq[from_bus] vmsq_to_bus = m.vmsq[to_bus] g = tx_calc.calculate_conductance(branch) b = tx_calc.calculate_susceptance(branch) bc = branch['charging_susceptance'] tau = 1.0 shift = 0.0 if branch['branch_type'] == 'transformer': tau = branch['transformer_tap_ratio'] shift = math.radians(branch['transformer_phase_shift']) g11 = g / tau**2 g12 = g * math.cos(shift) / tau g21 = g * math.sin(shift) / tau g22 = g b11 = (b + bc / 2) / tau**2 b12 = b * math.cos(shift) / tau b21 = b * math.sin(shift) / tau b22 = b + bc / 2 m.eq_pf_branch[branch_name] = \ m.pf[branch_name] == \ g11 * vmsq_from_bus - \ (g12 * m.c[(from_bus,to_bus)] + g21 * m.s[(from_bus,to_bus)] + b12 * m.s[(from_bus,to_bus)] - b21 * m.c[(from_bus,to_bus)]) m.eq_pt_branch[branch_name] = \ m.pt[branch_name] == \ g22 * vmsq_to_bus - \ (g12 * m.c[(from_bus,to_bus)] + g21 * m.s[(from_bus,to_bus)] - b12 * m.s[(from_bus,to_bus)] + b21 * m.c[(from_bus,to_bus)]) m.eq_qf_branch[branch_name] = \ m.qf[branch_name] == \ -b11 * vmsq_from_bus + \ (b12 * m.c[(from_bus,to_bus)] + b21 * m.s[(from_bus,to_bus)] - g12 * m.s[(from_bus,to_bus)] + g21 * m.c[(from_bus,to_bus)]) m.eq_qt_branch[branch_name] = \ m.qt[branch_name] == \ -b22 * vmsq_to_bus + \ (b12 * m.c[(from_bus,to_bus)] + b21 * m.s[(from_bus,to_bus)] + g12 * m.s[(from_bus,to_bus)] - g21 * m.c[(from_bus,to_bus)])
def declare_eq_branch_power(model, index_set, branches, branch_attrs, coordinate_type=CoordinateType.POLAR): """ Create the equality constraints for the real and reactive power in the branch """ m = model bus_pairs = zip_items(branch_attrs['from_bus'], branch_attrs['to_bus']) unique_bus_pairs = list(set([val for idx, val in bus_pairs.items()])) declare_expr_c(model, unique_bus_pairs, coordinate_type) declare_expr_s(model, unique_bus_pairs, coordinate_type) con_set = decl.declare_set("_con_eq_branch_power_set", model, index_set) m.eq_pf_branch = pe.Constraint(con_set) m.eq_pt_branch = pe.Constraint(con_set) m.eq_qf_branch = pe.Constraint(con_set) m.eq_qt_branch = pe.Constraint(con_set) for branch_name in con_set: branch = branches[branch_name] if not branch['in_service']: continue from_bus = branch['from_bus'] to_bus = branch['to_bus'] if coordinate_type == CoordinateType.POLAR: vmsq_from_bus = m.vm[from_bus]**2 vmsq_to_bus = m.vm[to_bus]**2 elif coordinate_type == CoordinateType.RECTANGULAR: vmsq_from_bus = m.vr[from_bus]**2 + m.vj[from_bus]**2 vmsq_to_bus = m.vr[to_bus]**2 + m.vj[to_bus]**2 g = tx_calc.calculate_conductance(branch) b = tx_calc.calculate_susceptance(branch) bc = branch['charging_susceptance'] tau = 1.0 shift = 0.0 if branch['branch_type'] == 'transformer': tau = branch['transformer_tap_ratio'] shift = math.radians(branch['transformer_phase_shift']) g11 = g / tau**2 g12 = g * math.cos(shift) / tau g21 = g * math.sin(shift) / tau g22 = g b11 = (b + bc / 2) / tau**2 b12 = b * math.cos(shift) / tau b21 = b * math.sin(shift) / tau b22 = b + bc / 2 m.eq_pf_branch[branch_name] = \ m.pf[branch_name] == \ g11 * vmsq_from_bus - \ (g12 * m.c[(from_bus,to_bus)] + g21 * m.s[(from_bus,to_bus)] + b12 * m.s[(from_bus,to_bus)] - b21 * m.c[(from_bus,to_bus)]) m.eq_pt_branch[branch_name] = \ m.pt[branch_name] == \ g22 * vmsq_to_bus - \ (g12 * m.c[(from_bus,to_bus)] + g21 * m.s[(from_bus,to_bus)] - b12 * m.s[(from_bus,to_bus)] + b21 * m.c[(from_bus,to_bus)]) m.eq_qf_branch[branch_name] = \ m.qf[branch_name] == \ -b11 * vmsq_from_bus + \ (b12 * m.c[(from_bus,to_bus)] + b21 * m.s[(from_bus,to_bus)] - g12 * m.s[(from_bus,to_bus)] + g21 * m.c[(from_bus,to_bus)]) m.eq_qt_branch[branch_name] = \ m.qt[branch_name] == \ -b22 * vmsq_to_bus + \ (b12 * m.c[(from_bus,to_bus)] + b21 * m.s[(from_bus,to_bus)] + g12 * m.s[(from_bus,to_bus)] - g21 * m.c[(from_bus,to_bus)])
def create_hot_start_lpac_model(model_data, voltages, lower_bound=-pi / 3, upper_bound=pi / 3, cosine_segment_count=20, include_feasibility_slack=False, mode="uniform"): """ The hot start LPAC model assumes that voltages are known, e.g. from an AC base point solution. """ ###Grid data md = model_data.clone_in_service() tx_utils.scale_ModelData_to_pu(md, inplace=True) gens = dict(md.elements(element_type='generator')) buses = dict(md.elements(element_type='bus')) branches = dict(md.elements(element_type='branch')) loads = dict(md.elements(element_type='load')) shunts = dict(md.elements(element_type='shunt')) gen_attrs = md.attributes(element_type='generator') bus_attrs = md.attributes(element_type='bus') branch_attrs = md.attributes(element_type='branch') inlet_branches_by_bus, outlet_branches_by_bus = \ tx_utils.inlet_outlet_branches_by_bus(branches, buses) gens_by_bus = tx_utils.gens_by_bus(buses, gens) model = pe.ConcreteModel() ###declare (and fix) the voltage magnitudes and squares of voltage magnitudes bus_voltage_magnitudes = voltages #Assumes voltages is given as a dictionary libbus.declare_var_vm(model, bus_attrs['names'], initialize=bus_voltage_magnitudes) model.vm.fix() libbus.declare_var_vmsq( model=model, index_set=bus_attrs['names'], initialize={k: v**2 for k, v in bus_attrs['vm'].items()}, bounds=zip_items({k: v**2 for k, v in bus_attrs['v_min'].items()}, {k: v**2 for k, v in bus_attrs['v_max'].items()})) ### declare the polar voltages libbus.declare_var_va(model, bus_attrs['names'], initialize=bus_attrs['va']) ### declare the cosine approximation variables cos_hat_bounds = {k: (0, 1) for k in branch_attrs['names']} decl.declare_var('cos_hat', model, branch_attrs['names'], bounds=cos_hat_bounds) ### fix the reference bus ref_bus = md.data['system']['reference_bus'] #ref_angle = md.data['system']['reference_bus_angle'] model.va[ref_bus].fix(radians(0.0)) ### declare the fixed shunts at the buses bus_bs_fixed_shunts, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts( buses, shunts) ### declare (and fix) the loads at the buses bus_p_loads, bus_q_loads = tx_utils.dict_of_bus_loads(buses, loads) libbus.declare_var_pl(model, bus_attrs['names'], initialize=bus_p_loads) libbus.declare_var_ql(model, bus_attrs['names'], initialize=bus_q_loads) model.pl.fix() model.ql.fix() ### include the feasibility slack for the bus balances p_rhs_kwargs = {} q_rhs_kwargs = {} if include_feasibility_slack: p_rhs_kwargs, q_rhs_kwargs, penalty_expr = _include_feasibility_slack( model, bus_attrs, gen_attrs, bus_p_loads, bus_q_loads) ### declare the generator real and reactive power pg_init = { k: (gen_attrs['p_min'][k] + gen_attrs['p_max'][k]) / 2.0 for k in gen_attrs['pg'] } libgen.declare_var_pg(model, gen_attrs['names'], initialize=pg_init, bounds=zip_items(gen_attrs['p_min'], gen_attrs['p_max'])) qg_init = { k: (gen_attrs['q_min'][k] + gen_attrs['q_max'][k]) / 2.0 for k in gen_attrs['qg'] } libgen.declare_var_qg(model, gen_attrs['names'], initialize=qg_init, bounds=zip_items(gen_attrs['q_min'], gen_attrs['q_max'])) ### declare the current flows in the branches vr_init = { k: bus_attrs['vm'][k] * pe.cos(bus_attrs['va'][k]) for k in bus_attrs['vm'] } vj_init = { k: bus_attrs['vm'][k] * pe.sin(bus_attrs['va'][k]) for k in bus_attrs['vm'] } s_max = {k: branches[k]['rating_long_term'] for k in branches.keys()} s_lbub = dict() for k in branches.keys(): if s_max[k] is None: s_lbub[k] = (None, None) else: s_lbub[k] = (-s_max[k], s_max[k]) pf_bounds = s_lbub pt_bounds = s_lbub qf_bounds = s_lbub qt_bounds = s_lbub pf_init = dict() pt_init = dict() qf_init = dict() qt_init = dict() for branch_name, branch in branches.items(): from_bus = branch['from_bus'] to_bus = branch['to_bus'] y_matrix = tx_calc.calculate_y_matrix_from_branch(branch) ifr_init = tx_calc.calculate_ifr(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) ifj_init = tx_calc.calculate_ifj(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) itr_init = tx_calc.calculate_itr(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) itj_init = tx_calc.calculate_itj(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) pf_init[branch_name] = tx_calc.calculate_p(ifr_init, ifj_init, vr_init[from_bus], vj_init[from_bus]) pt_init[branch_name] = tx_calc.calculate_p(itr_init, itj_init, vr_init[to_bus], vj_init[to_bus]) qf_init[branch_name] = tx_calc.calculate_q(ifr_init, ifj_init, vr_init[from_bus], vj_init[from_bus]) qt_init[branch_name] = tx_calc.calculate_q(itr_init, itj_init, vr_init[to_bus], vj_init[to_bus]) libbranch.declare_var_pf(model=model, index_set=branch_attrs['names'], initialize=pf_init, bounds=pf_bounds) libbranch.declare_var_pt(model=model, index_set=branch_attrs['names'], initialize=pt_init, bounds=pt_bounds) libbranch.declare_var_qf(model=model, index_set=branch_attrs['names'], initialize=qf_init, bounds=qf_bounds) libbranch.declare_var_qt(model=model, index_set=branch_attrs['names'], initialize=qt_init, bounds=qt_bounds) #################### #Constraints #################### ###Balance equations in a bus #p balance libbus.declare_eq_p_balance(model=model, index_set=bus_attrs['names'], bus_p_loads=bus_p_loads, gens_by_bus=gens_by_bus, bus_gs_fixed_shunts=bus_gs_fixed_shunts, inlet_branches_by_bus=inlet_branches_by_bus, outlet_branches_by_bus=outlet_branches_by_bus, **p_rhs_kwargs) #q balance libbus.declare_eq_q_balance(model=model, index_set=bus_attrs['names'], bus_q_loads=bus_q_loads, gens_by_bus=gens_by_bus, bus_bs_fixed_shunts=bus_bs_fixed_shunts, inlet_branches_by_bus=inlet_branches_by_bus, outlet_branches_by_bus=outlet_branches_by_bus, **q_rhs_kwargs) ### Power in a branch branch_con_set = decl.declare_set('_con_eq_p_q_lpac_branch_power', model, branch_attrs['names']) model.eq_pf_branch_t = pe.Constraint(branch_con_set) model.eq_pt_branch_t = pe.Constraint(branch_con_set) model.eq_qf_branch_t = pe.Constraint(branch_con_set) model.eq_qt_branch_t = pe.Constraint(branch_con_set) for branch_name in branch_con_set: branch = branches[branch_name] from_bus = branch['from_bus'] to_bus = branch['to_bus'] g = tx_calc.calculate_conductance(branch) b = tx_calc.calculate_susceptance(branch) model.eq_pf_branch_t[branch_name] = \ model.pf[branch_name] == \ g*model.vmsq[from_bus] - model.vm[from_bus]*model.vm[to_bus]*(g * model.cos_hat[branch_name] + b * (model.va[from_bus] - model.va[to_bus])) model.eq_pt_branch_t[branch_name] = \ model.pt[branch_name] == \ g*model.vmsq[to_bus] - model.vm[from_bus]*model.vm[to_bus]*(g * model.cos_hat[branch_name] + b * (model.va[to_bus] - model.va[from_bus])) model.eq_qf_branch_t[branch_name] = \ model.qf[branch_name] == \ -b*model.vmsq[from_bus] - model.vm[from_bus]*model.vm[to_bus]*(g*(model.va[from_bus] - model.va[to_bus]) - b*model.cos_hat[branch_name]) model.eq_qt_branch_t[branch_name] = \ model.qt[branch_name] == \ -b*model.vmsq[to_bus] - model.vm[from_bus]*model.vm[to_bus]*(g*(model.va[to_bus] - model.va[from_bus]) - b*model.cos_hat[branch_name]) ### Piecewise linear cosine constraints model.N = pe.Set(initialize=list(range(cosine_segment_count + 1))) declare_pwl_cosine_bounds(model=model, index_set=branch_attrs['names'], branches=branches, lower_bound=lower_bound, upper_bound=upper_bound, cosine_segment_count=cosine_segment_count, mode=mode) ### Objective is to maximize cosine hat variables obj_expr = sum(model.cos_hat[branch_name] for branch_name in branch_attrs['names']) if include_feasibility_slack: obj_expr += penalty_expr model.obj = pe.Objective(expr=obj_expr) return model, md
def create_cold_start_lpac_model(model_data, cosine_segment_count=20, lower_bound=-pi / 3, upper_bound=pi / 3, include_feasibility_slack=False, mode="uniform"): """ The cold start LPAC model assumes that no target voltages are available and that all voltages are initially approximated as 1 pu. """ ###Grid data md = model_data.clone_in_service() tx_utils.scale_ModelData_to_pu(md, inplace=True) gens = dict(md.elements(element_type='generator')) buses = dict(md.elements(element_type='bus')) branches = dict(md.elements(element_type='branch')) loads = dict(md.elements(element_type='load')) shunts = dict(md.elements(element_type='shunt')) gen_attrs = md.attributes(element_type='generator') bus_attrs = md.attributes(element_type='bus') branch_attrs = md.attributes(element_type='branch') inlet_branches_by_bus, outlet_branches_by_bus = \ tx_utils.inlet_outlet_branches_by_bus(branches, buses) gens_by_bus = tx_utils.gens_by_bus(buses, gens) model = pe.ConcreteModel() ### declare the polar voltages libbus.declare_var_va(model, bus_attrs['names'], initialize=bus_attrs['va']) libbus.declare_var_vmsq( model=model, index_set=bus_attrs['names'], initialize={k: v**2 for k, v in bus_attrs['vm'].items()}, bounds=zip_items({k: v**2 for k, v in bus_attrs['v_min'].items()}, {k: v**2 for k, v in bus_attrs['v_max'].items()})) ### declare the voltage change variables decl.declare_var('phi', model, bus_attrs['names']) ### declare the cosine approximation variables cos_hat_bounds = {k: (0, 1) for k in branch_attrs['names']} decl.declare_var('cos_hat', model, branch_attrs['names'], bounds=cos_hat_bounds) ### fix the reference bus ref_bus = md.data['system']['reference_bus'] #ref_angle = md.data['system']['reference_bus_angle'] model.va[ref_bus].fix(radians(0.0)) ### declare (and fix) the loads at the buses bus_p_loads, bus_q_loads = tx_utils.dict_of_bus_loads(buses, loads) libbus.declare_var_pl(model, bus_attrs['names'], initialize=bus_p_loads) libbus.declare_var_ql(model, bus_attrs['names'], initialize=bus_q_loads) model.pl.fix() model.ql.fix() ### declare the fixed shunts at the buses bus_bs_fixed_shunts, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts( buses, shunts) ### include the feasibility slack for the bus balances p_rhs_kwargs = {} q_rhs_kwargs = {} if include_feasibility_slack: p_rhs_kwargs, q_rhs_kwargs, penalty_expr = _include_feasibility_slack( model, bus_attrs, gen_attrs, bus_p_loads, bus_q_loads) ### declare the generator real and reactive power pg_init = { k: (gen_attrs['p_min'][k] + gen_attrs['p_max'][k]) / 2.0 for k in gen_attrs['pg'] } libgen.declare_var_pg(model, gen_attrs['names'], initialize=pg_init, bounds=zip_items(gen_attrs['p_min'], gen_attrs['p_max'])) qg_init = { k: (gen_attrs['q_min'][k] + gen_attrs['q_max'][k]) / 2.0 for k in gen_attrs['qg'] } libgen.declare_var_qg(model, gen_attrs['names'], initialize=qg_init, bounds=zip_items(gen_attrs['q_min'], gen_attrs['q_max'])) ### declare the current flows in the branches vr_init = { k: bus_attrs['vm'][k] * pe.cos(bus_attrs['va'][k]) for k in bus_attrs['vm'] } vj_init = { k: bus_attrs['vm'][k] * pe.sin(bus_attrs['va'][k]) for k in bus_attrs['vm'] } s_max = {k: branches[k]['rating_long_term'] for k in branches.keys()} s_lbub = dict() for k in branches.keys(): if s_max[k] is None: s_lbub[k] = (None, None) else: s_lbub[k] = (-s_max[k], s_max[k]) pf_bounds = s_lbub pt_bounds = s_lbub qf_bounds = s_lbub qt_bounds = s_lbub pf_init = dict() pt_init = dict() qf_init = dict() qt_init = dict() for branch_name, branch in branches.items(): from_bus = branch['from_bus'] to_bus = branch['to_bus'] y_matrix = tx_calc.calculate_y_matrix_from_branch(branch) ifr_init = tx_calc.calculate_ifr(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) ifj_init = tx_calc.calculate_ifj(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) itr_init = tx_calc.calculate_itr(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) itj_init = tx_calc.calculate_itj(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus], vj_init[to_bus], y_matrix) pf_init[branch_name] = tx_calc.calculate_p(ifr_init, ifj_init, vr_init[from_bus], vj_init[from_bus]) pt_init[branch_name] = tx_calc.calculate_p(itr_init, itj_init, vr_init[to_bus], vj_init[to_bus]) qf_init[branch_name] = tx_calc.calculate_q(ifr_init, ifj_init, vr_init[from_bus], vj_init[from_bus]) qt_init[branch_name] = tx_calc.calculate_q(itr_init, itj_init, vr_init[to_bus], vj_init[to_bus]) libbranch.declare_var_pf(model=model, index_set=branch_attrs['names'], initialize=pf_init, bounds=pf_bounds) libbranch.declare_var_pt(model=model, index_set=branch_attrs['names'], initialize=pt_init, bounds=pt_bounds) libbranch.declare_var_qf(model=model, index_set=branch_attrs['names'], initialize=qf_init, bounds=qf_bounds) libbranch.declare_var_qt(model=model, index_set=branch_attrs['names'], initialize=qt_init, bounds=qt_bounds) ################################ #Constraints ################################ ### Balance equations at a bus (based on Kirchhoff Current Law) #Should be able to just use DC OPF approximation of B-theta type? ### declare the p balance libbus.declare_eq_p_balance(model=model, index_set=bus_attrs['names'], bus_p_loads=bus_p_loads, gens_by_bus=gens_by_bus, bus_gs_fixed_shunts=bus_gs_fixed_shunts, inlet_branches_by_bus=inlet_branches_by_bus, outlet_branches_by_bus=outlet_branches_by_bus, approximation_type=ApproximationType.BTHETA, **p_rhs_kwargs) #Need one also for q balance libbus.declare_eq_q_balance(model=model, index_set=bus_attrs['names'], bus_q_loads=bus_q_loads, gens_by_bus=gens_by_bus, bus_bs_fixed_shunts=bus_bs_fixed_shunts, inlet_branches_by_bus=inlet_branches_by_bus, outlet_branches_by_bus=outlet_branches_by_bus, **q_rhs_kwargs) ### Constraints for power in a branch branch_con_set = decl.declare_set('_con_eq_p_q_lpac_branch_power', model, branch_attrs['names']) model.eq_pf_branch_t = pe.Constraint(branch_con_set) model.eq_pt_branch_t = pe.Constraint(branch_con_set) model.eq_qf_branch_t = pe.Constraint(branch_con_set) model.eq_qt_branch_t = pe.Constraint(branch_con_set) for branch_name in branch_con_set: branch = branches[branch_name] from_bus = branch['from_bus'] to_bus = branch['to_bus'] g = tx_calc.calculate_conductance(branch) b = tx_calc.calculate_susceptance(branch) model.eq_pf_branch_t[branch_name] = \ model.pf[branch_name] == \ g - g * model.cos_hat[branch_name] - b * (model.va[from_bus] - model.va[to_bus]) model.eq_pt_branch_t[branch_name] = \ model.pt[branch_name] == \ g - g * model.cos_hat[branch_name] - b * (model.va[to_bus] - model.va[from_bus]) model.eq_qf_branch_t[branch_name] = \ model.qf[branch_name] == \ -b - g*(model.va[from_bus] - model.va[to_bus]) + b*model.cos_hat[branch_name] - b*(model.phi[from_bus] - model.phi[to_bus]) model.eq_qt_branch_t[branch_name] = \ model.qt[branch_name] == \ -b - g*(model.va[to_bus] - model.va[from_bus]) +b*model.cos_hat[branch_name] - b*(model.phi[to_bus] - model.phi[from_bus]) ### Piecewise linear cosine constraints model.N = pe.Set(initialize=list(range(cosine_segment_count + 1))) declare_pwl_cosine_bounds(model=model, index_set=branch_attrs['names'], branches=branches, lower_bound=lower_bound, upper_bound=upper_bound, cosine_segment_count=cosine_segment_count, mode=mode) ### Objective is to maximize cosine hat variables # obj_expr = sum(model.cos_hat[branch_name] for branch_name in branch_attrs['names']) # if include_feasibility_slack: # obj_expr += penalty_expr # model.obj = pe.Objective(expr=obj_expr) ###Objective to match with acopf.py ### declare the generator cost objective libgen.declare_expression_pgqg_operating_cost(model=model, index_set=gen_attrs['names'], p_costs=gen_attrs['p_cost'], q_costs=gen_attrs.get( 'q_cost', None)) obj_expr = sum(model.pg_operating_cost[gen_name] for gen_name in model.pg_operating_cost) if include_feasibility_slack: obj_expr += penalty_expr if hasattr(model, 'qg_operating_cost'): obj_expr += sum(model.qg_operating_cost[gen_name] for gen_name in model.qg_operating_cost) model.obj = pe.Objective(expr=obj_expr) return model, md