Constraints not satisfied for the generated optimal solutions

Hi,

I have an optimization problem, which indicates an optimal solution is given. But the "ApparantPowerLimitEV" constraints are apparently not satisfied. I would appreciate any insight for that.

Best regards,

Sen

import gurobipy as gp
from gurobipy import GRB, quicksum
import pandas as pd
import numpy as np
import math

def func_optimization(c_loss, c_baseload, c_ev, c_hp_up, c_hp_down, c_pv, p_pv_fore, p_ev_max, p_hp_set, p_baseload):
    # units in kA, kV, MW, MVA, MVar, Euro
    # values for single phase
    s_pv = 3.75E-3/3# apparant power limits, 4.5/1.2, divided by 3 phase, inverter size
    s_ev = 3.7E-3/3
    s_trafo = 0.63/3
    n_bus = 195
    n_houses = 182
    p_hp_max = [] # HP capacity in kW
    for i in range(n_houses):
        p_hp_max.append(math.ceil(max(np.genfromtxt("load182\\hpload_customer{}.csv".format(i+1))))/3 * 1E-3)
    house_index = []
    for i in range(n_bus):
        if i not in [0,17,24,45,52,62,64,78,93,135,140,144,167]:
            house_index.append(i)
    pf = 0.92 # baseload & HP
    tan_phi_load = (np.sqrt(1-pf**2))/pf
    pf_ev_pv_limit = 0.95
    tan_phi_evpv = (np.sqrt(1-pf_ev_pv_limit**2))/pf_ev_pv_limit
    q_baseload = p_baseload * tan_phi_load
    v_ref = 0.23 # kV
    v_lb = 0.96 #pu
    v_ub = 1.04
    epse_network = pd.read_excel("epse_network.xlsx")
    m = gp.Model("GEC")
    # m.Params.LogToConsole = 0
    # define variables
    p = m.addVars(n_bus, lb = -float('inf'), vtype = GRB.CONTINUOUS, name = "PBusInjection")
    p_houses = m.addVars(n_houses, lb = -float('inf'), vtype = GRB.CONTINUOUS, name = "PHouseBusInjection") 
    q = m.addVars(n_bus, lb = -float('inf'),  vtype = GRB.CONTINUOUS, name = "QBusInjection")
    q_houses = m.addVars(n_houses, lb = -float('inf'),  vtype = GRB.CONTINUOUS, name = "QHouseBusInjection") 
    P = m.addVars(n_bus-1, lb = -float('inf'),  vtype = GRB.CONTINUOUS, name = "PLine")
    Q = m.addVars(n_bus-1, lb = -float('inf'),  vtype = GRB.CONTINUOUS, name = "QLine")
    v = m.addVars(n_bus, lb = (v_lb*v_ref)**2, ub = (v_ub*v_ref)**2, vtype = GRB.CONTINUOUS, name = "VoltSquare")
    l = m.addVars(n_bus-1, lb = 0, vtype = GRB.CONTINUOUS, name = "CurrentSquare")
    p_pv = m.addVars(n_houses, lb = 0, vtype = GRB.CONTINUOUS, name = "PVactivePower")
    q_pv = m.addVars(n_houses, lb = -float('inf'),  vtype = GRB.CONTINUOUS, name = "PVreactivePower")
    p_ev = m.addVars(n_houses, lb = 0, vtype = GRB.CONTINUOUS, name = "EVactivePower")
    q_ev = m.addVars(n_houses, lb = -float('inf'),  vtype = GRB.CONTINUOUS, name = "EVreactivePower")
    p_hp = m.addVars(n_houses, lb = 0, vtype = GRB.CONTINUOUS, name = "HPactivePower")
    q_hp = m.addVars(n_houses, lb = 0,  vtype = GRB.CONTINUOUS, name = "HPreactivePower")
    p_pv_down = m.addVars(n_houses, lb = 0,  vtype = GRB.CONTINUOUS, name = "PVcurtailedActivePower")
    p_ev_down = m.addVars(n_houses, lb = 0,  vtype = GRB.CONTINUOUS, name = "EVcurtailedActivePower")
    p_hp_down = m.addVars(n_houses, lb = 0, vtype = GRB.CONTINUOUS, name = "HPcurtailedActivePower")
    p_hp_up = m.addVars(n_houses, lb = 0, vtype = GRB.CONTINUOUS, name = "HPincreasedActivePower")
    p_base_curtailed = m.addVars(n_houses, lb = 0, ub = 0, vtype = GRB.CONTINUOUS, name = "CurtailedBaseActivePower")
    # define constraints
    
    # for slack bus, power balance
    m.addConstr(p[0] == P[0] + P[25] + P[63] + P[94] + P[136])
    m.addConstr(q[0] == Q[0] + Q[25] + Q[63] + Q[94] + Q[136])
    m.addQConstr(p[0]*p[0] + q[0]*q[0] <= s_trafo**2, "trafoLimit") # transformer loading constraints, #1 additional constraint
    # for non-slack bus, power balance
    for j in range(1,n_bus):
        P_outFlow = 0
        for i in range(n_bus-1):
            if epse_network.at[i,'startNode'] == j:
                P_outFlow += P[epse_network.at[i,'endNode']-1]
        m.addConstr(p[j] == P_outFlow - (P[j-1]-l[j-1]*epse_network.at[j-1,'r_ohm']))       
    for j in range(1,n_bus):
        Q_outFlow = 0
        for i in range(n_bus-1):
            if epse_network.at[i,'startNode'] == j:
                Q_outFlow += Q[epse_network.at[i,'endNode']-1]
        m.addConstr(q[j] == Q_outFlow - (Q[j-1]-l[j-1]*epse_network.at[j-1,'x_ohm']))
    # voltage relation
    for i in range(n_bus-1):
        m.addConstr(v[epse_network.at[i,'endNode']] == v[epse_network.at[i,'startNode']]\
                    -2*(epse_network.at[i,'r_ohm']*P[epse_network.at[i,'endNode']-1] \
                        + epse_network.at[i,'x_ohm']*Q[epse_network.at[i,'endNode']-1])
                        +(epse_network.at[i,'r_ohm']**2+epse_network.at[i,'x_ohm']**2)*l[epse_network.at[i,'endNode']-1])
    # socp constraints
    for i in range(n_bus-1):
        m.addQConstr(P[epse_network.at[i,'endNode']-1] * P[epse_network.at[i,'endNode']-1]\
                     +Q[epse_network.at[i,'endNode']-1] * Q[epse_network.at[i,'endNode']-1] <=
                          l[epse_network.at[i,'endNode']-1] * v[epse_network.at[i,'startNode']], name = "SOCP{}".format(i))
    for i in range(n_bus):
        if i not in house_index and i != 0: # slack bus + residential loads
            m.addConstr(p[i] == 0)
            m.addConstr(q[i] == 0)
    m.addConstrs(p_houses[i] == p[house_index[i]] for i in range(n_houses))
    m.addConstrs(q_houses[i] == q[house_index[i]] for i in range(n_houses))
    m.addConstrs(p_houses[i] == p_pv[i] + p_base_curtailed[i] - p_baseload[i] - p_ev[i] - p_hp[i] for i in range(n_houses))
    m.addConstrs(q_houses[i] == q_pv[i] +p_base_curtailed[i] * tan_phi_load - q_baseload[i] + q_ev[i] - q_hp[i] \
                 for i in range(n_houses))
    
    for i in range(n_houses):
        m.addQConstr(p_pv[i]*p_pv[i] + q_pv[i]*q_pv[i] <= s_pv**2, name = "ApparantPowerLimitPV{}".format(i))
        m.addQConstr(p_ev[i]*p_ev[i] + q_ev[i]*q_ev[i] <= s_ev**2, name = "ApparantPowerLimitEV{}".format(i)) 
        m.addConstr(-p_pv[i] * tan_phi_evpv <= q_pv[i])
        m.addConstr(q_pv[i] <= p_pv[i] * tan_phi_evpv)
        m.addConstr(-p_ev[i] * tan_phi_evpv <= q_ev[i])   
        m.addConstr(q_ev[i] <= p_ev[i] * tan_phi_evpv )
        m.addConstr(q_hp[i] == p_hp[i] * tan_phi_load)
        m.addConstr(p_ev[i] <= p_ev_max[i])
        m.addConstr(p_ev_down[i] == p_ev_max[i] - p_ev[i])       
        m.addConstr(p_pv[i] <= p_pv_fore[i])
        m.addConstr(p_pv_down[i] == p_pv_fore[i] - p_pv[i])
        m.addConstr(p_hp[i] <= p_hp_max[i])
        m.addConstr(p_hp_down[i] >= p_hp_set[i] - p_hp[i])
        m.addConstr(p_hp_up[i] >= p_hp[i] - p_hp_set[i])
        m.addConstr(p_base_curtailed[i] <= p_baseload[i]) #2 additional constraint
    for i in range(n_bus-1):
        m.addConstr(l[i] <= (epse_network.at[i,'currentLim_kA'])**2)
    m.addConstr(v[0] == v_ref**2) #3 additional constraint
    # define objective
    obj = quicksum(l[i]*epse_network.at[i,'r_ohm'] * c_loss for i in range(n_bus-1))\
        + quicksum(c_baseload[i]*p_base_curtailed[i] for i in range(n_houses))\
            + quicksum(c_ev[i]*p_ev_down[i] for i in range(n_houses))\
                + quicksum(c_pv[i]*p_pv_down[i] for i in range(n_houses))\
                    + quicksum(c_hp_up[i]*p_hp_up[i] for i in range(n_houses))\
                        + quicksum(c_hp_down[i]*p_hp_down[i] for i in range(n_houses))       
    m.setObjective(obj, GRB.MINIMIZE)
    # m.setParam('MIPGap', 1E-10)
    # m.setParam('NonConvex', 2)
    # m.setParam('NumericFocus', 3)
    m.optimize()
    m.write("model.mps")
    dict_optimizedResults = {
        "p": [p[i].X for i in range(n_bus)],
        "q": [q[i].X for i in range(n_bus)],
        "p_ev": [p_ev[i].X for i in range(n_houses)],
        "p_houses": [-p_houses[i].X for i in range(n_houses)], # minus for consistency with power flow
        "v": [np.sqrt(v[i].X)/v_ref for i in range(n_bus)],
        "l": [np.sqrt(l[i].X)/epse_network.at[i,'currentLim_kA'] for i in range(n_bus-1)],
        "p_ev_down": [p_ev_down[i].X for i in range(n_houses)],
        "p_pv_down": [p_pv_down[i].X for i in range(n_houses)],
        "p_hp_up": [p_hp_up[i].X for i in range(n_houses)],
        "p_hp_down": [p_hp_down[i].X for i in range(n_houses)],
        "q_ev": [q_ev[i].X for i in range(n_houses)],
        "q_pv": [q_pv[i].X for i in range(n_houses)],
        "P": [P[i].X for i in range(n_bus-1)],
        "Q": [Q[i].X for i in range(n_bus-1)],
        "q_houses": [-q_houses[i].X for i in range(n_houses)],
        "p_pv": [p_pv[i].X for i in range(n_houses)],
        "p_hp": [p_hp[i].X for i in range(n_houses)],
        "q_hp": [q_hp[i].X for i in range(n_houses)],
        "p_base_curtailed": [p_base_curtailed[i].X for i in range(n_houses)] 
        } #.X squeeze out values from single element array, same as np.squeeze
    return dict_optimizedResults
                        

if __name__ == "__main__":
    n_houses = 182    
    c_loss = 40
    c_baseload = np.ones(n_houses) * 5000
    c_ev = np.ones(n_houses) * 200
    c_hp_up = np.ones(n_houses) * 200
    c_hp_down = np.ones(n_houses) * 200
    c_pv = np.ones(n_houses) * 400
    p_pv_fore = np.ones(n_houses) * 5e-3/3
    p_ev_max = np.ones(n_houses) * 3.7e-3/3
    p_hp_set = np.ones(n_houses) * 1e-3/3
    p_baseload = np.ones(n_houses) * 1.5e-3/3
    dict_optimizedResults = func_optimization(c_loss, c_baseload, c_ev, c_hp_up,\
                      c_hp_down, c_pv, p_pv_fore, p_ev_max, p_hp_set, p_baseload)
    p = dict_optimizedResults["p"]
    q = dict_optimizedResults["q"]
    p_ev = dict_optimizedResults["p_ev"]
    p_houses = dict_optimizedResults["p_houses"]
    v = dict_optimizedResults["v"]
    l = dict_optimizedResults["l"]
    p_ev_down = dict_optimizedResults["p_ev_down"]
    p_pv_down = dict_optimizedResults["p_pv_down"]
    p_hp_up = dict_optimizedResults["p_hp_up"]
    p_hp_down = dict_optimizedResults["p_hp_down"]
    q_ev = dict_optimizedResults["q_ev"]
    q_pv = dict_optimizedResults["q_pv"]   
    P = dict_optimizedResults["P"]
    Q = dict_optimizedResults["Q"]
    q_houses = dict_optimizedResults["q_houses"]
    p_pv = dict_optimizedResults["p_pv"]
    p_hp = dict_optimizedResults["p_hp"]
    q_hp = dict_optimizedResults["q_hp"]
    p_base_curtailed = dict_optimizedResults["p_base_curtailed"]
    # np.array(p_pv)*np.array(p_pv) + np.array(q_pv)*np.array(q_pv) <= (3.75E-3/3)**2
    print(np.array(p_ev)*np.array(p_ev) + np.array(q_ev)*np.array(q_ev) <= (3.7E-3/3)**2)

Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (win64)
Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
Optimize a model with 3897 rows, 3533 columns and 9295 nonzeros
Model fingerprint: 0x34a91ef3
Model has 559 quadratic constraints
Coefficient statistics:
Matrix range [3e-06, 1e+00]
QMatrix range [1e+00, 1e+00]
Objective range [6e-02, 5e+03]
Bounds range [5e-02, 6e-02]
RHS range [2e-04, 8e-02]
QRHS range [2e-06, 4e-02]
Presolve removed 1873 rows and 1133 columns
Presolve time: 0.02s
Presolved: 2959 rows, 2971 columns, 7804 nonzeros
Presolved model has 377 second-order cone constraints
Ordering time: 0.00s

Barrier statistics:
AA' NZ : 1.052e+04
Factor NZ : 2.751e+04 (roughly 3 MBytes of memory)
Factor Ops : 3.046e+05 (less than 1 second per iteration)
Threads : 1

Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 2.05070280e+05 -3.08660958e+04 1.29e+01 3.31e+02 1.73e+03 0s
1 2.19335888e+05 -1.02472862e+04 3.27e+00 1.45e-01 4.11e+02 0s
2 2.24320909e+03 -5.09929184e+03 2.70e-02 1.53e-03 4.44e+00 0s
3 2.64225397e+02 -1.64580346e+03 2.30e-03 2.08e-04 5.75e-01 0s
4 8.40633504e+01 -7.31873593e+02 2.88e-04 7.31e-05 1.77e-01 0s
5 4.63350240e+01 -1.70545059e+02 3.98e-05 1.74e-05 4.34e-02 0s
6 3.51567556e+01 -3.72334243e+00 1.70e-06 2.66e-06 7.57e-03 0s
7 3.20440355e+01 1.62213111e+01 2.54e-07 1.08e-06 3.07e-03 0s
8 3.14501810e+01 2.66238038e+01 9.16e-08 3.16e-07 9.37e-04 0s
9 3.11540917e+01 2.95557412e+01 4.46e-08 9.54e-08 3.11e-04 0s
10 3.09653096e+01 3.03441617e+01 2.11e-08 3.24e-08 1.21e-04 0s
11 3.08616565e+01 3.06376577e+01 8.08e-09 1.40e-08 4.36e-05 0s
12 3.08057390e+01 3.07469451e+01 1.46e-09 3.12e-09 1.14e-05 0s
13 3.07947295e+01 3.07861565e+01 7.10e-10 2.28e-09 1.67e-06 0s
14 3.07918198e+01 3.07889494e+01 3.02e-10 1.41e-10 5.58e-07 0s
15 3.07902874e+01 3.07895271e+01 8.00e-11 2.09e-10 1.48e-07 0s
16 3.07898735e+01 3.07896256e+01 2.29e-11 6.29e-10 4.82e-08 0s
17 3.07897457e+01 3.07896622e+01 6.13e-12 7.69e-10 1.62e-08 0s

Barrier solved model in 17 iterations and 0.08 seconds
Optimal objective 3.07897457e+01

p_ev
Out[10]: 
[0.001233333252782066,
0.0012333332525010464,
0.0012333332517102484,
0.001233333250372892,
0.0012333332499916679,
0.0012333332499489874,
0.0012333332503263114,
0.0012333332506982873,
0.0012333332542703067,
0.0012333332512244383,
0.00123333325139316,
0.0012333332550746,
0.0012333332515416682,
0.0012333332523684715,
0.0012333332513185624,
0.0012333332501297115,
0.0012333332502187594,
0.001233333249433389,
0.0012333332495219358,
0.001233333249329937,
0.001233333249406215,
0.0012333332494701102,
0.0012333332496593885,
0.0012333332563687852,
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0.0012333332511307675,
0.0012333332497659521,
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0.0012333332448267917,
0.0012333332447901704,
0.001233333244587632,
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0.0012333332447169662]

q_ev
Out[11]: 
[-1.5277253314616634e-05,
0.00037360614173411865,
0.00037523855694493235,
0.0003765956302091952,
0.00037816883005703403,
0.00037974221467751933,
0.00038077320343655183,
0.0003806983641203059,
0.000378949278803331,
0.00037877414492769454,
0.00037733767984386593,
0.000373569203437942,
0.0003729283065512942,
0.00034982145577331416,
0.0003627096131320957,
0.0003707261378307198,
0.0003749966199803653,
0.00037234999798129256,
0.0003720984050397518,
0.00036933765927170176,
0.0003668374077416811,
0.0003641113646304407,
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q_ev
Out[12]: 
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