Exemple #1
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 def testDcOpf(self):
     """ Test solving the auction case using DC OPF.
     """
     solver = OPF(self.case, True, opt={"verbose": False})
     solution = solver.solve()
     self.assertTrue(solution["converged"])
     self.assertAlmostEqual(solution["f"], -517.81, 2)
Exemple #2
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class OPFModelTest(unittest.TestCase):
    """ Test case for the OPF model.
    """

    def setUp(self):
        """ The test runner will execute this method prior to each test.
        """
        self.case = Case.load(POLY_FILE)
        self.opf = OPF(self.case)


    def test_dc_linear_constraints(self):
        """ Test linear OPF constraints.
        """
        self.opf.dc = True
        om = self.opf._construct_opf_model(self.case)

        A, l, u = om.linear_constraints()

        self.assertEqual(A.shape, (28, 9))
        self.assertEqual(l.shape, (28, ))
        self.assertEqual(u.shape, (28, ))

        pl = 4
        self.assertAlmostEqual(A[0, 0], 13.3333, pl)
        self.assertAlmostEqual(A[4, 2], -3.8462, pl)
        self.assertAlmostEqual(A[2, 8], -1.0000, pl)
        self.assertAlmostEqual(A[9, 1],  4.0000, pl)
        self.assertAlmostEqual(A[27, 5], 3.3333, pl)

        self.assertAlmostEqual(l[0], 0.0000, pl)
        self.assertAlmostEqual(l[3], -0.7000, pl)
        self.assertEqual(l[6], -Inf)
        self.assertEqual(l[27], -Inf)

        self.assertAlmostEqual(u[0],  0.0000, pl)
        self.assertAlmostEqual(u[3], -0.7000, pl)
        self.assertAlmostEqual(u[6],  0.4000, pl)
        self.assertAlmostEqual(u[7],  0.6000, pl)
        self.assertAlmostEqual(u[23], 0.9000, pl)


    def test_ac_linear_constraints(self):
        """ Test linear OPF constraints.
        """
        self.opf.dc = False
        om = self.opf._construct_opf_model(self.case)

        A, l, u = om.linear_constraints()

        self.assertEqual(A, None)
        self.assertEqual(l.shape, (0, ))
        self.assertEqual(u.shape, (0, ))
Exemple #3
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 def setUp(self):
     """ The test runner will execute this method prior to each test.
     """
     self.case = Case.load(join(DATA_DIR, self.case_name,
                                self.case_name + ".pkl"))
     self.case.sort_generators() # ext2int
     self.opf = OPF(self.case, dc=False)
     self.om = self.opf._construct_opf_model(self.case)
     self.solver = PIPSSolver(self.om)
Exemple #4
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 def setUp(self):
     """ The test runner will execute this method prior to each test.
     """
     self.case = Case.load(POLY_FILE)
     self.opf = OPF(self.case)
Exemple #5
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 def setUp(self):
     """ The test runner will execute this method prior to each test.
     """
     self.case = Case.load(join(DATA_DIR, self.case_name,
                                self.case_name + ".pkl"))
     self.opf = OPF(self.case, dc=True)
Exemple #6
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class PIPSSolverTest(unittest.TestCase):
    """ Defines a test case for the PIPS AC OPF solver.
    """

    def __init__(self, methodName='runTest'):
        super(PIPSSolverTest, self).__init__(methodName)

        self.case_name = "case6ww"
        self.case = None
        self.opf = None
        self.om = None
        self.solver = None


    def setUp(self):
        """ The test runner will execute this method prior to each test.
        """
        self.case = Case.load(join(DATA_DIR, self.case_name,
                                   self.case_name + ".pkl"))
        self.case.sort_generators() # ext2int
        self.opf = OPF(self.case, dc=False)
        self.om = self.opf._construct_opf_model(self.case)
        self.solver = PIPSSolver(self.om)


    def test_constraints(self):
        """ Test equality and inequality constraints.
        """
        msg = self.case_name
        AA, ll, uu = self.solver._linear_constraints(self.om)

        if AA is not None:
            mpA = mmread(join(DATA_DIR, self.case_name, "opf", "A_AC.mtx"))
            mpl = mmread(join(DATA_DIR, self.case_name, "opf", "l_AC.mtx"))
            mpu = mmread(join(DATA_DIR, self.case_name, "opf", "u_AC.mtx"))

            self.assertTrue(mfeq2(AA, mpA.tocsr()), msg)
            self.assertTrue(mfeq1(ll, mpl.flatten()), msg)
            self.assertTrue(mfeq1(uu, mpu.flatten()), msg)


    def test_var_bounds(self):
        """ Test bounds on optimisation variables.
        """
        msg = self.case_name
        _, xmin, xmax = self.solver._var_bounds()

        mpxmin = mmread(join(DATA_DIR, self.case_name, "opf", "xmin_AC.mtx"))
        mpxmax = mmread(join(DATA_DIR, self.case_name, "opf", "xmax_AC.mtx"))

        self.assertTrue(mfeq1(xmin, mpxmin.flatten()), msg)
        self.assertTrue(mfeq1(xmax, mpxmax.flatten()), msg)


    def test_initial_point(self):
        """ Test selection of an initial interior point.
        """
        b, l, g, _ = self.solver._unpack_model(self.om)
        _, LB, UB = self.solver._var_bounds()
        _, _, _, _, _, ny, _ = self.solver._dimension_data(b, l, g)
        x0 = self.solver._initial_interior_point(b, g, LB, UB, ny)

        mpx0 = mmread(join(DATA_DIR, self.case_name, "opf", "x0_AC.mtx"))

        self.assertTrue(mfeq1(x0, mpx0.flatten()), self.case_name)


    def test_solution(self):
        """ Test AC OPF solution.
        """
        msg = self.case_name
        solution = self.solver.solve()
        lmbda = solution["lmbda"]

        f = mmread(join(DATA_DIR, self.case_name, "opf", "f_AC.mtx"))
        x = mmread(join(DATA_DIR, self.case_name, "opf", "x_AC.mtx"))

        diff = 1e-4

        # FIXME: Improve accuracy.
        self.assertAlmostEqual(solution["f"], f[0], places=3)
        self.assertTrue(mfeq1(solution["x"], x.flatten(), diff))

        if len(lmbda["mu_l"]) > 0:
            mu_l = mmread(join(DATA_DIR, self.case_name, "opf", "mu_l_AC.mtx"))
            self.assertTrue(mfeq1(lmbda["mu_l"], mu_l.flatten(), diff), msg)

        if len(lmbda["mu_u"]) > 0:
            mu_u = mmread(join(DATA_DIR, self.case_name, "opf", "mu_u_AC.mtx"))
            self.assertTrue(mfeq1(lmbda["mu_u"], mu_u.flatten(), diff), msg)

        if len(lmbda["lower"]) > 0:
            muLB = mmread(join(DATA_DIR, self.case_name, "opf", "muLB_AC.mtx"))
            # FIXME: Improve accuracy.
            self.assertTrue(mfeq1(lmbda["lower"], muLB.flatten(), diff), msg)

        if len(lmbda["upper"]) > 0:
            muUB = mmread(join(DATA_DIR, self.case_name, "opf", "muUB_AC.mtx"))
            # FIXME: Improve accuracy.
            self.assertTrue(mfeq1(lmbda["upper"], muUB.flatten(), diff), msg)

#        if len(lmbda["nl_mu_l"]) > 0:
#            nl_mu_l = mmread(
#                join(DATA_DIR, self.case_name, "opf", "nl_mu_l.mtx"))
#            self.assertTrue(
#                mfeq1(lmbda["nl_mu_l"], nl_mu_l.flatten()), msg)
#
#        if len(lmbda["nl_mu_l"]) > 0:
#            nl_mu_u = mmread(
#                join(DATA_DIR, self.case_name, "opf", "nl_mu_u.mtx"))
#            self.assertTrue(
#                mfeq1(lmbda["nl_mu_u"], nl_mu_u.flatten()), msg)


    def test_integrate_solution(self):
        """ Test integration of AC OPF solution.
        """
        self.solver.solve()

        bus = mmread(join(DATA_DIR, self.case_name, "opf", "Bus_AC.mtx"))
        gen = mmread(join(DATA_DIR, self.case_name, "opf", "Gen_AC.mtx"))
        branch = mmread(join(DATA_DIR, self.case_name, "opf", "Branch_AC.mtx"))

        # FIXME: Improve accuracy.
        pl = 4

        # bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vmin lam_P lam_Q mu_Vmax mu_Vmin
        for i, bs in enumerate(self.case.buses):
            self.assertAlmostEqual(bs.v_magnitude, bus[i, 7], pl) # Vm
            self.assertAlmostEqual(bs.v_angle, bus[i, 8], pl) # Va
            self.assertAlmostEqual(bs.p_lmbda, bus[i, 13], pl) # lam_P
            self.assertAlmostEqual(bs.q_lmbda, bus[i, 14], pl) # lam_Q
            # FIXME: Improve accuracy
            self.assertAlmostEqual(bs.mu_vmax, bus[i, 15], pl) # mu_Vmax
            self.assertAlmostEqual(bs.mu_vmin, bus[i, 16], pl) # mu_Vmin

        # bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin Pc1 Pc2 Qc1min Qc1max
        # Qc2min Qc2max ramp_agc ramp_10 ramp_30 ramp_q apf mu_Pmax mu_Pmin
        # mu_Qmax mu_Qmin
        for i, gn in enumerate(self.case.generators):
            # FIXME: Improve accuracy
            self.assertAlmostEqual(gn.p, gen[i, 1], pl) # Pg
            self.assertAlmostEqual(gn.q, gen[i, 2], pl) # Qg
            self.assertAlmostEqual(gn.v_magnitude, gen[i, 5], pl) # Vg
            self.assertAlmostEqual(gn.mu_pmax, gen[i, 21], pl) # mu_Pmax
            self.assertAlmostEqual(gn.mu_pmin, gen[i, 22], pl) # mu_Pmin
            self.assertAlmostEqual(gn.mu_qmax, gen[i, 23], pl) # mu_Qmax
            self.assertAlmostEqual(gn.mu_qmin, gen[i, 24], pl) # mu_Qmin

        # fbus tbus r x b rateA rateB rateC ratio angle status angmin angmax
        # Pf Qf Pt Qt mu_Sf mu_St mu_angmin mu_angmax
        for i, ln in enumerate(self.case.branches):
            self.assertAlmostEqual(ln.p_from, branch[i, 13], pl) # Pf
            self.assertAlmostEqual(ln.q_from, branch[i, 14], pl) # Qf
            self.assertAlmostEqual(ln.p_to, branch[i, 15], pl) # Pt
            self.assertAlmostEqual(ln.q_to, branch[i, 16], pl) # Qt
            self.assertAlmostEqual(ln.mu_s_from, branch[i, 17], pl) # mu_Sf
            self.assertAlmostEqual(ln.mu_s_to, branch[i, 18], pl) # mu_St
            self.assertAlmostEqual(ln.mu_angmin, branch[i, 19], pl)
            self.assertAlmostEqual(ln.mu_angmax, branch[i, 20], pl)
Exemple #7
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class DCOPFTest(unittest.TestCase):
    """ Defines a test case for DC OPF.
    """

    def __init__(self, methodName='runTest'):
        super(DCOPFTest, self).__init__(methodName)

        #: Name of the folder in which the MatrixMarket data exists.
        self.case_name = "case6ww"

        self.case = None
        self.opf = None


    def setUp(self):
        """ The test runner will execute this method prior to each test.
        """
        self.case = Case.load(join(DATA_DIR, self.case_name,
                                   self.case_name + ".pkl"))
        self.opf = OPF(self.case, dc=True)


    def testVa(self):
        """ Test voltage angle variable.
        """
        msg = self.case_name
        bs, _, _ = self.opf._remove_isolated(self.case)
        _, refs = self.opf._ref_check(self.case)
        Va = self.opf._get_voltage_angle_var(refs, bs)

        mpVa0 = mmread(join(DATA_DIR, self.case_name, "opf", "Va0.mtx"))
        mpVal = mmread(join(DATA_DIR, self.case_name, "opf", "Val.mtx"))
        mpVau = mmread(join(DATA_DIR, self.case_name, "opf", "Vau.mtx"))

        self.assertTrue(mfeq1(Va.v0, mpVa0.flatten()), msg)
        self.assertTrue(mfeq1(Va.vl, mpVal.flatten()), msg)
        self.assertTrue(mfeq1(Va.vu, mpVau.flatten()), msg)


    def testVm(self):
        """ Test voltage magnitude variable.
        """
        bs, _, gn = self.opf._remove_isolated(self.case)
        Vm = self.opf._get_voltage_magnitude_var(bs, gn)

        mpVm0 = mmread(join(DATA_DIR, self.case_name, "opf", "Vm0.mtx"))

        self.assertTrue(mfeq1(Vm.v0, mpVm0.flatten()), self.case_name)


    def testPg(self):
        """ Test active power variable.
        """
        msg = self.case_name
        self.case.sort_generators() # ext2int
        _, _, gn = self.opf._remove_isolated(self.case)
        Pg = self.opf._get_pgen_var(gn, self.case.base_mva)

        mpPg0 = mmread(join(DATA_DIR, self.case_name, "opf", "Pg0.mtx"))
        mpPmin = mmread(join(DATA_DIR, self.case_name, "opf", "Pmin.mtx"))
        mpPmax = mmread(join(DATA_DIR, self.case_name, "opf", "Pmax.mtx"))

        self.assertTrue(mfeq1(Pg.v0, mpPg0.flatten()), msg)
        self.assertTrue(mfeq1(Pg.vl, mpPmin.flatten()), msg)
        self.assertTrue(mfeq1(Pg.vu, mpPmax.flatten()), msg)


    def testQg(self):
        """ Test reactive power variable.
        """
        msg = self.case_name
        self.case.sort_generators() # ext2int
        _, _, gn = self.opf._remove_isolated(self.case)
        Qg = self.opf._get_qgen_var(gn, self.case.base_mva)

        mpQg0 = mmread(join(DATA_DIR, self.case_name, "opf", "Qg0.mtx"))
        mpQmin = mmread(join(DATA_DIR, self.case_name, "opf", "Qmin.mtx"))
        mpQmax = mmread(join(DATA_DIR, self.case_name, "opf", "Qmax.mtx"))

        self.assertTrue(mfeq1(Qg.v0, mpQg0.flatten()), msg)
        self.assertTrue(mfeq1(Qg.vl, mpQmin.flatten()), msg)
#        self.assertTrue(mfeq1(Qg.vu, mpQmax.flatten()), msg)
        self.assertTrue(mfeq1(Qg.vu, mpQmax.flatten()), msg)


    def testPmis(self):
        """ Test active power mismatch constraints.
        """
        msg = self.case_name
        case = self.case
        case.sort_generators() # ext2int
        B, _, Pbusinj, _ = case.Bdc
        bs, _, gn = self.opf._remove_isolated(case)
        Pmis = self.opf._power_mismatch_dc(bs, gn, B, Pbusinj, case.base_mva)

        mpAmis = mmread(join(DATA_DIR, self.case_name, "opf", "Amis.mtx"))
        mpbmis = mmread(join(DATA_DIR, self.case_name, "opf", "bmis.mtx"))

        self.assertTrue(mfeq2(Pmis.A, mpAmis.tocsr(), 1e-12), msg)
        self.assertTrue(mfeq1(Pmis.l, mpbmis.flatten()), msg)
        self.assertTrue(mfeq1(Pmis.u, mpbmis.flatten()), msg)


    def testPfPt(self):
        """ Test branch flow limit constraints.
        """
        msg = self.case_name
        _, ln, _ = self.opf._remove_isolated(self.case)
        _, Bf, _, Pfinj = self.case.Bdc
        Pf, Pt = self.opf._branch_flow_dc(ln, Bf, Pfinj, self.case.base_mva)

        lpf = mmread(join(DATA_DIR, self.case_name, "opf", "lpf.mtx"))
        upf = mmread(join(DATA_DIR, self.case_name, "opf", "upf.mtx"))
        upt = mmread(join(DATA_DIR, self.case_name, "opf", "upt.mtx"))

        self.assertTrue(mfeq1(Pf.l, lpf.flatten()), msg)
        self.assertTrue(mfeq1(Pf.u, upf.flatten()), msg)
        self.assertTrue(mfeq1(Pt.l, lpf.flatten()), msg)
        self.assertTrue(mfeq1(Pt.u, upt.flatten()), msg)


    def testVang(self):
        """ Test voltage angle difference limit constraint.
        """
        msg = self.case_name
        self.opf.ignore_ang_lim = False
        bs, ln, _ = self.opf._remove_isolated(self.case)
        ang = self.opf._voltage_angle_diff_limit(bs, ln)

        if ang.A.shape[0] != 0:
            Aang = mmread(join(DATA_DIR, self.case_name, "opf", "Aang.mtx"))
        else:
            Aang = None
        lang = mmread(join(DATA_DIR, self.case_name, "opf", "lang.mtx"))
        uang = mmread(join(DATA_DIR, self.case_name, "opf", "uang.mtx"))

        if Aang is not None:
            self.assertTrue(mfeq2(ang.A, Aang.tocsr()), msg)
        self.assertTrue(mfeq1(ang.l, lang.flatten()), msg)
        self.assertTrue(mfeq1(ang.u, uang.flatten()), msg)


    def testVLConstPF(self):
        """ Test dispatchable load, constant power factor constraints.
        """
        msg = self.case_name
        _, _, gn = self.opf._remove_isolated(self.case)
        vl = self.opf._const_pf_constraints(gn, self.case.base_mva)

        if vl.A.shape[0] != 0:
            Avl = mmread(join(DATA_DIR, self.case_name, "opf", "Avl.mtx"))
            self.assertTrue(mfeq2(vl.A, Avl.tocsr()), msg)

        lvl = mmread(join(DATA_DIR, self.case_name, "opf", "lang.mtx"))
        self.assertTrue(mfeq1(vl.l, lvl.flatten()), msg)

        uvl = mmread(join(DATA_DIR, self.case_name, "opf", "uang.mtx"))
        self.assertTrue(mfeq1(vl.u, uvl.flatten()), msg)


#    def testPQ(self):
#        """ Test generator PQ capability curve constraints.
#        """
##        Apqh = mmread(join(DATA_DIR, self.case_name, "opf", "Apqh.mtx"))
##        ubpqh = mmread(join(DATA_DIR, self.case_name, "opf", "ubpqh.mtx"))
##        Apql = mmread(join(DATA_DIR, self.case_name, "opf", "Apql.mtx"))
##        ubpql = mmread(join(DATA_DIR, self.case_name, "opf", "ubpql.mtx"))
#        self.fail("Generator PQ capability curve constraints not implemented.")


    def testAy(self):
        """ Test basin constraints for piece-wise linear gen cost variables.
        """
        msg = self.case_name
        self.case.sort_generators() # ext2int
        _, _, gn = self.opf._remove_isolated(self.case)
        _, ycon = self.opf._pwl_gen_costs(gn, self.case.base_mva)

        if ycon is not None:
            Ay = mmread(join(DATA_DIR, self.case_name, "opf", "Ay_DC.mtx"))
            by = mmread(join(DATA_DIR, self.case_name, "opf", "by_DC.mtx"))

            self.assertTrue(mfeq2(ycon.A, Ay.tocsr()), msg)
            self.assertTrue(mfeq1(ycon.u, by.flatten()), msg)
Exemple #8
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class DCOPFSolverTest(unittest.TestCase):
    """ Defines a test case for the DC OPF solver.
    """

    def __init__(self, methodName='runTest'):
        super(DCOPFSolverTest, self).__init__(methodName)

        self.case_name = "case6ww"
        self.case = None
        self.opf = None
        self.om = None
        self.solver = None


    def setUp(self):
        """ The test runner will execute this method prior to each test.
        """
        self.case = Case.load(join(DATA_DIR, self.case_name,
                                   self.case_name + ".pkl"))
        self.case.sort_generators() # ext2int
        self.opf = OPF(self.case, dc=True)
        self.om = self.opf._construct_opf_model(self.case)
        self.solver = DCOPFSolver(self.om)


    def test_constraints(self):
        """ Test equality and inequality constraints.
        """
        AA, ll, uu = self.solver._linear_constraints(self.om)

        mpA = mmread(join(DATA_DIR, self.case_name, "opf", "A_DC.mtx"))
        mpl = mmread(join(DATA_DIR, self.case_name, "opf", "l_DC.mtx"))
        mpu = mmread(join(DATA_DIR, self.case_name, "opf", "u_DC.mtx"))

        self.assertTrue(mfeq2(AA, mpA.tocsr()), self.case_name)
        self.assertTrue(mfeq1(ll, mpl.flatten()), self.case_name)
        self.assertTrue(mfeq1(uu, mpu.flatten()), self.case_name)


    def test_var_bounds(self):
        """ Test bounds on optimisation variables.
        """
        _, xmin, xmax = self.solver._var_bounds()

#        mpx0 = mmread(join(DATA_DIR, self.case_name, "opf", "x0_DC.mtx"))
        mpxmin = mmread(join(DATA_DIR, self.case_name, "opf", "xmin_DC.mtx"))
        mpxmax = mmread(join(DATA_DIR, self.case_name, "opf", "xmax_DC.mtx"))

#        self.assertTrue(alltrue(x0 == mpx0.flatten()), self.case_name)
        self.assertTrue(mfeq1(xmin, mpxmin.flatten()), self.case_name)
        self.assertTrue(mfeq1(xmax, mpxmax.flatten()), self.case_name)


    def test_initial_point(self):
        """ Test selection of an initial interior point.
        """
        b, l, g, _ = self.solver._unpack_model(self.om)
        _, LB, UB = self.solver._var_bounds()
        _, _, _, _, _, ny, _ = self.solver._dimension_data(b, l, g)
        x0 = self.solver._initial_interior_point(b, g, LB, UB, ny)

        mpx0 = mmread(join(DATA_DIR, self.case_name, "opf", "x0_DC.mtx"))

        self.assertTrue(mfeq1(x0, mpx0.flatten(), 1e-9), self.case_name)


    def test_pwl_costs(self):
        """ Test piecewise linear costs.
        """
        msg = self.case_name
        b, l, g, _ = self.solver._unpack_model(self.om)
        _, ipwl, _, _, _, ny, nxyz = self.solver._dimension_data(b, l, g)
        Npwl, Hpwl, Cpwl, fparm_pwl, _ = \
            self.solver._pwl_costs(ny, nxyz, ipwl)

        if Npwl is not None:
            mpNpwl = mmread(join(DATA_DIR, self.case_name, "opf", "Npwl.mtx"))
            mpHpwl = mmread(join(DATA_DIR, self.case_name, "opf", "Hpwl.mtx"))
            mpCpwl = mmread(join(DATA_DIR, self.case_name, "opf", "Cpwl.mtx"))
            mpfparm = mmread(join(DATA_DIR, self.case_name, "opf","fparm_pwl.mtx"))

            self.assertTrue(mfeq2(Npwl, mpNpwl.tocsr()), msg)
            self.assertTrue(mfeq2(Hpwl.todense(), mpHpwl), msg)
            self.assertTrue(mfeq1(Cpwl, mpCpwl.flatten()), msg)
            self.assertTrue(mfeq1(fparm_pwl.flatten(), mpfparm.flatten()), msg)


    def test_poly_costs(self):
        """ Test quadratic costs.
        """
        msg = self.case_name
        base_mva = self.om.case.base_mva
        b, l, g, _ = self.solver._unpack_model(self.om)
        ipol, _, _, _, _, _, nxyz = self.solver._dimension_data(b, l, g)
        Npol, Hpol, Cpol, fparm_pol, _, _ = \
            self.solver._quadratic_costs(g, ipol, nxyz, base_mva)

        if Npol is not None:
            mpNpol = mmread(join(DATA_DIR, self.case_name, "opf", "Npol.mtx"))
            mpHpol = mmread(join(DATA_DIR, self.case_name, "opf", "Hpol.mtx"))
            mpCpol = mmread(join(DATA_DIR, self.case_name, "opf", "Cpol.mtx"))
            mpfparm = mmread(join(DATA_DIR, self.case_name, "opf","fparm_pol.mtx"))

            self.assertTrue(mfeq2(Npol, mpNpol.tocsr()), msg)
            self.assertTrue(mfeq2(Hpol, mpHpol.tocsr()), msg)
            self.assertTrue(mfeq1(Cpol, mpCpol.flatten()), msg)
            self.assertTrue(mfeq2(fparm_pol, mpfparm), msg)


    def test_combine_costs(self):
        """ Test combination of pwl and poly costs.
        """
        msg = self.case_name
        base_mva = self.om.case.base_mva
        b, l, g, _ = self.solver._unpack_model(self.om)
        ipol, ipwl, _, _, nw, ny, nxyz = self.solver._dimension_data(b, l, g)
        Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl = self.solver._pwl_costs(ny, nxyz,
                                                                      ipwl)
        Npol, Hpol, Cpol, fparm_pol, _, npol = \
            self.solver._quadratic_costs(g, ipol, nxyz, base_mva)
        NN, HHw, CCw, ffparm = \
            self.solver._combine_costs(Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl,
                                       Npol, Hpol, Cpol, fparm_pol, npol, nw)

        mpNN = mmread(join(DATA_DIR, self.case_name, "opf", "NN.mtx"))
        mpHHw = mmread(join(DATA_DIR, self.case_name, "opf", "HHw.mtx"))
        mpCCw = mmread(join(DATA_DIR, self.case_name, "opf", "CCw.mtx"))
        mpffparm = mmread(join(DATA_DIR, self.case_name, "opf", "ffparm.mtx"))

        self.assertTrue(mfeq2(NN, mpNN.tocsr()), msg)
        self.assertTrue(mfeq2(HHw, mpHHw.tocsr()), msg)
        self.assertTrue(mfeq1(CCw, mpCCw.flatten()), msg)
        self.assertTrue(mfeq2(ffparm, mpffparm), msg)


    def test_coefficient_transformation(self):
        """ Test transformation of quadratic coefficients for w into
            coefficients for X.
        """
        msg = self.case_name
        base_mva = self.om.case.base_mva
        b, l, g, _ = self.solver._unpack_model(self.om)
        ipol, ipwl, _, _, nw, ny, nxyz = self.solver._dimension_data(b, l, g)
        Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl = \
            self.solver._pwl_costs(ny, nxyz, ipwl)
        Npol, Hpol, Cpol, fparm_pol, polycf, npol = \
            self.solver._quadratic_costs(g, ipol, nxyz, base_mva)
        NN, HHw, CCw, ffparm = \
            self.solver._combine_costs(Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl,
                                       Npol, Hpol, Cpol, fparm_pol, npol, nw)
        HH, CC, _ = \
            self.solver._transform_coefficients(NN, HHw, CCw, ffparm, polycf,
                                                any_pwl, npol, nw)

        mpHH = mmread(join(DATA_DIR, self.case_name, "opf", "HH.mtx"))
        mpCC = mmread(join(DATA_DIR, self.case_name, "opf", "CC.mtx"))

        self.assertTrue(mfeq2(HH, mpHH.tocsr()), msg)
        self.assertTrue(mfeq1(CC, mpCC.flatten()), msg)


    def test_solution(self):
        """ Test DC OPF solution.
        """
        msg = self.case_name
        solution = self.solver.solve()
        lmbda = solution["lmbda"]

        mpf = mmread(join(DATA_DIR, self.case_name, "opf", "f_DC.mtx"))
        mpx = mmread(join(DATA_DIR, self.case_name, "opf", "x_DC.mtx"))
        mpmu_l = mmread(join(DATA_DIR, self.case_name, "opf", "mu_l_DC.mtx"))
        mpmu_u = mmread(join(DATA_DIR, self.case_name, "opf", "mu_u_DC.mtx"))
        mpmuLB = mmread(join(DATA_DIR, self.case_name, "opf", "muLB_DC.mtx"))
        mpmuUB = mmread(join(DATA_DIR, self.case_name, "opf", "muUB_DC.mtx"))

        diff = 1e-09

        self.assertAlmostEqual(solution["f"], mpf[0], places=6)
        self.assertTrue(mfeq1(solution["x"], mpx.flatten(), diff), msg)
        self.assertTrue(mfeq1(lmbda["mu_l"], mpmu_l.flatten(), diff), msg)
        self.assertTrue(mfeq1(lmbda["mu_u"], mpmu_u.flatten(), diff), msg)
        self.assertTrue(mfeq1(lmbda["lower"], mpmuLB.flatten(), diff), msg)
        self.assertTrue(mfeq1(lmbda["upper"], mpmuUB.flatten(), diff), msg)


    def test_integrate_solution(self):
        """ Test integration of DC OPF solution.
        """
        self.solver.solve()

        bus = mmread(join(DATA_DIR, self.case_name, "opf", "Bus_DC.mtx"))
        gen = mmread(join(DATA_DIR, self.case_name, "opf", "Gen_DC.mtx"))
        branch = mmread(join(DATA_DIR, self.case_name, "opf", "Branch_DC.mtx"))

        pl = 2

        # bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vmin lam_P lam_Q mu_Vmax mu_Vmin
        for i, bs in enumerate(self.case.buses):
            self.assertAlmostEqual(bs.v_magnitude, bus[i, 7], pl) # Vm
            self.assertAlmostEqual(bs.v_angle, bus[i, 8], pl) # Va
            self.assertAlmostEqual(bs.p_lmbda, bus[i, 13], pl) # lam_P
            self.assertAlmostEqual(bs.q_lmbda, bus[i, 14], pl) # lam_Q
            self.assertAlmostEqual(bs.mu_vmax, bus[i, 15], pl) # mu_Vmax
            self.assertAlmostEqual(bs.mu_vmin, bus[i, 16], pl) # mu_Vmin

        # bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin Pc1 Pc2 Qc1min Qc1max
        # Qc2min Qc2max ramp_agc ramp_10 ramp_30 ramp_q apf mu_Pmax mu_Pmin
        # mu_Qmax mu_Qmin
        for i, gn in enumerate(self.case.generators):
            self.assertAlmostEqual(gn.p, gen[i, 1], pl) # Pg
            self.assertAlmostEqual(gn.q, gen[i, 2], pl) # Qg
            self.assertAlmostEqual(gn.v_magnitude, gen[i, 5], pl) # Vg
            self.assertAlmostEqual(gn.mu_pmax, gen[i, 21], pl) # mu_Pmax
            self.assertAlmostEqual(gn.mu_pmin, gen[i, 22], pl) # mu_Pmin
            self.assertAlmostEqual(gn.mu_qmax, gen[i, 23], pl) # mu_Qmax
            self.assertAlmostEqual(gn.mu_qmin, gen[i, 24], pl) # mu_Qmin

        # fbus tbus r x b rateA rateB rateC ratio angle status angmin angmax
        # Pf Qf Pt Qt mu_Sf mu_St mu_angmin mu_angmax
        for i, ln in enumerate(self.case.branches):
            self.assertAlmostEqual(ln.p_from, branch[i, 13], pl) # Pf
            self.assertAlmostEqual(ln.q_from, branch[i, 14], pl) # Qf
            self.assertAlmostEqual(ln.p_to, branch[i, 15], pl) # Pt
            self.assertAlmostEqual(ln.q_to, branch[i, 16], pl) # Qt
            self.assertAlmostEqual(ln.mu_s_from, branch[i, 17], pl) # mu_Sf
            self.assertAlmostEqual(ln.mu_s_to, branch[i, 18], pl) # mu_St
            self.assertAlmostEqual(ln.mu_angmin, branch[i, 19], pl) # mu_angmin
            self.assertAlmostEqual(ln.mu_angmax, branch[i, 20], pl) # mu_angmax