Notebooks · lib/power/matpower_ref

The power flow against MATPOWER's own solution

MATPOWER's test suite solves its 9-bus case t_case9_pf (lib/t/t_case9_pf.m, bus 3 renumbered 30) and stores the result in lib/t/soln9_pf.mat (AC) and soln9_dcpf.mat (DC), in the MATPOWER repository (commit 80b6e16, 2026-10-12; BSD-3-Clause, see lib/power/cases/LICENSE-MATPOWER). The numbers below are those files' result columns, read with scipy.io.loadmat and printed with every digit.

Newton's method and the DC solve agree with MATPOWER to rounding. The fast-decoupled method converges to the same equations at the same tolerance (mismatch below 10⁻⁸ per unit) along a different path, so it is held to that tolerance: about 10⁻⁶ MVAr and 10⁻⁷ degrees here.

Look inside this program

Atlas
The program’s map: every function and which calls which.
There’s no recorded run of this program yet.

This program declares a record type (Expected), and records run only in compiled C for now, so the Run buttons here are off. Open it in the workbench and use its C tab to compile it.

Shift+Enter in a cell runs it and moves to the next. Running a cell runs every cell above it too, as one program.

[1]lines 18–110

from power.case import PF, PG, PT, QF, QG, QMAX, QMIN, QT, VA, VM, read_case
from power.pf import DC, FDXB, NR, runpf

TOL: Num = 1e-8
#: rounding of Newton's answer, in per unit, degrees and MW (MATPOWER's values carry about 13 digits)
NR_ATOL: Num = 1e-10
#: the fast-decoupled answer is right to the mismatch tolerance, magnified in MW by baseMVA
FD_ATOL: Num = 1e-5
MAX_IT: Int = 30
#: a held generator sits on its limit; the others are inside it by more than the solve's error
QLIM_SLACK: Num = 1e-6

PF_VM = [1.0, 0.9999999999999998, 0.9999999999999999, 0.9870068523919053, 0.975472177085053, 1.0033754364528003, 0.9856448817249466, 0.9961852458090698, 0.957621040429904]
PF_VA = [0.0, 9.668741126628127, 4.771073237177321, -2.406643919519411, -4.01726432670755, 1.9256016868285664, 0.6215445553889333, 3.7991201926923224, -4.34993357656101]
PF_PG = [71.9547015892219, 85.0, 163.0]
PF_QG = [24.068957772759347, -3.649025534209524, 14.460119531125173]
PF_PF = [71.9547015892219, 30.728280279736758, -59.445314441944795, 84.99999999999997, 24.10613416723329, -75.98935222105762, -162.99999999999972, 86.50443565720315, -40.960113134644104]
PF_QF = [24.068957772759347, -0.5858508226422805, -16.312049500578592, -3.649025534209524, 4.536791179891787, -10.599237559223031, 2.276189879408795, -2.5324293491302003, -35.71801701219844]
PF_PT = [-71.95470158922191, -30.55468555805444, 60.89386583276659, -84.99999999999997, -24.010647778941497, 76.49556434279414, 162.99999999999974, -84.03988686535044, 41.2264213094818]
PF_QT = [-20.753044538740305, -13.687950499421419, -12.427469531088455, 7.890678351196219, -24.400762440777147, 0.25623946972257383, 14.460119531125173, -14.281982987799147, 21.33889536138395]

DC_VM = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
DC_VA = [0.0, 9.796018855085988, 5.060560045142459, -2.211158722968871, -3.7380912469925134, 2.2066572675958294, 0.8224410569767293, 3.9590113171907273, -4.06340049078228]
DC_PG = [66.99999999999994, 85.0, 163.0]
DC_QG = [0.0, 0.0, 0.0]
DC_PF = [66.99999999999994, 28.9673913043478, -61.03260869565219, 84.99999999999999, 23.96739130434781, -76.03260869565217, -162.99999999999997, 86.96739130434786, -38.032608695652144]
DC_QF = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
DC_PT = [-66.99999999999994, -28.9673913043478, 61.03260869565219, -84.99999999999999, -23.96739130434781, 76.03260869565217, 162.99999999999997, -86.96739130434786, 38.032608695652144]
DC_QT = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

CASE = read_case("lib/power/cases/t_case9_pf.m")

#: MATPOWER's result columns for one solve
record Expected {
    vm: Arr
    va: Arr
    pg: Arr
    qg: Arr
    pf: Arr
    qf: Arr
    pt: Arr
    qt: Arr
}

def agrees(m: Int, atol: Num, e: Expected) {
    r = runpf(CASE, m, false, TOL, MAX_IT)
    assert_true(r.success)
    assert_allclose(r.bus[:, VM], e.vm, atol)
    assert_allclose(r.bus[:, VA], e.va, atol)
    assert_allclose(r.gen[:, PG], e.pg, atol)
    assert_allclose(r.gen[:, QG], e.qg, atol)
    assert_allclose(r.branch[:, PF], e.pf, atol)
    assert_allclose(r.branch[:, QF], e.qf, atol)
    assert_allclose(r.branch[:, PT], e.pt, atol)
    assert_allclose(r.branch[:, QT], e.qt, atol)
}

AC = Expected { vm: PF_VM, va: PF_VA, pg: PF_PG, qg: PF_QG, pf: PF_PF, qf: PF_QF, pt: PF_PT, qt: PF_QT }
DCX = Expected { vm: DC_VM, va: DC_VA, pg: DC_PG, qg: DC_QG, pf: DC_PF, qf: DC_QF, pt: DC_PT, qt: DC_QT }

test "Newton-Raphson reproduces MATPOWER's soln9_pf" {
    agrees(NR, NR_ATOL, AC)
}

test "the fast-decoupled method reproduces soln9_pf to its tolerance" {
    agrees(FDXB, FD_ATOL, AC)
}

test "the DC power flow reproduces MATPOWER's soln9_dcpf" {
    agrees(DC, NR_ATOL, DCX)
}

test "with Q limits enforced every generator ends inside its limits" {
    c = read_case("lib/power/cases/case14.m")
    free = runpf(c, NR, false, TOL, MAX_IT)
    held = runpf(c, NR, true, TOL, MAX_IT)
    assert_true(held.success)
    #: case14's slack generator (bus 1) falls below its Qmin of 0 when the limits are ignored;
    #: held there, its bus stops being the reference and bus 2 takes over
    over: Int = 0
    ng: Int = int(shape(free.gen)[0])
    for g to ng {
        if free.gen[g, QG] > free.gen[g, QMAX] or free.gen[g, QG] < free.gen[g, QMIN] {
            over += 1
        }
        assert_true(held.gen[g, QG] <= held.gen[g, QMAX] + QLIM_SLACK and held.gen[g, QG] >= held.gen[g, QMIN] - QLIM_SLACK)
    }
    assert_true(over == 1)
    assert_near(held.gen[0, QG], held.gen[0, QMIN], 0.0)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors

from power.case import PF, PG, PT, QF, QG, QMAX, QMIN, QT, VA, VM, read_case
from power.pf import DC, FDXB, NR, runpf

TOL: Num = 1e-8
#: rounding of Newton's answer, in per unit, degrees and MW (MATPOWER's values carry about 13 digits)
NR_ATOL: Num = 1e-10
#: the fast-decoupled answer is right to the mismatch tolerance, magnified in MW by baseMVA
FD_ATOL: Num = 1e-5
MAX_IT: Int = 30
#: a held generator sits on its limit; the others are inside it by more than the solve's error
QLIM_SLACK: Num = 1e-6

PF_VM = [1.0, 0.9999999999999998, 0.9999999999999999, 0.9870068523919053, 0.975472177085053, 1.0033754364528003, 0.9856448817249466, 0.9961852458090698, 0.957621040429904]
PF_VA = [0.0, 9.668741126628127, 4.771073237177321, -2.406643919519411, -4.01726432670755, 1.9256016868285664, 0.6215445553889333, 3.7991201926923224, -4.34993357656101]
PF_PG = [71.9547015892219, 85.0, 163.0]
PF_QG = [24.068957772759347, -3.649025534209524, 14.460119531125173]
PF_PF = [71.9547015892219, 30.728280279736758, -59.445314441944795, 84.99999999999997, 24.10613416723329, -75.98935222105762, -162.99999999999972, 86.50443565720315, -40.960113134644104]
PF_QF = [24.068957772759347, -0.5858508226422805, -16.312049500578592, -3.649025534209524, 4.536791179891787, -10.599237559223031, 2.276189879408795, -2.5324293491302003, -35.71801701219844]
PF_PT = [-71.95470158922191, -30.55468555805444, 60.89386583276659, -84.99999999999997, -24.010647778941497, 76.49556434279414, 162.99999999999974, -84.03988686535044, 41.2264213094818]
PF_QT = [-20.753044538740305, -13.687950499421419, -12.427469531088455, 7.890678351196219, -24.400762440777147, 0.25623946972257383, 14.460119531125173, -14.281982987799147, 21.33889536138395]

DC_VM = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
DC_VA = [0.0, 9.796018855085988, 5.060560045142459, -2.211158722968871, -3.7380912469925134, 2.2066572675958294, 0.8224410569767293, 3.9590113171907273, -4.06340049078228]
DC_PG = [66.99999999999994, 85.0, 163.0]
DC_QG = [0.0, 0.0, 0.0]
DC_PF = [66.99999999999994, 28.9673913043478, -61.03260869565219, 84.99999999999999, 23.96739130434781, -76.03260869565217, -162.99999999999997, 86.96739130434786, -38.032608695652144]
DC_QF = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
DC_PT = [-66.99999999999994, -28.9673913043478, 61.03260869565219, -84.99999999999999, -23.96739130434781, 76.03260869565217, 162.99999999999997, -86.96739130434786, 38.032608695652144]
DC_QT = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

CASE = read_case("lib/power/cases/t_case9_pf.m")

#: MATPOWER's result columns for one solve
record Expected {
    vm: Arr
    va: Arr
    pg: Arr
    qg: Arr
    pf: Arr
    qf: Arr
    pt: Arr
    qt: Arr
}

def agrees(m: Int, atol: Num, e: Expected) {
    r = runpf(CASE, m, false, TOL, MAX_IT)
    assert_true(r.success)
    assert_allclose(r.bus[:, VM], e.vm, atol)
    assert_allclose(r.bus[:, VA], e.va, atol)
    assert_allclose(r.gen[:, PG], e.pg, atol)
    assert_allclose(r.gen[:, QG], e.qg, atol)
    assert_allclose(r.branch[:, PF], e.pf, atol)
    assert_allclose(r.branch[:, QF], e.qf, atol)
    assert_allclose(r.branch[:, PT], e.pt, atol)
    assert_allclose(r.branch[:, QT], e.qt, atol)
}

AC = Expected { vm: PF_VM, va: PF_VA, pg: PF_PG, qg: PF_QG, pf: PF_PF, qf: PF_QF, pt: PF_PT, qt: PF_QT }
DCX = Expected { vm: DC_VM, va: DC_VA, pg: DC_PG, qg: DC_QG, pf: DC_PF, qf: DC_QF, pt: DC_PT, qt: DC_QT }

test "Newton-Raphson reproduces MATPOWER's soln9_pf" {
    agrees(NR, NR_ATOL, AC)
}

test "the fast-decoupled method reproduces soln9_pf to its tolerance" {
    agrees(FDXB, FD_ATOL, AC)
}

test "the DC power flow reproduces MATPOWER's soln9_dcpf" {
    agrees(DC, NR_ATOL, DCX)
}

test "with Q limits enforced every generator ends inside its limits" {
    c = read_case("lib/power/cases/case14.m")
    free = runpf(c, NR, false, TOL, MAX_IT)
    held = runpf(c, NR, true, TOL, MAX_IT)
    assert_true(held.success)
    #: case14's slack generator (bus 1) falls below its Qmin of 0 when the limits are ignored;
    #: held there, its bus stops being the reference and bus 2 takes over
    over: Int = 0
    ng: Int = int(shape(free.gen)[0])
    for g to ng {
        if free.gen[g, QG] > free.gen[g, QMAX] or free.gen[g, QG] < free.gen[g, QMIN] {
            over += 1
        }
        assert_true(held.gen[g, QG] <= held.gen[g, QMAX] + QLIM_SLACK and held.gen[g, QG] >= held.gen[g, QMIN] - QLIM_SLACK)
    }
    assert_true(over == 1)
    assert_near(held.gen[0, QG], held.gen[0, QMIN], 0.0)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors