MixedIntegerPrograming(MIP)-BasedFaultLocation...

9-11 September 2018 - 50th North American Power Symposium

Mixed Integer Programing(MIP)-Based Fault LocationIdentification Using MicroPMUs

Presentation at 50th North American Power Symposium

Mohammed AlqahtaniDepartment of Electrical Engineering

University of South FloridaPrince Sattam bin Abdulaziz University

Dr. Zhixin Miao & Dr. Lingling FanDepartment of Electrical Engineering

University of South Florida

September 10, 2018


Outline

IntroductionUtility performance evaluationA common used methodOur objective

The Advantages of the MIP-Based Proposed method

MIP Formulation for a Simple Single Phase Network

MIP formulation for Three-Phase Distribution Systems

Numerical example


Outline





Numerical example


Utility performance evaluation

I Nowadays, the electric utility industry is a competitive field. Each utility wants to increase productivityand reduce economic losses.

I Reliability indices are a way of evaluating the performance of the utilities. To be a competitive in theutilities market, improve these indices.

I Accoring to IEEE Std 1366 (IEEE Guide for Electric Power Distribution Reliability Indices).– The System Average Interruption Duration Index (SAIDI)=∑

Customer Minutes of Interruption

Total Number of Served Customers

– The Customer Average Interruption Duration Index (CAIDI)=∑Customer Minutes of Interruption

Total Number of Served Customers

I Reducing the interruption duration will ensure improvement in these indices.


A Common Used MethodImpedance Based Method 1

– Uses voltage and current measurements at the substation to estimate the impedance and then thedistance to the fault point.

– a standard feature in most microprocessor-based relays.– Adopted from the transmission system.– In Distribution systems, The method suffers from multi-estimation due to the radial topology of the

system (multiple points may have the same distance.)

Common practices to improve it: to use external information to narrow the searching area- History of events- Weather status- Construction areas- Costumers calls!! (Do we really want to wait for an angry customer call?!)

1(J. Mora-Florez, J. Melendez, and G. Carrillo-Caicedo, “Comparison of impedance based fault location methods for power distributionsystems,” Electric Power Systems Research, vol. 78, no. 4, pp. 657–666, 2008)


Example2

Figure: Fault event screen capture

Figure: Spreadsheet for the line parameters

2(K. Zimmerman and D. Costello, “Impedance-based fault location experience,” in Proc. 58th Annu. Conf. Protect. Relay Eng., Apr. 2005, pp.211–226)


Continue

Two Possible locations

Figure: Distribution Feeder


IEEE-123How many points will have the same distance to the substation?

Figure: IEEE-123 test feeder


Our objective

I To reduce the outage time in order to improve the reliability indices and reducerevenue loss caused by outages.

I To achieve that goal: a fast fault location method is required to speed up therestoration process.


Outline





Numerical example



I Does not yield to multiple locations.I Only requires the pre and during fault voltages at the end of the branches in

addition to the impedance bus matrix. (no need for current measurements)I Applicable for grounded and ungrounded systems.I The implementation of the proposed method is simple and does not require

multiple stages or iterations.I It determines the fault type, location and magnitude. While other methods rely on

protective devises in substations to classify the fault type or determine the faultmagnitude.


Outline





Numerical example



Figure: Simple 6-Node Network

Only one voltage phasor is required tofind If4, if more than one voltage phasorsare measured, it will be anoverdetermined problem.

[0 0 −If4 0 0

]T = YNN ∆VN (1)

∆V = V post − V pre

∆VN = ZNN

[0 0 −If4 0 0

]T (2)

ZNN =z12 z12 z12 z12 z12z12 z12 + z23 z12 + z23 z12 + z23 z12z12 z12 + z23 z12 + z23 + z34 z12 + z23 + z34 z12z12 z12 + z23 z12 + z23 + z34 z12 + z23 + z34 + z45 z12z12 z12 z12 z12 z26


MIP Formulation For a Simple Single Phase Network

I Now we will assume that the fault location and magnitude are unknown.I Hence a binary variable is introduced for each bus ui as shown in (3). If there a

fault on bus i then ui=1 , If not ui = 0

∆VN = ZNN

[−u2If2 −u3If3 −u4If4 −u5If5 −u6If6

]T(3)


MIP Formulation For a Simple Single Phase Network

I Now will replace uiIfi with Ixi

∆VN = ZNN

[−Ix2 −Ix3 −Ix4 Ix5 Ix6

]T(4)

Ixi ={

Ifi, if ui = 10, if ui = 0

(5)

I If the system has only one fault, then the inequality constrains is imposed

6∑i=2

ui ≤ 1 (6)


MIP formulation for a simple single phase networkI Note that If is a phasor so its real and imaginary parts will be considered

separately using the big-M technique as shown in (6)

− (1 − ui)M + Re(Ifi) ≤ Re(Ixi) ≤ Re(Ifi) + (1 − ui)M− (1 − ui)M + Im(Ifi) ≤ Im(Ixi) ≤ Im(Ifi) + (1 − ui)M− uiM ≤ Re(Ixi) ≤ +uiM

− uiM ≤ Im(Ixi) ≤ +uiM

(7)

if ui = 1

Re(Ixi) = Re(Ifi)Im(Ixi) = Im(Ifi)

−M ≤ Re(Ixi) ≤ M

−M ≤ Im(Ixi) ≤ M

if ui = 0

Re(Ixi) = 0Im(Ixi) = 0


The Overall MIP Problem FormulationI The objective function is the sum of the norm 2 of the error between the

measured and estimated voltage deviation values.I The measured voltage values are collected using MicroPMUs located at the end of

the branched + the first bus after the source bus.

minimize∑i∈E

‖∆Vmeas

i −∆Vi‖ (8a)

subject to∑i∈N

ui ≤ 1 (8b)

∆VN = −ZNN Ix (8c)

−uiM ≤ Re(Ixi) ≤ +uiM (8d)

−uiM ≤ Im(Ixi) ≤ +uiM (8e)

−(1− ui)M + Re(Ifi) ≤ Re(Ixi) ≤ Re(Ifi) + (1− ui)M (8f)

−(1− ui)M + Im(Ifi) ≤ Im(Ixi) ≤ Im(Ifi) + (1− ui)M (8g)

(8h)

where E is the set of the buses located at the end of each branch and the bus closest to the substation bus, N is the set of the buses exceptthe substation bus.


Outline





Numerical example


MIP Formulation for Three-Phase Distribution SystemsI If three phase fault occurs at Bus4, the faults currents can be calculated as shown

in (8).

Figure: Simple 6-Node Network

A fault location binary variable ui isdesignated to each phase in each busexcept substation bus

0...0−Ia

f4−Ib

f4−Ic

f40...0

= Y

abcNN

∆V a

2∆V b

2∆V c

2...

∆V a6

∆V b6

∆V c6

(9)

∆Vabc

N = ZabcNN

−u2 Ia

f2−u3 Ib

f2−u4 Ic

f2...

−u14 Iaf6

−u15 Ibf6

−u16 Icf6

(10)


MIP Formulation For Three-Phase Distribution SystemsI To exclude the possibility of having faults between phases from different buses,

Another location binary variable ki is designated to each bus except thesubstation bus.

I For the 6-node network, The dimension of u is 15, and the dimension of k is 5.

u2 + u3 + u4 = 3(k2)u5 + u6 + u7 = 3(k3)u8 + u9 + u10 = 3(k4)u11 + u12 + u13 = 3(k5)u14 + u15 + u16 = 3(k6)

(11)

∑ki = 1 (12)

I When a fault happened at Bus 2 , k2 = 1 and all the phase binaries at that busare equal to 1, however that does not mean all the phases are under fault.

I The magnitude of the current will determine the faulted phase.


The Overall Three-Phase MIP Problem Formulation

minimize∑i∈E

‖∆V abc,measi −∆V abc

i ‖

subject to ∆V abcN = −Zabc

NN Iabcx (13a)

−uiM ≤ Re(Ixi) ≤ +uiM (13b)−uiM ≤ Im(Ixi) ≤ +uiM (13c)

−(1− ui)M + Re(Ifi) ≤ Re(Ixi) ≤ Re(Ifi) + (1− ui)M (13d)−(1− ui)M + Im(Ifi) ≤ Im(Ixi) ≤ Im(Ifi) + (1− ui)M (13e)

for all i ∈ Bua + ub + uc = 3(ki) (13f)∑i∈E

ki = 1 (13g)

for all i ∈ N

where E is the set of the microPMU phases, N is the set of the buses except the substation bus. B is the set ofthe phases except the substation bus’s phases.


Outline





Numerical example


Numerical example

I Very unbalanced feeder.I (PQ,I and Z) loads.I UngroundedI micro-PMUs are placed at the end of

the branches as shown in the figure.

799

701 742

705 702 720

704 713

707 722

703 744 729

728

727 706

725 718

714

730

731 709

708 732

775 733 736

734 710

735 737 738 711 741

740

724

712

Micro-PMU

Figure: Modified version IEEE-37 Test Feeder


Numerical exampleI All the single phase faults were identified correctly. (108 tests for each transformer

configuration)

Table: Phase-to-Ground faults (∆ - ∆)

Identification Results OpenDSS MeasurementsLocation Obj IF ∠IF Iflow ∠Iflow729.b 0.070 2.111 -36 2.225 -33.5711.c 0.170 2.064 -158.9 2.188 -156.1702.b 0.053 2.124 -36 2.240 -33.5775.a 0.002 4.9e10−4 -97.5 5.3e10−4 -94.2

Table: Phase-to-Ground faults (∆ - Y )

Identification Results OpenDSS MeasurementsLocation Obj IF ∠IF Iflow ∠Iflow702.a 89.6 2636.2 -100.4 2832.9 -97.3741.c 100.2 1210 38.5 1285.4 41.5707.b 94.2 1513 159.8 1591.9 162.2710.c 99.88 1414.1 36.9 1503.3 39.9


Double and Three Phase faults

I More than 97% of the double and Three-phase faults were identified correctly.I Only 2-3p Faults at 707 were identified as faults at Bus 722, which is adjacent bus

to Bus 707. By excluding Bus 722 from the searching space, the proposed methodcorrectly identified the faulted bus, which means it was at the second leastobjective function value.


Double and Three Phase Faults

Table: Double-Phase to Ground faults (∆ - ∆)

Identification Results OpenDSS MeasurementsLocation Obj Ia

F IbF Ia

flow Ibflow

736.ab 155.1 1147.7 1168.5 1263.8 1262.9714.ab 165.8 1992.8 2027.1 2191.5 2191742.ab 153.3 1954.4 1990 2151.1 2150.4775.ab 39.07 10630.7 10869.4 11796 11796

Table: Double-Phase Faults (∆ - Y )


F IbF Ia

flow Ibflow

735.ab 140.6 1581.4 1446.2 1706.4 1583.4704.ab 172.7 2407.3 2172 2576.5 2375.5728.ab 119 2150.6 1934.4 2309.4 2120.3731.ab 84.5 2018.3 1788.3 2171.7 1962

Table: Three-Phase Faults (∆ - ∆)


F IbF Ic

F Iaflow Ib

flow Icflow

727.abc 131.69 2231.8 2377.5 2242 2500.8 2573.9 2434.4708.abc 140.2 1998.6 2159.2 2027.1 2242.2 2337.3 2197.2738.abc 216.4 1545.8 1715.9 1606.5 1741.1 1859.7 1738.3720.abc 257 2030.3 2188.6 2070.9 2261.3 2366.7 2253.6

Table: Three-phase faults (∆ - Y )


F IbF Ib

F Iaflow Ib

flow Ibflow

725.abc 265 1757.7 1904.1 1807.7 1956.6 2059.5 1966.6744.abc 152.7 2142.3 2282.5 2152.9 2399.9 2472.2 2336.3732.abc 153.2 1864.8 2015.8 1899.3 2092.1 2182.2 2058.3737.abc 204 1631.1 1787.8 1683.1 1836.2 1938.5 1820.9


THANK YOU

Date post:	17-Jul-2020
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

MixedIntegerPrograming(MIP)-BasedFaultLocation...

Documents