Optimization of Phasor Measurement Unit (PMU) Placement in Supervisory Control and Data Acquisition (SCADA)-Based Power System for Better State-Estimation Performance
Abstract
:1. Introduction
2. Modified Weighted Least Square with Phasor Measurements
- The phasor measurements and the traditional measurements are taken at the same snapshot—there is no time skew between them.
- A PMU should be always available at the slack bus so that the reference angle of both measurements is the same.
- When a PMU is installed at a certain bus, it can read the bus voltage phasor in addition to all the branch current phasors connected to that bus and flowing away from that bus.
3. Heuristic Approach to Optimization
- z: the measurement vector with white noise;
- R: the vector of measurement error variance;
- p: number of PMUs required to be placed in the system;
- AllBus: contains all the numbers of candidate buses;
- BusWithPMU: includes the bus numbers which have been assigned a PMU;
- BusToPlace: the vector which includes the bus numbers that will be equipped with PMUs. It is acquired by eliminating BusWithPMU from AllBus;
- Num: the length of BusToPlace vector;
- BusNum: the parameter that includes the bus number that will be equipped with a PMU;
- KnownPMUBus: composed by merging BusWithPMU vector and BusNum variable;
- Ind_array: contains NCE values of state estimation.
4. Optimization with Genetic Algorithm
4.1. Problem Formulation of Optimal Phasor Measurement Unit (PMU) Placement:
4.2. Basic Working Principle of the Binary Genetic Algorithm (BGA)
- Selection or reproduction: this phase generates the chromosomes or parents based on their fitness value. Error indicator of the state estimation is used as the fitness for this work. A lower indicator represents better chromosome or a PMU location set.
- Crossover: this creates the children or off-springs from the parents with the view that the child could be fitter than the parents. Off-springs are formed by taking the best characteristics from both parents based on a user-defined probability. Crossover could be done on a single or multiple point based on the size of the chromosomes.
- Mutation: this works on the off-springs, checking each bit individually to search for a better solution.
5. Test Case Preparation
6. Results
6.1. Comparison with Heuristic Approach
6.2. Optimal PMU Locations by Covering Critical Zones
6.3. Optimization when the Critical Zones are Non-Interacting
6.4. Significance of Covering Critical Locations
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Measurement Description | 30-Bus System | 118-Bus System |
---|---|---|
Total measurements | 126 | 440 |
Redundancy | 2.13 | 1.87 |
Number of voltage-magnitudes (Vm) | 14 | 62 |
Number of real power-injections (PG) | 16 | 55 |
Number of reactive power-injections (QG) | 15 | 55 |
Number of real power-flows from a bus (PF) | 25 | 68 |
Number of reactive power-flows from a bus (QF) | 24 | 68 |
Number of real power-flows to a bus (PT) | 16 | 66 |
Number of reactive power-flows to a bus (QT) | 16 | 66 |
Measurement Type | Measurement Locations |
---|---|
Voltage-magnitude buses | 1, 6, 24 |
Voltage-angle buses | 1, 6, 24 |
Current flow branches (real and reactive) | 1-2, 1-3, 6-7, 6-8, 6-9, 6-10, 6-28, 24-25 |
Measurement Type | Standard Deviation σ (Per Unit) |
---|---|
SCADA voltage magnitude | 0.01 |
Real power injection | 0.02 |
Reactive power injection | 0.04 |
Real power flow | 0.02 |
Reactive power flow | 0.04 |
PMU voltage magnitude | 0.0001 |
PMU voltage angle | 0.006 |
PMU current magnitude | 0.0001 |
PMU current angle | 0.006 |
Criteria | Considered Parameter |
---|---|
Population size | 100 |
Selection probability | 1 |
Crossover probability | 0.9 |
Mutation probability | 0.25 |
Maximum number of iterations | 250 |
Elite chromosome (PMU must be installed) | Slack bus: Bus-1 for 30-bus and bus-69 for 118-bus system |
Buses which cover the critical zones | |
Crossover point | 30-bus: Double |
118-bus: Triple | |
Stopping criteria | 1. Reaching the maximum number of iterations |
2. If the fitness value does not change for consecutive 100 iterations |
Number of PMUs | Heuristic | BGA | ||
---|---|---|---|---|
Optimal PMU Locations | Normalized Cumulative Error (NCE) Value | Optimal PMU Locations | NCE Value | |
2 | 1, 6 | 2.89 × 10−4 | 1, 6 | 2.89 × 10−4 |
3 | 1, 6, 25 | 1.81 × 10−4 | 1, 10, 25 | 1.78 × 10−4 |
4 | 1, 6, 22, 25 | 1.28 × 10−4 | 1, 6, 12, 24 | 1.27 × 10−4 |
5 | 1, 6, 12, 22, 25 | 7.69 × 10−5 | 1, 6, 12, 22, 25 | 7.69 × 10−5 |
Number of PMUs | Heuristic | BGA | ||
---|---|---|---|---|
Optimal PMU Locations | NCE Value | Optimal PMU Locations | NCE Value | |
2 | 69, 100 | 6.35 × 10−4 | 69, 100 | 6.35 × 10−4 |
3 | 69, 100, 30 | 5.41 × 10−4 | 69, 38, 26 | 5.397 × 10−4 |
4 | 69, 100, 30, 25 | 4.63 × 10−4 | 26, 38, 69, 100 | 4.362 × 10−4 |
5 | 69, 100, 30, 25, 64 | 3.83 × 10−4 | 69, 100, 30, 25, 64 | 3.83 × 10−4 |
6 | 69, 100, 30, 25, 64, 32 | 3.32 × 10−4 | 69, 100, 30, 25, 64, 32 | 3.32 × 10−4 |
7 | 69, 100, 30, 25, 64, 32, 1 | 2.97 × 10−4 | 69, 100, 30, 25, 64, 32, 1 | 2.97 × 10−4 |
Number of PMUs | NCC (Not Covering Critical) | CC (Covering Critical) | ||
---|---|---|---|---|
Optimal PMU Locations | NCE Value | Optimal PMU Locations | NCE Value | |
2 | 1, 6 | 2.89 × 10−4 | 1, 12 | 4.5202 × 10−4 |
3 | 1, 10, 25 | 1.7755 × 10−4 | 1, 12, 6 | 2.3653 × 10−4 |
4 | 1, 6, 12, 24 | 1.2792 × 10−4 | 1, 6, 12, 24 | 1.2792 × 10−4 |
5 | 1, 6, 25, 22, 12 | 7.69 × 10−5 | 1, 6, 25, 22, 12 | 7.69 × 10−5 |
Number of PMUs | NCC (Not Covering Critical) | CC (Covering Critical) | ||
---|---|---|---|---|
Optimal PMU Locations | NCE Value | Optimal PMU Locations | NCE Value | |
2 | 69, 100 | 6.35 × 10−4 | 39, 69 | 7.095 × 10−4 |
3 | 69, 38, 26 | 5.396 × 10−4 | 39, 69, 100 | 6.08 × 10−4 |
4 | 26, 38, 69, 100 | 4.362 × 10−4 | 39, 49, 69, 100 | 5.226 × 10−4 |
5 | 69, 100, 30, 25, 64 | 3.83 × 10−4 | 39, 69, 31, 100, 116 | 4.699 × 10−4 |
6 | 69, 100, 30, 25, 64, 32 | 3.32 × 10−4 | 39, 69, 26, 29, 38, 100 | 4.12 × 10−4 |
7 | 69, 100, 30, 25, 64, 32, 1 | 2.97 × 10−4 | 39, 69, 12, 61, 19, 100, 32 | 3.59 × 10−4 |
Critical Measurements | Elite Chromosomes | Optimization Results | ||
---|---|---|---|---|
PF_12-13, QF_12-13, QF_25-26, Vm_26 | 1 (slack bus), 12, 26 | No of PMUs | Optimal PMU Locations | NCE Indicator |
2 | 1, 12 | 8.198 × 10−4 | ||
3 | 1, 12, 26 | 6.707 × 10−4 | ||
4 | 1, 6, 12, 26 | 4.004 × 10−4 | ||
5 | 1, 6, 12, 24, 26 | 2.245 × 10−4 | ||
6 | 1, 6, 12, 24, 26, 4 | 1.011 × 10−4 |
Cases | Bad-Data Location | NCC (Not Covering Critical) (PMUs in 1, 10, 25) | CC (Covering Critical) (PMUs in 1, 6,12) |
---|---|---|---|
White noises only | N/A | 1.7755 × 10−4 | 2.3653 × 10−4 |
Single bad-data around critical locations | Vm_12 | 1.155 × 10−3 | 2.370 × 10−4 |
QT_15-12 | 6.733 × 10−4 | 2.415 × 10−4 | |
PF_12-14 | 6.294 × 10−4 | 2.358 × 10−4 | |
PF_12-16 | 1.035 × 10−3 | 2.366 × 10−4 | |
QF_12-14 | 2.453 × 10−4 | 2.373 × 10−4 | |
QF_12-16 | 3.157 × 10−4 | 2.375 × 10−4 |
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Shahriar, M.S.; Habiballah, I.O.; Hussein, H. Optimization of Phasor Measurement Unit (PMU) Placement in Supervisory Control and Data Acquisition (SCADA)-Based Power System for Better State-Estimation Performance. Energies 2018, 11, 570. https://doi.org/10.3390/en11030570
Shahriar MS, Habiballah IO, Hussein H. Optimization of Phasor Measurement Unit (PMU) Placement in Supervisory Control and Data Acquisition (SCADA)-Based Power System for Better State-Estimation Performance. Energies. 2018; 11(3):570. https://doi.org/10.3390/en11030570
Chicago/Turabian StyleShahriar, Mohammad Shoaib, Ibrahim Omar Habiballah, and Huthaifa Hussein. 2018. "Optimization of Phasor Measurement Unit (PMU) Placement in Supervisory Control and Data Acquisition (SCADA)-Based Power System for Better State-Estimation Performance" Energies 11, no. 3: 570. https://doi.org/10.3390/en11030570