Optimal Placement of PMU to Enhance Supervised Learning-Based Pseudo-Measurement Modelling Accuracy in Distribution Network
Abstract
:1. Introduction
2. Pseudo-Measurement Modeling
3. Problem Formulation
3.1. Genetic Algorithms
- 1.
- Generate population: The combinations are chosen at random from a set of , where N is the total number of buses and is the number of PMU-installed buses. Selected buses are used as input buses for LR, which estimates pseudo-measurement.
- 2.
- Evaluate average TVE: Using voltage magnitude and phase angle data and active power and reactive power of the slack bus as inputs, voltage magnitude and phase angle of unmeasured points are estimated, where is a number of unmeasured buses. After that, convert the estimated voltage magnitude and phase angle for unmeasured points to TVE through Equation (4). The evaluation of that combination is based on the average TVE of unmeasured buses.
- 3.
- Selection: The combinations with the lowest average TVE value based on fitness values and the combinations chosen at random as lucky survivors are chosen to be the parents of the next generation.
- 4.
- Crossover: A total of combinations surviving from the selection process are grouped into to create five combinations for each pair through the crossover process. A total of 20 pairs produce 100 combinations, resulting in 100 new combinations. The crossover process was carried out by combining the PMU placement information of each pair and then choosing the number of random extraction.
- 5.
- Mutation: of the generated combinations are selected as mutation and one of the information (bus position that PMU is installed) is changed to a random value. After completing this process, a new generation consisting of 100 combinations is born.
- 6.
- Return to the “Evaluate average TVE” process. These processes are repeated until the th generation. The information (PMU position) of the gene that had the best value since the th generation is selected as the optimal PMU.
3.2. Particle Swarm Optimization
- 1.
- Initialization: combinations of PMU placement were generated. The combinations were generated at random from the combination set , where N is the system size (total bus number) and is the number of PMU-installed buses. The combinations that occurred were applied as the PMU installation point in the simulation.
- 2.
- Evaluate the fitness value: The average TVE of unmeasured buses becomes the evaluation of that combination. The calculation of fitness values was carried out with Equation (4), such as the approach used with the GA described earlier.
- 3.
- Update and : Based on the fitness value, the position with the lowest average TVE value for an individual particle and the position with the lowest TVE value for all particles are updated.
- 4.
- If the number of iterations is reaches , the process moves on to step 6, otherwise, it moves on to step 5.
- 5.
- Velocity and position were updated: the velocity equation reflecting inertial, social, and cognitive factors was used to update the position of each particle. The parameter information is shown in Table 2. The position of each updated particle moves back to step 2, and the process is repeated.
- 6.
- After all iterations are terminated, the coordinate of is selected as the optimal placement.
4. Simulation Result
4.1. Optimal PMU Placement
4.1.1. Case 1—IEEE 33-Bus System
4.1.2. Case 2—IEEE 69-Bus System
4.2. State Estimation
- 1.
- Measurement uncertainty of PMU: 1% for voltage magnitude, 0.573 for phase angle [34].
- 2.
- Pseudo-measurements based on OP and WP: Uncertainty in values estimated by LR.
- 3.
- Pseudo-measurements based on LP: 50% for active/reactive power.
4.2.1. Case 1—IEEE 33-Bus System
4.2.2. Case 2—IEEE 69-Bus System
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Description | Values |
---|---|---|
Population sizes | 100 | |
Best samples | 20% | |
Lucky samples | 20% | |
Number of children | 5 | |
Chance of mutation | 20% | |
Final generation | 20 |
Parameter | Description | Values |
---|---|---|
Cognitive factor | 2.0 | |
Social factor | 2.0 | |
w | Inertia weight | 0.9 |
Particles | 100 | |
Max iteration | 20 | |
d | Dimension |
Method | Rank (Top %) | Exploration | IB | |
---|---|---|---|---|
GA | 3 | 1 (top) | 900 | 9, 16, 31 |
4 | 1 (top) | 900 | 9, 16, 24, 31 | |
5 | 8 (0.004) | 1200 | 6, 10, 16, 24, 31 | |
PSO | 3 | 1 (top) | 900 | 9, 16, 31 |
4 | 1 (top) | 600 | 9, 16, 24, 31 | |
5 | 1 (top) | 900 | 10, 16, 24, 26, 31 | |
RS | 3 | 3 (0.06) | 2000 | 10, 16, 31 |
4 | 18 (0.05) | 2000 | 9, 16, 24, 32 | |
5 | 101 (0.05) | 2000 | 6, 10, 17, 23, 31 | |
BF | 3 | 1 (top) | 4960 | 9, 16, 31 |
4 | 1 (top) | 35,960 | 9, 16, 24, 31 | |
5 | 1 (top) | 201,376 | 10, 16, 24, 26, 31 |
Method | Rank (Top %) | Exploration | IB | |
---|---|---|---|---|
GA | 3 | 4 (0.008) | 1800 | 20, 60, 67 |
4 | 38 (0.005) | 2000 | 20, 43, 62, 67 | |
5 | 680 (0.007) | 1000 | 20, 43, 62, 63, 66 | |
PSO | 3 | 1 (top) | 1900 | 10, 20, 60 |
4 | 19 (0.002) | 1300 | 20, 44, 60, 67 | |
5 | 371 (0.004) | 1600 | 10, 20, 46, 63, 64 | |
RS | 3 | 24 (0.048) | 2000 | 10, 24, 60 |
4 | 402 (0.049) | 2000 | 11, 19, 60, 64 | |
5 | 5077 (0.049) | 2000 | 6, 13, 20, 43, 60 | |
BF | 3 | 1 (top) | 50,116 | 10, 20, 60 |
4 | 1 (top) | 814,385 | 10, 20, 43, 60 | |
5 | 1 (top) | 10,424,128 | 10, 20, 43, 60, 65 |
Indicator | Magnitude ( p.u) | Angle ( Degree) | |||||
---|---|---|---|---|---|---|---|
OP | LP | WP | OP | LP | WP | ||
3 | Avg | 71.294 | 175.094 | 15,556.095 | 1.977 | 15.514 | 2074.534 |
Max | 621.567 | 780.11 | 66,611.141 | 14.991 | 84.133 | 8413.159 | |
Min | 0 | 0 | 0 | 0 | 0 | 0 | |
4 | Avg | 55.443 | 155.081 | 16,795.932 | 1.096 | 14.629 | 1974.514 |
Max | 349.5 | 755.405 | 67,255.438 | 3.3869 | 49.88 | 8398.775 | |
Min | 0 | 0 | 0 | 0 | 0 | 0 | |
5 | Avg | 41.741 | 147.8 | 17,136.878 | 0.41 | 9.2 | 1578.64 |
Max | 409.756 | 762.125 | 59,708.604 | 2.993 | 35.865 | 7263.886 | |
Min | 0 | 0 | 0 | 0 | 0 | 0 |
Indicator | Magnitude ( p.u) | Angle ( Degree) | |||||
---|---|---|---|---|---|---|---|
OP | LP | WP | OP | LP | WP | ||
3 | Avg | 111.105 | 270.418 | 2156.975 | 0.999 | 13.665 | 136.253 |
Max | 3187.87 | 4257.55 | 13,625.349 | 11.88 | 81.883 | 693.295 | |
Min | 0 | 0 | 0 | 0 | 0 | 0 | |
4 | Avg | 106.465 | 204.701 | 2164.774 | 0.894 | 6.695 | 101.866 |
Max | 3222.997 | 4327.7 | 13,616.621 | 12.059 | 81.866 | 691.581 | |
Min | 0 | 0 | 0 | 0 | 0 | 0 | |
5 | Avg | 106.503 | 133.918 | 2161.948 | 0.613 | 5.098 | 136.065 |
Max | 3227.337 | 3816.824 | 10,186.182 | 12.429 | 91.925 | 692.318 | |
Min | 0 | 0 | 0 | 0 | 0 | 0 |
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Lee, K.-Y.; Park, J.-S.; Kim, Y.-S. Optimal Placement of PMU to Enhance Supervised Learning-Based Pseudo-Measurement Modelling Accuracy in Distribution Network. Energies 2021, 14, 7767. https://doi.org/10.3390/en14227767
Lee K-Y, Park J-S, Kim Y-S. Optimal Placement of PMU to Enhance Supervised Learning-Based Pseudo-Measurement Modelling Accuracy in Distribution Network. Energies. 2021; 14(22):7767. https://doi.org/10.3390/en14227767
Chicago/Turabian StyleLee, Kyung-Yong, Jung-Sung Park, and Yun-Su Kim. 2021. "Optimal Placement of PMU to Enhance Supervised Learning-Based Pseudo-Measurement Modelling Accuracy in Distribution Network" Energies 14, no. 22: 7767. https://doi.org/10.3390/en14227767
APA StyleLee, K. -Y., Park, J. -S., & Kim, Y. -S. (2021). Optimal Placement of PMU to Enhance Supervised Learning-Based Pseudo-Measurement Modelling Accuracy in Distribution Network. Energies, 14(22), 7767. https://doi.org/10.3390/en14227767