A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables
The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush–Kuhn–Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-10-01
|
| Series: | Energies |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1996-1073/10/10/1623 |
| _version_ | 1828283568293412864 |
|---|---|
| author | Xiaoyang Deng Jinghan He Pei Zhang |
| author_facet | Xiaoyang Deng Jinghan He Pei Zhang |
| author_sort | Xiaoyang Deng |
| collection | DOAJ |
| description | The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush–Kuhn–Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from large-scale wind power and loads, a novel P-OPF method is proposed, where the correlations among input variables are also taken into account. Firstly, the inverse Nataf transformation and Cholesky decomposition are used to obtain samples of wind speeds and loads with a given correlation matrix. Then, the K-means algorithm is introduced to group the samples of wind power outputs and loads into a number of clusters, so that in each cluster samples of stochastic variables have small variances. In each cluster, the CM for P-OPF is conducted to obtain the cumulants of system variables. According to these cumulants, the moments of system variables corresponding to each cluster are computed. The moments of system variables for the total samples are obtained by combining the moments for all grouped clusters through the total probability formula. Then, the moments for the total samples are used to calculate the corresponding cumulants. Finally, Cornish–Fisher expansion is introduced to obtain the probability density functions (PDFs) of system variables. IEEE 9-bus and 118-bus test systems are modified to examine the proposed method. Study results show that the proposed method can produce more accurate results than traditional CM for P-OPF and is more efficient than Monte Carlo simulation (MCS). |
| first_indexed | 2024-04-13T08:47:13Z |
| format | Article |
| id | doaj.art-f42e48f6d2aa4c1e949b6f973b6b18cf |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-04-13T08:47:13Z |
| publishDate | 2017-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-f42e48f6d2aa4c1e949b6f973b6b18cf2022-12-22T02:53:38ZengMDPI AGEnergies1996-10732017-10-011010162310.3390/en10101623en10101623A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic VariablesXiaoyang Deng0Jinghan He1Pei Zhang2School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, ChinaSchool of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, ChinaSchool of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, ChinaThe traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush–Kuhn–Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from large-scale wind power and loads, a novel P-OPF method is proposed, where the correlations among input variables are also taken into account. Firstly, the inverse Nataf transformation and Cholesky decomposition are used to obtain samples of wind speeds and loads with a given correlation matrix. Then, the K-means algorithm is introduced to group the samples of wind power outputs and loads into a number of clusters, so that in each cluster samples of stochastic variables have small variances. In each cluster, the CM for P-OPF is conducted to obtain the cumulants of system variables. According to these cumulants, the moments of system variables corresponding to each cluster are computed. The moments of system variables for the total samples are obtained by combining the moments for all grouped clusters through the total probability formula. Then, the moments for the total samples are used to calculate the corresponding cumulants. Finally, Cornish–Fisher expansion is introduced to obtain the probability density functions (PDFs) of system variables. IEEE 9-bus and 118-bus test systems are modified to examine the proposed method. Study results show that the proposed method can produce more accurate results than traditional CM for P-OPF and is more efficient than Monte Carlo simulation (MCS).https://www.mdpi.com/1996-1073/10/10/1623cumulant method (CM)probabilistic optimal power flow (P-OPF)large fluctuationsK-means algorithm |
| spellingShingle | Xiaoyang Deng Jinghan He Pei Zhang A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables Energies cumulant method (CM) probabilistic optimal power flow (P-OPF) large fluctuations K-means algorithm |
| title | A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables |
| title_full | A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables |
| title_fullStr | A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables |
| title_full_unstemmed | A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables |
| title_short | A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables |
| title_sort | novel probabilistic optimal power flow method to handle large fluctuations of stochastic variables |
| topic | cumulant method (CM) probabilistic optimal power flow (P-OPF) large fluctuations K-means algorithm |
| url | https://www.mdpi.com/1996-1073/10/10/1623 |
| work_keys_str_mv | AT xiaoyangdeng anovelprobabilisticoptimalpowerflowmethodtohandlelargefluctuationsofstochasticvariables AT jinghanhe anovelprobabilisticoptimalpowerflowmethodtohandlelargefluctuationsofstochasticvariables AT peizhang anovelprobabilisticoptimalpowerflowmethodtohandlelargefluctuationsofstochasticvariables AT xiaoyangdeng novelprobabilisticoptimalpowerflowmethodtohandlelargefluctuationsofstochasticvariables AT jinghanhe novelprobabilisticoptimalpowerflowmethodtohandlelargefluctuationsofstochasticvariables AT peizhang novelprobabilisticoptimalpowerflowmethodtohandlelargefluctuationsofstochasticvariables |