Probabilistic Power Flow Calculation Research Articles

Optimal scheduling of active distribution network based on RBF-stochastic response surface method

As the high proportion of distributed generation (DG) and diversification of loads increase, the distribution network faces increasingly greater impact. To address the high-dimensional stochastic problems arising from the multi-dimensional uncertainty of power source and load, this paper proposes a two-stage optimization scheduling scheme for AC distribution networks based on RBF-stochastic response surface method (RBF-SRSM). This scheme takes into account economy, environmental protection and safety, and consists of day-ahead and intra-day stages. The day-ahead decision scheduling is based on an optimal low-carbon economy operation plan, while the intra-day reactive power optimization is achieved by converting nonlinear integral indicators into discrete linear indicators through probabilistic power flow calculation and the first moment derivation principle inspired by SRSM. The mixed integer second-order cone programming (MISOCP) method is used to solve the dispatching plan, and the results suggest that the proposed method is more efficient than the SRSM.

Risk assessment of distribution network operation with scale distributed photovoltaics

In the context of large-scale photovoltaic integration into the distribution network, it is of great significance to comprehensively consider the uncertainty of photovoltaic output and load and scientifically and effectively evaluate the operational risks of the distribution network, in order to ensure the reliable and economic operation of the distribution network. At the same time, with the increase of distributed photovoltaic installed capacity, the small interference stability caused by it has an increasing impact on the operation of the distribution network. In this paper, we first establish a probabilistic model of photovoltaic output and load. Then, we propose a risk calculation method based on the non-sequential Monte Carlo method and probabilistic power flow calculation. Then, a risk analysis of large-scale photovoltaic access to the distribution network was carried out. A new small interference stability risk index was constructed to evaluate the risk of system oscillation caused by photovoltaic access. On this basis, the comprehensive risk value is calculated, and the risk levels are divided based on the voltage over-limit risk and power flow over-limit risk. Finally, the feasibility and effectiveness of the risk assessment model are verified through case analysis.

Hierarchical Blocking Control for Mitigating Cascading Failures in Power Systems with Wind Power Integration

The increasing uncertainty of wind power brings greater challenges to the control for mitigation of cascading failures. In order to minimize the risk of cascading failures in large-scale wind power systems at a lower economic cost, a multi-stage blocking control model is proposed based on sensitivity analysis. Firstly, the propagation mechanism of cascading failures in power systems with wind power integration is analyzed, and the propagation path of such failures is predicted. Subsequently, sensitive lines that are prone to failure are identified using the power sensitivity matrix, taking into account the effects of blocking control on the propagation path. By constraining the power flow of these sensitive lines, a multi-stage blocking control model for the predicted cascading failure path is proposed with the objective of minimizing the control cost and cascading failure probability. Based on probabilistic optimal power flow calculations, the constraints related to wind power uncertainty are transformed into opportunity constraints. To validate the effectiveness of the proposed model, the IEEE 39-node system is used as an example, and the results show that the obtained control method is able to balance economy and safety. In addition, the control costs for the same initial failure are higher as the wind power penetration rates and confidence levels increase.

An Improved Three-point Method for Power Flow Calculation based on Halton Sequence

With the development of electric power system, it is necessary to expand the scale of new energy power generation to meet the demand of peak cutting and valley filling. The new energy power generation presents intermittenity and volatility, so it is a hot research topic to use the theory of point estimation method to study the power system planning based on uncertainty quantity. This paper improved the three-point estimation method in probabilistic power flow calculation, combined with Halton sequence sampling method to make sampling samples more uniform, and then added a pair of estimation points on the basis of the three-point estimation method, so as to improve the precision of power flow calculation without calculating the fourth moment. The proposed method is verified on IEEE14 and IEEE33 node systems, and the results verify the rationality of the improved three-point method based on Halton sequence.

Time sequence three-phase probabilistic power flow calculation for power system including traction station load of high-speed railway

The increasing traction station load of high-speed railway with single-phase, high-power, spatiotemporal mobility, and uncertainty has brought major impacts and challenges to the power system. The non-negligible characteristics are the spatial distribution of traction stations on high-speed railway lines, the time sequence of traction load moving with EMUs, as well as the nonparametric probabilistic features and correlation of traction load. A method of time sequence three-phase probabilistic power flow (3PPF) calculation for power system including traction station load of high-speed railway is proposed in this paper. Firstly, through the port transformation of traction power supply system (TPSS), the three-phase equivalent model of TPSS is established to construct an unbalanced three-phase power flow calculation model of grid with traction station load. Secondly, considering the spatial correlation, time sequence and non-parametric probabilistic feature of traction load, the time sequence probabilistic models of multiple traction station loads are built based on diffusion-based kernel density estimator (DKDE). Then, the algorithm of time sequence 3PPF calculation based on three-point estimation method (3PEM) is applied to deal with the computational efficiency and accuracy problems of 3PPF considering correlation and timing. Finally, the two modified three-phase power systems are employed for case studies in combination with the measured data of traction station of a high-speed railway. The validity and computing efficiency of the proposed method are verified.

A novel deep learning based probabilistic power flow method for Multi-Microgrids distribution system with incomplete network information

With the massive deployment of microgrids (MGs) and energy communities, various stakeholders have been involved in distribution networks. Due to the underdeveloped information infrastructure, especially in rural distribution networks, there is an increasing number of “blind areas” in the operation of distribution networks. The calculation of probabilistic power flow (PPF) with incomplete parameters have become an urgent issue to be solved for ensuring safe operation. Based on the deep learning and mechanism models, a novel PPF method is proposed for multi-microgrids distribution systems considering incomplete network information. Firstly, accessible power exchange data as well as public and independent information are utilized to realize equivalent modeling for microgrids area with incomplete parameters, based on a novel Kriging surrogate enhanced Gate Recurrent Unit-Temporal Convolutional Network (GRU-TCN). Then, the PPF calculation is effectively conducted by the distribution system operator (DSO) through the point estimation method (PEM), in which the equivalent GRU-TCN models and model-based power flow are integrated. Therefore, the complicated interactive iteration of the power flow equation is avoided, and the PPF calculation efficiency is effectively improved. In addition, user privacy is protected because only the trained GRU-TCN deep learning models will be used by DSO for the PPF calculation. The proposed method is validated in a modified IEEE 33-node distribution network, a modified American PG&E 69-node distribution network as well as the modified three-phase unbalanced IEEE 123-node distribution network including several MGs with unknown internal network parameters. The results show that the proposed method can improve the PPF calculation efficiency greatly while ensuring high-precision calculation results. The required evaluation time can be reduced by 64.01% and 99.31% compared with the DNN-based Monte Carlo sampling method and the traditional mechanism model-based Monte Carlo sampling method with complete information, respectively.

Probabilistic power flow calculation using principal component analysis-based compressive sensing

The increasing scale of the injection of renewable energy has brought about great uncertainty to the operation of power grid. In this situation, probabilistic power flow (PPF) calculation has been introduced to mitigate the low accuracy of traditional deterministic power flow calculation in describing the operation status and power flow distribution of power systems. Polynomial chaotic expansion (PCE) method has become popular in PPF analysis due to its high efficiency and accuracy, and sparse PCE has increased its capability of tackling the issue of dimension disaster. In this paper, we propose a principal component analysis-based compressive sensing (PCA-CS) algorithm solve the PPF problem. The l1-optimization of CS is used to tackle the dimension disaster of sparse PCE, and PCA is included to further increase the sparsity of expansion coefficient matrix. Theoretical and numerical simulation results show that the proposed method can effectively improve the efficiency of PPF calculation in the case of random inputs with higher dimensions.

Risk assessment of photovoltaic distribution network based on adaptive kernel density estimation and cumulant method

In order to efficiently and accurately evaluate the out of limit risk of photovoltaic power distribution network, the adaptive kernel density estimation (AKDE) method is introduced to fit the actual light intensity sequence, and the probability distribution model of photovoltaic power station output characteristics is established. At the same time, the Cornish–Fisher series combined with the cumulant method (CM) is used to calculate the probabilistic power flow of photovoltaic distribution network, the accuracy of probabilistic power flow calculation (PPFC) is verified by Monte Carlo Method (MCM), the system level voltage out of limit risk index (VOLRI) and branch power flow out of limit risk index (BPFOLRI) are established. Finally, MATLAB is used to verify the accuracy and efficiency of the algorithm for photovoltaic distribution network risk assessment.

Gaussian Mixture Model for Multivariate Wind Power Based on Kernel Density Estimation and Component Number Reduction

The Gaussian mixture model (GMM) is a powerful tool to establish the probability distributions of random variables in power system analyses. GMM can model arbitrary probability distributions by increasing the number of its Gaussian components, but the commonly used expectation-maximization (EM) algorithm fails to obtain accurate GMM for large component numbers, which limits the application of GMM to multivariate wind power modeling. In this letter, a parameter estimation method for GMM with large component numbers is proposed based on kernel density estimation (KDE) and the improved density-preserving hierarchical EM algorithm. Then, the closed-form solution to probabilistic power flow (PPF) calculation is derived based on piecewise linearization and GMM, which validates the importance of large component numbers. Finally, the proposed uncertainty modeling method is compared with EM-based GMM, Copula functions, KDE, k-nearest neighbors and block neural autoregressive flow on actual wind speed data to validate its superiority in describing the details of probability densities of wind power. PPF calculation is performed to show the efficiency and accuracy of the proposed uncertainty analysis method.

Nonparametric Probabilistic Optimal Power Flow

With the increasing penetration of renewable energy, accurate and efficient probabilistic optimal power flow (POPF) calculation becomes more and more important to provide decision support for secure and economic operation of power systems. This paper develops a novel nonparametric probabilistic optimal power flow (N-POPF) model describing the probabilistic information by quantiles, which avoids any parametric probability distribution assumptions of random variables. A novel critical region integral method (CRIM) which combines the multiparametric programming theory and discrete integral is proposed to efficiently solve the N-POPF problem. In the CRIM, the critical region partitioning algorithm is firstly introduced into the POPF model to directly establish the mapping relationship from wind power to optimal solutions of the POPF problem. Besides, a discrete integral method is developed in the CRIM to achieve the probability convolution calculation based on quantiles. Comprehensive numerical experiments verify the superior performance of the proposed CRIM in estimation accuracy and computational efficiency, and demonstrate that N-POPF model significantly improves the accuracy of uncertainty analysis. In general, the proposed N-POPF model and CRIM form a new framework of POPF problem for power system analysis and operation.

Probabilistic power flow calculation considering electro-thermo-mechanical dynamics of overhead conductor

Conductor temperature and tension are important physical states that determine the security of the overhead line. The states are sensitive to the line power flow and the meteorological conditions around the conductor that have strong uncertainty. In this paper, the electro-thermo-mechanical coupling dynamics of the power system are modeled. Then, focusing on the calculation of the distributions of the electro-thermo-mechanical dynamics (ETMDs) of critical spans under the uncertain operational environment of the power system, the implementation framework and the fast calculation methods for the probabilistic power flow considering electro-thermo-mechanical dynamics (PPF-ETMD) are proposed. The work presented in this paper provides an effective method for operators to capture distributions of the ETMDs of critical spans under the uncertain environment and detect the underlying system security risk based on the thermal and mechanical essence of the security of the overhead line. Numerical simulations based on a regional power system in China and the IEEE 300-node system are carried out to verify the effectiveness of the proposed method.

An Assessment Method for the Impact of Electric Vehicle Participation in V2G on the Voltage Quality of the Distribution Network

In order to further evaluate the impact of vehicle-to-grid (V2G) on the distribution network, this paper studies a method to assess the influence of electric vehicles participating in charge and discharge on the voltage quality of the distribution network. First, considering the state of charge of the EV, the participation of the owner and other factors, the charging and discharging model is built. Then, the probabilistic power flow calculation based on Latin hypercube sampling is used to obtain the probability distribution of the voltage amplitude of the charge and discharge load connected to the distribution network, and finally the evaluation index is established to quantify and calculate the voltage quality of the distribution network participating in the V2G process of electric vehicles. Simulation results show that the evaluation method has the advantage of fast calculation speed while ensuring known accuracy, introduces the probability distribution of expected value and variance quantification of voltage amplitude, more intuitively understands the degree of influence on voltage quality before and after V2G, and can effectively assess the impact of electric vehicles accessing the distribution network in V2G mode on the power quality of low-voltage residential areas and industrial and commercial areas, and this evaluation method can provide useful reference for the formulation of future V2G control strategies and the planning of future urban power grids.

Statistical machine learning model for capacitor planning considering uncertainties in photovoltaic power

New energy integration and flexible demand response make smart grid operation scenarios complex and changeable, which bring challenges to network planning. If every possible scenario is considered, the solution to the planning can become extremely time-consuming and difficult. This paper introduces statistical machine learning (SML) techniques to carry out multi-scenario based probabilistic power flow calculations and describes their application to the stochastic planning of distribution networks. The proposed SML includes linear regression, probability distribution, Markov chain, isoprobabilistic transformation, maximum likelihood estimator, stochastic response surface and center point method. Based on the above SML model, capricious weather, photovoltaic power generation, thermal load, power flow and uncertainty programming are simulated. Taking a 33-bus distribution system as an example, this paper compares the stochastic planning model based on SML with the traditional models published in the literature. The results verify that the proposed model greatly improves planning performance while meeting accuracy requirements. The case study also considers a realistic power distribution system operating under stressed conditions.

Probabilistic Load Flow–Based Optimal Placement and Sizing of Distributed Generators

Distributed generation (DG) is gaining importance as electrical energy demand increases. DG is used to decrease power losses, operating costs, and improve voltage stability. Most DG resources have less environmental impact. In a particular region, the sizing and location of DG resources significantly affect the planned DG integrated distribution network (DN). The voltage profiles of the DN will change or even become excessively increased. An enormous DG active power, inserted into an improper node of the distribution network, may bring a larger current greater than the conductor’s maximum value, resulting in an overcurrent distribution network. Therefore, DG sizing and DG location optimization is required for a systematic DG operation to fully exploit distributed energy and achieve mutual energy harmony across existing distribution networks, which creates an economically viable, secure, stable, and dependable power distribution system. DG needs to access the location and capacity for rational planning. The objective function of this paper is to minimize the sum of investment cost, operation cost, and line loss cost utilizing DG access. The probabilistic power flow calculation technique based on the two-point estimation method is chosen for this paper’s load flow computation. The location and size of the DG distribution network are determined using a genetic algorithm in a MATLAB environment. For the optimum solution, the actual power load is estimated using historical data. The proposed system is based on the China distribution system, and the currency is used in Yuan. After DG access, active and reactive power losses are reduced by 53% and 26%, respectively. The line operating cost and the total annual cost are decreased by 53.7% and 12%, respectively.

Probabilistic optimal power flow calculation method considering sequential features and correlations of multi-uncertain source-load scenarios

In order to accurately evaluate the influence of the correlation and sequential feature of wind power, PV power, and load on the economic operation of a power system, a sequential probabilistic optimal power flow calculation method based on multi-uncertain source-load scenarios generated by a multi-generative adversarial network (MGAN) is proposed. First, the historical datasets of wind power, PV power, and load in adjacent areas were collected, and their probability distributions in 24 time periods were analyzed. The results showed that the probability distribution of different periods had obvious differences, which were defined as time sequence differences in this paper. Second, a novel neural network called MGAN for scenario generation was designed. Based on the historical data of each time period, the correlated wind power, photovoltaic (PV) power, and load scenarios were generated by MGAN. Finally, in the modified IEEE 118-bus system, in which two wind power sources, two PV power sources, and two loads with correlation were integrated, probabilistic optimal power flow calculations were carried out for 24 periods with the goal of the lowest power generation cost of thermal power units. The experimental results showed that the power generation cost fluctuation ranges that considered the time sequence difference were reduced by 60% on average compared with the nonconsidered. The proposed method can effectively reduce the power generation cost budget.

Research on Optimal Power Flow Calculation Method for Multi-wind Power Distribution Network

The comprehensive consideration of the uncertainty and correlation factors in the power system is of great significance for the comprehensive evaluation of the optimal power flow. For the edge distribution of wind speed in wind fields, the non-parametric kernel density estimation method is adopted in this paper. For the wind speed combined distribution model of multiple wind fields, due to its own characteristics and the complexity of taking the correlation into account, the vine copula function was used in this paper to construct the model. Then, the three-point estimation method is used to generate independent random vectors in the standard normal space, and based on the combined distribution model, Rosenblatt inverse transformation is used to map the random vectors into correlated wind speed vectors. Finally, 2N+1 deterministic optimal power flow calculation is completed according to the interior point method, and the probability statistics information of each state quantity of power system is obtained. Taking the actual wind speed in a certain area as an example, the combined distribution model of multiple wind fields is constructed, and the probabilistic optimal power flow calculation is carried out in the power supply system containing multiple wind fields. The simulation results show that the method presented in this paper gives consideration to the accuracy and efficiency of the calculation.

Research on Probabilistic Power Flow Calculation of DC Distribution Network

With the development of distributed power sources based on wind power and photovoltaics and the increase of DC loads, DC power grids have attracted more and more attention. Compared with the AC distribution network, the DC distribution network can save a lot of commutation links while absorbing a large amount of renewable energy and DC load, reducing losses and improving economic benefits. This paper combines the probabilistic power flow calculation method based on the three-point estimation method and the Nataf inverse transform used in the AC power grid with the DC power flow model, and proposes a method suitable for the probabilistic power flow calculation of the DC distribution network. Comparing the results and analyzing the in fluence of the load distortion rate and the increase in the capacity of new energy absorbed on the calculation error of the estimation method, it demonstrates the accuracy and effectiveness of the calculation method in this paper.

Assessment of the importance of branches considering new energy access

Under the background of increasing penetration rate of new energy, the risk level of power system is getting higher and higher. Identifying the key branches of the system quickly and accurately is of great significance for improving the stability of power grid operation and preventing the occurrence of blackouts. This paper models the uncertain factors after the new energy is connected and establishes a grid risk assessment system. Based on the probabilistic power flow calculation, the comprehensive system risk index under the decommissioning of each branch is obtained as the branch importance through five indicators like power flow fluctuation risk and line active power over-limit risk The improved IEEE-39 node system is used as an example for simulation calculation. The results verify the effectiveness of this method, which can distinguish the importance of branches, and provide references for safety early warning and differentiated planning.

Probabilistic power flow calculation based on importance-Hammersley sampling with Eigen-decomposition

This paper presents a novel probabilistic power flow calculation method for power systems with integrated wind farms, based on importance sampling and Hammersley sequence with eigen-decomposition. The method proposed in this paper adopts importance sampling to build probability density functions in a desired range to compress the sampling space and hence reduce the calculation burden. The Hammersley sequence, a kind of low discrepancy sequence, is used to obtain uniform samples for improving the sampling efficiency. In addition, since the traditional Cholesky method is unable to decompose the non-positive definite correlation matrix, this paper applies the eigen-decomposition to solve this problem for multiple correlated wind sources. Case studies are conducted on modified IEEE test systems, where the advantages of the proposed method are verified. According to the simulation results, the proposed method shows greater accuracy and efficiency, compared to the traditional methods.

Static Stability Analysis Based on Probabilistic Power Flow Calculation considering P2G Technology

At present, integrated energy systems have received extensive attention, but there is no basic framework for stability analysis of coupled systems. The injection of a large amount of renewable energy also has a great impact on the stability of the system. This paper focuses on how to analyze the static stability of the coupling system with uncertainty, which mainly considers the uncertainty of wind power generation and photovoltaic power generation and also considers the influence of P2G technology on the whole system. Firstly, this paper analyzes the principles of wind power generation and photovoltaic power generation and constructs the probability model of renewable energy power generation power. Then, the three-point estimation method is used to process the data, and the probability distribution of the unknown quantity is obtained by probabilistic power flow analysis. Finally, the probability distribution of each eigenvalue is obtained by analyzing the sensitivity of the characteristic roots to the voltage. Thus, the static stability of the system is judged. The applicability of proposed methodology is demonstrated by analyzing an integrated IEEE 14-bus power system and a Belgian 20-node gas system in this paper.