Probabilistic Power Flow Research Articles

Identification and Evaluation of Vulnerable Links in a Distribution Network with Renewable Energy Source Based on Minimum Discriminant Information

With the increase in the proportion of photovoltaic and wind power access, the scale and form of distribution networks are becoming more and more complex. The traditional single distribution network vulnerability assessment method is difficult to use to identify the vulnerable links in the distribution network. Therefore, this paper proposes a method for identifying and evaluating vulnerable links in distribution networks based on minimum discriminant information. First, considering the influence of distributed grid connection, an improved probabilistic power flow calculation method is proposed, which improves the calculation efficiency and accuracy. Second, considering the correlation degree, transmission capacity, and voltage stability of branches in the distribution network, the identification index of vulnerable lines is defined. Based on power quality and operating state, the identification index of vulnerable nodes in a distribution network is defined. Finally, based on the indicators of vulnerable nodes and vulnerable lines, the vulnerable links in the distribution network are comprehensively evaluated based on the principle of minimum discriminant information, and the vulnerable links of the entire distribution network are evaluated according to different degrees of vulnerability. The rationality and effectiveness of the proposed method are verified via an example analysis of actual power grid data.

Voltage over-limit risk assessment of wind power and photovoltaic access distribution system based on day-night segmentation and Gaussian mixture model

The access of distributed power sources such as wind power and photovoltaic (PV) with randomness and uncertainty makes the operation of distribution system more complicated. It is particularly necessary to comprehensively and efficiently evaluate the risk of voltage over-limit in distribution systems with wind power and photovoltaic. Firstly, aiming at the problem of centralized sampling of Monte Carlo method in risk assessment of distribution system, a day-night segmented Monte Carlo (MC) sampling method is proposed to generate a large number of day-night sampling scenarios. Secondly, the Gaussian mixture model is used to fit the probability density of the voltage obtained from probabilistic power flow calculations, concurrently, the utility preference exponential function characterizes the severity of the over-limit, and a comprehensive evaluation model of voltage over-limit risk is constructed. Finally, the effectiveness and accuracy of the proposed method are verified by taking the improved IEEE 33-bus distribution system as an example. These results offer actionable insights for future risk assessments of new energy grid connections.

Fractional Moments Based Adaptive Scaled Unscented Transformation for Probabilistic Power Flow of AC-DC Hybrid Grids

Fractional Moments Based Adaptive Scaled Unscented Transformation for Probabilistic Power Flow of AC-DC Hybrid Grids

Impact of electric vehicles and wave energy systems on OPF of power networks using hybrid Osprey-PSO approach

In this article, a novel optimization algorithm named hybrid Osprey Optimization and Particle Swarm Optimization (OOPSO) is proposed to solve the Probabilistic Optimal Power Flow (POPF) problem in power systems with high penetration of renewable energy resources (RERs), such as photovoltaic, wind, and wave energy and integration of electric vehicles (EVs). The algorithm's results are compared with established optimization algorithms like Osprey Optimization Algorithm (OOA), Particle Swarm Optimization (PSO), and Heap Optimization. Applied to the 30 and 118-bus IEEE test systems, the OOPSO algorithm efficiently deals with the uncertainties produced by RERs generation. This research study includes EV charging profiles for weekdays and weekends. It considers home and work-level charging scenarios. The RERs and EVs penetration ensure system reliability while minimizing generation costs and satisfying power flow constraints. Compared to existing algorithms, the OOPSO algorithm achieves superior performance, faster convergence, and higher solution accuracy. The simulation results show the effectiveness of OOPSO. It appears to be a robust tool for POPF, integrating RERs in power systems with EVs. This work highlights the potential of OOPSO as a feasible approach for power system optimization in the context of RERs and EV integration, paving the way for further research into unconventional grid optimization techniques.

Probabilistic power flow based on physics-guided graph neural networks

Under the high-dimensional and nonlinear stochastic power system environment, artificial intelligence (AI) is becoming a promising alternative to the urgent demand for probabilistic power flow (PPF). However, traditional AI only learns from experiences in data and is unable to satisfy physical constraints. This may result in an undesired infeasible inference for PPF. To solve this issue, a physics-guided graph neural network (PG-GNN)-based PPF analysis method is proposed. At the outset, alternating current power flow equation is analyzed to produce gradients for connecting physical component and AI. The proposed PG-GNN then incorporates the sensitivities into the training tensor graph such that it enables in-depth physical learning. At the same time, the GNN serves to enhance generalizability in varying topology. The well-trained PG-GNN is finally leveraged to surrogate traditional power flow solver in Monte-Carlo method, such that real-time PPF is realized. Numerical tests on benchmarks demonstrate that, in unseen scenarios, the proposed method enables only little gap versus the exact baseline, but beats other rivals with over tenfold computing efficiency. Moreover, comparisons with traditional AIs manifest that our method holds better generalizability.

Probabilistic optimal power flow computation for power grid including correlated wind sources

AbstractThis paper sets out to develop an efficient probabilistic optimal power flow (POPF) algorithm to assess the influence of wind power on power grid. Given a set of wind data at multiple sites, their marginal distributions are fitted by a newly developed generalized Johnson system, whose parameters are specified by a percentile matching method. The correlation of wind speeds is characterized by a flexible Liouville copula, which allows to model the asymmetric dependence structure. In order to improve the efficiency for solving POPF problem, a lattice sampling method is developed to generate wind samples at multiple sites, and a logistic mixture model is proposed to fit distributions of POPF outputs. Finally, case studies are performed, the generalized Johnson system is compared with Weibull distribution and the original Johnson system for fitting wind samples, Liouville copula is compared against Archimedean copula for modelling correlated wind samples, and lattice sampling method is compared with Sobol sequence and Latin hypercube sampling for solving POPF problem on IEEE 118‐bus system, the results indicate the higher accuracy of the proposed methods for recovering the joint cumulative distribution function of correlated wind samples, as well as the higher efficiency for calculating statistical information of POPF outputs.

The planning method of new energy distribution network in plateau area based on local accommodation

Abstract The planning method of new energy distribution network in plateau area based on local accommodation is studied to improve the local accommodation capacity of new energy distribution network in plateau area. The framework of new energy distribution network planning in the plateau area is constructed, and the distribution network equipment suitable for the plateau environment is selected based on the harsh environment in the plateau area; in the framework of new energy distribution network planning in plateau area, a bi-level planning model considering multi-flexible resource coordinated scheduling and energy storage is established. The upper level planning model takes the maximum accommodation of new energy as the objective, and the lower level planning model takes the optimal daily operation benefit of energy storage under the given configuration as the optimization objective; the probabilistic power flow method and C-PSO are used to solve the bi-level model. The experiment shows that this method ensures the stability of the new energy distribution network in the plateau area, reduces the amount of abandoned wind energy and the operating cost, and improves the local accommodation capacity of the core higher than the distribution network.

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.

Deep learning-based correlation analysis for probabilistic power flow considering renewable energy and energy storage

Developing photovoltaic (PV) and wind power is one of the most efficient approaches to reduce carbon emissions. Accumulating the PV and wind energy resources at different geographical locations can minimize total power output variance as injected into the power systems. To some extent, a low degree of the variance amplitude of the renewable resources can reduce the requirement of in-depth regulation and dispatch for the fossil fuel-based thermal power plants. Such an issue can alternatively reduce carbon emissions. Thus, the correlation problem by minimizing the variance of total PV and wind power plays a vital role in power system planning and operation. However, the synergistic effect of power output correlation is mainly considered on the generation side, and it is often neglected for the correlation relationship between the power grid components. To address this problem, this paper proposes a correlation coefficient analysis method for the power grid, which can quantify the relationship between energy storage and the probabilistic power flow (PPF) of the grid. Subsequently, to accelerate the mapping efficiency of power correlation coefficients, a novel deep neural network (DNN) optimized by multi-task learning and attention mechanism (MA-DNN) is developed to predict power flow fluctuations. Finally, the simulation results show that in IEEE 9-bus and IEEE14-bus systems, the strong correlation grouping percentage between the power correlation coefficients and power flow fluctuations reached 92% and 51%, respectively. The percentages of groups indicating weak correlation are 4% and 38%. In the modified IEEE 23-bus system, the computational accuracy of MA-DNN is improved by 37.35% compared to the PPF based on Latin hypercube sampling. Additionally, the MA-DNN regression prediction model exhibits a substantial improvement in assessing power flow fluctuations in the power grid, achieving a speed enhancement of 758.85 times compared to the conventional probability power flow algorithms. These findings provide the rapid selection of the grid access point with the minimum power flow fluctuations.

Probabilistic Voltage Optimization Considering Load Static Voltage Characteristics

In the conventional power flow calculation, the load is mostly treated as a constant power node. When the voltage deviation occurs, the static voltage characteristics of the load will change, resulting in the change of the power flow calculation. This situation is more likely to occur in the distribution network with distributed power supply. Therefore, it is very important to consider the static voltage response characteristics of the load in the power flow calculation. In the existing literature, when evaluating and optimizing voltage stability, deterministic indicators are usually used to evaluate the voltage level of the system. In the active distribution network with uncertain new energy output, this method has its limitations. Based on the above analysis, this paper uses the power flow calculation method considering the static voltage characteristics of the load to solve the node voltage distribution of the distribution network system. Considering the uncertainty of new energy output and load, the semi-invariant method is used to analyze the probabilistic power flow. An evaluation index considering the digital characteristics of voltage deviation distribution is proposed. The voltage optimization model is established according to the proposed index, and the genetic algorithm is used to solve the problem. The IEEE33 node standard example is simulated to verify the correctness and feasibility of the proposed method.

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.

An active multiphase probabilistic power flow based on a clustering approach

Probabilistic methods for analyzing power systems have become more widespread, mainly due to the increase in load and generation uncertainties and the current need for planning problems that are sufficiently accurate to take appropriate actions. However, some characteristics need to be better investigated in the Distribution Systems (DS) analysis, such as the input random variables’ modeling using real databases and, mainly, the probabilistic treatment of unbalance and scalability studies. This paper proposes an active Multiphase Probabilistic Power Flow (MPPF) evaluation, considering real measurement databases to represent customer demand uncertainties. It is called Multiphase Probabilistic Power Flow Based on K-Means (MPPFKM), and it encompasses a mixture of a clustering technique and an analytical method. The K-Means algorithm divides the input database into a set of clusters that models the scenarios to be evaluated in the multiphase power flow problem, which considers the distribution network with its inherent unbalance. Subsequently, the output variables’ higher order statistical moments are calculated using the obtained responses for each cluster. Finally, their PDFs and CDFs are recovered using the Gram-Charlier Expansion analytical method. While the clustering algorithm allows working with real data, giving the proposed work greater proximity to real-world results, the analytical tool provides an accurate recovery of the probability functions, because it detects their distortions caused by the nature of the multiphase problem. Estimating the correct number of clusters is a key factor in obtaining the precision required by power systems engineers and achieving significant computational time reduction, especially for large-scale unbalanced systems. Simulations are carried out using several DS feeders to test the proposed method, which specifically addresses DS issues not yet well explored in the literature, such as probabilistic simulations under different unbalance situations, applications with single-phase DGs, and scalability studies are conducted using the IEEE 8500 test feeder. Comparisons are made with usual MPPF algorithms, including Monte Carlo Simulation (MCS) and Point Estimation Methods (PEM). Simulations using large-scale unbalanced systems proved that the output variables' probability functions might present distortions, becoming more challenging for other methods. Under this perspective, MPPFKM presents better exactness in the calculation of higher order statistical moments and, consequently, can estimate the PDFs of the MPPF output variables with great precision, which is crucial for statistical models that use actual input data.

K-Medoids clustering applications for high-dimensionality multiphase probabilistic power flow

Actual power systems’ planning studies require the stochastic modeling of networks due to their increasing penetration of uncertain parameters, such as probabilistic-nature loads and renewable generation features. Although numerous Probabilistic Power Flow (PPF) methods have been presented in the literature, the scalability of such tools is still under study due to the ‘curse of dimensionality’, which states that the probabilistic methods lose their accuracy with the increase of random input variables. Since many authors are using clustering algorithms to solve the PPF, mainly because of their easy implementation and good computational precision, this paper proposes for the first time the K-Medoids clustering method to model uncertainties in unbalanced distribution systems. Modifications in the clustering algorithm are included to improve its accuracy in view of a large set of input variables. The multiphase modeling of networks is also considered to represent the inherent unbalance of distribution systems correctly. Simulations were carried out using the IEEE unbalanced test-feeders IEEE 123 and the large-scale system IEEE 8500, which includes more than 2000 input variables. Results show that K-Medoids are a better alternative in relation to other numerical/approximation approaches, such as Monte Carlo Simulation or Point Estimate Methods, because it is faster and presents great accuracy, especially for large-scale applications. Comparisons were also made regarding other clustering approaches, highlighting the benefits of the proposed one in scalability.

Calculation of probabilistic harmonic power flow based on improved three-point estimation method and maximum entropy as distributed generators access to distribution network

Uncertainty and volatility are the features of distributed generation (DG), which can impact greatly on the operational status of distribution network. Thus, an improved three-point estimation method and maximum entropy theory (ITPEM&ME) for calculating the probabilistic harmonic power flow in distribution network is proposed in this study. Firstly, the probabilistic model is constructed according to the uncertainty of input variables and the improved three-point estimate method is utilized to convert a probabilistic problem into a deterministic problem. Secondly, in order to obtain the distribution of the random harmonics in distribution network, the maximum entropy theory is adopted to reconstruct the statistical characteristics after the deterministic calculation is realized for each harmonic voltages. The case of an IEEE-33 system under various conditions is conducted. The results by the different algorithms indicate that the proposed method ITPEM&ME has a smaller error than the traditional method, as well as the fitting effect of the probability density function (PDF) is much closer to the practical engineering. It is feasible and accurate in dealing with probabilistic harmonic power flow problems.

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.

Efficient surrogate-assisted importance sampling for rare event assessment in probabilistic power flow

In recent years, the increasing integration of renewable energy and electric vehicles has exacerbated uncertainties in power systems. Operators are interested in identifying potential violation events such as overvoltage and overload via probabilistic power flow calculations. Evaluating the violation probabilities requires sufficient accuracy in tail regions of the output distributions. However, the conventional Monte Carlo simulation and importance sampling typically require numerous samples to achieve the desired accuracy. The required power flow simulations result in substantial computational burdens. This study addresses this challenge by proposing a surrogate-assisted importance sampling method. Specifically, a high-fidelity radial basis function-based surrogate is constructed to approximate the nonlinear power flow model. Subsequently, the surrogate is embedded in the conventional importance sampling technique to evaluate the rare probabilities with high efficiency and reasonable accuracy. The computational strengths of the proposed method are validated in the IEEE 14-bus, 118-bus, and realistic 736-bus systems through comparisons with several well-developed methods. The comparisons provide a reference for system operators to select the appropriate method for evaluating violations based on the intended applications.

Probabilistic Reactive Power Flow Optimization of Distribution System in Presence of Distributed Units Uncertainty Using Combination of Improved Taguchi Method and Dandelion Algorithm

Probabilistic Reactive Power Flow Optimization of Distribution System in Presence of Distributed Units Uncertainty Using Combination of Improved Taguchi Method and Dandelion Algorithm

Probabilistic Optimal Power Flow Computation Using Stratified Quadrature Rule

In this paper, the probabilistic optimal power flow (POPF) problem is modeled as a black box uncertainty quantification problem. If distribution functions of POPF inputs are unknown, only samples are available, the multivariate Gaussian mixture model is suggested to recover the joint cumulative distribution function of POPF inputs, and a probability selection method is introduced to relate POPF inputs to an independent standard normal vector. Then, moment matching equations are proposed to characterize the uncertainty effects of POPF inputs on outputs, whereby some properties of the POPF problem are revealed, and a stratified quadrature rule (SQR) is proposed for POPF computation by combining a Hadamard matrix based quadrature rule and a discrete sine transformation matrix based quadrature rule. This newly developed SQR has a computational burden linear with the number of POPF inputs, and performs well in estimating means and standard deviations POPF outputs. Finally, case studies are conducted on a modified IEEE 118-bus system to illustrate the accuracy and efficiency of the proposed method.

Analysis of probabilistic optimal power flow in the power system with the presence of microgrid correlation coefficients

Analysis of probabilistic optimal power flow in the power system with the presence of microgrid correlation coefficients

Congestion forecast framework based on probabilistic power flow and machine learning for smart distribution grids

The increase in renewable energy sources and new technologies such as electric vehicles and storage can generate uncertainties in distribution grid operations, increasing the likelihood of congestions in power lines. Distribution system operators (DSOs) face several challenges while operating their grids in such conditions. These congestions deteriorate the electrical equipment in the long term, reducing its life span. This work proposes a framework to predict grid asset congestions on a daily basis. A congestion forecast framework is proposed by combining probabilistic power flows and machine learning algorithms to support DSOs in their daily decision-making. The framework is tested on a modified IEEE-33 bus system and CINELDI MV Reference system with hourly synthetic data. The results showed that the framework is able to closely predict the congestions on the lines. Computational capabilities are reported and discussed. The study indicates that the framework is a suitable tool for day-to-day congestion predictions in smart distribution grids yielding low error in expected values.