Probabilistic Power Flow Research Articles

Fault Reconfiguration of Distribution Networks with Soft Open Points Considering Uncertainties of Photovoltaic Outputs and Loads

Conventional fault reconfiguration methods assume determinant values for loads and distributed generators outputs, which may lead to a reconfiguration solution that cannot satisfy operational constraints. This paper proposes a fault reconfiguration method for distribution networks with soft open points (SOPs) considering the uncertainties of photovoltaic (PV) output power and loads. Firstly, a fast probabilistic power flow method based on voltage sensitivity for distribution networks with SOPs is proposed to evaluate each reconfiguration scheme. Then a fault reconfiguration model considering uncertainties of PV output powers and loads is formulated and solved to minimize load shedding and line losses. The effectiveness of the proposed reconfiguration method is verified using the modified 33 and 69-bus distribution systems. The proposed method is shown to be very fast and can provide reliable reconfiguration schemes satisfying all system operation constraints.

Probabilistic optimal power flow analysis incorporating correlated wind sources

Probabilistic optimal power flow analysis incorporating correlated wind sources

Efficient uncertainty quantification in economic re-dispatch under high wind penetration considering interruptible load

Due to the high variability and intermittency of wind power generation, operators tend to have a corrective stage to adjust their predictive dispatch schedules for re-balancing the system following a contingency in the real-time market. This paper presents a new probabilistic real-time re-dispatch model integrating interruptible load (IL) programs with the aim to minimize the total operational cost. The problem is formulated in a probabilistic optimal power flow (P-OPF) framework, accounting for uncertainties on both IL response and wind power forecasts. To address this problem, we develop a probabilistic collocation method (PCM) combining techniques of sparse grids and correlation control, which enables efficient and accurate propagation of correlated uncertain variables with relatively low computational cost. The effectiveness of the proposed model and computational strategy are demonstrated on the modified IEEE RTS 24-bus test case and a simplified regional Jiangsu power grid, where the impacts of IL pricing and capacity on the re-dispatch results are further explored.

Probabilistic Power Flow Based on a Gaussian Process Emulator

In this letter, a novel Gaussian process emulator is proposed, for the first time, to conduct the probabilistic power-flow calculation. Based on Bayesian inference, a Gaussian process emulator is trained and served as a nonparametric, reduced-order model of the nonlinear power-flow model. This emulator allows us to evaluate the time-consuming power-flow solver at the sampled values with a negligible computational cost. The simulations reveal the excellent performance of this method.

Reliability-Based Probabilistic Network Pricing With Demand Uncertainty

The future energy system embraces growing flexible demand and generation, which bring large-scale uncertainties and challenges to current deterministic network pricing methods. This paper proposes a novel reliability-based probabilistic network pricing method considering demand uncertainty. Network reliability performance, including probabilistic contingency power flow (PCPF) and tolerance loss of load (TLoL), are used to assess the impact of demand uncertainty on actual network investment cost, where PCPF is formulated by the combined cumulant and series expansion. The tail value at risk (TVaR) is used to generate analytical solutions to determine network reinforcement horizons. Then, final network charges are calculated based on the core of the Long-run incremental cost (LRIC) algorithm. A 15-bus system is employed to demonstrate the proposed method. Results indicate that the pricing signal is sensitive to both demand uncertainty and network reliability, incentivising demand to reduce uncertainties. This is the first-ever network pricing method that determines network investment costs considering both supply reliability and demand uncertainties. It can guide better sitting and sizing of future flexible demand in distribution systems to minimise investment costs and reduce network charges, thus enabling a more efficient system planning and cheaper integration.

A data‐driven probabilistic power flow method based on convolutional neural networks

A data‐driven probabilistic power flow method based on convolutional neural networks

Improving the scalability of deep neural network for probabilistic power flow

Improving the scalability of deep neural network for probabilistic power flow

Fast Cumulant Method for Probabilistic Power Flow Considering the Nonlinear Relationship of Wind Power Generation

Currently, the increasing wind power penetration, with consequent randomness and variability, presents great challenges to power system planning and operation. Probabilistic power flow (PPF) has been developed to calculate the power flow under uncertain circumstances. However, the current wind power models are subject to specific probability distributions, limiting their accuracies in wider applications. Additionally, the cumulant method (CM)-based PPF, if nonlinear relationship is considered in, would face an impractically high computational complexity. To address these problems in modeling and cumulant calculation, this article proposes a novel generalized density/distribution fitting method (GDFM) combining with the Copula function to establish a joint probability model for wind power generation. A special impulse- mixed probability density (IMPD) integration method is also introduced to derive the input cumulants from the model. Finally, a fast cumulant method (FCM) is proposed to reduce the computational burden of output cumulant calculation while retaining a high accuracy in a nonlinear context. Case study on the IEEE-118 test system validates the effectiveness of the proposed methods, and a real application to a provincial power grid in China provides some useful power flow risk information for decision making. The whole FCM-based PPF scheme can be helpful for future power flow examination in power system planning and operation.

Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

Probabilistic Optimal Power Flow for Day-Ahead Dispatching of Power Systems with High-Proportion Renewable Power Sources

With the increasing proportion of uncertain power sources in the power grid; such as wind and solar power sources; the probabilistic optimal power flow (POPF) is more suitable for the steady state analysis (SSA) of power systems with high proportions of renewable power sources (PSHPRPSs). Moreover; PSHPRPSs have large uncertain power generation prediction error in day-ahead dispatching; which is accommodated by real-time dispatching and automatic generation control (AGC). In summary; this paper proposes a once-iterative probabilistic optimal power flow (OIPOPF) method for the SSA of day-ahead dispatching in PSHPRPSs. To verify the feasibility of the OIPOPF model and its solution algorithm; the OIPOPF was applied to a modified Institute of Electrical and Electronic Engineers (IEEE) 39-bus test system and modified IEEE 300-bus test system. Based on a comparison between the simulation results of the OIPOPF and AC power flow models; the OIPOPF model was found to ensure the accuracy of the power flow results and simplify the power flow model. The OIPOPF was solved using the point estimate method based on Gram–Charlier expansion; and the numerical characteristics of the line power were obtained. Compared with the simulation results of the Monte Carlo method; the point estimation method based on Gram–Charlier expansion can accurately solve the proposed OIPOPF model

Probabilistic optimal power flow of AC/DC system with multiport current flow controller

To evaluate the impact of the randomness and correlation of photovoltaic (PV) and load on AC/DC systems with a multiport current flow controller (M-CFC), this paper proposes a probabilistic optimal power flow calculation for AC/DC systems based on a nonparametric kernel density estimation. First, according to the M-CFC model, the DC power flow calculation method with M-CFC was deduced, and its influence on line loss was analyzed. Second, a nonparametric kernel density estimation with an adaptive bandwidth was used to accurately describe the probability distribution of the PV and load, and correlation samples of the PV and load were obtained by the mixed copula function. Then an optimization model that considers system loss and static security was established, and a fast nondominated sorting genetic algorithm based on the elite strategy (NSGA-II) was used to calculate the multi-objective probability optimal power flow of the AC/DC system. Finally, a case study was performed on the modified IEEE39 bus system using measured PV and load data. We verified the nonparametric kernel density estimation with an adaptive bandwidth can better adapt to random component uncertainty, and M-CFC can improve the static security of the system.

Learning-Based Probabilistic Power Flow Calculation Considering the Correlation Among Multiple Wind Farms

Wind power generation provides a new route for the sustainable development of energy. However, with the large scale integration of wind farms, the volatile wind energy and the correlation among various wind speeds bring a considerable quantity of uncertainty for the power system operation. In this paper, a probabilistic power flow (PPF) analysis model for the power system incorporating the correlation among various wind speeds is proposed. As distinct from existing studies, in this paper, we introduce the relevance vector machine (RVM) into correlation modeling of wind speeds via historical learning samples to construct bivariate joint distribution. Compared with the conventional parameter estimation methods, the proposed method has higher flexibility and computational efficiency. On this basis, the regular vine copula approach is adopted further to build the multivariate joint distribution model of wind speeds. To calculate the PPF of power system with the integration of wind power, we employ the three-point estimation method (3PEM) while the Rosenblatt Transformation technique is proposed to transform the input variables into independent variables. The effectiveness of the proposed calculation framework is examined through simulation studies, and the obtained results illustrate the advantages of the proposed method.

Arbitrary Polynomial Chaos Based Simulation of Probabilistic Power Flow Including Renewable Energies

In this paper, a method is introduced for probabilistic power flow calculations based on arbitrary polynomial chaos. For the polynomial chaos, orthogonal polynomial sets are used to represent the uncertainties of renewable power generation, and these orthogonal polynomials are generated from actual data. The aforementioned method is applied to probabilistic power flow calculations, and its applicability is confirmed in application to an actual transmission network. The calculation time and accuracy achieved using the arbitrary polynomial-chaos method are compared with those achieved using the popular Monte Carlo method. The results show that the calculation speed is 246-680 times greater than that with the direct Monte Carlo method, while the accuracy is almost same.

Risk Assessment of Multi-area Interconnected Power System under Gas Station Network Attacked

Abstract This paper mainly investigates the risk assessment of multi-area interconnected power system with probabilistic optimal power flow (POPF) for charging load of plug-in hybrid electric vehicle (PHEV) under gas station network attacked. Firstly, the PHEV charging model is developed by analyzing the change of PHEV operation mode after running out of gasoline. Secondly, in a multi-region interconnected power system, a line overload risk index is established to evaluate the impact of PHEV charging on the tie-line powers with the gas station network unavailable, and POPF considering PHEVs, wind and photovoltaic generation is employed to reduce the risk of system operation. Finally, the method is tested on IEEE 118-bus system to analyze the impacts of PHEV charging on tie-line powers and the entire system under gas station network attacked, and the economy and safety of system operation are evaluated before and after optimization.

Fast Probabilistic Voltage Control for Distribution Networks With Distributed Generation Using Polynomial Surrogates

Renewable distributed generation will be a key component of future power distribution networks. In order to control the voltage conditions for distribution networks integrated with distributed generation (DG) units, it is vital to quantify the impacts of control variables on voltage magnitudes under consumption and generation uncertainties. To do so, we need to run, for each control action, several power flow simulations for various consumption and generation realizations. This is computationally infeasible for systems with many uncertain inputs. In this work, we address this challenge by developing surrogates, or metamodels, that analytically estimate the random voltage as a function of input variables which include random parameters (consumption and generation levels) and control actions (power factors). Specifically, we propose a model reduction method for building these surrogates, which reduces the number of simulations needed for training. This method identifies and includes only the consumption and generation variables that are influential on the voltage at a given bus. Using this `reduced' surrogate, we then develop a sensitivity-based approach for probabilistic voltage control. We demonstrate the computational efficacy of the control approach on a IEEE 69-bus system with a large number of correlated input parameters. The highlights of computational efficiency in this case study include (1) accurate probabilistic power flow analysis using surrogates constructed by only 500 training simulations for a system with more than 150 random parameters, and (2) successful surrogate-based voltage control approach which only requires 150 additional simulation samples, as opposed to the conventional perturb-and-observe voltage control which needs more than 500,000 samples.

Single- and multi-objective optimization for photovoltaic distributed generators implementation in probabilistic power flow algorithm

In this study, probabilistic power flow (PPF) for radial distribution systems (RDSs) integrated with photovoltaic (PV) distributed generators (DGs) is presented. The PPF is carried out using a combined approach of cumulants generating function and Gram–Charlier expansion. To express the intermittent nature of the PV power generation and demand powers, the random probabilities for solar irradiance and load demand are considered and modeled in the PPF. The benefits of PVDGs integration into RDS can be accomplished by their optimal placement and sizing. Hence, two optimization approaches are implemented to allocate the PVDG in the RDS. The first optimization approach utilizes a single-objective function based on particle swarm optimization (PSO) to minimize the total power losses in RDSs, while the second approach uses the multi-objective PSO (MOPSO) to minimize the total power losses and voltage deviation. However, in case of MOPSO, a fuzzy logic decision making is developed to adopt a suitable solution from the optimal Pareto set according to the decision-maker preference. The developed algorithm is verified using two standard IEEE radial distribution systems: IEEE 33-bus and 69-bus. The obtained results prove the ability of the developed algorithm in solving the PPF considering the optimal PVDG allocation with low computational time.

A Data Clustering Based Probabilistic Power Flow Method for AC/VSC-MTDC

This paper investigates the role of modified clustering methods to account correlated uncertainties in the probabilistic power flow problem for alternate current/voltage source control-multiple terminal direct current (ac/VSC-MTdc). Such uncertainties are introduced by stochastic renewable generation units or variable loads. The wind farm is a type of stochastic generation units that grows dramatically in power networks. Due to the increase of penetration level of renewable generations, number of uncertainty sources is increased. Clustering methods are suitable tools for handling stochastic power system problems, because these methods provide acceptable results with less computation in comparison to other common methods such as Monte Carlo simulations. In this paper, two modified methods are used for clustering uncertainty sets. These methods include modified K-means algorithm, and modified self-organized map neural network. After clustering, the power flow of ac/VSC-MTdc is carried out for cluster centers of each method. Results of the probabilistic power flow for case study that is based on the IEEE 24-bus and IEEE 118-bus test systems are presented and compared with different clustering techniques, Monte Carlo simulation, and Latin hypercube sampling (LHS) methods. Such results show that power flow calculation with clustering methods is more accurate than LHS method and is faster than Monte Carlo simulation method.

Fast Calculation of Probabilistic Power Flow: A Model-Based Deep Learning Approach

Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to overcome the computational challenge. A deep neural network (DNN) is used to approximate the power flow calculation and is trained according to the physical power flow equations to improve its learning ability. The training process consists of several steps: 1) the branch flows are added into the objective function of the DNN as a penalty term, which improves the approximation accuracy of the DNN; 2) the gradients used in the back propagation process are simplified according to the physical characteristics of the transmission grid, which accelerates the training speed while maintaining effective guidance of the physical model; and 3) an improved initialization method for the DNN parameters is proposed to improve the convergence speed. The simulation results demonstrate the accuracy and efficiency of the proposed method in standard IEEE and utility benchmark systems.

Probabilistic Optimal Power Flow Calculation Method Based on Adaptive Diffusion Kernel Density Estimation

In order to accurately evaluate the influence of the uncertainty and correlation of photovoltaic (PV) output and load on the running state of power system, a probabilistic optimal power flow calculation method based on adaptive diffusion kernel density estimation is proposed in paper. Firstly, based on the distribution characteristics of PV output, the adaptive diffusion kernel density estimation model of PV output is constructed, which can fit the distribution of arbitrary distribution of PV power. This model can improve the local adaptability of PV output model and reflect the uncertainty and volatility of PV output more accurately. Secondly, The Kendall rank correlation coefficient and the least Euclidean distance are used as correlation measure and index of fitting to select the optimal Copula function, and the joint probability distribution model of PV output and load is constructed. After extracting the correlated PV output and load samples, a probabilistic optimal power flow calculation method considering the correlation of PV output and load is proposed. Finally, simulation studies are conducted with the measured data of a PV power plant of China and the IEEE 30-bus power system. The results show that considering the correlation between PV output and load can improve the accuracy of probabilistic optimal power flow calculation and effectively reduce the power generation cost of power system.

Probabilistic power flow with topology changes based on deep neural network

The uncertainty of power systems is rapidly increasing with the continuing development of renewable energy. Probabilistic power flow (PPF) is an effective tool for addressing these uncertainties. However, the high computational burden is a major bottleneck for the practical application of PPF. This paper proposes an efficient method for solving the PPF based on deep neural network (DNN). Stacked denoising auto-encoders (SDAE) is selected to extract the nonlinear features of the power flow model with discrete topology status. The following two aspects are investigated to improve the DNN performance: (1) construction of the feature vector that effectively characterizes the renewable energy, load, and topology and (2) knowledge transfer of DNN parameters to improve the training efficiency of the DNN for evolutionary scenarios. After training, the power flow solutions of all samples generated by Monte-Carlo simulation (MCS) can be directly projected through the DNN with high accuracy, rapid speed and low computational burden. Finally, the effectiveness of the proposed method is verified on the modified IEEE 39-bus and 118-bus systems.