Probabilistic Power Flow Method Research Articles

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.

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.

The Effect of Power Flow Entropy on Available Load Supply Capacity under Stochastic Scenarios with Different Control Coefficients of UPFC

With the sharp increase in fluctuant sources in power systems, the deterministic power flow (DPF) calculation has been unable to meet the demands of practical applications; thus, the probabilistic method becomes indispensable for the reliable and stable operation of power systems. This paper adopts the probabilistic power flow (PPF) method, which is a Monte Carlo simulation (MCS) based on the Latin hypercube sampling (LHS) method, to analyze the uncertainties of power systems. Specifically, the available load supply capability (ALSC) based on the branch loading rate is used to analyze the safety margin of the whole system, while the improved power flow entropy is introduced to quantify the equilibrium of power flow distribution. The repeated power flow (RPF) calculation is combined with the PPF method, and, hence, the probabilistic repeated power flow (PRPF) method is proposed to calculate the power flow entropy at the initial state and the probabilistic ALSC. To flexibly control the power flow, the unified power flow controller (UPFC) is added to the AC power system. The different control coefficients of UPFC are set to reveal the relationship between power flow entropy and available load supply capability under the stochastic scenarios. Finally, the modified IEEE14 test system is used to study the adjustment abilities of UPFC. With consideration of uncertainties in the test case, the positive effect of UPFC on the power flow entropy and the probabilistic ALSC under stochastic scenarios is deeply studied.

Probabilistic Power Flow Method for Hybrid AC/DC Grids Considering Correlation among Uncertainty Variables

For a new power system using high-penetration renewable energy, the traditional deterministic power flow analysis method cannot accurately represent the stochastic characteristics of each state variable. The aggregation of renewable energy with different meteorological characteristics in the AC/DC interconnected grid significantly increases the difficulty of establishing a steady-state model. Therefore, this study proposes an improved Latin hypercube sampling algorithm using the van der Waerden scores and diffusion kernel density estimation to overcome the limitations of a priori assumption on probability distributions in uncertainty modeling and to retain the correlations among random variables in the sampling data. Interconnected grids are constructed with IEEE 9-bus and IEEE 14-bus and modified with IEEE 57-bus to describe common application cases of aggregated renewable energy. On this basis, the approximation errors of the proposed probabilistic power flow algorithm to the statistical characteristics of the power parameters are evaluated by setting the Nataf algorithm and the Latin hypercube algorithm using adaptive kernel density estimation as the control group. The results show that the improved Latin hypercube sampling algorithm can exhibit high computational accuracy and strong adaptability, both in severe operating scenarios with large amplitude of load fluctuations and with nonlinear power balance equations incorporating high dimensional random variables.

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 harmonic forecasting of the distribution system considering time-varying uncertainties of the distributed energy resources and electrical loads

Distributed energy resources (DER) and electrical loads have grown rapidly in response to concerns about energy sustainability and rising energy demand. However, to realize energy conversion, a large number of power electronic converters are used, resulting in serious harmonic issues in the distribution system. Meanwhile, the random and intermittent characteristics of DER and electrical load bring strong uncertainties to the distribution system. It not only affects the safe and stable operation but also leads to the new stochastic characteristics of harmonics. The study proposes a novel probabilistic harmonic power flow method that takes into account DER and electrical load uncertainties in order to effectively forecast and analyze the uncertain harmonic distortion. Firstly, the time-varying states with stochastic characteristics are determined to represent the uncertainties of electrical load, distributed photovoltaic power, and distributed wind power. The proposed method adapts to time-varying uncertain variable analysis while requiring less computation. Then, a novel constant-weight point estimate method based on the Nataf transformation is proposed to obtain the statistical features of the uncertainties. By simplifying the approximation process, the uncertain variable can be estimated more rapidly and effectively. Moreover, the interaction between multiple uncertain variables is also considered with the correlation coefficient matrix, which can analyze the harmonic coupling interaction in the system. Finally, the probabilistic harmonic power flow is developed considering the time-varying stochastic characteristic of uncertainties. On this basis, the proposed method can be used to forecast the harmonic distortion and also analyze the daily or seasonal statistical features. The proposed probabilistic harmonic power flow method's effectiveness is validated using real-field measured data.

풍력 발전과 부하 사이의 상관성을 고려한 확률론적 전력 조류 해석 기법 제안

Due to the increase of the renewable energy and variation of the distributed sources, the power system experience more variability and uncertainty than before. In this paper, we propose an framework for steady-state analysis of power systems using the joint probabilistic information about the wind speeds and loads. Vine copula is employed to capture the the complex dependencies between wind speeds and loads in the multiple regions. In addition, we investigate probabilistic modeling based on the parametric estimation and Wasserstein distance to depict the marginal distribution of wind speed and load. The effectiveness of the proposed method was tested on an IEEE 39-bus system using Python and MATLAB. From the simulation, it was found that the probabilistic power flow method (PPF) that combined vine copula sampling outperforms the deterministic approach and the PPF with random simple sampling in terms of the quantitative risk assessment in the power system.

Comparison of solving probabilistic optimal power flow methods in the presence of wind and solar sources

Power system control and operation studies have been experienced essential changes due to increasing the penetration of uncertain renewable energy resources. One of the most critical issues in this regard is the optimal power flow (OPF). As a result, the deterministic methods do not have the capability of different modeling uncertainties raised in new power systems, and there is a need to investigate the effective models in this regard. This paper focuses on probabilistic optimal power flow (POPF) methods applied to power systems with uncertain wind and Photovoltaic power generations. In this paper, the Monte Carlo simulation (MCS) and analytical methods such as the three-point estimation method (3PEM), unscented transformation (UT), and Interior-Point method (IPM) are applied to solve the probabilistic optimal power flow problem. MCS has been widely applied as a framework to assess the ability of analytical methods. The mentioned techniques are applied to a sample case study extracted from the IEEE 300-bus system. The main contribution of this work is the comparison of analytical methods concluding 3PEM, UT, and IPM, and with MCS as well. The obtained results on the studied networks by the suggested techniques show that in the 3PEM, due to the limited points, the optimal solution is achieved in less calculation time than the other methods. From another perspective, the voltage changes at the buses would be more stable in the IPM. Also, this method is much faster than the MCS method in terms of the convergence rate. To show the effectiveness of the mentioned methods, this paper presents probabilistic load flow method based on the statistical methods to deal with fluctuations because of large-scale renewable energy integration. The proposed methods are validated on the improved industrial 85–bus system of Kermanshah region (in the west of Iran) by adding solar and wind farms.

Collaborative Management of Multi-Type Energy for Optimal Control of Voltage and Loss of Distribution Systems with DGs and SVCs

Aiming at the deficiencies and shortcomings of traditional reactive power compensation devices in controlling and improving voltage quality, a bilevel programming model for the coordinated optimal allocation of active and reactive power capacity of photovoltaic power generation systems, wind-driven generators, shunt capacitors and static var compensators is established based on chance-constrained programming. In the optimization model, the randomness and intermittence of the output power of the distributed generation and the reactive power regulation ability of the distributed generation are considered. The correlation of illumination, wind speed and load fluctuation is considered and affected by seasonal variation. Latin hypercube sampling method is used to deal with the correlation of random variables. Monte Carlo probabilistic power flow method is used to calculate the power flow of distribution network with intermittent distributed generation systems. The location and capacity of active and reactive power sources in outer programming are optimized by adaptive artificial fish swarm algorithm, and the allocation scheme of active and reactive power sources determined by outer programming is optimized by inner adaptive artificial fish swarm algorithm. The two-layer nested adaptive artificial fish swarm algorithm is used to solve the optimal allocation problem constructed in this paper, and the optimal allocation scheme of active and reactive power supply capacity is determined. Taking IEEE33 distribution system as an example, the feasibility and applicability of the proposed model and algorithm are verified.

Day-Ahead Optimal Dispatch for Active Distribution Network Considering Probability Model of Controllable Distributed Generation

In this paper, the probabilistic model of the controllable distributed generation in active distribution network is developed and applied to the daily stochastic optimal dispatch. The probabilistic characteristics of photovoltaic power generation system with active control capability are explored, and the relationship between the reference value of active power and its cumulative distribution function and mean value is obtained. The active power probability model of wind power generation system is improved according to the actual wind speed power curve. By fully utilizing the inverter capacity and coordinating active power, the reactive power of distributed generation is actively controlled under the constraint of power factor. Then considering the chance constraints, a daily optimal scheduling model for active distribution network with the goal of minimizing the operating cost of distribution network is developed, and the constraints that can calculate the charge and discharge times of the energy storage system are designed. The chance constrained programming is solved by the heuristic method, and the deterministic optimization steps are solved by the second-order cone programming method, respectively. The probabilistic power flow method based on stochastic response surface method is utilized to test chance constraints. Finally, the modified IEEE33 node distribution system example shows that the obtained models and algorithms are correct and can meet the requirements of safe and economic operation.

Advanced Probabilistic Power Flow Method Using Vine Copulas for Wind Power Capacity Expansion

As the use of renewable energy is continuously increasing, power systems are currently exposed to greater uncertainty and variability, which can lead to severe power system stability issues. Therefore, a power system analysis tool should be devised to assess the impact of renewable energy integration along with an accurate modeling of their stochastic characteristics. In this study, an advanced probabilistic power flow (PPF) method is developed using vine copulas that captures the complex dependency of the stochastic wind power generated from multiple wind sites. The proposed method also involves the use of a function for selecting the probability models of wind speeds by regions in a sophisticated manner. The effectiveness of the proposed method is tested on an IEEE bus system as well as, on a South Korean power system with thousands of buses and transmission lines using PSS/E with Python API. The simulations demonstrate that the proposed method can more accurately evaluate the power system risks with the sophisticated modeling of wind power in multiple sites as compared to the deterministic approach or the PPF with independent sampling.

Probabilistic Assessment of Power Systems with Renewable Energy Sources based on an Improved Analytical Approach

The increasing penetration of renewable energy sources has introduced great uncertainties and challenges into computation and analysis of electric power systems. To deal with uncertainties, probabilistic approaches need to be used. In this paper, we propose a new framework for probabilistic assessment of power systems taking into account uncertainties from input random variables such as load demands and renewable energy sources. It is based on the cumulant-based Probabilistic Power Flow (PPF) in combination with an improved clustering technique. The improved clustering technique is also developed in this study by making use of Principal Component Analysis (PCA) and Particle Swarm Optimization (PSO) to reduce the range of variation in the input data, thus increasing the accuracy of the traditional cumulant-based PPF (TCPPF) method. In addition, thanks to adopting PCA for dimensionality reduction, the improved clustering technique can be effectively dealt with a large number of input random variables so that the proposed framework for probabilistic assessment can be applied for large power systems. The IEEE-118 bus test system is modified by adding five wind and eight solar photovoltaic power plants to examine the proposed method. Uncertainties from input random variables are represented by appropriate probabilistic models. Extensive testing on the test system indicates good performance of the proposed approach in comparison to the traditional cumulant-based PPF and Monte Carlo simulation. The IEEE-118 bus test system is modified by adding five wind and eight solar photovoltaic power plants to examine the proposed method. Extensive testing on the test system, using Matlab (R2015a) on an Intel Core i5 CPU 2.53 GHz/4.00 GB RAM PC, indicates good performance of the proposed approach (PPPF) in comparison to the TCPPF and Monte Carlo simulation (MCS): In terms of computation time, PPPF needs 4.54 seconds, while TCPPF and MCS require 2.63 and 251 seconds, respectively; ARMS errors are calculated for methods using benchmark MCS and their values clearly demonstrate the higher accuracy of PPPF in estimating probability distributions compared to TCPPF, i.e., the maximum (Max) and mean (Mean) values of ARMS errors of all output random variables are: ARMSPPPFmax = 0.11%, ARMSTCPPFmax = 0.55%, and ARMSPPPFmean = 0.06%, ARMSTCPPFmean = 0.35%.

Hybrid‐adaptive differential evolution with decay function applied to transmission network expansion planning with renewable energy resources generation

As the country implements the reform of the electricity market and a large number of renewable energy resources (RES) are connected to the grid, the model and algorithm of traditional transmission network expansion planning (TNEP) are not suitable. A model of TNEP is built, in which the investment cost of new lines and the market-based annual congestion surplus are selected as objective functions. A probabilistic DC power flow method is used to describe uncertainties of RES generation. A new algorithm, Hybrid-Adaptive Differential Evolution with Decay Function (HyDE-DF), is applied to solve the model of TNEP for the first time. Analysis and comparison in the IEEE 18-bus system and the 52-bus system in an area of Sichuan Province prove the feasibility, effectivity, and practicability of the model and solving algorithm. Some comparisons are performed using other variants of Differential Evolution (DE) and a swarm intelligence optimization algorithm to demonstrate the performance superiority of the new algorithm and new application. It is worth mentioning that in the 52-bus system of an area of Sichuan Province, the investment cost obtained by the new algorithm is at least one or two orders of magnitude lower than other algorithms.

Probabilistic impact of wind energy integration on distribution transformers

In traditional power grid, the direction of power flow of transformers is usually fixed in one direction. However, with the integration of the renewable energy sources, such as wind farms, the power flow in the grid becomes fluctuating and uncertain, which may cause the reverse power flow passing the transformer. For example, excessive reverse power flow may lead to the increase of transformer power loss and challenge the thermal stability of the transformer. This paper investigates the impact of wind energy integration on the existing power system infrastructure, such as distribution transformers. Probabilistic power flow (PPF) method is used for the analysis. Firstly, a sampling method based on Halton sequence is applied for PPF calculation. Then, to ensure the accuracy of probabilistic power flow calculation, the correlation between wind speeds of different wind farms is considered. A 30-Bus system is used for the probabilistic analysis of the transformer reverse power flow with different level of wind penetration. The results show that the reverse power flow of transformer may occur before 100% wind penetration is achieved. The higher the total wind power capacity in the grid causes the greater probability of transformer reverse power flow. Also, the location of wind farms will also affect the probability of transformer reverse power flow.

A clustering-based analytical method for hybrid probabilistic and interval power flow

Various probabilistic power flow (PPF) and interval power flow (IPF) methods have been developed to deal with random and interval variables in power systems, respectively. However, the co-existence of these two types of variables poses great challenges to PPF and IPF calculations. To cope with this issue, we propose a clustering-based analytical method for hybrid probabilistic and interval power flow (HPIPF) calculation. The uncertainties of load demands and wind power outputs are treated as random and interval variables, respectively. The remarkable feature of this method is to propose an assumption called the unified optimal scenarios of wind power. On this basis, HPIPF calculation is transformed into IPF and PPF calculations, which can be solved by the optimal-scenarios method and the cumulant method, respectively. The accuracy and efficiency of the proposed method are validated on the IEEE 14-bus and 118-bus test systems through the comparisons with the double-layer Monte-Carlo simulation. Furthermore, the impacts of correlated interval variables are analyzed. The simulations indicate that the estimations of output variables may be conservative without considering the correlations of interval variables.

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.

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

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

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 Power Flow for Hybrid AC/DC Grids with Ninth-Order Polynomial Normal Transformation and Inherited Latin Hypercube Sampling

This paper proposes a new probabilistic power flow method for the hybrid AC/VSC-MTDC (Voltage Source Control-Multiple Terminal Direct Current) grids, which is based on the combination of ninth-order polynomial normal transformation (NPNT) and inherited Latin hypercube sampling (ILHS) techniques. NPNT is utilized to directly handle historical records of uncertain sources to build the accurate probability model of random inputs, and ILHS is adopted to propagate the randomness from inputs to target outputs. Regardless of whether the underlying probability distribution is known or unknown, the proposed method has the ability to adaptively evaluate the sample size according to a specific operational scenario of the power systems, thus achieving a good balance between computational accuracy and speed. Meanwhile, the frequency histograms, probability distributions, and some more statistics of the results can be accurately and efficiently estimated as well. The modified IEEE 118-bus system, together with the realistic data of wind speeds and diverse consumer behaviors following irregular distributions, is used to demonstrate the effectiveness and superiority of the proposed method.

A probabilistic power flow calculation method considering the uncertainty of the static frequency characteristic

In a power system, power generation and load have frequency response characteristics, which randomly fluctuate with changes in operating status. This study investigates a probabilistic power flow method that considers the unit and load uncertainty of the static frequency characteristic. Firstly, a calculation model is established on the basis of the characteristics of the frequency modulation performance of the unit and load. Then a calculation method is developed using the concept of dynamic power flow in order to determine the probability distribution of the active power flow of each line under the occurrence of a fault in the system. In the method, Monte Carlo sampling with the semi-invariant method is applied for analysis and calculation. The IEEE-30-buses system is taken as an example to analyze the impact of different responses of units on the power flow distribution of various branches. The method discussed herein is compared with the Monte Carlo simulation method to verify its effectiveness.