Probabilistic Load Flow Algorithm Research Articles

Novel risk index integrating practical operation limits enhances probabilistic contingency ranking for large-scale photovoltaic plant planning

This research addresses the pressing need for heightened grid security amid increasing uncertainties in photovoltaic PV generation. The research problem lies in the limitations of conventional contingency analysis metrics, failing to adequately consider both contingency occurrences and uncertainties inherent in PV generation. In response, a comprehensive algorithm is proposed that introduces a novel severity function framework, enhancing traditional contingency ranking metrics. This approach incorporates grid remedial actions and refines line and bus voltage classification by considering available correction time, aiming to offer a more robust security assessment. Motivated by the imperative to address uncertainty in PV generation, the proposed work builds on established analysis tools. A probabilistic load flow algorithm manages PV generation uncertainties, utilizing historical data for contingency incidence uncertainty. Additionally, a probabilistic model for PV plants integrates historical solar data, deriving hourly probability density functions to meet grid code requirements, including reactive power considerations. The justification for this work lies in the algorithm's demonstrated efficacy, validated on the IEEE 14-bus network. Results highlight its ability to identify risks associated with line overloading and bus voltage breaches. Comparative evaluations underscore proper coupling buses for security, favoring distributed capacity to mitigate line overloading risks. The study's key results emphasize voltage risk amplification with reactive power omission, stressing the significance of compensation strategies. This research addresses a critical problem, presenting a comprehensive algorithmic solution to enhance grid security amidst uncertainties in PV integration. Findings offer valuable insights for strategically interaction between large scale PV plants and electrical grid, contributing to an improved grid security paradigm in a dynamic and uncertain energy model.

Predictability and Voltage Profile Improvement of Distribution Networks with a D-STATCOM Model

This paper presents a modeling for D-STATCOM device into Monte Carlo probabilistic load flow algorithm. The model is used to improve the predictability and voltage profile of distribution networks. In this model, the D-STATCOM’s bus is represented as a special generator bus which injects reactive power only. The injected reactive power of D-STATCOM is updated during the iterative process to maintain the voltage magnitude at the specified value. The model can be easily implemented in the original PLF code without deeply modifications. The probabilistic load flow (PLF) with D-STATCOM model is validated using various standard IEEE tests systems; 33-bus, and 69-bus systems. The PLF algorithm with DSTATCOM model has been evaluated based on MATLAB package. However, the obtained results prove the effectiveness of D-STATCOM implementation in the test systems regarding to predictability and voltage profile issues. Moreover, the standard deviation of the systems is decreased.

Probabilistic Load Flow Algorithm of Distribution Networks with Distributed Generators and Electric Vehicles Integration

Probabilistic Load Flow (PLF) calculations are important tools for analysis of the steady-state operation of electrical energy networks, especially for electrical energy distribution networks with large-scale distributed generators (DGs) and electric vehicle (EV) integration. Traditional PLF has used the Cumulant Method (CM) and Latin Hypercube Sampling (LHS) method. However, traditional CM requires that each input variable be independent of one another, and the Cholesky decomposition adopted by the traditional LHS has limitations in that it is only applicable for positive definite matrices. To solve these problems, taking into account the Q-MCS theory of LHS, this paper proposes a CM PLF algorithm based on improved LHS (ILHS-CM). The cumulants of the input variables are obtained based on sampling results. The probability distribution of the output variables is obtained according to the Gram-Charlier series expansion. Moreover, DGs, such as wind turbines, photovoltaic (PV) arrays, and EVs integrated into the electrical energy distribution networks are comprehensively considered, including correlation analysis and dynamic load flow analysis for EV-coordinated charging. Four scenarios are analyzed based on the IEEE-30 node network, including with/without DGs and EVs, error analysis and performance evaluation of the proposed algorithm, correlation analysis of DGs and EVs, and dynamic load flow analysis with EV integration. The results presented in this paper demonstrate the effectiveness, accuracy, and practicability of the proposed algorithm.

Probabilistic direct load flow algorithm for unbalanced distribution networks considering uncertainties of PV and load

The increasing penetration of distributed generations such as rooftop photovoltaics (PVs) brings about great challenges to distribution network planning and operation, due to the great uncertainty and intermittence. Although many probabilistic load flow (PLF) approaches have been proposed to handle uncertainties in power systems, PLFs for unbalanced distribution networks with superior computational performance are still under demand. Therefore, this study presents a novel PLF algorithm for unbalanced distribution networks considering the uncertainties introduced by PVs and loads. Taking PVs and loads as the random inputs while three-phase voltages and network loss as the random outputs, the proposed PLF integrates the cumulant method and the Gram–Charlier expansion with the advanced direct load flow (DLF) approach to effectively address the unbalanced distribution PLF problems. Finally, the effectiveness and superior performance in terms of efficiency, accuracy, and robustness of the proposed PLF algorithm are verified by detailed simulations and compared with the Monte–Carlo Simulation method on a real Australian unbalanced distribution network.

Direct Probabilistic Load Flow in Radial Distribution Systems Including Wind Farms: An Approach Based on Data Clustering

The ongoing study aims to establish a direct probabilistic load flow (PLF) for the analysis of wind integrated radial distribution systems. Because of the stochastic output power of wind farms, it is very important to find a method which can reduce the calculation burden significantly, without having compromising the accuracy of results. In the proposed approach, a K-means based data clustering algorithm is employed, in which all data points are bunched into desired clusters. In this regard, probable agents are selected to run the PLF algorithm. The clustered data are used to employ the Monte Carlo simulation (MCS) method. In this paper, the analysis is performed in terms of simulation run-time. Also, this research follows a two-fold aim. In the first stage, the superiority of data clustering-based MCS over the unsorted data MCS is demonstrated properly. Moreover, the impact of data clustering-based MCS and unsorted data-based MCS is investigated using an indirect probabilistic forward/backward sweep (PFBS) method. Thus, in the second stage, the simulation run-time comparison is carried out rigorously between the proposed direct PLF and the indirect PFBS method to examine the computational burden effects. Simulation results are exhibited on the IEEE 33-bus and 69-bus radial distribution systems.

Dependent Discrete Convolution Based Probabilistic Load Flow for the Active Distribution System

Active distribution system (ADS) plays a significant role in enabling the integration of distributed generation. The stochastic nature of renewable energy resources injects the complex uncertainties of power flow into ADS. This paper proposes a discrete convolution methodology for probabilistic load flow (PLF) of ADS considering correlated uncertainties. First, the uncertainties of load and renewable energy are modeled using the distribution of the corresponding forecasting error, and the correlation is formulated using a Copula function. A novel reactive power-embedded DC power flow model with high accuracy in both branch flow and node voltage is introduced into ADS. Finally, the distribution of power flow is calculated using dependent discrete convolution, which is capable of handling nonanalytical probability distribution functions. In addition, a reduced dimension approximation method is proposed to further reduce the computational burden. The proposed PLF algorithm is tested on the IEEE 33-nodes system and 123-nodes system, and the results show that the proposed methodology requires less computation and produces higher accuracy compared with current methods.

Capacity allocation of hybrid solar-wind energy system based on discrete probabilistic method

Complementary renewable energies like wind and solar power may be more sufficient to satisfy reliability requirements. This paper proposes a quantitative capacity allocation method of a hybrid wind and solar energy system. First, discrete probability distributions are established to model the random factors including the volatility of power outputs and the failure of components. Then a multiobjective optimization model is formulated with objectives of minimization of the total investment, the nodal voltages violating limits probability, and power supply inadequacy probability. For the purpose of fast probability computing with a satisfactory precision degree, an innovative probabilistic load flow algorithm is introduced, which deals with means and increments of random variables separately and uses cumulants as well as Gram--Charlier series to obtain probabilistic distributions of state variables. A modified parallel elitist nondominated sorting genetic algorithm II is used to search the Pareto optimal configuration solutions.

Power system reliability assessment suitable for a deregulated system via the method of cumulants

In this paper a technique for calculation of overall power system reliability and its corresponding cost, is presented. The technique has been developed for a de-regulated system where plant loading is done based on price offer or ‘bid’. The main variables of the system, bus load and generating plant availability, are represented by random variables. System reliability is calculated using a probabilistic load flow algorithm and its corresponding cost is calculated using a probabilistic production costing algorithm. The technique allows the power system planner to assess different loading strategies to achieve a required reliability level.