Optimal Power Flow Calculation Research Articles

Optimal Power Flow Calculation Based on Improved Crossover Algorithm

Abstract Aiming at the optimization problem of power flow distribution in power system, this paper puts forward a method for calculating the optimal power flow of power network based on the improved crisscross algorithm. The fast convergence crisscross optimization algorithm (FCSO) is based on the traditional crisscross optimization algorithm (CSO) to improve the efficiency and accuracy of solving the Optimal Power Flow, OPF) problem. Based on the original double crossover operator, the improved algorithm puts forward a brand-new operator-central crossover operator, which alternates with transverse crossover operator according to certain rules, In order to improve the quality of single search and accelerate convergence, each individual in the population performs crossover operation with the current optimal individual in turn, and then performs competition operator to selectively approach the current global optimal individual. Finally, combined with experimental verification, the optimal power flow calculation of reactive power optimization based on FSCO has obvious practical effects in improving network voltage quality and reducing line loss, The average voltage increase ratio of 220kV bus and 110kV bus is 0.676% and 0.855% respectively, and the loss reduction rate reaches 3.51%, Compared with CSO, the convergence and calculation speed of FSCO proposed in this paper is faster, the convergence curve is smoother, and the average time consumption is increased to 59.53% compared with CSO, In the case of obtaining the same precision solution, the optimization time is obviously shortened, the timeliness of the optimal solution in regulation operation is effectively improved, and the problem of reactive power optimization in power system can be well solved.

A Fully Analytical Approach for the Real-Time Dynamic Reliability Evaluation of Composite Power Systems with Renewable Energy Sources

Renewable energy sources (RES) have strong uncertainties, which significantly increase the risks of power imbalance and load shedding in composite power systems. It is thus necessary to evaluate the operational reliability for guiding economic dispatch and reducing the risks. Current methods cannot meet the requirement for the operational timeliness of reliability evaluations due to the high computational complexity of the optimal power flow (OPF) calculations of massive contingencies. This paper proposes a fully analytical approach to construct fast-to-run analytical functions of reliability indices and avoid reassessments when the load and RES change. The approach consists of uniform design (UD)-based contingency screening and a modified stochastic response surface method (mSRSM). The contingency screening method is used to select critical contingencies while considering the uncertainties. The mSRSM is used to construct the analytical functions of the load shedding to the load and RES generation for the selected contingencies. An analytical function of a smooth virtual variable that maps to the load shedding is established in such a way that, when the load and RES vary, the reliability can be assessed within a very short time rather than using laborious OPF calculations. Case studies illustrate the excellent performance of the proposed method for real-time reliability evaluation.

Optimal Placement of HVDC-VSC in AC System Using Self-Adaptive Bonobo Optimizer to Solve Optimal Power Flows: A Case Study of the Algerian Electrical Network

Modern electrical power networks make extensive use of high voltage direct current transmission systems based on voltage source converters due to their advantages in terms of both cost and flexibility. Moreover, incorporating a direct current link adds more complexity to the optimal power flow computation. This paper presents a new meta-heuristic technique, named self-adaptive bonobo optimizer, which is an improved version of bonobo optimizer. It aims to solve the optimal power flow for alternating current power systems and hybrid systems AC/DC, to find the optimal location of the high voltage direct current line in the network, with a view to minimize the total generation costs and the total active power transmission losses. The self-adaptive bonobo optimizer was tested on the IEEE 30-bus system, and the large-scale Algerian 114-bus electric network. The obtained results were assessed and contrasted with those previously published in the literature in order to demonstrate the effectiveness and potential of the suggested strategy.

Optimal power flow in hybrid AC-DC systems considering N-k security constraints in the preventive-corrective control stage

The optimal power flow methods for AC-DC systems containing VSC-HVDC generally only consider the economy during normal operation, overlooking the distribution of line transmission power in fault conditions. As a result, lines that continue to operate after a fault may experience overloading or operate at full capacity. Thus, a method for optimal power flow calculation is proposed that incorporates N-k security constraints in the preventive-corrective control stage for secure and economic operation of hybrid AC-DC systems. This method ensures that the line transmission power in the system meets the limits in the normal, short-term fault, and long-term fault states. In addition to the optimal power flow in the normal state, the method incorporates the system's imbalance as an indicator to evaluate system resilience. It combines this indicator with the economic, network loss, and performance metrics of the system, forming a two-stage bi-level multi-objective optimization model. Furthermore, to address the curse of dimensionality in anticipating system fault sets, a method for generating the anticipated fault set using non-sequential Monte Carlo simulation is proposed, along with a fault scenario search approach based on robust thinking to identify the most severe faults. Finally, the traditional IEEE 30-bus system was improved, and simulation verification was conducted using examples of an AC/DC system with a three-terminal DC network and a wind-solar-storage hybrid AC/DC system with a three-terminal DC network. The simulation results indicate that the proposed optimal power flow method considering the preventive-corrective control stage with N-k security constraints can effectively enhance system resilience. Furthermore, it improves the economic efficiency while ensuring the secure operation of the system.

Dynamic Calculation Method for Zonal Carbon Emissions in Power Systems Based on the Theory of Production Simulation and Carbon Emission Flow Theory

Power systems are the main source of carbon emissions. Currently, coordinated operation strategies of the source–grid–load–storage model considering carbon emissions is primarily expanded from the generation side. For practical power systems, where multiple types of generating units coexist at a single node, it is difficult to develop unit combination strategies that simultaneously consider carbon emission factors and power flow constraints. Therefore, a new power flow calculation method based on connectivity matrix theory was proposed, aiming to address the issues of existing approaches that are too coarse and unable to accurately represent the operating states of multiple units under each node. Furthermore, a new method for dynamic calculation of regional carbon emission based on connectivity matrix and carbon emissions flow was introduced to improve the accuracy of carbon emission measurements. Firstly, a simulation model for a coordinated optimization operation based on the minimum system cost for the source–grid–load was established and an optimal flow calculation method using a connectivity matrix was introduced. Second, a dynamic carbon emission calculation method, considering electricity sources, was developed by combining the results of the optimal power flow calculation with carbon emission flow theory. Finally, the effectiveness of the approach in this article was verified by the IEEE 14-bus system example and a provincial power grid, ensuring strict adherence to the conservation principle of carbon emissions between the supply and demand sides and satisfying power flow constraints.

Optimal power flow method with consideration of uncertainty sources of renewable energy and demand response

Optimal power flow (OPF) calculation methods are important for the power system operation and mainly focus on the deterministic power flow calculation, neglecting the impact of demand response on online security calculation of power systems with renewable energy sources. Therefore, this paper proposes an OPF calculation method that considers the uncertainties of wind power, photovoltaic (PV) power generation and demand-side response. Firstly, the research focuses on the renewable energy grid, considering the uncertainties of wind power and PV power generation, and establishes uncertainty models for wind power and PV output. Secondly, based on cloud model theory, an uncertainty model for demand response is established. According to the established models, an efficient OPF model is constructed with a linearized submodels considering multiple uncertainties. By testing on the IEEE 30-bus system as a typical example, we found the effectiveness and superiority of the proposed OPF calculation method can benefit the power system economic operation and demand side resource utilization.

Optimal Power Flow Calculation Based on SplitNN-DNN

Abstract Optimal power flow computation in power systems is an important aspect to ensure the smooth operation of power grids, but there are some challenges in terms of computing speed and data privacy protection in traditional methods. To address these issues, this study proposes a new method based on SplitNN-DNN. Firstly, we use a deep neural network to design a model that directly maps load data to voltage results, thereby improving computational efficiency. Second, we introduce a longitudinal federated learning technique to enable model training without data breaches. Finally, we conducted validation experiments on IEEE 118 and IEEE 300 node systems, and the results show that this approach not only protects data privacy, but also approaches the traditional centralized computation methods in performance, and has potential for practical applications.

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.

On the operation and implications of grid-interactive renewable energy communities

The increasing installations of photovoltaic systems, electric vehicle chargers, heat pumps, and battery storage systems challenge distribution system operators to prevent critical grid operations. Nonetheless, flexibility potential from customer-owned assets remains untapped due to lacking federated coordination and incentives. In Europe, emerging renewable energy communities can address this challenge by facilitating collective optimal operation of flexible assets and providing grid services. This paper presents an approach for renewable energy communities to offer participants’ flexibility through grid-interactive operations. Distribution system operators then based on optimal power flow calculations request flexibility use to prevent voltage violations, transformer overloads, and line overloads. A case study with simulations for a future rural low-voltage grid is conducted. The results show that, compared to business-as-usual operations or renewable energy communities with fixed import and export limits, the grid-interactive approach ensures non-critical grid operations cost-efficiently and reduces curtailment by 60% to 90%, down to 1.1% of total generation. By providing both upward and downward flexibility and aligning with distribution system operators’ requirements, grid-interactive renewable energy communities can be key in enhancing the efficient use and stability of distribution grids.

Optimal power flow calculation method for regional integrated energy system based on double-layer optimization

In this paper, a two-layer optimization calculation method is proposed to improve the practical application efficiency of the integrated energy system and to improve the different problems of power flow calculation. Firstly, the power flow model is constructed and the optimization function is established based on indicators such as economy and environmental protection. The two-layer optimization method is proposed by combining the quadratic programming method and the particle swarm algorithm. Then, the obtained operating conditions of each energy equipment are used as the input of the power flow. The processing of each device and the energy flow of the power flow network are calculated and the effectiveness of the algorithm is verified by MATLAB power analysis.

Simulation of flow based optimal activation of reserves in regional balancing markets

The objective of this paper is to introduce an approach for enabling optimal activation of balancing energy resources within a regional balancing market. In order to take into account the constraints from the transmission network, the paper proposes a modified technique for optimal power flow calculation. This novel approach results in a more effective usage of transmission network capacities during reserve activation on a regional level compared to the conventional Common Merit Order List (CMOL) approach, which only considers the available cross-zonal transmission capacity (CZC) and disregards the physical power flows. The paper provides details on a procedure that includes simulation of electricity markets, as well as simulation on imbalances in the system. The methodology is used for evaluating the proposed approach on an IEEE test system comprising of three zones. The paper shows a significant reduction of balancing costs by implementation of regional balancing market it also investigates and shows the impact of the increased RES penetration to the amount of needed balancing energy in the system.

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.

A Physics-Guided Graph Convolution Neural Network for Optimal Power Flow

The data-driven method with strong approximation capabilities and high computational efficiency provides a promising tool for optimal power flow (OPF) calculation with stochastic renewable energy. However, the topology change dramatically increases the learning difficulties and the demand for learning samples. In this work, we propose a physics-guided graph convolution neural network (GCNN) for OPF calculation with consideration of varying topologies, including the physics-guided graph convolution kernel, feature construction, and loss function formulation. Specifically, a physics-embedded graph convolution kernel is derived by aggregating the features from local neighborhoods utilizing the nodal OPF model formulation. An iterative feature construction method is also developed that encodes both the physical feature and practical constraints into the node vector. Finally, a correlative learning loss function to optimize the unbalanced power injection is developed. Extensive numerical results carried out on various IEEE test systems show that the prediction accuracy of OPF using the proposed method under varying topology changes can be improved by an average of 13.30% and up to 32.63% compared with state-of-the-art methods.

A Lagrange-Multiplier-Based Reliability Assessment for Power Systems Considering Topology and Injection Uncertainties

With the expansion of power grids and the growth of renewable energy generation, more uncertainties of topology (e.g. components outages) and injection (e.g. renewable energy outputs variations) need to be analyzed. As a result, large numbers of system states have to be evaluated by optimal power flow (OPF) and this brings a significant challenge to the efficiency of reliability assessment. To address this, a Lagrange-multiplier-based reliability assessment method (LM-T&I) is proposed to accelerate the evaluation of system states. The Lagrange-multiplier-based function is constructed to obtain the optimal load shedding of topology changes and injection variations, avoiding time-consuming OPF computations. Moreover, combined with the impact-increment-based state enumeration method (IISE), the computational efficiency can be further improved. Case studies are conducted on the RTS-79 and IEEE 118-bus systems. The scalability of the LM-T&I method is verified on the practical Brazilian system. The results demonstrate that the LM-T&I method has a superior performance on the reliability assessment compared with traditional methods.

On the robustness of machine-learnt proxies for security constrained optimal power flow solvers

In this paper, we focus on the robustness of machine learning based proxies used to speed up, alone or jointly with state-of-the-art mathematical optimization methods, optimal power flow and security-constrained optimal power flow calculations. On data sets for the Nordic32 alternative current security-constrained optimal power flow benchmark, we evaluate the robustness of proxies with respect to load distribution, power factors, on-line generators and network topology, and generator costs. We show that simplified random load sampling procedures that are used in most published academic studies, are insufficient to yield robust machine learnt proxies, and consequently limit their usefulness in the real world. Based on these results, we formulate recommendations for future research.

Optimal power flow calculation in hybrid power system involving solar, wind, and hydropower plant using weighted mean of vectors algorithm

One of the most complex and motivating issues in power system is optimal power flow (OPF), which is a constrained optimization problem characterized by non-linearity and non-convexity. From these specifications, researchers competed in the past decades to find optimal solutions to OPF problem while keeping system stability. This paper presents an efficient optimization approach to deal with OPF problem in the hybrid renewable energy systems involving wind turbines, solar photovoltaic and small hydropower plant using optimization method depends on weighted mean of vectors INFO. Total generation cost, active power losses, and combined cost and emission are the principle goal, taking into account both reserve and penalty cost appropriate to over and under estimation respectively in the generation cost model. To evaluate the performance of INFO in solving OPF problem, modified IEEE 30-bus and IEEE 57-bus test systems will be utilized. The obtained results are compared with several algorithms such as Gorilla troop optimizer GTO, artificial ecosystem-based optimization AEO, Barnacles Mating Optimizer BMO for the same test systems keeping the same conditions. Simulation results have indicated the superiority of INFO while respecting all constraints. INFO can minimize total generation cost to 788.9417 $/h for IEEE 30-bus and 5259.2040 $/h for IEEE 57-bus. The results demonstrate clearly that the INFO is a highly efficient algorithm that is an encouraging tool for solving OPF problem. The promising findings highlight the potential of the INFO algorithm to smoothest the integration of RES, and its role in promoting sustainable energy solutions. Furthermore, the one-way analysis of variance (ANOVA) test, a statistical approach, was employed to evaluate the superiority of the proposed algorithm and to highlight a certain level of confidence to our study.

Multi-Objective Optimal Power Flow Calculation Considering Carbon Emission Intensity

In keeping with China’s dual carbon goals, optimal low-carbon power system dispatch has become a necessary component of the greening of the power system. However, typically, research considers only the economics of such efforts. Based on our power flow analysis of the power grid and the correlation properties of carbon emission flow, an optimal power flow calculation model targeting the total carbon emission rate of the power system’s power generation cost, active network loss, and load and network loss was constructed. Next, the NSGA-III algorithm was used to solve the model, and the decision was to coordinate and optimize the output schemes of various types of power plants, such as wind, water, and thermal. The modified IEEE39 node simulation system was built with Matlab software (MATLAB R2020b). The results of the calculation showed that, compared to the traditional method of determining the optimal power flow, the proposed method reduced the system carbon emissions by 20% while the power generation cost increased by less than 2%, which proves the effectiveness and practicability of the proposed method.

A Real-Time Adaptive Energy Optimization Method for Urban Rail Flexible Traction Power Supply System

In urban rail traction power supply systems, the optimal power flow method is mostly utilized for energy optimization. Conventional power flow optimization adopts offline calculation methods to obtain the optimal strategy under given scenarios. However, this method cannot continuously realize the ideal optimization effect for the time-varying flexible traction power supply system. For this reason, this paper proposes a real-time adaptive energy optimization method to solve the problem above. Firstly, the control objective of the optimal power flow is determined based on analyzing the system power flow. Secondly, a hierarchical control system is designed to achieve adaptive optimal control for the flexible traction power supply system. Moreover, a swarm intelligence optimization algorithm-based optimal power flow calculation method is employed to realize the real-time optimal power flow. Finally, some simulations are performed to verify the effectiveness and accuracy of the proposed real-time optimal power flow. It is demonstrated that the real-time optimal power flow method makes it possible to consider the low delay and high accuracy of control commands at the same time. Compared with the conventional offline method, the proposed real-time method can reduce the input electricity consumption by 1.47%, which is valuable in practical applications.

Distributed bi-level optimal power flow calculation for SVSM interval of integrated transmission and distribution networks considering the uncertain renewables

To accurately and efficiently calculate the static voltage stability margin (SVSM) interval of integrated transmission and distribution networks (ITDNs) considering the uncertain fluctuation of renewables, a distributed bi-level optimal power flow (OPF) calculation method based on the alternating direction method of multipliers for the SVSM interval of ITDNs is proposed in this paper. Due to the different structure characteristics of transmission network (TN) and distribution network (DN), a hybrid node-branch OPF method for calculating the SVSM of ITDNs is proposed, which has better convergence than the traditional node OPF method. Different reactive power-voltage control modes of renewable energy stations (RESs) are also considered in the calculation. Considering the uncertain fluctuation of RESs, two distributed bi-level OPF models for calculating the upper and lower bounds of the SVSM interval of ITDNs are established. Based on the alternating direction method of multipliers, the SVSM interval bounds of ITDNs can be obtained by solving the sub-optimization models and transmitting the boundary coupling variables and the load growth parameter between the TN and multiple DNs iteratively until the given convergence criterion is satisfied. Test results on two ITDNs, the modified IEEE 39–33 & 69 bus system and an actual 2285-bus ITDNs, demonstrate the high computation accuracy and efficiency of the proposed distributed bi-level OPF method compared with other calculation methods.

Estimation Method for Transmission Line Overloads Due to Renewable Energy Source (RES) Output Forecast Errors in Daily Supply and Demand Planning

AbstractWe propose a method to estimate transmission‐line overloads due to forecast errors of power output of renewable energy sources. The proposed method involves particle swarm optimization and optimal power flow calculations. The effectiveness of the method is confirmed via numerical simulations using a modified IEEE RTS 24‐bus system model. The results indicate that the proposed method can determine the forecast errors of the renewable power output that causes thermal overload, and further predict the occurrences of transmission‐line overload under generator activation in supply and demand planning. Furthermore, we explain the occurrence mechanism of transmission‐line overload due to forecast errors, which may contribute to improve the daily supply and demand planning. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.