Optimal Power Flow Calculation Research Articles

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.

Power flow analysis of 110kV power supply system based on PowerWorld

With the growing global interest in various economic and environmental benefits of the power system, it is essential to ensure the safe and stable operation of the power grid. The optimal power flow calculation method is studied using the PowerWorld and Newton-Ralfsnn methods. The results calculated by the Simulator LP OPF function are compared with the manual calculation of the 110 kV power supply system grid. After optimization, the total cost is saved by 623.05 ¥/h. The simulation results can directly and vividly reflect the power distribution and optimize the power supply and distribution power flow.

Nonisothermal optimal power and gas flow considering energy storage

The isothermal assumption that treats the gas temperature as a constant is widely adopted in the traditional research. However, the gas temperature has a noticeable effect on the optimal power and gas flow (OPGF) calculation. Moreover, the rational allocation of energy storage can enhance the flexibility and economy of the power and gas system. This paper presents a nonisothermal OPGF considering energy storage, which effectively avoids the constant assumptions on the gas temperature. A simplified partial differential equation which only has bilinear constraints is introduced to depict the temperature change of natural gas. Then, the partial differential equation is discretized by the finite difference scheme and an algebraic pipeline thermal model is developed to avoid the mathematical complexity of the energy conservation equation. The energy storage model is embedded into the OPGF model to enhance the system economy and flexibility. Coupling the DC power flow model and the nonisothermal gas flow model, the nonisothermal OPGF model considering energy storage is formulated. Comprehensive simulations illustrates that the proposed nonisothermal OPGF model considering energy storage can better evaluate the operation state of the integrated energy system. In addition, the energy storage can improve the operation flexibility of systems, thereby significantly reducing the operation costs of the integrated energy systems.

Achieving Optimal Reactive Power Compensation in Distribution Grids by Using Industrial Compensation Systems

This paper presents a method for integrating industrial consumers owning compensation systems as alternative reactive power sources into grid operating processes. In remuneration, they receive a market-based provision of reactive power. The aim is to analyze the potential of reactive power compensation systems of industrial companies connected to medium-voltage (10 kV–30 kV) AC grids in order to increase the reactive power ability of distribution grids. Measurement methods and reactive power potential results of six industrial companies are presented to characterize the amount and temporal availability of their reactive power potential. The presented approach for using the decentralized reactive power potential is a centralized reactive power control method and is based on optimal power flow (OPF) calculations. An optimization algorithm based on linear programming is used to coordinate a reactive power retrieval tuned to the actual demand. The influencing quantities are the current grid status (voltage and load flow capacity reserves at grid nodes and power lines) and the current reactive power potential of the reactive power sources. The compensation impact of six measured industrial companies on an exemplary medium-voltage grid is shown by an application example.

A Novel Loss Sensitivity Based Linearized OPF and LMP Calculations for Active Balanced Distribution Networks

The distribution system operator performs optimal power flow calculations for efficient and economical scheduling of the distributed energy resources (DERs) and congestion management of the active distribution network. A linearized version of the ac optimal power flow (ACOPF) model is more suitable for practical implementation due to its simplicity and fast convergence. Thus, this article proposes a linearized ACOPF framework and locational marginal price (LMP) calculations for a generalized (i.e., radial and meshed) active balanced distribution system. The proposed linearized ACOPF for the distribution level market is formulated based on novel active and reactive power loss sensitivities by considering the effects of high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{R/X}$</tex-math></inline-formula> ratio and network constraints. The distribution LMPs are mathematically derived for active and reactive power generations and loads. Different reactive power loads are represented as a function of active power loads using the concept of power-factors. Thus, the load portfolio consists of nominal active power demand and nominal power-factor. Different LMPs are calculated for loads with different power-factors. DERs submit a separate offer for active and reactive power generations. Thus, separate LMPs are derived for DERs. The efficacy and efficiency of the proposed ACOPF framework are illustrated and compared on different radial and meshed distribution systems.

Exploiting Internet Data Centers as Energy Prosumers in Integrated Electricity-Heat System

In some emerging Internet data center (IDC) projects, the waste heat dissipated from IT facilities is being captured and supplied to the district heating systems for energy efficiency concerns. From the perspective of electricity consumption and heat production, IDCs can be regarded as energy prosumers, whose spatial and temporal flexibility of energy behaviors is of great significance for the operation of integrated electricity-heat systems (IEHSs). To explore the potential benefits, the required modeling and dispatching techniques are investigated in this paper. Firstly, an Internet-service based energy prosumer model of IDCs is formulated. Especially, the heat production capability is represented considering the complete dynamic heat flow including the heat dissipation, exchange, recovery, and upgrading. And fuzzy parameters are utilized to characterize the uncertainties of the forecasted workloads in advance of the dispatch for IDCs. Moreover, an integrated operation framework for the IDC-IEHS is constructed. Specifically, a hierarchical dispatch scheme is further proposed to achieve privacy-constrained cooperative scheduling between the energy system and IDCs. In the scheme, the energy requirements for IDCs are obtained from the integrated optimal heat and power flow calculation where the temporal scale difference between the electric power and heating systems is considered. The obtained energy requirements are then regarded as the target values for the workload scheduling of IDCs. A deviation correction mechanism is designed to achieve the overall optimality of the IDC-IEHS. Finally, the hydraulic-thermal decomposition and trapezoid fuzzy value equivalence methods are used to solve the optimization problems. Simulation results demonstrate that exploiting IDCs as energy prosumers can promote the accommodation of renewables and reduce system cost in the IEHS, as well as improving the self energy efficiency of IDCs.

A Data-Driven Linear Optimal Power Flow Model for Distribution Networks

The linearized power flow (PF) model is mainly used to make the optimal power flow (OPF) problem convex. However, existing data-driven linear PF models are not applicable for OPF calculation since the Kirchhoff's law (KCL) constraints are neglected. In this letter, we propose a data-driven linear PF model incorporating the KCL constraints and can be embedded in OPF for distribution networks (DNs). By combining the support vector regression (SVR) and ridge regression (RR) algorithms, the proposed method is robust against bad data in measurements. Numerical tests show that the proposed model has much higher accuracy than the existing linear models, especially for OPF calculation.

A Modified Multiparameter Linear Programming Method for Efficient Power System Reliability Assessment

Power systems face adequacy risks because of the high integration of renewable energy. It is urgent to develop efficient methods for power system operational reliability assessment. Conventional power system reliability assessment methods cannot achieve real-time assessment of system risk because of the high computational complexity and long calculation time. The high computational complexity is mainly caused by a large number of optimal power flow (OPF) calculations. To reduce the computational complexity, this paper transfers the optimal power flow model as a multiparameter linear programming model. Then, the optimal power flow can be obtained by linear calculations. Furthermore, this paper proposes a state reduction method considering the importance index of transmission lines for further improving the calculation efficiency. Case studies are carried out on IEEE standard systems and a provincial power grid in China. Compared with the conventional reliability assessment method, the reliability assessment efficiency of the proposed method increases by 10–40 times, and the assessment error is less than 1%.

Development and application of equilibrium optimizer for optimal power flow calculation of power system

This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC’20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon’s rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.