Optimal Power Flow Research Articles

An Approach for Hybrid Optimal Power Flow Strategies with Optimal Allocation of Distributed Generators for a Power Network

The OPF difficulties are characterized by the presence of four distinct objective functionswhich are: active powerlosses,fuel operating costs and voltage variations. The volatile and variable nature of distributed generator (DG) sources contributes to the convolutionof the optimum power flow (OPF) issue. This paperemployed bat algorithms to tackle the issue of optimumpower flow (OPF)and PSO algorithm to optimal allocation of DG. The goal was to enhance the effectiveness of energy use, environmental sustainability, and cost efficiency of the electricity grid. The test cases include a wide range of scenarios, including the existence of Distributed Generation (DG), different locations of DG within the network, various kinds of load expansion, and occasional breakdowns of transmission lines. These possibilities are considered in order to address the problem presented by the suggested solution OPF. The incidents are assessed utilizing bus systems, such as the 30 bus systemin MATLAB.

Optimal Power Flow of Multi-objective Combined Heat and Power with Wind-Solar-Electric Vehicle-Tidal Using Hybrid Evolutionary Approach

Optimal Power Flow of Multi-objective Combined Heat and Power with Wind-Solar-Electric Vehicle-Tidal Using Hybrid Evolutionary Approach

Framework design of distributed P2P2G energy transaction considering photovoltaic power and dispatch of manufacturing facilities

In this paper, a distributed peer-to-peer-to-grid (P2P2G) energy transaction framework considering photovoltaic generation and dispatch of manufacturing facilities is designed to increase the penetration of renewable energy resource. The factory with typical manufacturing assembly production task, photovoltaic panels and battery is regarded as a micro-grid (MG) to participate in the energy transaction market. The designed framework contains two levels. In the upper level, each MG determines the scheduling of manufacturing facilities and battery and the quantities of P2P2G energy transactions based on the given P2P energy transaction price and distribution locational marginal price (DLMP), in which the complex typical manufacturing assembly process is formulated as a kind of deferable load and the DLMP is updated according to the optimal power flow (OPF) of the network. In the lower level, peer-to-peer (P2P) energy transaction prices are updated by non-cooperative games and the homologous Rosen-Nash equilibrium points are obtained by using Nikaido-Isoda relaxation and alternating direction method of multipliers (ADMM) algorithm. The efficacy of the designed framework is demonstrated by a case study, and the results indicate the designed framework can improve the utilisation rate of renewable energy.

A coordinated active and reactive power optimization approach for multi-microgrids connected to distribution networks with multi-actor-attention-critic deep reinforcement learning

As a promising approach to managing distributed energy, the use of microgrids has attracted significant attention among those managing continuous connections to distribution networks. However, the barriers of the data sharing among different microgrids, the uncertainty of the distributed renewable sources and loads, and the nonlinear optimization of power flow make traditional model-based optimization methods difficult to be applied. In this paper, a data-driven coordinated active and reactive power optimization method is proposed for distribution networks with multi-microgrids. A multi-agent deep reinforcement learning (MADRL) method is used to protect the data privacy of each microgrids. Moreover, attention mechanism, which pays attention to crucial information, is presented to overcome the problem of slow convergence caused by the dimensionality explosion of the optimized variables. Two types of agents, controlling discrete action and continuous action devices, respectively, are formulated in coordinated optimization, which reduces voltage violations and improves the system operation efficiency. In addition, in order to improve the performance of the online agent model under variable operation conditions, the transfer learning is embedded in the training process of the MADRL. The proposed method is verified on a modified IEEE 33-bus distribution network with nine microgrids.

Impact of phase selection on accuracy and scalability in calculating distributed energy resources hosting capacity

Hosting capacity (HC) and dynamic operating envelopes (DOEs), defined as dynamic, time-varying HC, are calculated using three-phase optimal power flow (OPF) formulations. Due to the computational complexity of such optimisation problems, HC and DOE are often calculated by introducing certain assumptions and approximations, including the linearised OPF formulation, which we implement in the Python-based tool ppOPF. Furthermore, we investigate how assumptions of the distributed energy resource (DER) connection phase impact the objective function value and computational time in calculating HC and DOE in distribution networks of different sizes. The results are not unambiguous and show that it is not possible to determine the optimal connection phase without introducing binary variables since, no matter the case study, the highest objective function values are calculated with mixed integer OPF formulations. The difference is especially visible in a real-world low-voltage network in which the difference between different scenarios is up to 14 MW in a single day. However, binary variables make the problem computationally complex and increase computational time to several hours in the DOE calculation, even when the optimality gap different from zero is set.

Augmented Two-Stage Hierarchical Controller for Distributed Power Generation System Powered by Renewable Energy: Development and Performance Analysis

The sustainable development of an area is highly reliant on a reliable electrical energy supply. Microgrids are important in integrating distributed energy resources (DERs) using power electronic converters. However, microgrid control becomes challenging with the increasing number of distributed generators and loads. With the conventional droop control method, power contributions from DER converters cannot be accurately shared due to a mismatch of line impedances. In this paper, an augmented hierarchical control mechanism is proposed to solve the issues mentioned above. This hierarchical control mechanism consists of primary and secondary controllers. The primary stage utilized the droop controller to improve optimal power flow, mainly for the resistive network. The secondary stage is based on an improved methodology to compensate for the voltage and frequency variations during small and large signal disturbances. Moreover, the modelling and analysis for PMSG-based wind energy conversion systems are also presented. The response of the primary controller for active and reactive power sharing is investigated. The analysis emphasizes the demonstration of optimal power-sharing under normal and abnormal conditions for the considered load. Finally, the suggested robust controller’s performance is evaluated in a MATLAB environment, and simulation results show the proposed scheme’s superiority under different operating conditions. The frequency is stable at 50 Hz after a 50 KW load is added.

Hybrid strategy of flexibility regulation and economic energy management in the power system including renewable energy hubs based on coordination of transmission and distribution system operators

Energy management of energy hubs in the power system impacts both transmission and distribution networks and their operations. Hence, to enhance efficiency, there should be bilateral coordination between distribution and transmission networks. Moreover, thanks to including power sources, storage, and responsive loads, hubs can earn financial benefits from the energy and ancillary services market. Therefore, this paper presents the operation of distribution and transmission networks in the presence of flexible-renewable energy hubs based on transmission system operator (TSO)-distribution system operator (DSO) coordination according to the market clearing price modeling in energy and flexibility markets. The proposed scheme minimizes the sum of the expected operating costs of the networks and hubs minus the expected flexibility profit of the hubs. The scheme is constrained to optimal power flow equations of the networks, flexibility limit of the networks, and flexibility-operation model of renewable energy hubs located in transmission and distribution networks. The unscented transformation method is used to model the uncertainties of load, renewable sources, and stationary storage (aggregation of electric vehicles). Energy price and flexibility are among the dual variables of the problem. To simultaneously calculate these variables and the main variables of the problem, an integrated model of the suggested scheme based on the penalty function technique is extracted. Eventually, numerical results validate the capability of the scheme in enhancing the operation, economic, and flexibility status of the proposed scheme, in which renewable sources along with storage and responsive load in the energy hub can obtain 100 % flexibility conditions for the networks. They help enhance the economic and operation indices of distribution and transmission networks by about 26 %-44 % and 22 %-33 % compared to the case without hubs and renewable sources.

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.

A hybrid quantum–classical algorithm for mixed-integer optimization in power systems

Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing has been tested as a potential solution towards reducing the computational burden imposed by these problems, providing promising results, motivating the can be used to speedup the solution of MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs’ sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid “quantum–classical” approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum–classical algorithms for power system mixed integer optimization problems.

Bucketized Active Sampling for learning ACOPF

This paper considers optimization proxies for Optimal Power Flow (OPF), i.e., machine-learning models that approximate the input/output relationship of OPF. Recent work has focused on showing that such proxies can be of high fidelity. However, their training requires significant data, each instance necessitating the (offline) solving of an OPF. To meet the requirements of market-clearing applications, this paper proposes Bucketized Active Sampling (BAS), a novel active learning framework that aims at training the best possible OPF proxy within a time limit. BAS partitions the input domain into buckets and uses an acquisition function to determine where to sample next. By applying the same partitioning to the validation set, BAS leverages labeled validation samples in the selection of unlabeled samples. BAS also relies on an adaptive learning rate that increases and decreases over time. Experimental results demonstrate the benefits of BAS.

Applications of Multi-Objective OPF Solutions with Optimal Placement of Multiple and Multi-Type FACTS Units to IEEE System: Comparison of Different Approaches

Optimal power flow (OPF) problem and its implications for power system stability and efficiency is investigated in this study. OPF, a restricted optimization query with non-linearity and non-convexity, is one of the most challenging and fascinating problems in the recent power system. Based on these parameters, researchers have been working hard over the past few decades to identify the best solutions to the OPF issue that maintain system stability. This work presents multi-objective OPF solutions utilizing Newton's technique with numerous multi-type FACTS units. First, the GA is applied to identify the perfect size and location of the FACTS units. Next, the generator and FACTS settings are optimized. In this instance, four scenarios are taken into consideration and three OFs are employed to see how the OFs affect the positioning and dimensions of FACTS devices. The OF is suggested to consider the reduction of both generation costs and transmission losses while also optimizing the power transfer capacity of designated corridors. A full analysis relating to the IEEE-30 bus system is presented and analyzed.

MPNG: A MATPOWER-Based Tool for Optimal Power and Natural Gas Flow Analyses

MPNG is an open-source simulation package for solving Optimal Power and Natural Gas Flow (OPNGF) problems. It is coded in <small>Matlab</small> and developed using the widely-used tool for power systems research and education, <small>Matpower</small>. MPNG assembles a nonlinear steady state OPNGF formulation for analyzing the integration of electricity and natural gas networks with order-of-priority classes of consumers and gas nodal price-controlled storage facilities. This paper presents the details of the nonlinear optimization model behind MPNG, as well as several features that were designed into it for the purpose of achieving robustness. These include an approximation of the Weymouth equation for handling bi-directional gas flows in pipelines, a per-unit representation for the natural gas network, and penalized slack variables for power and gas balances. Simulation results using a test case and the Colombian power and natural gas networks are presented to highlight MPNG&#x0027;s capabilities to solve OPNGF problems.

An Enhanced SD-GS-AL Algorithm for Coordinating the Optimal Power and Traffic Flows With EVs

An Enhanced SD-GS-AL Algorithm for Coordinating the Optimal Power and Traffic Flows With EVs

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.

Linear optimal power flow model for modern distribution systems: Management of normally closed loop grids and on-load tap changers

Modern distribution systems face new challenges due to the rise of small-scale renewable energy resources and the electrification of energy demand. Additionally, the complexity of network management increases with the exchange of flexibility services between distribution and higher voltage levels. The system operator's role involves optimizing the planning and operation of the distribution network. In current scenarios, this includes managing flexibility resources (such as generators, demand response, and on-load tap changers) and implementing new operating strategies (such as closed-loop topologies and dynamic reconfiguration). This paper proposes a reformulation of one of the most used linear approximations of the Optimal Power Flow model for distribution networks. The novelty of this reformulation lies in integrating equations to handle tap-changing transformers with closed-loop/meshed network operation, while preserving the original linear formulation and computational tractability.

Ensuring data privacy in AC Optimal Power Flow with a distributed co-simulation framework

During the energy transition, the significance of collaborative management among institutions is rising, confronting challenges posed by data privacy concerns. Prevailing research on distributed approaches, as an alternative to centralized management, often lacks numerical convergence guarantees or is limited to single-machine numerical simulation. To address this, we present a distributed approach for solving AC Optimal Power Flow (OPF) problems within a geographically distributed environment. This involves integrating the energy system Co-Simulation (eCoSim) module in the eASiMOV framework with the convergence-guaranteed distributed optimization algorithm, i.e., the Augmented Lagrangian based Alternating Direction Inexact Newton method (aladin). Comprehensive evaluations across multiple system scenarios reveal a marginal performance slowdown compared to the centralized approach and the distributed approach executed on single machines—a justified trade-off for enhanced data privacy. This investigation serves as empirical validation of the successful execution of distributed AC OPF within a geographically distributed environment, highlighting potential directions for future research.

Distributed sequential optimal power flow under uncertainty in power distribution systems: A data-driven approach

Modern distribution systems with high penetration of distributed energy resources face multiple sources of uncertainty. This transforms the traditional Optimal Power Flow problem into a problem of sequential decision-making under uncertainty. In this framework, the solution concept takes the form of a policy, i.e., a method of making dispatch decisions when presented with a real-time system state. Reasoning over the future uncertainty realization and the optimal online dispatch decisions is especially challenging when the number of resources increases and only a small dataset is available for the system’s random variables. In this paper, we present a data-driven distributed policy for making dispatch decisions online and under uncertainty. The policy is assisted by a Graph Neural Network but is constructed in such a way that the resulting dispatch is guaranteed to satisfy the system’s constraints. The proposed policy is experimentally shown to achieve a performance close to the optimal-in-hindsight solution, significantly outperforming state-of-the-art policies based on stochastic programming and plain machine-learning approaches.

Topology-aware reinforcement learning for tertiary voltage control

Transmission systems have experienced an increase in the occurrence frequency and intensity of high voltage events over the past few years. Since traditional approaches to optimal power flow do not scale well to real-life systems, it has become urgent to develop new methods to help operators improve tertiary voltage control. In this paper, we propose to train a graph neural network to choose voltage setpoints by interacting with a power grid simulator using reinforcement learning techniques. Moreover, we introduce the hyper heterogeneous multi graph formalism to account for topology variations of real-life systems (assets disconnection, bus-splitting, etc.). Our approach is validated on an artificial case study based on the case60nordic power grid.

Improved algebraic inverter modeling for four-wire power flow optimization

This paper discusses the modeling of inverters used in distributed energy resources in steady state. Modeling the interaction between distribution grids and inverter-based resources is crucial to understand the consequences for the network’s operational and planning processes. This work highlights the limitations of existing models and emphasizes the need for better representations of inverters and their control laws in decision-making contexts. Improved steady-state grid-following and grid-forming inverter models are presented, including both three-leg and four-leg converter variants. The advantages of these improved models in mathematical optimization contexts are showcased by investigating the power quality improvement capabilities of the inverters. Numerical studies integrating the proposed inverter models in a four-wire unbalanced optimal power flow engine are presented, and trade-offs between modeling detail and computational intensity are illustrated.

An iterative two‐stage PSCOPF method considering line fault uncertainty under typhoon influence

AbstractTyphoon weather poses a significant threat to the security and stability of the power system, as it can potentially lead to the disconnection of transmission lines. Concurrently, there exists substantial uncertainty regarding which specific lines may become disconnected under such weather conditions. The preventive security constrained optimal power flow (PSCOPF) is one of the main methods to address this issue. However, the current PSCOPF exhibits low computational efficiency due to the requirement of analysing all line faults through the N‐1 check. Therefore, this paper proposes a PSCOPF method based on two‐stage optimization. Firstly, the concentric relaxation method is employed to screen and obtain the critical line faults, thereby reducing the total quantity of security constraints associated with N‐1 line fault scenarios. Secondly, the incorporation of scenario transition constraints is introduced to decompose the PSCOPF model into OPF (optimal power flow) models under N‐0 scenarios and N‐1 critical line fault scenarios, then solve iteratively to achieve multi‐scenario decoupling. Finally, the proposed method was validated on the IEEE30 test system to demonstrate its capability to ensure economics in the N‐0 scenario and security in N‐1 scenarios.