Power Flow Solution Research Articles

Three‐phase four‐wire power flow solution for multi‐grounded distribution networks with non‐bolted grounding

AbstractThis study proposes a direct three‐phase four‐wire power flow method to accurately analyse the neutral line and multiple grounding characteristics. In particular, the proposed grounding impedance building‐based solution method was used to analyse the neutral grounding impedance in power flow studies based on the slack bus grounding impedance. The accuracy of the proposed method was verified using a neutral‐to‐earth voltage test system. IEEE 13‐bus and 123‐bus test systems were used to compare the advantages and disadvantages of the proposed method. Compared to the current injection full Newton and forward–backward sweep methods, the proposed method achieves a significant reduction in iteration numbers of up to 76.92% and 77.78%, respectively. For different grounding scenarios, stable convergence characteristics were exhibited by the proposed method after six to seven iterations.

Security constrained optimal power flow solution for practical transmission grid using hybrid use of generating plant and network restructuring

This paper presented a study on the security constrained optimal power flow (SCOPF) of a practical transmission utility grid network (TUGN). The objectives of reduction in the transmission losses of TUGN (TLGN) and to minimize the bus voltage deviations (BVD) are achieved by addition of thermal power plant (TPP) and network restructuring (NR). Identification of best fit node for generation injection is achieved using the method based on hybrid combination of analytic approach and genetic algorithm (GA). Efficacy of the proposed study is evaluated using the computation of energy equivalent to network loss saving, percentage derating of the load (PDOL), voltage profile, bus voltage deviations, and financial analysis (FA). Study is performed without and with contingency (N-1) for the base case network, TUGN with addition of TPP and TUGN with addition of TPP and NR. This is established that addition of TPP, addition of TPP with NR are effective to reduce the TLGN, improve the voltage profile and minimize the bus voltage deviations. This study is more efficient compared to various studies reported in literature.

Optimal Power Flow Solution Integrated with TCSC to Improved Voltage Profile and Losses Reduction in Power System Using Effective Intelligent Technique

Optimal Power Flow Solution Integrated with TCSC to Improved Voltage Profile and Losses Reduction in Power System Using Effective Intelligent Technique

Optimal operation of three-phase unbalanced active distribution system based on semidefinite relaxation and convex-concave procedure

The three-phase distribution optimal power flow (D-OPF) problem has attracted much attention in recent years due to practical requirements for managing distributed energy resources and multi-energy customers in unbalanced active distribution systems. To deal with the strong nonconvexity of the three-phase OPF problem, this paper develops the semidefinite programming (SDP) formulation of three-phase OPF problems considering the mutual coupling in multi-phase networks. Instead of directly dropping the rank-one constraints, a sequential convex optimization algorithm based on the convex-concave procedure (CCP) is proposed for recovering a feasible and optimal solution of three-phase power flow. The proposed iterative algorithm not only has high computational efficiency but also guarantees the optimality when the semidefinite relaxation or second-order cone relaxation method is inexact. Case studies on various IEEE testing distribution systems verify that the proposed algorithm recovers the feasible and optimal power flow solution. It also exhibits a relatively low number of iterations and short solving time in large-scale IEEE testing systems.

Nash–Cournot Equilibrium and Its Impact on Network Transmission Congestion

This paper evaluates the impact of congestion on transmission lines when the operation cost is minimized using economic dispatch (ED), comparing the results obtained with the Nash–Cournot Equilibrium (NCE). A methodology is developed for the optimal power flow solution through the NCE, considering the network topology (upper and lower generation limits, upper and lower limits of the transmission lines, and power balance) for a nine-node system without and considering two bilateral power transactions. The results show that the operation cost is higher when the NCE is implemented than ED. However, the problem of congestion in the transmission lines is reduced due to the equilibrium obtained in the power dispatch against minimizing the operation cost in the dispatch; the transmission lines with the most significant participation tend to become congested when additional bilateral transactions occur. Finally, the above is verified by obtaining the mean and median of the transmission line percentages used in the two simulations.

Three-phase power flow using binary tree search algorithm for unbalanced distribution networks

The main objective of this study is to examine a binary tree (BT) three-phase (3Φ) power flow analysis method for unbalanced distribution networks. A simple and efficient 3Φ power flow solution method for unbalanced radial distribution networks was proposed. This method is based on the BT search structure. Large-scale distribution network problems can be evaluated using current-injection techniques and two-port network models. The power flow solution process was simplified into a set of 3 × 3 matrix operations using the BT-based method. The solution complexity remained unchanged, regardless of the size of the power system. In other words, the performance and robustness of the proposed algorithm were maintained at relatively high values with increasing system size. Furthermore, programming complexity was reduced by standardising the solution process. The effectiveness and accuracy of the proposed model and algorithm were validated using four IEEE standard benchmark feeders and a series of random cases.

An in-depth examination of artificial intelligence-based methods for optimal power flow solutions

An in-depth examination of artificial intelligence-based methods for optimal power flow solutions

Unsupervised learning for equitable DER control

In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.

Long solution times or low solution quality: On trade-offs in choosing a power flow formulation for the Optimal Power Shutoff problem

The Optimal Power Shutoff (OPS) problem is an optimization problem that makes power line de-energization decisions in order to reduce the risk of igniting a wildfire, while minimizing the load shed of customers. This problem, with DC linear power flow equations, has been used in many studies in recent years. However, using linear approximations for power flow when making decisions on the network topology is known to cause challenges with AC feasibility of the resulting network, as studied in the related contexts of optimal transmission switching or grid restoration planning. This paper explores the accuracy of the DC OPS formulation and the ability to recover an AC-feasible power flow solution after de-energization decisions are made. We also extend the OPS problem to include variants with the AC, Second-Order-Cone, and Network-Flow power flow equations, and compare them to the DC approximation with respect to solution quality and time. The results highlight that the DC approximation overestimates the amount of load that can be served, leading to poor de-energization decisions. The AC and SOC-based formulations are better, but prohibitively slow to solve for even modestly sized networks thus demonstrating the need for new solution methods with better trade-offs between computational time and solution quality.

Adaptive convergence enhancement strategies for Newton–Raphson power flow solutions in distribution networks

AbstractThis study introduces a series of strategies to enhance convergence in the Newton–Raphson power flow method for unbalanced distribution networks. The proposed approach incorporates graph theory, Kron reduction, and current injection techniques. The network components, including transmission conductors, power transformers, power conductors, shunt capacitors/reactors, and demand loads, were merged into the bus impedance matrix. Using two identification processes (based on mismatches for bus voltages and bus power injections) and optimal multipliers (μ), the proposed approach estimates the initial bus voltages by approximating the converged solutions. To verify the effectiveness of the proposed approach, the authors performed a comparative analysis of five IEEE test feeders in various scenarios. The results confirmed the effectiveness of the proposed approach, particularly for unbalanced distribution systems with diverse transformer connections.

Chaotic-quasi-oppositional-phasor based multi populations gorilla troop optimizer for optimal power flow solution

This paper proposes an efficient modified Gorilla Troops Optimizer (MGTO) to address the problem of prone to local optima and stagnation possibility in the standard Gorilla Troops Optimizer (GTO). The proposed MGTO is based on multiple strategies including chaotic initialization, quasi-oppositional based learning, phasor motion, and multi-populations strategy. The proposed MGTO is applied to resolve the non-convex single objectives optimal power flow (OPF) problem to reduce the fuel cost without and with vple, the emissions, the fuel cost considering prohibted zones (POZs) and piecewise functions, while for multiple objective cases the fuel cost is optimized with the power losses, the voltage deviation and the emissions. To validate the effectiveness of the proposed optimizer, it is tested on IEEE 30-bus and 57-bus systems, as well as 23 standard benchmark functions and the obtained outcomes are compared with the other seven well-known optimization techniques such as SCSO, GWO, WOA, SCA, PF, BWO and GTO. The simulation results verified that the proposed MGTO provides a remarkable and robust solution for the OPF problem solution compared to the other state-of-the-arts algorithms.

Network equivalent-based VQ Curve method and its application in a novel real-time voltage stability assessment methodology

The PV and VQ curves have been widely accepted tools for monitoring voltage stability. Although these curves have been used in offline studies, their online applications are not trivial, involving specific issues and complexities concerning real-time environment. The literature presents some approaches to determine quantities related to voltage stability limit in real-time analysis of the PV curve. However, it does not occur with the corresponding quantities for the VQ curve, making it difficult to analyze these curves jointly. This work presents two significant innovative contributions, based on the use of real-time network equivalents estimated through measurement data. The first is a technique suitable for real-time applications to calculate the complete VQ curve, called Network Equivalent-based VQ Curve. The second is a methodology for determining voltage stability margins using information from both PV and VQ curves. Simulations were carried out in RVS Test System, and 9, 14, 30 and 118 Bus Test Cases available in MATPOWER. The results of Network Equivalent-based VQ Curve application were validated by power flow solution. The voltage stability assessment methodology proposed in this paper represents a significant advance, going beyond the traditional approaches.

Graph‐based solution for smart grid real‐time operation and control

Graph‐based solution for smart grid real‐time operation and control

Risk Assessment of Radial Distribution Systems using Modified Jelly Fish Search Algorithm to analyse the Performance Indices

One of the essential techniques for figuring out Power Distribution System performance is reliability evaluation. With time, the range of methods for assessing reliability has grown, and the distribution system's evolution has also become more intricate. The likelihood of a network failing grows with time once it begins to function, especially if it is used for an extended period. Reliability indices have been evaluated using different algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and various modified versions of algorithms. The Jelly Fish Search Algorithm has been used in various power system applications such as to determine the most cost-effective way to dispatch generating units' loads, integrate Distributed Generation (DG) units, track the maximum power of photovoltaic systems, and determine optimal power flow solutions, among other uses. The performance indices for the Radial Distribution System (RDS) have not been evaluated using JFSA.Variation of performance indices with respect to unavailability has not been discussed in the literature. Here an attempt is made to analyse the variation of the indices with the unavailability. The proposed algorithm is evaluated first on 3 load point radial distribution system and the computations are performed on the popular IEEE-RBTS Bus2 test system. Based on the output it is observed that for the both the systems the behaviour of the indices with respect to the unavailability is in similar fashion. The equations are derived for the performance indices using the Minitab. With the equations obtained the Performance indices values can be predicted for the given unavailability value. It is the better appropriate method for the assessing the performance indices of Radia Distribution System.

Real-Time Testing Optimal Power Flow in Smart-Transformer-Based Meshed Hybrid Microgrids: Design and Validation

The smart transformer (ST) is a multiport and multi-stage converter that allows for the formation of meshed hybrid microgrids (MHMs) by enabling AC-DC ports in medium and low voltage. This type of microgrid has advantages over the performance of conventional hybrid AC-DC microgrids (HMGs); however, the number of degrees of freedom of the ST increases the complexity of the energy management systems (EMSs), which require adequate and accurate modeling of the power flow of the converters and the MG to find the feasible solution of optimal power flow (OPF) problems in the MHM. An ST’s equivalent power flow model is proposed for formulating the MHM OPF problem and developing low-frequency equivalent models integrated with a decoupled hierarchical control architecture under a real-time simulation approach to the ST-based MHM. A simulation model of the MHM in the Simulink® environment of Matlab® 9.12 is developed and implemented under a digital real-time simulation (DRTS) approach on the OPAL-RT® platform. This model allows for determining the accuracy of the developed equivalent models, both low-frequency and power flow, and determining the MHM performance based on optimal day-ahead scheduling. Simulation test results demonstrated the ST equivalent model’s accuracy and the MHM’s accuracy for OPF problems with an optimal day-ahead scheduling horizon based on the model-in-the-loop (MIL) and DRTS approach.

Optimal power flow solution using a learning-based sine–cosine algorithm

Optimal power flow solution using a learning-based sine–cosine algorithm

Learning model combining convolutional deep neural network with a self-attention mechanism for AC optimal power flow

Alternating current optimal power flow (OPF) analysis is critical for efficient and reliable operation of power systems. For large systems or repetitive computations, the traditional methods such as the direct and gradient methods, or non-traditional methods, such as the genetic algorithm and simulating annealing, are time-consuming and unsuitable for real-time computing. The work in this paper proposes a novel framework to obtain the optimal solution of power flow in real-time using a combination of convolutional neural networks and a self-attention mechanism. All parameters of the power networks are rearranged in an image-like shape of a multi-channel image where each channel is a two-dimensional matrix. The proposed approach is adaptive with every input size of power systems as well as frequent variations of network topologies without intervention to the framework core. The encompassment of all power system contexts in which all parameters of internal elements, generation costs, and topology information are included, contributes to the higher accuracy of inference compared to other current machine-learning-based OPF-solving methods. Besides, the proposed framework established on ubiquitous platforms is effortlessly integrated into current infrastructures of power systems, and the great efficiency along with the computation speed may serve as a critical point for practical implications, such as enabling faster decision-making during real-time operations, predicting system contingencies, and remedial actions based on an offline pre-trained model. This supervised learning process is applied to the dataset of four case studies of meshed power systems: the IEEE 5-bus system (IEEE-5), the IEEE 30-bus system (IEEE-30), the IEEE 39-bus system (IEEE-39), and the IEEE 57-bus system (IEEE-57) to prove the efficacy of the proposed method.

A novel solution to optimal power flow problems using composite differential evolution integrating effective constrained handling techniques

Optimal power flow is a complex and highly non-linear problem in which steady-state parameters are needed to find a network’s efficient and economical operation. In addition, the difficulty of the Optimal power flow problem becomes enlarged when new constraints are added, and it is also a challenging task for the power system operator to solve the constrained Optimal power flow problems efficiently. Therefore, this paper presents a constrained composite differential evolution optimization algorithm to search for the optimum solution to Optimal power flow problems. In the last few decades, numerous evolutionary algorithm implementations have emerged due to their superiority in solving Optimal power flow problems while considering various objectives such as cost, emission, power loss, etc. evolutionary algorithms effectively explore the solution space unconstrainedly, often employing the static penalty function approach to address the constraints and find solutions for constrained Optimal power flow problems. It is a drawback that combining evolutionary algorithms and the penalty function approach requires several penalty parameters to search the feasible space and discard the infeasible solutions. The proposed a constrained composite differential evolution algorithm combines two effective constraint handling techniques, such as feasibility rule and ɛ constraint methods, to search in the feasible space. The proposed approaches are recognized on IEEE 30, 57, and 118-bus standard test systems considering 16 study events of single and multi-objective optimization functions. Ultimately, simulation results are examined and compared with the many recently published techniques of Optimal power flow solutions owing to show the usefulness and performance of the proposed a constrained composite differential evolution algorithm.

Fuzzy logic-based approach for optimal allocation of distributed generation in a restructured power system

Fuzzy logic emerges as a powerful tool for optimizing power flow solutions, particularly in the context of deregulated power systems. By employing fuzzy logic controls, the ideal placement of distribution generators (DGs) can be determined, ensuring the reliability indices are identified through optimal power flow solutions and fuzzy logic controllers to maintain system feasibility. In a deregulated power system, strategic placement of distribution generator units plays a crucial role in minimizing power loss and enhancing overall system performance by mitigating fluctuations. To identify areas of weakness, especially within transmission companies, accessing optimal power flow algorithms becomes essential in a deregulated power system. Both transmission and distribution networks should be appropriately adjusted to alleviate congestion within the respective companies. The aggregator must assess system performance, utilizing data obtained from distribution and transmission companies within the deregulated power system.

Economical-environmental-technical optimal power flow solutions using a novel self-adaptive wild geese algorithm with stochastic wind and solar power.

This study introduces an enhanced self-adaptive wild goose algorithm (SAWGA) for solving economical-environmental-technical optimal power flow (OPF) problems in traditional and modern energy systems. Leveraging adaptive search strategies and robust diversity capabilities, SAWGA distinguishes itself from classical WGA by incorporating four potent optimizers. The algorithm's application to optimize an OPF model on the different IEEE 30-bus and 118-bus electrical networks, featuring conventional thermal power units alongside solar photovoltaic (PV) and wind power (WT) units, addresses the rising uncertainties in operating conditions, particularly with the integration of renewable energy sources (RESs). The inherent complexity of OPF problems in electrical networks, exacerbated by the inclusion of RESs like PV and WT units, poses significant challenges. Traditional optimization algorithms struggle due to the problem's high complexity, susceptibility to local optima, and numerous continuous and discrete decision parameters. The study's simulation results underscore the efficacy of SAWGA in achieving optimal solutions for OPF, notably reducing overall fuel consumption costs in a faster and more efficient convergence. Noteworthy attributes of SAWGA include its remarkable capabilities in optimizing various objective functions, effective management of OPF challenges, and consistent outperformance compared to traditional WGA and other modern algorithms. The method exhibits a robust ability to achieve global or nearly global optimal settings for decision parameters, emphasizing its superiority in total cost reduction and rapid convergence.