Power Flow Method Research Articles

Decentralized Operations of Industrial Complex Microgrids Considering Corporate Power Purchase Agreements for Renewable Energy 100% Initiatives in South Korea

With the rise of environmental policies and advanced technologies, power systems are transitioning from centralized to decentralized systems, incorporating more distributed energy resources (DERs). This shift has increased interest in the operational functions of microgrids (MGs). The “Renewable Energy 100%” (RE100) campaign is pushing companies to adopt renewable energy. In South Korea, industrial complex microgrids (ICMGs) aim to achieve RE100 through corporate power purchase agreements (PPAs) with renewable energy providers. ICMGs need to operate in both grid-connected and islanded modes, facing challenges in power transactions due to different operating agents. This study proposes a decentralized optimal power flow (OPF) method using the separable augmented Lagrangian relaxation (SALR) algorithm to solve these power transaction problems without disclosing internal information. The proposed method decomposes the centralized OPF problem into subproblems for each ICMG and solves them in a distributed manner, sharing only transaction prices and amounts. Numerical results from the case study validate the effectiveness of the proposed method.

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.

Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow

Multi-Dimensional Optimal Power Flow (MDOPF) is a fundamental task in power systems engineering aimed at optimizing the operation of electrical networks while considering various constraints such as power generation, transmission, and distribution. The mathematical model of MDOPF involves formulating it as a non-linear, non-convex optimization problem aimed at minimizing specific objective functions while adhering to equality and inequality constraints. The objective function typically includes terms representing the Fuel Cost (FC), Entire Network Losses (ENL), and Entire Emissions (EE), while the constraints encompass power balance equations, generator operating limits, and network constraints, such as line flow limits and voltage limits. This paper presents an innovative Improved Kepler Optimization Technique (IKOT) for solving MDOPF problems. The IKOT builds upon the traditional KOT and incorporates enhanced local escaping mechanisms to overcome local optima traps and improve convergence speed. The mathematical model of the IKOT algorithm involves defining a population of candidate solutions (individuals) represented as vectors in a high-dimensional search space. Each individual corresponds to a potential solution to the MDOPF problem, and the algorithm iteratively refines these solutions to converge towards the optimal solution. The key innovation of the IKOT lies in its enhanced local escaping mechanisms, which enable it to explore the search space more effectively and avoid premature convergence to suboptimal solutions. Experimental results on standard IEEE test systems demonstrate the effectiveness of the proposed IKOT in solving MDOPF problems. The proposed IKOT obtained the FC, EE, and ENL of USD 41,666.963/h, 1.039 Ton/h, and 9.087 MW, respectively, in comparison with the KOT, which achieved USD 41,677.349/h, 1.048 Ton/h, 11.277 MW, respectively. In comparison to the base scenario, the IKOT achieved a reduction percentage of 18.85%, 58.89%, and 64.13%, respectively, for the three scenarios. The IKOT consistently outperformed the original KOT and other state-of-the-art metaheuristic optimization algorithms in terms of solution quality, convergence speed, and robustness.

Restructured electricity market strategies for the Indian utility system using support vector regression and energy valley optimizer

Restructuring the electricity market has led to the establishment of a competitive open market environment. The electricity market has introduced uncertainty and risk in the economic sector conventionally owned by the state. The power generated in the generating station is transferred to the distribution side in the power markets, which share a common transmission network. The power transfer will be in bulk amounts and needed to operate the electricity market securely and economically. The bulk amount of power transfer relies on accurately estimating Available Transfer Capability (ATC), representing the maximum allowable power flow through the existing transmission network while maintaining system reliability. The estimation of the ATC using a proposed hybrid method. The hybrid method comprises Repeated Power Flow (RPF) and Support Vector Regression (SVR) methods. The electricity market participants such as sellers and buyers submit bids to maximize their profit with the help of ATC values. The linear bid function is proposed to formulate participant strategies. Each participant will submit the availability of power requirement and willing price in the linear bid function. The Energy Valley Optimizer (EVO) algorithm is proposed to maximize the profit of each participant. The EVO algorithm efficiently explores a vast solution space, considering complex constraints and uncertainties inherent in the market dynamics to enhance economic gains. The proposed work is tested on the practical UPSEB (Uttar Pradesh State Electricity Board) 75-bus Indian utility system.

A novel stochastic power flow calculation and optimal control method for microgrid based on multivariate stochastic factors fusion – Sensitivity

The stochasticity of power flow of distributed generations (DGs) and load in the microgrid has great influence on power flow distribution and voltage quality of the distribution network. For improving the voltage quality of the distribution network, the questions need to be further studied, which include the description of the stochasticity of the power flow in the microgrid and the impact of the microgrid into the distribution network on the power flow. Therefore, a novel stochastic power flow calculation and optimal control method for the microgrid based on multivariate stochastic factors fusion-sensitivity (MSFF-sensitivity) is proposed in this paper. Firstly, the multivariate stochastic factors fusion (MSFF) function is developed by using the probability density function to extract the stochasticity and correlation of power flow among different stochastic factors in the microgrid, which are effectively unified. Furthermore, the fusion-sensitivity (F-sensitivity) of the power flow in the microgrid integrated into the distribution network is constructed to accurately characterize the influence degree of various stochastic factors in the microgrid on the power flow of the distribution network. Based on this, the output power of the stochastic factor is adjusted to optimally control the power flow of the distribution network. Finally, the algorithm verification suggests that, compared with the conventional power flow methods, the method proposed in this paper is more suitable for the microgrid. The influence of stochastic power flow on the distribution network can be effectively reduced and the voltage quality of the distribution network can be improved by optimizing control of the power flow in the microgrid integrated into the distribution network.

Dynamic compensation of active and reactive power in distribution systems through PV-STATCOM and metaheuristic optimization

This article presents a heuristic methodology to address the operation problem of PV-STATCOMs, focusing on the dynamic compensation of active and reactive power to minimize daily energy losses and costs associated with purchasing energy in distribution networks. The methodology is developed using a master-slave type optimization approach. In the master stage, potential solutions are generated using an optimization algorithm based on the salp swarm. In contrast, the slave stage evaluates these solutions using the power flow method by successive approximations. The methodology was evaluated in two test systems, with 33 and 69 nodes, varying the power factor of each PV-STATCOM. The results demonstrate a significant reduction in both energy losses in the network and the cost of purchasing energy at the substation. Furthermore, the efficiency of the salp swarm algorithm for effective resolution of the problem is confirmed. This approach contributes to optimizing the operation of PV-STATCOMs and highlights the proposed algorithm's applicability and effectiveness in practical distribution network environments.

The planning method of new energy distribution network in plateau area based on local accommodation

Abstract The planning method of new energy distribution network in plateau area based on local accommodation is studied to improve the local accommodation capacity of new energy distribution network in plateau area. The framework of new energy distribution network planning in the plateau area is constructed, and the distribution network equipment suitable for the plateau environment is selected based on the harsh environment in the plateau area; in the framework of new energy distribution network planning in plateau area, a bi-level planning model considering multi-flexible resource coordinated scheduling and energy storage is established. The upper level planning model takes the maximum accommodation of new energy as the objective, and the lower level planning model takes the optimal daily operation benefit of energy storage under the given configuration as the optimization objective; the probabilistic power flow method and C-PSO are used to solve the bi-level model. The experiment shows that this method ensures the stability of the new energy distribution network in the plateau area, reduces the amount of abandoned wind energy and the operating cost, and improves the local accommodation capacity of the core higher than the distribution network.

A novel solution methodology for electrical vehicles charging schedule in coordinated with full flexible resources in microgrid

This paper proposes a new model for the day-ahead Electric Vehicle charging schedule in Microgrids (MGs) with flexible resources such as Wind Turbine (WT) and Photovoltaic (PV) electrical power, Combined Heat and Power (CHP), Energy Storage Source (ESS), and load Demand Responses (DR). The proposed Mixed Integer Nonlinear Multi-Objective Optimization (MINMO) model considers uncertainty properties with optimal operation objects. The cost function, and power loss minimization are the proposed model's objects for considering optimal operation objects. This model is solved by a three-level decomposition method in master-sub problem presentation and Binary-Continues PSO algorithm (BC PSO) to quickly calculate the optimal solution. In the first layer, the main constraint of electric vehicle aggregators (EVAs) is satisfied by the binary PSO algorithm. According to the top-layer solution, flexible recourses are managed to satisfy the operation objects by the Bi-level Continues PSO algorithm in the second layer. Then, after converging to the optimum solution of these two layers, Electric Vehicles (EVs) charging stations are solved at the last layer by algebraic equations. Finally, the efficiency of the proposed method is illustrated via its application in IEEE 33-bus MG system. The numerical results show that the proposed solution methodology reduces the runtime of the problem up to 95 % compared to intelligence-based and full Newton–Raphson AC power flow method. Also, numerical results illustrate that considering CHP and DR in addition to the other flexible resources reduces the operation cost and power loss up to 21 % and 5 % respectively. In top of that the minimum total cost for day-ahead EV charging schedule by the proposed model and solution methodology is 578,312.7$.

Intelligent method for Power flow using Artificial Neural Network with UPFC

It is slightly difficult to transmit such a large amount of electricity in very flexible and efficient way as the size of conventionally used relay and protective devices will increase while transmitting such a large amount of electricity which will increase the operating cost. So for transmission of such a large amount of electricity, Flexible Alternating Current Transmission Systems (FACTS) will have been found to be promising aspect in terms of the analysis of the power system. In this paper the comparative analysis of unified power flow controller(upfc) is presented in presence of LG fault. ANN controllers are applied in UPFC in MATLAB/SIMULINK environment. There is significant reductions in oscillations in rotor angle deviation of multimachine systems using ANN controller compare to conventional PI controller. Hardware prototype model of UPFC also shows improvement in voltage stably in multimachine. There is improvement in rotor angle stability of power system using ANN controller compared to conventional PI controller. Oscillations are reduced.

Linear Power Flow Method for Radial Distribution Systems Including Voltage Control Devices

Linear Power Flow Method for Radial Distribution Systems Including Voltage Control Devices

Large scale penetration impact of PMS-WTGS on voltage profile and power loss for 5-bus, 330kV system of the Nigerian grid

In recent times, adverse environmental changes and the gradual reduction in fossil fuel deposits is making integration of renewable energy secure global attention. This paper therefore investigates the effect of high penetration of wind power on power loss and voltage profile of 52-bus, 330kV Nigerian grid. Modeling and simulation of the study were successfully done using the Continuation Power Flow method and Power System Analysis Toolbox in the Matrix Laboratory environment. The Ant Colony Optimization (ACO) technique codes were used to determine the best sites and sizes of Permanent Magnet Synchronous-based Wind Turbine Generators (PMS-WTGs) on the grid as nonoptimal placement and size of PMS-WTGs will result into active power losses and poor voltage profile. The ACO and power flow analysis indicated two load buses, Aladja bus and Yola bus as best sites for PMS-WTGs with optimal sizes of 100MW and 197MW respectively. The result shows a decrease in the system's active (42.1%) and reactive (43.9%) power losses while heightening voltage magnitudes of critical buses to statutory values and enhancing the grid power quality. The overall results indicate that integrating 297MW PMS-WTGs improves voltage stability and power loss reduction by maximizing system loadability and reducing line losses.

Dynamic vulnerability assessment of hybrid system considering wind power uncertainty

The stochastic volatility of wind power introduces numerous uncertainties to the security and stability of the hybrid system, which in turn affects the overall vulnerability level of the system. In this study, a wind power output model incorporating the effects of wind abandonment and uncertainty factors is established. Additionally, a hybrid optimal power flow (OPF) method considering economic dispatch, stochastic trip, and islanding strategies is developed to simulate the power flow dispatch during cascading failures. Furthermore, a set of indexes describing the global dynamic vulnerability of the hybrid system is proposed to reveal the effects of changes in wind power uncertainty and penetration levels on the hybrid system in the short term. Simulations were conducted on an adapted IEEE118 system, and the results demonstrate that an increase in wind power uncertainty and penetration will exacerbate the system’s vulnerability. This severity is particularly pronounced during peak and valley load periods, making the hybrid system more susceptible to large-scale outages. When the wind power uncertainty level grows to 4, the overall vulnerability level of the hybrid system increases by 102.3% compared to the initial uncertainty case. When the wind penetration level reaches 46%, the overall vulnerability level rises by 75.9% compared to the initial system. These findings emphasize the sensitivity of the hybrid system to different levels of wind power uncertainties and penetrations, providing evidence-based support for the prevention of system cascade failures.

Complex affine arithmetic based uncertain sensitivity analysis of voltage fluctuations in active distribution networks

The uncertainties of distribution generations (DGs) and loads lead to severe voltage fluctuations in active distribution networks (ADNs). Meanwhile, energy storage systems (ESSs) and static var compensators (SVCs) can mitigate the uncertainties of power injections by regulating the active and reactive power. Considering the variations of multiple uncertain factors, this paper proposes a complex affine arithmetic (CAA) based uncertain sensitivity analysis method of voltage fluctuations in ADNs. First, affine models of active and reactive power injections are established. The correlations of noisy symbols are used to reflect the mitigation effects of ESSs and SVCs on the uncertainties introduced by DGs and loads. Next, sensitivity indicators of voltage fluctuations are defined based on the transitivity of noisy symbols. Then, a calculation method for sensitivity indicators based on the micro-increments of coefficients is proposed. Combined with the obtained indicators, a fast sensitivity method for calculating interval values of voltages is further proposed. The modified IEEE 33-bus system is tested to validate the accuracy and efficiency of the proposed method by comparison with the continuous utilization of power flow method. Moreover, the 292-bus system is tested to validate its applicability in a large distribution system. Facts have proved that this method improves the efficiency and reliability of calculations, and in different scenarios, it can achieve fast calculation of nodes and online analysis of the voltage fluctuation range in uncertain environments, provides an effective tool for voltage quality management in active distribution networks.

Assessment of photovoltaic generation penetration effect on the maximum loadability of the system

This paper proposed a method to investigate the effect of increasing PV penetration on the voltage stability of an IEEE 14-bus test system considering maximum PV penetration and system loadability limit. The critical bus of the test system has been decided based on nose curve analysis. The solar PV system is deployed with the most critical bus of the system. The effect of increasing PV penetration on the improvement in the loading capacity of various power system components like transmission lines, transmission line transformers, and generators is investigated over the adopted test system. Based on solar PV penetration up to 100 MW, the maximum loadability limit of the IEEE 14-bus test system increases, as shown by the results. Bus 14 is found to be the most severe bus of the test system using the continuation power flow (CPF) method. However, in some cases, overloading situations develop after a certain limit of PV penetration in the power system. In this condition, the overloading of the power system equipment is improved by the use of a Static Synchronous Compensator (STATCOM) at bus number 14, a double circuit line in the critical line (9–14), and Static Synchronous Series Compensator (SSSC) in the most severe line (9–14) in the system. The maximum loadability of the system gets maximum enhanced from 4.0349 p.u. to 4.5602 p.u. under simultaneous use of solar PV generation, SSSC, and STATCOM at the most critical bus and in most severe line of the system. As evidence, the enhancement in maximum loadability of the system found using the proposed method has been also compared with the existing research. The maximum system loadability has been also enhanced under normal and (N-1) contingency conditions by the use of PV penetration in the system. PSAT/MATLAB software is used for simulation and maximum loadability has been investigated by continuation power flow (CPF) method.

K-Medoids clustering applications for high-dimensionality multiphase probabilistic power flow

Actual power systems’ planning studies require the stochastic modeling of networks due to their increasing penetration of uncertain parameters, such as probabilistic-nature loads and renewable generation features. Although numerous Probabilistic Power Flow (PPF) methods have been presented in the literature, the scalability of such tools is still under study due to the ‘curse of dimensionality’, which states that the probabilistic methods lose their accuracy with the increase of random input variables. Since many authors are using clustering algorithms to solve the PPF, mainly because of their easy implementation and good computational precision, this paper proposes for the first time the K-Medoids clustering method to model uncertainties in unbalanced distribution systems. Modifications in the clustering algorithm are included to improve its accuracy in view of a large set of input variables. The multiphase modeling of networks is also considered to represent the inherent unbalance of distribution systems correctly. Simulations were carried out using the IEEE unbalanced test-feeders IEEE 123 and the large-scale system IEEE 8500, which includes more than 2000 input variables. Results show that K-Medoids are a better alternative in relation to other numerical/approximation approaches, such as Monte Carlo Simulation or Point Estimate Methods, because it is faster and presents great accuracy, especially for large-scale applications. Comparisons were also made regarding other clustering approaches, highlighting the benefits of the proposed one in scalability.

Checking Loadability Limits and Finding Optimal Location and Size of SVC to Improve Loadability

Voltage instability is a significant issue that could happen in power systems and sometimes leads to the outage of the system. Voltage instability study is important in power system planning and continual operation. In addition, the maximum loadability ranking process of buses can be performed by computing line stability while increasing the reactive power loads.In this paper, by using Power System Analysis Toolbox (PSAT); the IEEE 30 bus system is used to identify the voltage instability by using the Continuation Power Flow (CPF) method. Also, optimal sizing and location of SVC devices to improve the loadability in the system.

An Extended Continuation Power Flow Method for Static Voltage Stability Assessment of Renewable Power Generation-Penetrated Power Systems

The continuation power flow method (CPF) has been extensively used for obtaining the static voltage stability limit of power systems, which provides important guidance for the stable operation. However, the conventional CPF cannot account for the dynamic characteristics of renewable power generation, thus resulting in prominent errors for renewable power generation-penetrated power systems. In this paper, we investigate the static voltage stability assessment (SVSA) of power systems with high penetration of rgb0,0,0renewable power generation (RPG). An extended Jacobian matrix is firstly established by considering the dynamic characteristics of synchronous generators (SG) and renewable power generation in constant AC voltage control mode (CVRPG). Based on the extended Jacobian matrix, an extended CPF method is proposed for SVSA of the power system and a reactive power sensitivity index is proposed to indicate the voltage support capability of nodes. Simulation results show that the proposed extended CPF method has higher accuracy than conventional CPF in assessing the static voltage stability of power systems with high penetration of RPG. It is also revealed that that the voltage support capability of each node rises as the proportion coefficient is increases.

Flexible energy management of storage-based renewable energy hubs in the electricity and heating networks according to point estimate method

Hubs contain sources and storages that can transfer and store energy. It is predicted that the energy management of hubs enhances the network's economic and technical status. Therefore, the paper presents flexible energy management of energy hubs linked with electrical and thermal grids. In the energy hub, wind and photovoltaic systems generate electricity, and bio-waste units are utilized to concurrently produce electricity and heat power. Compressed air and thermal energy storage control the flexibility of the hubs. The objective function minimizes the expected cost of energy injected by the upstream grid. Constraints are network optimal power flow equations, operation model, and flexibility limit of the hub. The design has uncertain parameters caused by the load, energy price, and unpredictable renewable power. The point estimation technique helps model these uncertain variables to overcome the high volume of the problem and accurately evaluate the flexibility. Contributions include evaluating the performance of compressed-air storage and bio-waste units equipped with combined heat and power technology in the energy hub, considering the flexibility limit of hubs in both electrical and thermal sectors due to uncertain renewable power, using the point estimation method for modeling the uncertainties of hubs’ energy management to reduce computation time and provide accurate calculation of flexibility. The scheme is tested using a standard case, where the results show the ability of energy hubs to enhance and promote the economic and operation status of electricity and heating grids by about 36.5% and 36%− 43%, respectively, in comparison with the power flow method. Storages can extract 100% flexibility conditions for hubs. The scheme has succeeded in providing high flexibility conditions by proper energy management of compressed-air and thermal storage. Furthermore, the presence of the storage equipment beside wind, solar, and bio-waste renewable sources in the form of a hub, and energy management of the hubs have led to a more suitable economical and operational state of electrical and thermal networks compared to power flow studies.

Power Flow Solution on Multi-Terminal HVDC Systems: Supergrid Case

High Voltage Direct Current (HVDC) systems offer distinct advantages for the integration of offshore wind farms to inland grid system. HVDC transmission system based on Voltage Source Converter (VSC) enables multi-terminal use HVDC for the integration of large-scale wind power in the North Sea. That network requires a special formulation for power flow analysis as opposed to the conventional method employed on AC networks. This paper presents a sequential AC/DC power flow algorithm, which is proposed for the analysis of multi-terminal VSC HVDC (VSC-MTDC) systems. This sequential power flow method can be implemented easily in an existing AC power flow package and is very flexible when compared with unified methods. Gauss-Siedel is used to solve DC power balance equations, as it offers two keys advantages: very fast and simple computational implementation, and errors do not accumulate during the calculation. The algorithm is tested using the WSCC 3-machine, 9-bus system with a 3-terminal MTDC network and the results are compared with those obtained from DIgSILENT PowerFactoryTM demonstrating the validity of the proposed algorithm. As an aggregate value, a representative test case of the projected scheme for the phase I of the Supergrid project on the North Sea is presented. The proposed approach presented in this paper is used to calculate DC power flows for some scenarios.

A novel approach for hybrid system simulation and design based on an enhanced load flow calculation methodology

This article presents a modified method of performing power flow calculations as an alternative to pure energy-based simulations of off-grid hybrid systems. The enhancement consists in transforming the scenario-based power flow method into a discrete time dependent algorithm with the inclusion of bus and controller dynamics. The output of the simulation can be then used to run economic calculations as well as for the evaluation of the technical feasibility of a given network configuration.