Load Flow Method Research Articles

Reviews on Load Flow Methods in Electric Distribution Networks

Reviews on Load Flow Methods in Electric Distribution Networks

Competitive Analysis at the Cournot-Nash Equilibrium of an Interconnected Network

The electric power network has long been subject to monopolization, encompassing production, transportation, and distribution sectors. However, recent liberalization efforts have introduced competition into the electricity market. To understand and manage this competition, game theory, a prominent tool in economics, is frequently employed. Specifically, competition within the electricity market has been analyzed through various game-theoretical models, including Bertrand's atomicity, Cournot's homogeneity, and Nash's research competition. These models aim to achieve the Cournot-Nash equilibrium, where each participant in the market makes optimal decisions given the strategies of others. To effectively allocate production and ensure a balance between supply and demand, as well as to maintain the stability of the interconnected network, one has adopted a method that combines Load Flow techniques with game theory principles. This hybrid approach enables a strategic distribution of power production, taking into account the competitive dynamics of the market. By integrating these methodologies, one can address the complexities of competition while ensuring efficient and stable operation of the power grid. This innovative approach not only enhances the management of electricity production and distribution but also fosters a more competitive and resilient power network. Moreover, the application of game theory in this context allows for a deeper understanding of strategic interactions among market participants. It helps in predicting behaviors, formulating strategies, and anticipating market changes, thus providing a robust framework for decision-making. This is particularly crucial in a liberalized market where multiple entities vie for market share and profitability. By employing game-theoretical insights, one can simulate various market scenarios, optimize resource allocation, and enhance overall market efficiency. Furthermore, this approach supports the integration of renewable energy sources by ensuring that their variable nature is accommodated within the grid's operational dynamics. In summary, the intersection of game theory and load flow methods offers a comprehensive solution to the challenges posed by a competitive electricity market, paving the way for a sustainable and efficient energy future.

Analyzing Convergence and Accuracy of Load Flow Methods in the IEEE 39-Bus Power System

This research paper presents a comprehensive comparative analysis of load flow methods applied to the IEEE 39 bus system, focusing on Newton-Raphson, Gauss-Seidel, and two variations of the Fast Decoupled method, XB and BX. The study evaluates the convergence behavior and iteration performance of these methods across two widely used software platforms: MATLAB and Power World Simulator. Through extensive simulations, the research investigates the convergence characteristics and computational efficiency of each method, providing insights into their respective advantages and limitations. The findings offer valuable guidance for power system engineers and researchers in selecting suitable load flow methods for analyzing complex power systems.

Educational Interface of Load Flow Methods Using Matlab Graphic User’s Interface Software

this paper introduces a new created programapplication built based on MATLAB programing languageto solve power system networks at steady state problems,which include power flow studies with significant approach.The load flow solution uses iterative techniques that arenamely, Newton-Raphson, Gauss-Seidel and Fast Decouple.After obtaining their results, line changes like lineswitching, tap changer and bus changing such as busdeletion or any specific information at the same bus can beeasily achieved. Moreover, the users can enter their ownsystem, and save it to apply the pervious analysis. Thisfriendly interactive program designed to be simple for theusers with accurate results and it can be applied for anynetwork.

Optimal Frequency determination for Wind-Hydro hybrid unit using Telegrapher’s Method for Low frequency transmission lines

This study addresses the optimal load flow problem for low-frequency transmission lines connected to wind farms and pumped storage Hydropower (PSH). The losses in LF-HVac system and the voltage stability index heavily dependent on the operating frequency. Therefore, an optimal load flow (OLF) method must be incorporated to determine the proper solutions for these systems. This system analyses the load flow solutions in which newton Raphson with STATCOM requires large vector calculations with variables. So, to reduce the mathematical calculation a two-port equivalent model for transmission lines based on solutions to Telegrapher’s method has been proposed. The proposed OLF method is tested with other algorithms and implemented in IEEE 39-BUS system. The results obtained indicate that the LF method with the proposed metaheuristic algorithm gives optimal frequency for low-frequency HVac systems while maintaining the stability of system.

Photovoltaic hosting capacity assessment of a distributed network based on an improved holomorphic embedding load flow method and stochastic scenario simulation

The increasing proportion of distributed energy in the distribution network poses a significant challenge to effectively absorbing distributed generation (DG). On this premise, the DG hosting capacity (HC) assessment in the future distribution network based on the secure operation boundary of the power grid is necessary. In this paper, an improved holomorphic embedding load flow method (HELM) is employed to construct the relationship between the photovoltaic HC (PVHC) and each constraint to determine the upper limit of the comprehensive PVHC. Furthermore, a screening method of PV locations in the distribution network is constructed to screen the alternative PV locations with strong voltage regulation ability and reduce the alternative multi-point schemes, paving the way for simplifying the PVHC assessment based on a stochastic scenario simulation. Finally, a PVHC assessment based on the stochastic scenario simulation is proposed to expand the applicability of the assessment based on improved HELM. The negative impact of PV uncertainty is quantified by generating stochastic load flow scenarios based on the upper limit of the PVHC from improved HELM. The PVHC assessment in the high-voltage distribution network IEEE30 is analyzed to prove the efficiency and comprehensiveness of PVHC assessment in the distribution network.

Modified Harris Hawk algorithm-based optimal photovoltaics for Voltage Stability and Load Flow Analysis

ABSTRACT In the distribution system, proper placement of distributed generation (DG) is still a very challenging issue for getting their maximum potential benefits. Power system stability should be determined through load modeling, hybrid energy storage system (HESS), and photovoltaics (PV) modeling. This paper proposed the optimal sizing and location of photovoltaic using the Modified Harris Hawk Optimization (MHHO) algorithm. The energy generated from the photovoltaic (PV) is stored in the HESS, where the energy’s charging and discharging from the storage unit is framed with a reduced power loss (active and reactive power). The optimal sizing and placement of the PV system will provide better voltage stability. The Modified Harris Hawk Optimization Algorithm (MHHO) frames the system’s voltage stability. The Newton-Raphson load flow method is used to analyze the loading in the power system. The IEEE 33 and 69 bus systems are used to analyze the load flow to the consumers, thus analyzing the power system’s dynamic performance. The performance and voltage stability of the presented model are compared with the existing optimization techniques, which include the Firefly Algorithm (FA), Crow Search Optimization (CSO), Particle Swarm Optimization (PSO), Analytical PSO (APSO), Improved Cayote Optimization Algorithm (COA) and Whale optimization algorithm (WOA) through the MATLAB/Simulink platform.

Three‐phase steady‐state models of distributed generators with different control strategies

AbstractThis paper proposes three‐phase steady‐state models for distributed generators (DGs) with different negative control strategies. An augmented rectangular load flow method is used for three‐phase distribution systems. For two types of DGs with power electronic devices: photovoltaic power generators and doubly fed induction generators, the nodal voltage equations and output power equations are derived. Moreover, under unbalanced conditions, the strategies for mitigating the effects caused by negative sequence components are formulated as functions of the nodal voltage and the injected current. Furthermore, the models are incorporated into an augmented rectangular load flow method with nodal voltage and injected current as state variables in three‐phase systems. Case studies are conducted to verify the correctness and accuracy of the proposed models by comparing the results obtained from MATLAB and PSCAD.

Voltage Regulation in Low Voltage Distribution Networks with Embedded Photovoltaic Microgeneration

Low voltage distribution networks have been originally designed to feed loads. However, recently, small dispersed renewable generators, mainly photovoltaics, are being connected to the low voltage grids. This new operational framework represents a challenge to the planning and operation of distribution networks, since the multidimensional stochastic dependence structure of the joint behaviour of the generation and load can be very complex to model. This paper intends to give further insight to the subject by presenting a three-phase unbalanced load flow method suitable to deal with radial networks with embedded microgeneration. Some results concerning the voltage profile as obtained after Monte-Carlo simulations for different load scenarios are presented in the paper, as well as an assessment of the generation shedding procedures undertaken to control the voltage.

Interval Holomorphic Embedding Load Flow Method: A novel approach for interval analysis considering load and generation uncertainties

Interval Holomorphic Embedding Load Flow Method: A novel approach for interval analysis considering load and generation uncertainties

Cyber-constrained load shedding for smart grid resilience enhancement

With the further development of information and communication technology and their widespread use in power systems, our networks are moving towards cyber-physical systems. This paper proposes an optimal load flow method considering cyber constraints for the emergency response of smart networks to improve resilience. In the proposed method, not only the effect of cyber systems on physical systems but also the effect of physical systems on cyber systems is considered mutually. The mutual effect is that if the cyber nodes are interrupted, the cyber system can no longer send the information of generators and loads to the central controller. Also, if the load reduction in the bus exceeds a percentage in the physical network, it is practically no longer possible to feed the cyber system in that bus. In the following, the objective function is considered as the minimization of the sum of the cost of load shedding and generator production. Also, fast voltage stability index is used to determine weak buses. Finally, considering that the above model is non-linear, for this purpose, the problem is modeled by the PSO algorithm. Finally, a standard IEEE test system is used to evaluate the effectiveness of the proposed policy.

Area interchange control using the holomorphic embedding load flow method considering automatic generation control

Area interchange control using the holomorphic embedding load flow method considering automatic generation control

A novel load flow method for islanded microgrids with optimum droop coefficients

The integration of renewable energy resources into the power system has led to growing interest in the field of microgrids. These microgrids can operate in grid-connected or islanded modes.Load flow analysis is an important step for the operation and planning of the power system. The traditional load flow techniques, which use the concept of a reference bus, are not valid in microgrids, particularly when operating in islanded mode. Thus, in this study, a modified Gauss-Seidel method has been implemented in which to find the optimum values for droop coefficients, different optimisation techniques have been used. The value of droop gain impacts the load distribution among various DGs, as the fast action of droop is indicated by a higher value of droop gain. But the inappropriate value of droop gain affects the stability of the system, so typically the values are kept low due to steady state stability concerns. The optimum droop gain helps to keep the voltage and frequency within the permissible limits. The voltage profile has been improved with optimal gains for the droop coefficients, and about 4% loss reduction has been reported, proving the effectiveness of the proposed method. The method has been tested on 6-bus, 38-bus, and 40-bus islanded microgrid systems.

Analysis of Radial Distribution Systems by using Particle Swarm Optimization under Uncertain Conditions

Abstract: Losses in the network are one of the most important parts of a power distribution network, and work should be done to lower their value. The research used the Particle Swarm Optimisation (PSO) metaheuristic algorithm to investigate the impact of concurrently optimising phase balance and conductor size on the planning issues and objective functions of an imbalanced distribution system. These objective functions include power loss, voltage unbalance, total neutral current, and complicated power unbalance. Firstly, the optimisation process is applied to each goal function. Then, they are put together with weights to form a multi-objective optimisation problem. In this study, it was tried to find out how to minimise losses in electrical power distribution networks that aren't fair. Power flow and optimal DG placement are two PSO techniques that may be used to reduce losses. These changes may be applied to existing distribution systems using an effective load-flow method for a three-phase imbalanced radial distribution network. Knowing the node voltage, angle, branch current, actual power loss, wattles power loss, branch losses, etc. helps determine the network's true state. Simple formulae may be used to describe the relationship between the voltage at one end of the distribution system, the voltage at the other end, and the voltage drops throughout the whole system. An approach is developed to identify the relevant variables. The voltage's angle at the target is calculated with its magnitude. It's a process that requires time and effort. From the substation to each terminal node, the constant voltage of 1p.u. is considered. Voltage magnitude and phase angle are varied between repetitions, and voltage reductions are computed using the new parameters. The suggested approach has been applied to 19- and 25-node networks with unequal distribution. To demonstrate its efficacy, the recommended approach's speed requirements were compared to those of another recently developed technology. Good outcomes are achieved, and DG proves to be a viable option for reducing costs and improving performance.

Optimal allocation of distributed generation in active distribution power network considering HELM-based stability index

Traditionally, assessment of static voltage stability for distribution power networks with distributed generation (DG) utilizes the continuous power flow (CPF) method by calculating load margin index (LMI) at various load levels, which suffers from slow calculation speed and low accuracy when power flow calculation becomes ill-conditioned. To overcome this issue, this paper presents a novel holomorphic embedding load flow method (HELM)-based approach that calculates voltage stability indices for various types of nodes in a distribution network. Different orders of sensitivity information are calculated using the HELM method, and the criteria for assessing voltage stability are derived, which are used as constraints to optimize the location and capacity of DG. Such formulation of the optimization problem does not need to calculate the maximum load margin using CPF. Moreover, it can be effectively solved using the Genetic Algorithm and easily adaptable to various operating conditions of DG, which improve the calculation speed of the stability index. The effectiveness of the proposed approach is verified on IEEE 33-node and IEEE 69-node distribution power network models. Results show that considering the HELM VSI, the location, and capacity of DG in the distribution network can be better optimized. For the IEEE 33-node model, the total cost is reduced by approximately 2.33%, the network loss is reduced by 1.2%, and the HELM voltage stability criteria index is increased by about 4.23%; while for the IEEE 69-node system, the total cost is reduced by about 2.98%.

Holomorphic Embedding Load Flow Method in Three-Phase Distribution Networks With ZIP Loads

The Holomorphic Embedding Load flow Method (HELM) employs analytic continuation of complex analytic functions to calculate the practical (high voltage) load flow solution and provides promising convergence guarantees. Although HELM has been applied to various types of power systems, the literature has not thoroughly investigated three-phase distribution networks with common load types/connections. In this paper, we extend HELM to three-phase distribution networks with ZIP loads, while preserving its prominent convergence promises. Specifically, we introduce a HELM formulation, which emphasizes on accurate modeling of constant-current loads (and the voltage dependence of current injections) for both wye and delta connections. We perform extensive numerical experiments on standard test systems with various equipment/connection types to demonstrate the accuracy and efficacy of the proposed HELM compared with the existing literature.

A Literature Review on the Optimal Placement of Static Synchronous Compensator (STATCOM) in Distribution Networks

The existing distribution networks were designed at a time when there was virtually no embedded generation. The design methods ensured the voltage at various parts of the network remained within the limits required by standards, and for the most part, this was very successfully achieved. As Distributed Energy Resources (DERs) started to grow, the rise in voltage due to injected currents and the local impedances started to push network voltages toward, and even above, the desired upper limits. Voltage limits are based on typical appliance requirements, and long-term over-voltages will ultimately result in unacceptably short appliance life spans. Distribution Static Compensators (dSTATCOMs) are shunt-connected devices that can improve low-voltage networks’ performance by injecting currents that do not transfer real power. The currents can be reactive, negative or zero sequence, or harmonic. System performance can be improved by reducing conduction loss, improving voltage profile and voltage balance, or reducing Total Harmonic Distortion (THD). To obtain these benefits, optimal sizes of dSTATCOMs need to be placed at optimal locations within the distribution network. This paper has considered seventy research articles published over the past years related to the optimal placement and sizing of dSTATCOMs. In this study, minimization of power losses, voltage profile improvement, loadablity factor, voltage sag mitigation, and reduction in annual operating costs are considered fitness functions that are subjected to multiple constraint sets. The optimization algorithms found in the literature are categorized into six methods: analytical methods, artificial neural network-based methods, sensitivity approaches, metaheuristic methods, a combination of metaheuristic and sensitivity analysis, and miscellaneous. This study also presents a comparison among distribution network types, load flow methods optimization tools, etc. Therefore, a comprehensive review of optimal allocation and sizing of dSTATCOMs in distribution networks is presented in this paper, and guidance for future research is also provided.

MANA Formulation Based Load Flow Solution for DC Distribution Networks

This paper presents an efficient load-flow (LF) solution method for direct current distribution networks (DC-DNs). The principles of this method are based on the modified-augmented-nodal-analysis (MANA) formulation and Newton-Raphson (NR) algorithm. The guaranteed convergence and quadratic convergence conditions are also formulated using Kantorovich’s theorem. The modified IEEE 33 bus test feeder is simulated to test the proposed method and compare its performance with Laplacian Matrix based LF methods, Holomorphic Embedding LF method (HE-LFM) and classical Gauss-Seidel (GS) solution. Apart from the comparisons with these numerical methods the accuracy of the proposed method is also validated with Electromagnetic Transients (EMT) results. The proposed method offers much better convergence properties with a faster simulation speed.

A Novel Modified Decoupled Newton-Raphson Load Flow Method with Distributed Slack Bus for Islanded Microgrids Considering Frequency Variations

Microgrid load flow studies have recently attracted a lot of attention due to the introduction of independent microgrids with decentralized sources. These microgrids can be operated in grid-connected mode as well as in islanded mode. But the islanded mode operation of microgrids has some inherent limitations that cannot be addressed by conventional load flow approaches. Recent research has suggested some modifications to the traditional methods by treating system frequency as a variable parameter and leaving out the concept of slack bus. In this respect, a novel load flow method has been presented for microgrids that operate as droop-regulated distributed generations (DGs) employing distributed slack bus. The Jacobian matrix has been modified, which leads to improved convergence. Further, a comparison of the modified decoupled Newton Raphson and the modified Newton Raphson load flow techniques has been presented. Several case studies for 6-bus and 38-bus test systems, demonstrate the feasibility of the proposed load flow approach.

Fundamentals of State-Space Based Load Flow Calculation of Modern Energy Systems

Our current energy landscape is ever-changing, resulting from the ongoing energy transition and introducing a massive expansion of volatile generation feed-in and energy consumption (due to electrification). In turn, the energy supply’s requirements are also being affected. In this context, the energy system’s optimisation across all sectors will only grow in significance, especially in terms of future developments. Facilitating and researching methods for carrying out the aforementioned optimisation creates new demands pertaining to load flow simulation programmes. The volatility of specific participants and their interactions within existing power grids must be evaluated, wherefore the consideration of a large number of time steps but also dynamic simulations becomes inevitable. Carrying out such simulations is possible but very time-consuming. This article compared a variety of conventional load flow simulations such as the current iteration and Newton–Raphson methods and also introduced a novel, state-space based calculation approach, which boasts the potential of structurally increasing simulation speeds. Each of the method’s underlying principles, requirements, and mathematical correlations will be discussed and explained. In the second part of this article, the most important state-space equivalent circuit models of critical operating equipment are introduced. These models are essential for carrying out load flow simulation tests for an exemplary test network but could also be used for dynamic purposes. The previously showcased load flow methods were applied to a test network, with which the simulation methods should be validated. The results show that the state-space simulation has high accuracy while also being very flexible. All in all, the load flow calculation in state-space offers many advantages that could be an interesting alternative to conventional load flow simulations, especially for the analysis of complex, time series-based, and intelligently controlled smart grid power systems. In this context, the direct application of system theoretical methods for stability calculations, controllability, and dynamic system studies is to be mentioned. Optimisation options regarding the processes within the state-space calculation software still promise further significant increases in performance.