Multiple Power Flow Solutions Research Articles

Application of modified beetle antennae search algorithm and BP power flow prediction model on multi-objective optimal active power dispatch

The multi-objective optimal active power dispatch (MOAPD), an important part to realize the high-efficient and economic operation of power systems, widely considers the reduction of power loss, fuel cost and emission. To successfully solve the nonlinear MOAPD problems with contradictory objectives, the modified hybrid beetle antennae search (MHBAS) algorithm with adaptively-adjusted step factor is proposed in this paper. The suggested MHBAS algorithm integrates the preliminary optimization and mutation-crossover mechanisms of multi-objective differential evolution (MDE) algorithm, and has better population diversity. Furthermore, the novel fuzzy-object sorting method (FOSM) is put forward to determine the feasible Pareto fronts (PFs) of MOAPD. Seven testing cases on IEEE 30, 57, and 118-bus systems certify that, the best compromise solution (BCS) achieved by the MHBAS algorithm with FOSM is more desirable than traditional MDE and NSGA-II algorithms. Besides, the great superiority of MHBAS algorithm on PF diversity and PF uniformity are quantitatively validated by the hypervolume (HV) and inverted generational distance (IGD) indexes. Even more importantly, a feasible BP power flow prediction model which takes the basic fuel cost as the fulcrum is put forward for the first time. The innovative MHBAS-BP method, the combination of BP prediction model and MHBAS algorithm, provides great convenience for exploring the higher quality dispatching schemes near the current BCS. These multiple alternative power flow solutions obtained by NMBAS-BP method can meet the various requirements of decision makers with less time cost. In general, the proposed MHBAS-BP provides a representative application of computer technologies in solving complex MOAPD problems.

Novel Data-Driven Distributed Learning Framework for Solving AC Power Flow for Large Interconnected Systems

Recent advancement in power systems induces complexity in large-scale interconnected systems and poses challenges in performing security assessment studies at various operating conditions. Traditional model-based methods are computationally intensive and may not meet the requirements for real-time applications. This paper presents a novel data-driven framework for accelerating the process of obtaining multiple AC power flow (ACPF) solutions for large systems using deep convolutional neural networks (DCNN). DCNN models are designed and trained using various representative power flow cases from a system, whose outputs can be used to perform steady-state security assessment studies. Distributed training with multiple Graphical processing units (GPU)s is implemented using TensorFlow to reduce computation time. The proposed framework is implemented to identify critical buses and recognize the ACPF cases expected to cause steady-state bus voltage violations. The efficacy and feasibility of the proposed framework are evaluated on the Western Electricity Coordinating Council (WECC) 2028 system. Results demonstrate that the proposed framework is highly accurate and possess good interpretability in performing various transmission planning and operation assessment studies for large scale power networks.

Assessing Multiple Operationally-Stable Power Flow Solutions in Unbalanced Impedance-Grounded Systems: Initialization Procedure and Analysis

The power flow is usually formulated by nonlinear equations and may present multiple solutions. However, most of these solutions do not represent a practical situation but are mathematical findings. Remarkably, in unbalanced multiphase systems with impedance-grounded loads, a phenomenon can occur where two or more solutions may especially show practical significance. These solutions are called operationally-stable solutions (solutions which for a given loading level the nodal voltages, currents, and losses are feasible) and may be obtained in Distribution Systems (DS). In this paper, some relevant aspects regarding the multiple solutions in unbalanced grounded systems are explored: (i) the development of a simple analytical model considering the feeder and loads to analyze the multiple solutions generically; (ii) a direct procedure for initializing neutral voltages to find possible operationally-stable solutions or reduce the number of iterations to achieve convergence; (iii) a study on multiple solutions using the continuation power flow to analyze their behavior and verify their impacts on DS. The proposed assumptions have been confirmed with numerical experiments over IEEE 123, Simple NEV, and IEEE 8500 test feeders.

An efficient load flow solution for distribution system with addition of distributed generation using improved harmony search algorithms

The distribution system analysis is very important to know the system condition at any given point of time. This distribution power flow plays an important role. Many power flow techniques have been proposed in the past for distribution power flow (DPF). The implicit Z-bus Gauss–Seidel (GS) method is good when dispersed generations are modelled as PQ nodes in the distribution system but, when dispersed generations are modelled as PV nodes, it leads to divergence problems. In a Newton-like method, a slight change in the execution of the bus-type switching logic leads to an unlike convergence characteristic. Though backward/forward (BW/FW) method is effective and efficient, it slows down under heavy-load condition. Now, with the addition of distributed generation (wind/solar, etc.) at the distribution level, the classical configuration of the distribution system is also changed. This poses a need for more robust and efficient technique. This paper investigates the application of a new algorithm known as improved harmony search (IHS) for DPF. The IHS can determine multiple power flow solutions which fix the limitations of other methods while determining a solution for the highly stressed condition. The results for a standard test system are taken with IHS, Newton–Raphson (NR) and BW/FW method without and with the impact of the wind energy system, to show the potential of the proposed algorithm.

Reduced and aggregated distribution grid representations approximated by polyhedral sets

In this paper we present a novel tractable method to compute reduced and aggregated distribution grid representations that provide an interface in the form of active and reactive power (PQ) capability areas for improving transmission service operator – distribution service operator (TSO–DSO) interactions. Based on a lossless linear power flow approximation we derive polyhedral sets to determine a reduced PQ operating region capturing all voltage magnitude and branch power flow constraints of the entire distribution grid. To demonstrate the usefulness of our method, we compare the capability area obtained from the polyhedral approximation with an area generated by multiple optimal power flow (OPF) solutions for different distribution grids. While the approximation errors are reasonable, especially for low voltage (LV) grids, the computational complexity to compute the PQ capability area can be significantly reduced with our proposed method.

Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The holomorphicity, which provides global information of the curve at any regular point, enables large step sizes in the path-following procedure such that non-singular curve segments can be traversed with very few steps. When approaching singular points, we switch to the traditional predictor-corrector routine to pass through them and switch back afterward to the holomorphic embedding routine. We also propose a warm starter when switching to the predictor-corrector routine, i.e. a large initial step size based on the poles of the Pad\'{e} approximation of the derived holomorphic function, since these poles reveal the locations of singularities on the curve. Numerical analysis and experiments on many standard IEEE test cases are presented, along with the comparison to the full predictor-corrector routine, confirming the efficiency of the method.

Tracking Transformer Tap Position in Real-Time Distribution Network Power Flow Applications

The current injection power flow method is commonly used by the power distribution industry in real-time distribution management systems. The inclusion of reactive power control adjustments that simulate local voltage controllers is known to create multiple power flow solutions. The state-of-the-art for simulating local voltage controllers computes the most likely operational solution by considering the different precedences of the controlled devices, based on their speeds of response. This paper presents a novel sensitivity-based approach for simulating local controllers, which directly accounts for both controller interactions and the way in which the system state is reached. Numerical results are reported on networks with up to 3146 nodes and voltage dependent load models; the results show that the proposed approach yields probable power flow solutions that are virtually identical to those given by an implementation of the state-of-the-art time-coordinated method and with a speed-up factor around three on the large network cases.

A Sufficient Condition for Multiple Load Flow Solutions Existence in Three Phase Unbalanced Active Distribution Networks

This brief proposes an explicit sufficient condition which guarantees the existence of multiple power flow solutions in the active distribution networks. Compared to the existing methods, the proposed condition shows better result for the power flow solution space boundary limit. The solution space for node voltage has been plotted into a closed contour region where the power flow solution exists. Different cases of system unbalance have been studied to analyze their effect over multiple power flow solutions. As the proposed method depends only on present set of data, hence, it can be used as a tool for real time power flow analysis with lesser computational burden. The proposed theoretical derivation has been confirmed with numerical experiments over IEEE 13, 123 bus benchmark distribution systems.

Application of asymptotic numerical method with homotopy techniques to power flow problems

Traditional power flow methods such as the Newton-like methods are locally convergent and may be ineffective in some circumstances. In this paper, we propose a novel computational approach which associates a Newton homotopy with an asymptotic numerical method (ANM) to solve the nonlinear power flow equations. ANM is a family of algorithms based on the computation of Taylor series expansion per step. With ANM, as the homotopy path has been expressed into a closed analytical form section by section, the multiple power flow solutions on the path are computed by solving a simple polynomial equation. The proposed method provides a reliable way to study the ill-conditioned power flow problems thanks to the use of homotopy transformation and higher-order predictor of ANM. Numerical examples of several power systems are presented to validate the effectiveness of the method.

Multiple low voltage power flow solutions using hybrid PSO and optimal multiplier method

In this paper a method for computing multiple power flow solutions of power system is proposed. The proposed method determines the multiple solutions in pairs. Particle Swarm Optimization (PSO) technique is used to find the starting values of the rectangular Newton–Raphson power flow. From these starting values, the rectangular Newton–Raphson load flow determines a low voltage solution close to the first one. Optimal multipliers are then used to determine a second low voltage solution. Test results of standard IEEE 14 bus system have been shown.

Expert algorithm based on adaptive particle swarm optimization for power flow analysis

An Expert algorithm based on particle swarm optimization (PSO) technique with adaptive PSO parameters has been developed for power flow analysis under critical conditions and multiple power flow solutions. Depending on the objective functions of the current and best solutions in the present generation, unique and innovative formulas are designed for two sets of PSO parameters, inertia weight and learning factors. For faster, sure convergence and overcome the limitations of conventional methods, PSO parameters are so designed that they are highly adaptive. To the best of our knowledge, it is the first report of applying Adaptive PSO (APSO) to solve power flow problems. Multiple power flow solutions which are used for voltage stability analysis can be obtained if proposed method is used with local search as accelerating technique. The proposed algorithm proves its robustness providing reliable and better convergence under high R/X ratios and maximum loadability limits. The effectiveness and efficiency has been established showing results for standard and ill-conditioned test systems.

Robust load flow based on local search

A heuristic approach to the load flow solutions is proposed in this paper. The method is based on a perturbation technique. Voltage and phase angle of a bus is perturbed around their current values and the effect of perturbation is judged on a local network formed around the node concerned. Perturbations generating improved solutions are accepted. The method is slow but robust and is applicable in those cases when the conventional approaches fail. It can be used in finding the loadability limit, generating P-V/Q-V curves and also in finding multiple power flow solutions.

Developments in the analysis of unbalanced three-phase power flow solutions

This paper presents a new step size optimization factor to be used for solving unbalanced three-phase distribution current injection power flow. This optimization factor improves the performance of the iterative process namely at higher loading level and R/X ratio. In addition, this paper also proposes to extend the concept of this optimization factor to calculate the multiple unbalanced three-phase power flow solutions. In order to verify the effectiveness of the proposed methodologies, a practical Brazilian distribution test system and an ill-conditioned power network have been used.

The existence of multiple power flow solutions in unbalanced three-phase circuits

This paper presents a new phenomenon found for unbalanced power flow solutions: the existence of two voltage solutions at the neutral points of unbalanced three-phase circuits. The phenomenon is different from that found in traditional single-phase balanced power flow solutions. It is dependent on the degree of system or load unbalance. If the unbalance is reduced to zero, the two solutions will merge into one. This paper presents our observations and analysis on the problem. A test system is used to illustrate the practical significance of the phenomenon. We hope this work will stimulate further research on this challenging and interesting problem.

The Existence of Multiple Power Flow Solutions in Unbalanced Three-Phase Circuits

This paper presents a new phenomenon found for unbalanced power flow solutions: the existence of two voltage solutions at the neutral points of unbalanced three-phase circuits. The phenomenon is different from that found in traditional single-phase balanced power flow solutions. It is dependent on the degree of system or load unbalance. If the unbalance is reduced to zero, the two solutions will merge into one. This paper presents our observations and analysis on the problem. A test system is used to illustrate the practical significance of the phenomenon. We hope this work will stimulate further research on this challenging and interesting problem.

State-of-the-Art Methods for Electric Power Systems Voltage Stability Analysis

This paper presents a literature survey on the subject of voltage stability analysis of power systems. The survey describes several published methods and techniques used to determine voltage stability indices. These indices predict proximity to voltage instability and collapse problems. The Q-V and P-V curves; singular value decomposition; modal analysis; test function; reduced determinant; loading margin by multiple power flow solutions; local load margins; thevenin/load impedance; and energy function are the methods which have been decribed in the paper. The methods described are based on the original work that first proposed them. They are based on the power-flow system model, where the variation of real and reactive powers are assumed to be the main parameters driving the system to voltage instability. Some of the described methods were applied on the IEEE 30-bus power system.

Power system voltage stability and security assessment

The purpose of this investigation is to review the recent research progress in voltage stability and security assessment of power systems. This paper presents the fundamental concepts of voltage stability, gives a short recall of the classical voltage theory and different criteria currently available for predicting voltage collapse problems in power systems, which have been associated with multiple power flow solutions, bifurcation, dynamics of tap changers, stochastic loads, singular values, etc. The various methods for studying voltage collapse are compared. The application of expert system techniques to assist in the decision-making process of the reactive power/voltage control problem of power systems and future research directions towards voltage stability and security assessment will also be proposed in this paper.

A Generalized Circle Diagram Approach For Global Analysis Of Transmission System Performance

The global response of a power system to variations in the node constraints is considered. The relation of specific system variables to independent node parameters is calculated using a numerical technique which provides a generalization of the elementary power circle diagram. Curves which show system performance during disturbances, tradeoffs between design parameters, voltage stability limits and multiple power flow solutions are produced. The theory of the method is presented through geometrical concepts, and its application is illustrated with several examples.