Optimal Reactive Power Flow Problem Research Articles

Learning Provably Stable Local Volt/Var Controllers for Efficient Network Operation

This paper develops a data-driven framework to synthesize local Volt/Var control strategies for distributed energy resources (DERs) in power distribution grids (DGs). Aiming to improve DG operational efficiency, as quantified by a generic optimal reactive power flow (ORPF) problem, we propose a two-stage approach. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> stage involves learning the manifold of optimal operating points determined by an ORPF instance. To synthesize local Volt/Var controllers, the learning task is partitioned into learning local surrogates (one per DER) of the optimal manifold with voltage input and reactive power output. Since these surrogates characterize efficient DG operating points, in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">second</i> stage, we develop local control schemes that steer the DG to these operating points. We identify the conditions on the surrogates and control parameters to ensure that the locally acting controllers collectively converge, in a global asymptotic sense, to a DG operating point agreeing with the local surrogates. We use neural networks to model the surrogates and enforce the identified conditions in the training phase. AC power flow simulations on the IEEE 37-bus network empirically bolster the theoretical stability guarantees obtained under linearized power flow assumptions. The tests further highlight the optimality improvement compared to prevalent benchmark methods.

A novel solution for the optimal reactive power dispatch problem using an artificial neural network integrated with the firefly optimization algorithm

This article applies a novel intelligence technique to solve power system issues faced daily. Compensation for reactive power is a significant issue faced by power system operators in research. The solution can be obtained by handling a multi-objective task and multiconstraints by reducing the active power loss and minimizing the voltage deviation at the load end. The novelty of the research focuses on integrating artificial neural network techniques with the firefly algorithm, a novel optimization algorithm for attaining an objective function. The Levenberg–Marquardt back-propagation algorithm is most suited for proper tuning of the control variables. The objective of this research can be attained by appropriately tuning the control variables connected with the IEEE test bus systems, which helps to maximally improve the voltage profile. Existing research studies have focused on reactive power management, which is attained by solving optimal reactive power flow problems employing nature-inspired approach techniques such as the symbiotic organism search algorithm, the cuckoo search algorithm, the black hole algorithm, the krill herd algorithm, and whale optimization. The evolving strategy, the firefly algorithm (FFA), minimizes the multiconstraint functions more competently and effectively than any conventional algorithm. To showcase the strength of the firefly algorithm incorporating AI, it is examined on standard IEEE test bus systems, namely, the 14-, 30-, and 58-bus networks. The obtained results quantify the effectiveness of the proposed methodology, that is, the artificial intelligence technique implementing the firefly algorithm gives better results than conventional methods.

Improved adaptive gaining-sharing knowledge algorithm with FDB-based guiding mechanism for optimization of optimal reactive power flow problem

Improved adaptive gaining-sharing knowledge algorithm with FDB-based guiding mechanism for optimization of optimal reactive power flow problem

A Mathematical Programming Approach for Allocation and Analysis of TCSC in Power Transmission Systems

In this paper, a mathematical programming approach based on a branch and bound (BB) algorithm is proposed in order to determine the optimal allocation of thyristor-controlled series compensators (TCSC) in electrical power transmission systems, considering line thermal limits. The TCSC modeling is added in the Y-bus matrix, facilitating the computational implementation. BB-Y is the methodology used in this paper aiming to maximize the loading of the system considering a certain quantity of TCSC. In addition, the proposed algorithm is implemented for another test, using a determined number of TCSC, in order to improve the network voltage profile and minimize the total transmission losses. The methodology uses an interior point method to solve the problem relaxed, modeled as a reactive optimal power flow problem. Simulations are performed on the IEEE 118-bus test system, allocating different quantities of TCSC to find the maximum load the system can support. Given a certain number of TCSC, previously defined for a specific load, the TCSC are reallocated considering different objectives. For two TCSC the time for relocation is shorter than 4 seconds. The results also show that from three TCSC onwards, the maximum load increasing is not relevant, being around 0.3%. Therefore, the conclusion is that the algorithm has a low processing time, and conservative solutions allied with the presented methodology can be used in the optimal allocation of TCSC, what the aim is to optimize the systems performance.

Efficient Hybrid Algorithm Solution for Optimal Reactive Power Flow Using the Sensitive Bus Approach

This paper presents the design and application of an efficient hybrid algorithm for solving the Optimal Reactive Power Flow (ORPF) problem. The ORPF is formulated as a nonlinear constrained optimization problem where the active power losses must be minimized. The proposed approach is based on the hybridization of Particle Swarm Optimization (PSO) and Tabu-Search (TS) technique. The proposed PSO-TS approach is used to find the settings of the control variables (i.e. generation bus voltages, transformer taps, and shunt capacitor sizes) which minimize transmission active power losses. The bus locations of the shunt capacitors are identified according to sensitive buses. To show the effectiveness of the proposed method, it is applied to the IEEE 30 bus benchmark test system and is compared with PSO and TS without hybridization, along with some other published approaches. The obtained results reveal the effectiveness of the proposed method in dealing with the highly nonlinear constrained nature of the ORPF problem.

A primal–dual penalty-interior-point method for solving the reactive optimal power flow problem with discrete control variables

The Optimal Reactive Power Flow (ORPF) problem has been used as an important computational tool for power system planning and operation. Its mixed-discrete version (DORPF) is formulated as a non-convex, non-linear optimization problem with discrete and continuous variables, which is aimed at minimizing the transmission losses while meeting the power demand and enforcing operational and physical limits of the system. Although the DORPF problem has been solved by a myriad of methods, some of them present regularization problems associated with poor matrix-conditioning in the optimal solution, some do not provide for rapid infeasibility detection and some do not provide effective ways for handling the discrete nature of the control variables. Although some of these complicating issues have been tackled separately in the literature by various studies, a method that addresses all these issues has not yet been proposed for solving the DORPF problem. In this paper, an integration of optimization approaches is proposed for handling all such complicating issues. The basis of this approach is a primal–dual penalty-interior-point method, which integrates the good properties of penalty methods (e.g. regularization effects on the constraints and rapid infeasibility detection) and interior-point methods (e.g. scalability and good convergence behavior), without suffering from their disadvantages. In the proposed approach, this method is integrated with a sinusoidal penalty function method for handling the discrete nature of the control variables of the DORPF problem, together with a specific inertia correction strategy designed to avoid local maximizers associated with such a penalty function. Numerical tests carried out with the IEEE 30-, 57-, 118- and 300-bus systems focus on showing that all the complicating issues have been addressed by the proposed method. Comparisons with the results obtained by interior-point methods are also provided.

Solution of the Optimal Reactive Power Flow Problem Using a Discrete-Continuous CBGA Implemented in the DigSILENT Programming Language

The problem of the optimal reactive power flow in transmission systems is addressed in this research from the point of view of combinatorial optimization. A discrete-continuous version of the Chu &amp; Beasley genetic algorithm (CBGA) is proposed to model continuous variables such as voltage outputs in generators and reactive power injection in capacitor banks, as well as binary variables such as tap positions in transformers. The minimization of the total power losses is considered as the objective performance indicator. The main contribution in this research corresponds to the implementation of the CBGA in the DigSILENT Programming Language (DPL), which exploits the advantages of the power flow tool at a low computational effort. The solution of the optimal reactive power flow problem in power systems is a key task since the efficiency and secure operation of the whole electrical system depend on the adequate distribution of the reactive power in generators, transformers, shunt compensators, and transmission lines. To provide an efficient optimization tool for academics and power system operators, this paper selects the DigSILENT software, since this is widely used for power systems for industries and researchers. Numerical results in three IEEE test feeders composed of 6, 14, and 39 buses demonstrate the efficiency of the proposed CBGA in the DPL environment from DigSILENT to reduce the total grid power losses (between 21.17% to 37.62% of the benchmark case) considering four simulation scenarios regarding voltage regulation bounds and slack voltage outputs. In addition, the total processing times for the IEEE 6-, 14-, and 39-bus systems were 32.33 s, 49.45 s, and 138.88 s, which confirms the low computational effort of the optimization methods directly implemented in the DPL environment.

Minimizing Power Loss Using Modified Artificial Bee Colony Algorithm

Electrical energy losses are found in any part of the power system. In the power system, it is essential to minimize the real power loss in transmission lines. The voltage deviation at the load buses through controlling the reactive power flow is very important. This ensures the secured operation of power systems regarding voltage stability and the economics of the process due to loss minimization. In this paper, the Modified Artificial Bee Colony (MABC) algorithm is implemented to solve the power system's optimal reactive power flow problem. Generator bus voltages, transformer tap positions, and settings of switched shunt of compensators are used as decision variables to control the reactive power flow. These control variable values are adjusted for loss reduction. MABC algorithm is tested on the standard IEEE-30 bus test system. The results are compared with Firefly algorithm (FA) and Artificial Bee Colony (ABC) algorithm method to prove the effectiveness of the newest algorithm. The power loss results are quite productive, and the algorithm is the most efficient than the other methods such as ABC algorithm and FA algorithm. These results are produced by Matlab 2017b.

Reducing the Number of Control Actions in the Discrete Reactive Optimal Power Flow

This paper proposes a new formulation for the Discrete Reactive Optimal Power Flow problem (DROPF) that aims at reducing the number of control actions of the problem. For such a purpose, additional constraints are introduced in the classical model to the DROPF problem so as to represent specific behaviors of voltage control devices in the electrical system. These behaviors involve the actuation of a control device only when the voltage magnitude limit of the bus controlled by such device is effectively reached. The proposed DROPF model is solved by the branch-and-bound method implemented in the free solver BONMIN. Numerical tests were performed using the IEEE 14, 30 and 118 bus electrical systems and demonstrated the efficiency of the proposed model. The results are compared with the ones obtained by a classical DROPF.

An MISOCP-Based Solution Approach to the Reactive Optimal Power Flow Problem

In this letter, we present an alternative mixed-integer non-liner programming formulation of the reactive optimal power flow (ROPF) problem. We utilize a mixed-integer second-order cone programming (MISOCP) based approach to find global optimal solutions of the proposed ROPF problem formulation. We strengthen the MISOCP relaxation via the addition of convex envelopes and cutting planes. Computational experiments on challenging test cases show that the MISOCP-based approach yields promising results compared to a semidefinite programming based approach from the literature.

Optimal Reactive Power Flow for Large-Scale Power Systems Using an Effective Metaheuristic Algorithm

In this paper, stochastic fractal search method (SFS) is employed for solving the optimal reactive power flow (ORPF) problem with a target of optimizing total active power losses (TPL), voltage deviation (VD), and voltage stability index (VSI). SFS is an effective metaheuristic algorithm consisting of diffusion process and two update processes. ORPF is a complex problem giving challenges to applied algorithms by taking into account many complex constraints such as operating voltage from generators and loads, active and reactive power generation of generators, limit of capacitors, apparent power limit from branches, and tap setting of transformers. For verifying the performance, solutions of IEEE 30 and 118-bus system with TPL, VD, and VSI objectives are found by the SFS method with different control parameter settings. Result comparisons indicate that SFS is more favorable than other methods about finding effective solutions and having faster speed. As a result, it is suggested that SFS should be used for ORPF problem, and modifications performed on SFS are encouraged for better results.

Comparison of optimal reactive power flow model in the polar form and the mixed polar form

This paper establishes the optimal reactive power flow (ORPF) model in the polar form and the mixed polar form. The analysis shows that the ORPF model in the polar form not only has less calculation amount of equality constraints than the ORPF model in the mixed polar form, but also has more concise expressions, which makes it easier to understand, analyze, and remember. The test results of IEEE30, 118, 300, 1047 bus systems show that the ORPF model in the polar form obtains the same optimal value and iteration number as the ORPF model in the mixed polar form, but its calculation time is shorter, and the solving efficiency is higher. With the increasing scale of modern power system, the calculation time of ORPF problem rises, so it is necessary to improve its solving efficiency. The ORPF model in the polar form is more suitable for power system analysis and calculation because of its high solving efficiency.

Solving large-scale reactive optimal power flow problems by a primal–dual $$\hbox {M}^{2}\hbox {BF}$$ approach

In this paper, we propose a predictor–corrector primal–dual approach for the doubly modified logarithmic barrier function ($$\hbox {M}^{2}\hbox {BF}$$) method in order to solve Optimal Reactive Power Flow (ORPF) problems. The $$\hbox {M}^{2}\hbox {BF}$$ is a modification of the Polyak’s modified logarithmic barrier function (MBF) and is also a particular element of a recent family of nonquadratic penalty functions for augmented Lagrangian methods for handling convex problems only with inequality constraints. We also propose a global convergence strategy to be inserted in the proposed algorithm, which is developed over weak assumptions concerning the primal Hessian matrix. The resulting predictor–corrector primal–dual $$\hbox {M}^{2}\hbox {BF}$$ approach is applied for solving ORPF problems involving power systems with 57, 89, 118, 200, 300, 1354, 2007 and 2869 buses. A comparison with two state-of-the-art methods is performed. Numerical results show that the proposed approach is competitive and capable of solving ORPF problems for small to large-scale power systems.

Interior/exterior-point methods with inertia correction strategy for solving optimal reactive power flow problems with discrete variables

Interior/exterior-point methods have been widely used for solving Optimal Reactive Power Flow problems (ORPF). However, the utilization of such methods becomes difficult when transformer taps and/or capacitor/reactor banks are more rigorously represented in the problem formulation by means of discrete control variables. This work investigates the solution of the ORPF problem when transformer tap ratios are modeled as discrete variables. The solution method proposed handles discrete variables by means of sinusoidal penalty function, while the penalized problems are solved by an exterior-point method. An inertia correction strategy is proposed in order to assure that only local minima are obtained for the penalized problems. New search directions are also investigated that combine predictor and corrector directions. Numerical simulations are performed involving the IEEE 14, 30 and 57 bus systems. The results show the efficiency of the proposed inertia correction strategy and also reveals that the proposed exterior-point method outperforms traditional interior-point methods in terms of the number of iterations and computation times.

A distributed optimal reactive power flow for global transmission and distribution network

With the large-scale integration of distributed generators (DGs), the relationships between transmission network (TN) and distribution networks (DNs) are becoming more closely, especially in the aspects of reactive power and voltage. Optimal reactive power flow (ORPF) problems for TN and DNs are not suitable to be solved independently. Due to the fact that TN and DNs are operated by different control centers, a heterogeneous decomposition (HGD) based distributed ORPF method for global transmission and distribution (T&D) networks is presented in this paper. Considering the characteristics of the master–slave structure, the global T&D-ORPF problem can be decomposed into the TN-ORPF master sub-problem, the DN-ORPF slave sub-problems and the boundary consistency coordination sub-problem. Any of those optimization algorithms based on duality and gradient theory can be adopted to solve the TN-ORPF or DN-ORPF sub-problems. By incorporating a penalty function into optimization algorithm, the discrete control variables can successively discretized and therefore the augmented Lagrangian functions are differentiable. Boundary sensitivities constructed by the boundary dual multipliers are used to decouple the global ORPF problem of T&D networks. The same solution as the centralized optimization is achieved by transferring the boundary variables and sensitivities between the TN control center and DN control centers. The simulation results of IEEE 30-bus (TN) and modified IEEE 33-bus (DN) test systems containing multiple DGs show that the HGD algorithm is effective.

Linear inequalities convex transformation for optimal reactive power flow model based on MISOCP relaxations

A convex optimisation model for global optimum solution of optimal reactive power flow (ORPF) problem is proposed in this study, to solve the challenge of discrete variables of transformer taps involved in traditional ORPF models. Based on the second-order cone programming relaxation, a set of inequalities with 0-1 variables are introduced, to convexify the non-convex items that are products of discrete variables (or squares of discrete variables) and linear functions. After convexification, items containing second order of transformer ratio variables are dropped to the first order, and the non-convex non-linear nodal power equalities are equivalently transformed into linear equalities, thus formulating a mix-integer second-order cone programming (MISOCP) model of ORPF problem over feasible convex domain, which guarantees the global optimum theoretically. The results of IEEE-14, 30, 57, 118 bus systems show that, with stable numerical property and good optimum effect, the proposed model can give consideration to not only the quality of solution, but also the efficiency of calculation.

A primal-dual interior/exterior point method, with combined directions and quadratic test in reactive optimal power flow problems

In this paper, we propose a primal-dual interior/ exterior point method that uses the modified logarithmic barrier function together with a quadratic test strategy and new search direction procedures for solving the reactive optimal power flow problem. The quadratic test is proposed as an alternative strategy for the Cholesky procedure for calculating the positivity of the Hessian matrix of the problem. The new search directions investigated in the paper are determined by combining the search directions calculated in the predictor and corrector steps, and also by using information associated with the complementarity conditions. The method is implemented in Matlab and applied to solving the reactive optimal power flow problem for 9 and 39 bus systems, as well as for the IEEE 14, 30, 57 and 118 test systems.The results reinforce the efficiency of the method proposed for solving the problem.

A Modified Barrier and Barrier Method and the Optimal Power Flow Problem

This work proposes an approach that uses a union of methods based on logarithmic barrier function and modified logarithmic barrier function for the resolution of the reactive optimal power flow problem. In this proposed approach the inequality constraints are transformed into equalities by adding the slack variables, which are handled by logarithmic barrier function or modified logarithmic barrier function, and the equality constraints are handled by means of Lagrange multipliers. These methods are used in two steps. Initially, the method based on the logarithmic barrier function is applied until the transition condition is satisfied. After the method based on modified logarithmic barrier function is used until the stop condition is satisfied. Numerical tests carried out with the IEEE 14, 30, 57 and 118 bus electrical systems indicate that the proposed approach is efficient in the resolution of the reactive optimal power flow problem and the results obtained by the proposed approach were compared with the logarithmic barrier method and the logarithmic barrier method modified, separately.

A new approach for optimal reactive power flow of MTDC systems using the ABC algorithm

This paper presents a new approach to optimize reactive power flow of multiterminal high voltage direct current (HVDC) systems. Successful application of two-terminal DC systems worldwide makes the use of multiterminal direct current (MTDC) systems more attractive. Due to the economic and technical advantages of HVDC technology, MTDC systems have been used extensively in recent years. In this study, the artificial bee colony (ABC) algorithm is used for solution of the optimal reactive power flow problem of MTDC systems. In opposition to the current-balancing method used in the literature, this study represents a new approach for DC system power flow calculations. The proposed approach is tested on a sample IEEE MTDC test system. The results by the proposed approach are compared with those reported in the literature. Thus, the applicability and the efficiency of this approach used together with the ABC algorithm are shown.

Voltage stability constrained dynamic optimal reactive power flow based on branch-bound and primal–dual interior point method

Abstract A day-ahead voltage stability constrained dynamic optimal reactive power flow (VSC-DORPF) model is proposed in this paper. The amount of dynamic reactive power reserves (DRPR) is used as a measure of voltage stability of power system. The effective dynamic reactive power reserves (EDRPR) of reactive power sources are calculated to obtain DRPR of each area and the maximum variations in reactive power generation under contingency are taken as the required minimal DRPR for each area. Then the DRPR are introduced into the VSC-DORPF model as one of multiple objective functions and constraints in order to enhance the voltage stability of power system. A hybrid method, integrated by branch-bound method and primal–dual interior point (PDIP) method, is proposed to solve this VSC-DORPF problem. The discrete control variables and the time coupled constraints are handled by the proposed branching and pruning principles. As a result, the VSC-DORPF problem is decomposed into a series of optimal reactive power flow (ORPF) problems with continuous control variables only. Numerical tests with IEEE 30-bus system and IEEE 118-bus system show that the proposed model and method are effective.