Optimal Reactive Power Flow Research Articles

Voltage security constrained multi-period optimal reactive power flow using benders and optimality condition decompositions

This paper proposes a new coordinated voltage control scheme to ensure voltage security of power systems. The scheme schedules reactive power injection from VAR sources, including synchronous generators and condensers, capacitor banks, switchable reactors and FACTS devices, to ensure desired loading margin of power systems for a given horizon of time. The problem is treated as voltage security constrained multi-period optimal reactive power flow (VSC-MPORPF). To incorporate scheduling of both continuous and discrete VAR sources, the VSC-MPORPF is formulated as a mixed-integer nonlinear programming problem, and is solved using generalized Benders decomposition (GBD). Multi-period formulation ensures both optimal switching pattern of discrete voltage controllers and voltage security for a given future horizon. Also, to make the proposed method applicable for large-scale power systems, optimality condition decomposition approach is utilized, along with the GBD. The proposed methodology is examined through case studies conducted on a simple 6-bus, the IEEE 118-bus, and a 1180-bus test systems. The results demonstrate effectiveness and efficiency of the proposed framework in real-time operation of power systems.

An Adaptive Zone-Division-Based Automatic Voltage Control System With Applications in China

The power industry in China has grown significantly over the past decade, spurring the adoption of system-wide automatic voltage control (AVC) technology to meet stricter requirements for security and economical power system operation. To cope with the rapidly developing and frequently changing Chinese power grid, an AVC scheme based on adaptive zone division is introduced in this paper. Logically, this type of system has a three-level hierarchical structure, but, here, both secondary voltage control (SVC) and tertiary voltage control (TVC) are implemented via software at the same control center. The control zones are no longer fixed but are reconfigured online and updated in accordance with variations in the grid structure. The technical details of these procedures are presented here. The implementation of TVC (which is based on an online reactive optimal power flow) and SVC are also discussed, together with some technical details on improvements to their reliability and robustness. Some results obtained from field-site applications based on similar-days testing rather than simulations are employed to evaluate the performance and improvements of the AVC system. This system has been installed at over 20 control centers in China.

A hybrid artificial bee colony assisted differential evolution algorithm for optimal reactive power flow

Optimal Reactive Power Flow (ORPF) is a branch problem in the gradual development of the optimal power flow problem. Differential Evolution (DE) has been proved to be a promising evolutionary algorithm for solving the ORPF problem, but it requires a relatively large population size to avoid premature convergence, which will increase the algorithm convergence time. On the other hand, Artificial Bee Colony (ABC) algorithm has been proved to have good global search ability. Integrating the respective advantages of DE and ABC, a hybrid ABC assisted DE algorithm, denoted as DE–ABC, is proposed in this study to overcome DE’s disadvantage of requiring large population size and strengthen the global search ability. At the last, the effectiveness of DE–ABC is verified by the serial simulations on the IEEE 14-bus, 30-bus and 57-bus system test cases. The simulation results show, in the case of achieving the same effect, the required population size of DE–ABC hybrid algorithm is greatly less than that of DE algorithm, the algorithm convergence time is less too and the algorithm is robust.

AC–DC optimal reactive power flow model via predictor–corrector primal‐dual interior‐point method

This study presents a quadratic optimal reactive power flow (ORPF) models for ac-dc hybrid power system. In the ac system, the load tap changing transformer is represented by an ideal transformer and its series impedance with an artificial node located between them. The ideal transformer is further replaced by the current injections at the two terminal nodes. The artificial node voltage and the current injections are used to express the relationship between the quantities at both sides. For the dc system, some variables are introduced to formulate the dc equations. Finally, utilising their couplings, the ac and dc equations expressed in different coordinates can be integrated into a unified quadratic ac-dc ORPF model, which is simply expressed in the block form. The predictor-corrector primal-dual interior-point method is used to solve the optimisation problem. The quadratic model results in the constant Hessians that all have elements of 1 or −1, and mostly being zero and multiplication is not required to form the full Hessian, thereby accelerating the entire optimal process significantly. Extensive numerical simulations have shown the validity and superior performance of the proposed model than the conventional one.

PCPDIPM-based optimal reactive power flow model using augmented rectangular coordinates

A novel optimal reactive power flow (ORPF) model using augmented rectangular coordinates is established. The load tap changing (LTC) transformer is represented by an ideal transformer and its series impedance with a fictitious node located between them. The ideal transformer is replaced by the current injections at the two end nodes, and the constraint equations relating the current injections and voltages between two sides are formed. Meanwhile, the nodal voltages, injection currents, reactive power injections, and transformers turn ratio are considered as optimization variables. By the procedure, the ORPF model turns into quadratic and can be expressed in the blocked-matrix form. The predictor-corrector primal-dual interior point method is used to implement the optimization. The quadratic model results in the constant Hessians that all have elements of 1 or −1,and mostly being zero, and multiplication is not required to form the full Hessian, thereby accelerating the entire optimal process significantly. Column Approximate Minimum Degree algorithm is used to order the coefficient matrix, resulting in great reduction of the number of the fill-in elements. The proposed and the conventional methods are programmed in MATLAB for comparison. Extensive numerical simulations on test systems ranging from IEEE 14 to 300 buses have shown the validity and higher efficiency of the proposed model than the conventional one. Copyright © 2013 John Wiley & Sons, Ltd.

Optimal reactive power flow using multi-objective mathematical programming

This paper presents a multi-objective optimization methodology to solve the Optimal Reactive Power Flow (ORPF) problem. The ε-constraint approach is implemented for the Multi-objective Mathematical Programming (MMP) formulation. The solution procedure uses Mixed Integer Non-Linear Programming (MINLP) model due to discrete variables, such as the tap settings of transformers and the reactive power output of capacitor banks. The optimum tap settings of transformers are directly determined in terms of the admittance matrix of the network since the admittance matrix is constructed in the optimization framework as additional equality constraints. The optimization problem is modeled in General Algebraic Modeling System (GAMS) software and solved using DICOPT solver. Simulation results are implemented on the IEEE 14-, 30-, and 118-bus test systems to simultaneously optimize the total fuel cost, power losses and the system loadability as objective functions. The simulation results show that the proposed algorithm is suitable and effective for the reactive power planning.

Multi Objective For Optimal Reactive Power Flow Using Modified PSO Considering TCSC

Multi objective optimal reactive power flow considering FACTS technology is becoming one of the most important issue in power system planning and control. This paper presents a new variant of particle swarm algorithm with time varying acceleration coefficients (TVAC) to solve multi objective optimal reactive power flow (MOORPF) (power loss minimization and voltage deviation). The proposed algorithm is used to adjust dynamically the parameters setting of Thyristor controlled series capacitor (TCSC) in coordination with voltages of generating units. This study is implemented on the standard IEEE 30-Bus system and the results are compared with other evolutionary programs such as simple genetic algorithm (SGA) and the simple particle swarm algorithm (SPSO). Simulation results confirm robustness of this new variant based PSO in term of solution quality and convergence time.

Optimal VAR control for improvements in voltage profiles and for real power loss minimization using Biogeography Based Optimization

In this paper, a Biogeography Based Optimization (BBO) technique is introduced to solve multi-constrained optimal reactive power flow (ORPF) problem in power system. ORPF is a multi-objective nonlinear optimization problem that minimizes the bus voltage deviation and real power loss. The feasibility of the proposed algorithm is demonstrated for IEEE 30-bus system and IEEE 118-bus system. A comparison of simulation results reveals optimization efficacy of the proposed scheme over other well established population based optimization techniques like conventional particle swarm optimization (PSO), general passive congregation PSO (GPAC), local passive congregation PSO (LPAC), coordinated aggregation (CA) and interior point based OPF (IP-OPF).

Optimal Reactive Power Control in Hybrid Power Systems

Optimal reactive power flow accounts for the major reduction in active power loss as well as more stable system operation. This article presents a novel model for optimal reactive power flow in hybrid power systems. Hybrid systems consist of an AC-DC system and flexible AC transmission system devices. Contrary to conventional methods that approximate the reactive power optimization in hybrid AC/DC systems to a simple AC reactive power optimization joint with a DC-part re-initialization stage, this study yields the optimum reactive power flow by simultaneously adjusting the control factors of both AC and DC parts. Conventional control factors associated with the AC part consist of control bus voltage, transformer tab, and static VAR compensators. This work introduces a number of DC part-related control factors, including Vdc , Idc , and DC transformer tabs to be used beside the conventional control factors inferred from a unified power flow controller aided AC system. Also, the contribution of control parameters of the unified power flow controller is considered in the reactive power optimization modeling. The proposed method is performed on modified IEEE 14- and 30-bus systems, and it is shown to have less calculation burden and more minimized cost function than the conventional method.

Multi Objective Optimal Reactive Power Flow Based STATCOM Using Three Variant of PSO

This paper proposes, an efficient variant of particle swarm optimization (PSO) to solve the multi-objective optimal reactive power flow (ORPF) based flexible AC transmission system (FACTS) using multi STATCOM Controllers by adjusting dynamically their parameters setting. Two objectives function are considered (power loss and voltage devia- tion) to validate the robustness of the proposed approach. The performance of the proposed variant based PSO approach has been tested on the standard test system IEEE 30-bus; simulation results compared to the standard PSO confirm the effectiveness of the proposed variant to solving the multi-objective reactive power considering multi STATCOM Control- lers.

Artificial bee colony algorithm solution for optimal reactive power flow

Artificial bee colony (ABC) algorithm is an optimization algorithm based on the intelligent foraging behavior of honeybee swarm. Optimal reactive power flow (ORPF) based on ABC algorithm to minimize active power loss in power systems is studied in this paper. The advantage of ABC algorithm is that it does not require these parameters, because it is very difficult to determine external parameters such as cross over rate and mutation rate as in case of genetic algorithm and differential evolution. The other advantage is that global search ability of the algorithm is implemented by introducing a neighborhood source production mechanism which is similar to mutation process. Because of these features, ABC algorithm attracts much attention in recent years and has been used successfully in many areas. ORPF problem is one of these areas. In this paper, proposed algorithm is tested on both standard IEEE 30-bus test system and IEEE 118-bus test system. To show the effectiveness of proposed algorithms, the obtained results are compared with different approaches as available in the literature.

A GA approach to compare ORPF objective functions including Secondary Voltage Regulation

In the past, with vertically integrate utilities, Optimal Reactive Power Flow (ORPF) procedures were designed to minimize power system losses, keeping the voltage profile in an acceptable range. Nowadays, in the market environment, a new formulation of the ORPF, aimed at the system security maximization, is necessary. In particular, as congestions and overloads are usually taken into account by the energy market rules, voltage security could become the main goal of ORPFs. Voltage problems are caused by the increase in power transfer among areas of interconnected systems, by the lack of reactive power support and by the increasing limitations of transmission networks. In this paper, an analysis of several ORPF Objective Functions (OFs) is reported, where the goal considered is the network security maximization. To solve the optimization problem for the considered OFs, a Genetic Algorithm (GA) approach has been adopted, together with a particular formulation of the Power Flow (PF) taking into account the Secondary Voltage Regulation (SVR). Tests are performed on a detailed model of the Italian power system, comparing the results in terms of system losses, reactive power required, loadability limits and voltage collapse indices. Furthermore, the improvements achievable with the adoption of the SVR in the new market environment have been investigated.

Optimal reactive power flow via the modified barrier Lagrangian function approach

A new approach called the Modified Barrier Lagrangian Function (MBLF) to solve the Optimal Reactive Power Flow problem is presented. In this approach, the inequality constraints are treated by the Modified Barrier Function (MBF) method, which has a finite convergence property; i.e. the optimal solution in the MBF method can actually be in the bound of the feasible set. Hence, the inequality constraints can be precisely equal to zero. Another property of the MBF method is that the barrier parameter does not need to be driven to zero to attain the solution. Therefore, the conditioning of the involved Hessian matrix is greatly enhanced. In order to show this, a comparative analysis of the numeric conditioning of the Hessian matrix of the MBLF approach, by the decomposition in singular values, is carried out. The feasibility of the proposed approach is also demonstrated with comparative tests to Interior Point Method (IPM) using various IEEE test systems and two networks derived from Brazilian generation/transmission system. The results show that the MBLF method is computationally more attractive than the IPM in terms of speed, number of iterations and numerical conditioning.

Decomposition–coordination interior point method and its application to multi-area optimal reactive power flow

A decomposition–coordination interior point method (DIPM) is presented and applied to the multi-area optimal reactive power flow (ORPF) problem in this paper. In the method, the area distributed ORPF problem is first formed by introducing duplicated border variables. Then the nonlinear primal dual interior point method (IPM) is directly applied to the distributed ORPF problem in which a Newton system with border-matrix-blocks is formulated. Finally the overall ORPF problem is solved in decomposition iterations with the Newton system being decoupled. The proposed DIPM inherits the good performance of the traditional IPM with a feature appropriate for distributed calculations among multiple areas. It can be easily extended to other distributed optimization problems of power systems. Numeric results of five IEEE Test Systems are demonstrated and comparisons are made with those obtained using the traditional auxiliary problem principle (APP) method. The results show that the DIPM for the multi-area OPRF problem requires less iterations and CPU time, has better stability in convergence, and reaches better optimality compared to the traditional auxiliary problem principle method.

Proposed Shunt Rounding Technique for Large-Scale Security Constrained Loss Minimization

Optimal reactive power flow applications often model large numbers of discrete shunt devices as continuous variables, which are rounded to their nearest discrete value at the final iteration. This can degrade optimality. This paper presents novel methods based on probabilistic and adaptive threshold approaches that can extend existing security constrained optimal reactive power flow methods to effectively solve large-scale network problems involving discrete shunt devices. Loss reduction solutions from the proposed techniques were compared to solutions from the mixed integer nonlinear mathematical programming algorithm (MINLP) using modified IEEE standard networks up to 118 buses. The proposed techniques were also applied to practical large-scale network models of Great Britain. The results show that the proposed techniques can achieve improved loss minimization solutions when compared to the standard rounding method.

Improved Strength Pareto Evolutionary Algorithm with Local Search Strategies for Optimal Reactive Power Flow

Improved Strength Pareto Evolutionary Algorithm with Local Search Strategies for Optimal Reactive Power Flow

Multiobjective Optimal Reactive Power Flow Using Elitist Nondominated Sorting Genetic Algorithm: Comparison and Improvement

Elitist nondominated sorting genetic algorithm (NSGA-II) is adopted and improved for multiobjective optimal reactive power flow (ORPF) problem. Multiobjective ORPF, formulated as a multiobjective mixed integer nonlinear optimization problem, minimizes real power loss and improves voltage profile of power grid by determining reactive power control variables. NSGA-II-based ORPF is tested on standard IEEE 30-bus test system and compared with four other state-of-the-art multiobjective evolutionary algorithms (MOEAs). Pareto front and outer solutions achieved by the five MOEAs are analyzed and compared. NSGA-II obtains the best control strategy for ORPF, but it suffers from the lower convergence speed at the early stage of the optimization. Several problem-specific local search strategies (LSSs) are incorporated into NSGA-II to promote algorithm's exploiting capability and then to speed up its convergence. This enhanced version of NSGA-II (ENSGA) is examined on IEEE 30 system. Experimental results show that the use of LSSs clearly improved the performance of NSGA-II. ENSGA shows the best search efficiency and is proved to be one of the efficient potential candidates in solving reactive power optimization in the real-time operation systems.

Hybrid algorithm of differential evolution and evolutionary programming for optimal reactive power flow

Differential evolution (DE) is a promising evolutionary algorithm for solving the optimal reactive power flow (ORPF) problem, but it requires relatively large population size to avoid premature convergence, which will increase the computational time. On the other hand, evolutionary programming (EP) has been proved to have good global search ability. Exploiting this complementary feature, a hybrid algorithm of DE and EP, denoted as DEEP, is proposed in this study to reduce the required population size. The hybridisation is designed as a novel primary–auxiliary model to minimise the additional computational cost. The effectiveness of DEEP is verified by the serial simulations on the IEEE 14-, 30-, 57-bus system test cases and the parallel simulations on the IEEE 118-bus system test case.

Distributed Quasi-Newton Method and its Application to the Optimal Reactive Power Flow Problem

We consider a distributed system of N agents, on which we define a quadratic optimization problem subject to a linear equality constraint. We assume that the agents can estimate the gradient of the cost function element-wise by measuring the steady state response of the system. Even if the cost function cannot be decoupled into individual terms, and the linear constraint involves the whole system state, we are able to design a distributed, quasi-Newton optimization algorithm. We prove finite time convergence in its centralized version, and by using the tool of average consensus we design its distributed implementation in the case in which a communication graph is given. As a testbed for the proposed method, we consider the problem of optimal distributed reactive power compensation in smart microgrids.

Reactive Power Response of Wind Generators Under an Incremental Network-Loss Allocation Approach

The reactive power capability of wind generation (WG) producers can be used to provide volt/voltampere reactive (var) support in electrical distribution systems. In practice, the distribution network operator (DNO) is not able to dispatch reactive power of all generators, and such units are referred to as nondispatchable generators. Then, the reactive power of these nondispatchable generators is not a defined value, and it should accomplish the limits settled by national grid codes. This paper addresses the optimal reactive power provision of nondispatchable WG units under a loss allocation strategy based on incremental generation use of the system (GUoS) tariffs. The optimization problem is set from generators' viewpoint aiming to find the reactive power provision that minimizes the loss charges subject to operational constraints. Optimal solutions are compared with the DNOs mandatory dispatches using a reactive optimal power flow tool. Two test systems are analyzed: a 10-kV 28 bus and 60-kV 55-bus system throughout 672 and 168 h, respectively. The proposal permits to identify which units can be dispatched by the DNO due to its effect on the network.