Large-scale Optimal Power Flow Research Articles

A leader supply-demand-based optimization for large scale optimal power flow problem considering renewable energy generations

The supply-demand-based optimization (SDO) is among the recent stochastic approaches that have proven its capability in solving challenging engineering tasks. Owing to the non-linearity and complexity of the real-world IEEE optimal power flow (OPF) in modern power system issues and like the existing algorithms, the SDO optimizer necessitates some enhancement to satisfy the required OPF characteristics integrating hybrid wind and solar powers. Thus, a SDO variant namely leader supply-demand-based optimization (LSDO) is proposed in this research. The LSDO is suggested to improve the exploration based on the simultaneous crossover and mutation mechanisms and thereby reduce the probability of trapping in local optima. The LSDO effectiveness has been first tested on 23 benchmark functions and has been assessed through a comparison with well-regarded state-of-the-art competitors. Afterward, Three well-known constrained IEEE 30, 57, and 118-bus test systems incorporating both wind and solar power sources were investigated in order to authenticate the performance of the LSDO considering a constraint handling technique called superiority of feasible solutions (SF). The statistical outcomes reveal that the LSDO offers promising competitive results not only for its first version but also for the other competitors.

A Novel MOGNDO Algorithm for Security-Constrained Optimal Power Flow Problems

The current research investigates a new and unique Multi-Objective Generalized Normal Distribution Optimization (MOGNDO) algorithm for solving large-scale Optimal Power Flow (OPF) problems of complex power systems, including renewable energy sources and Flexible AC Transmission Systems (FACTS). A recently reported single-objective generalized normal distribution optimization algorithm is transformed into the MOGNDO algorithm using the nondominated sorting and crowding distancing mechanisms. The OPF problem gets even more challenging when sources of renewable energy are integrated into the grid system, which are unreliable and fluctuating. FACTS devices are also being used more frequently in contemporary power networks to assist in reducing network demand and congestion. In this study, a stochastic wind power source was used with different FACTS devices, including a static VAR compensator, a thyristor- driven series compensator, and a thyristor—driven phase shifter, together with an IEEE-30 bus system. Positions and ratings of the FACTS devices can be intended to reduce the system’s overall fuel cost. Weibull probability density curves were used to highlight the stochastic character of the wind energy source. The best compromise solutions were obtained using a fuzzy decision-making approach. The results obtained on a modified IEEE-30 bus system were compared with other well-known optimization algorithms, and the obtained results proved that MOGNDO has improved convergence, diversity, and spread behavior across PFs.

Distributed optimal power flow.

ObjectiveThe objectives of this paper are to 1) construct a new network model compatible with distributed computation, 2) construct the full optimal power flow (OPF) in a distributed fashion so that an effective, non-inferior solution can be found, and 3) develop a scalable algorithm that guarantees the convergence to a local minimum.Existing challengesDue to the nonconvexity of the problem, the search for a solution to OPF problems is not scalable, which makes the OPF highly limited for the system operation of large-scale real-world power grids—“the curse of dimensionality”. The recent attempts at distributed computation aim for a scalable and efficient algorithm by reducing the computational cost per iteration in exchange of increased communication costs.MotivationA new network model allows for efficient computation without increasing communication costs. With the network model, recent advancements in distributed computation make it possible to develop an efficient and scalable algorithm suitable for large-scale OPF optimizations.MethodsWe propose a new network model in which all nodes are directly connected to the center node to keep the communication costs manageable. Based on the network model, we suggest a nodal distributed algorithm and direct communication to all nodes through the center node. We demonstrate that the suggested algorithm converges to a local minimum rather than a point, satisfying the first optimality condition.ResultsThe proposed algorithm identifies solutions to OPF problems in various IEEE model systems. The solutions are identical to those using a centrally optimized and heuristic approach. The computation time at each node does not depend on the system size, and Niter does not increase significantly with the system size.ConclusionOur proposed network model is a star network for maintaining the shortest node-to-node distances to allow a linear information exchange. The proposed algorithm guarantees the convergence to a local minimum rather than a maximum or a saddle point, and it maintains computational efficiency for a large-scale OPF, scalable algorithm.

A Trajectory-Unified Method for Constructing the Feasible Region of OPF Problems

The feasible region plays an important role in optimal power flow (OPF) problems. However, constructing the feasible region of general optimal power flow problems is a challenging task. In this paper, a trajectory-unified (TJU) method is developed to compute the feasible region of general large-scale OPF problems. This is the first attempt, to our knowledge, to develop a numerical method to compute feasible regions of OPF problems. In addition, the projection of the computed feasible region into a desired low-dimensional sub-space is presented. By employing the proposed TJU method, we compute the feasible region of a 9-bus and the IEEE 118-bus OPF problem. It is shown that the feasible region of a power system grows in size from light-loading conditions to medium-loading conditions while it shrinks in size from medium-loading conditions to heavy-loading conditions. This discovery of a geometric property of the feasible solution asserts the observations that OPF problems are generally easy to solve during medium-loading conditions but are generally difficult to solve during heavy-loading conditions.

An Efficient Adaptive Moth Flame Optimization Algorithm for Solving Large-Scale Optimal Power Flow Problem with POZ, Multifuel and Valve-Point Loading Effect

This paper offers an enhanced adaptive moth flame optimization (AMFO) algorithm to solve the optimal power flow (OPF) problems efficiently. The idea of moth flame optimization (MFO) is motivated by the movement of moth headed about the moon direction. AMFO is primarily centered on the notion of MFO with adjusting the direction of moths in an adaptive manner around the flame. AMFO is compared with standard MFO for 14 different benchmark test suites. Standard IEEE 118-bus test system is used to substantiate the effectiveness and robustness of AMFO algorithm. The authentication of the suggested algorithm is established on 12 case studies for various single-objective functions like fuel cost minimization, emission minimization, active power loss minimization, voltage stability enhancement and voltage profile improvement. The simulation findings of the suggested algorithm are compared with those found by other well-known optimization methods. The achieved results demonstrate the ability and strength of AMFO approach to solving OPF problems. The outcomes divulge that AMFO algorithm can obtain accurate and improved OPF solutions compared with the other methods. A comparison among the convergence qualities of AMFO and the different techniques demonstrates the predominance of AMFO to achieve the optimal power flow solution with rapid convergence.

An efficient optimal power flow using bisection method

This paper presents an efficient approach using the bisection method for the solution of large-scale optimal power flow (OPF) problem. This method is proposed to overcome the major drawbacks of conventional/classical optimization techniques and the meta-heuristic techniques for solving the OPF problems. The conventional optimization techniques solve the OPF problem with less computational time, but they are not suitable for solving the problems with nonlinear/nonconvex and discrete variables. The evolutionary optimization techniques handle the nonconvex and discrete variables efficiently, but they demand high computational times. Therefore, to overcome the drawbacks of both conventional and evolutionary techniques, this paper proposes an efficient approach using the bisection method. In the bisection method, initially a generation schedule is determined, having an objective function value midway between its lower and upper bounds. Then, a load flow is performed for this solution to check the feasibility. If it is feasible, then the optimum solution lies between the midpoint and the lower bound. If it is infeasible, then it is between the midpoint and the higher bound. This concept is repeated until the optimum solution is found. Simulation results on two test systems (IEEE 30 bus and practical Indian 75 bus) are presented, and they are compared with the results of other competitive global approaches presented in the literature. The results show that the proposed approach can converge to the optimum solution and obtains the solution with high accuracy and least computational time.

Large-scale OPF based on voltage grading and network partition

In this paper, a model of a large-scale optimal power flow (OPF) under voltage grading and network partition and its algorithm is presented. Based on the principles of open loop operations, the node injecting current method is used to divide the large-scale power grid into voltage grading and district dividing structures. The power network is further divided into a high-voltage main network and several subnets according to voltage levels of 220 kV. The subnets are connected by means of boundary nodes, and the partition model is solved using the improved approximate Newton direction method, which achieves complete dynamic decoupling simply by exchanging boundary variables between the main network and the subnets. A largescale power grid thus is decomposed into many subnets, making the solution of the problem simpler and faster while helping to protect the information of individual subnets. The system is tested for correctness and effectiveness of the proposed model, and the results obtained are matched in real-time. Finally, the algorithm is seen to have good convergence while improving calculation speed.

Implementation of a Large-Scale Optimal Power Flow Solver Based on Semidefinite Programming

The application of semidefinite programming to the optimal power flow (OPF) problem has recently attracted significant research interest. This paper provides advances in modeling and computation required for solving the OPF problem for large-scale, general power system models. Specifically, a semidefinite programming relaxation of the OPF problem is presented that incorporates multiple generators at the same bus and parallel lines. Recent research in matrix completion techniques that decompose a single large matrix constrained to be positive semidefinite into many smaller matrices has made solution of OPF problems using semidefinite programming computationally tractable for large system models. We provide three advances to existing decomposition techniques: a matrix combination algorithm that further decreases solver time, a modification to an existing decomposition technique that extends its applicability to general power system networks, and a method for obtaining the optimal voltage profile from the solution to a decomposed semidefinite program.

Experiments with the interior-point method for solving large scale Optimal Power Flow problems

This paper reports extensive results obtained with the interior-point method (IPM) for nonlinear programmes (NLPs) stemming from large-scale and severely constrained classical Optimal Power Flow (OPF) and Security-Constrained Optimal Power Flow (SCOPF) problems. The paper discusses transparently the problems encountered such as convergence reliability and speed issues of the method.

Optimal power flow for large-scale power system with shunt FACTS using efficient parallel GA

The main disadvantage of GAs is the high CPU time execution and the qualities of the solution deteriorate with practical large-scale optimal power flow (OPF) problems. This paper presents an efficient parallel GA (EPGA) for the solution of large-scale OPF with consideration of practical generators constraints. The length of the original chromosome is reduced successively based on the decomposition level and adapted with the topology of the new partition. Partial decomposed active power demand added as a new variable and searched within the active power generation variables of the new decomposed chromosome. The strategy of the OPF problem is decomposed in two sub-problems, the first sub-problem related to active power planning to minimize the fuel cost function, and the second sub-problem designed to make corrections to the voltage deviation and reactive power violation based in an efficient reactive power planning of multi Static VAR Compensator (SVC). Numerical results on three test systems IEEE 30-Bus, IEEE 118-Bus and 15 generation units with prohibited zones are presented and compared with results of others competitive global approach. The results show that the proposed approach can converge to the optimum solution, and obtains the solution with high accuracy.

A Robust Approach to Optimal Power Flow With Discrete Variables

Optimal power flow (OPF) belongs to the nonlinear optimization problem with discrete variables. The interior point cutting plane method (IPCPM), which possesses the advantages of both the interior point method and the cutting plane method, becomes a very promising approach to the large-scale OPF. It employs a successive linearization process and iteratively solves the mixed integer linear programming problem. However, case studies have shown that: if the problem has multiple solutions, the optimal solutions will converge to the interior of the optimal face, and the cutting planes cannot be generated due to the failure to identify the optimal base. This paper presents a new general optimal base identification method for solving the problem. The new approach significantly improves the robustness and efficiency of IPCPM. Simulation results on IEEE test systems indicate that the algorithm proposed can not only properly deal with various types of optimal solutions but also greatly enlarge the application area of IPCPM.

A Study on the Convergency Property of the Auxiliary Problem Principle

This paper presents the convergency property of the Auxiliary Problem Principle when it is applied to large-scale Optimal Power Flow problems with Distributed or Parallel computation features. The key features and factors affecting the convergence ratio and solution stability of APP are also analyzed.

Numerical experiments with an optimal power flow algorithm based on parametric techniques

This paper presents the results of numerical experiments with a new optimal power flow (OPF) algorithm based on a parametric technique. The approach consists of relaxing the original OPF problem by incorporating parametric terms to the objective function, the equality, and inequality constraints. Such relaxation assures that any arbitrary initial solution, feasible or unfeasible, be the optimal solution of the OPF problem. As the scalar parameter changes, a family of OPF problems is created, whose necessary conditions are solved by Newton's method. An efficient strategy is proposed for updating the parameter and the optimal set of active inequality constraints of each intermediate problem. Two applications of the methodology are reported: the economic dispatch problem and the minimum transmission loss problem. These problems were solved for an 810-bus and a 2256-bus equivalent network of the South/Southeast interconnected Brazilian power system. The results show that the parametric approach is robust and efficient when applied to large-scale OPF problems.

Numerical Experiments with an Optimal Power Flow Algorithm Based on Parametric Techniques

This paper presents the results of numerical experiments with a new optimal power flow (OPF) algorithm based on a parametric technique. The approach consists of relaxing the original OPF problem by incorporating parametric terms to the objective function, the equality, and inequality constraints. Such relaxation assures that any arbitrary initial solution, feasible or unfeasible, be the optimal solution of the OPF problem. As the scalar parameter changes, a family of OPF problems is created, whose necessary conditions are solved by Newton's method. An efficient strategy is proposed for updating the parameter and the optimal set of active inequality constraints of each intermediate problem. Two applications of the methodology are reported: the economic dispatch problem and the minimum transmission loss problem. These problems were solved for an 810-bus and a 2256-bus equivalent network of the South/Southeast interconnected Brazilian power system. The results show that the parametric approach is robust and efficient when applied to large-scale OPF problems.

Advanced transformer control modeling in an optimal power flow using Newton's method

This paper reports on advanced transformer modeling facilities suitable for large-scale optimal power flow studies. The new transformer models are developed from first principles and incorporated into an existing Newton-based optimal power flow computer program for highly robust iterative solutions. A three-winding transformer model with tap ratios in all three windings is shown to be a general case for existing two-winding transformer models and the classic load tap-changing and phase-shifting transformer models. The newly developed transformer models add a great deal to software flexibility and are amenable to more realistic electric energy studies. This is partly due to the transformer models being fitted with complex tap changers in each winding and a nonlinear representation of the magnetizing branch. The three-winding transformer model interfaces easily with reactive power plant models, e.g., static VAr compensators.

Large Scale Optimal Power Flow Based on Interior Point Quadratic Programming of Solving Symmetric Indefinite System

This paper presents a new algorithm of the interior point quadratic programming which can solve large scale optimal power flow problems with profoundly less computational efforts and can start from either a feasible or an infeasible point. Numerical results on the IEEE test systems and a Japanese 344 bus system (2301 variables, 2222 equality constraints and 1534 inequality constraints) have verified that the proposed algorithm possesses enough robustness and reliability and is especially suitable for on-line use as well as off-line use for large scale systems

Optimal power flow sensitivity analysis

The authors present a method and the mathematical formulation for large-scale optimal power flow sensitivity analysis. The method has been implemented in a computer program (OPSENS) presently in use in the Pacific Gas and Electric Company. The results of using the OPSENS program for calculating the sensitivity of system losses for a 34 bus and a 1700 bus transmission network to bus load changes are reported and compared to the results of multiple OPF (optimal power flow) studies. The effectiveness of OPSENS in this application was demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Large-scale optimal power flow: effects of initialization, decoupling and discretization

Extensive numerical testing of a second-order OPF (optimal power flow) solution method was conducted using a 1500 bus network under various loading conditions. The results show that properly implemented second-order OPF solution methods are robust with respect to different starting points, the decoupled OPF solution is expected to be close to the full OPF solution, and the effects of discretization of load tap changing (LTC) transformer taps are very small and usually negligible. The test procedure required two optimizations. During the first optimization, the transformer taps were treated as continuous variables. Using the continuous solution, the LTC taps were moved to their closest allowable discrete values. During the second optimization the LTC transformer taps were held fixed at their discretized values. The second solution was compared to the first. A small difference between these two solutions indicates that the effects of the transformer tap discretization were minimal.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>