Optimal power flow for distribution networks using gravitational search algorithm

This paper presents a gravitational search algorithm (GSA)-based approach to solve the optimal power flow (OPF) problem in a distribution network with distributed generation (DG) units. The OPF problem is formulated as a nonlinear optimization problem with equality and inequality constraints, where optimal control settings in case of fuel cost minimization of DG units, power loss minimization in the distribution network, and finally simultaneous minimization of the fuel cost and power loss are obtained. The proposed approach is tested on an 11-node test system and on a modified IEEE 34-node test system. Simulation results obtained from the proposed GSA approach are compared with that obtained using a genetic algorithm approach. The results show the effectiveness and robustness of the proposed GSA approach.     

Optimal power flow solution of two-terminal HVDC systems using genetic algorithm

The usage extensively of high voltage direct current (HVDC) transmission links in recent years makes it necessary further work in this area. Therefore, two-terminal HVDC transmission link is one of most important elements in electrical power systems. HVDC link representation is mostly ignored and simplified for optimal power flow (OPF) studies in power systems. OPF problem of purely alternating current (AC) power systems is defined as minimization of the fuel cost to subjected equality and inequality constraints. Hence, OPF software of purely AC power systems is extended by taking into consideration power transfer control characteristics of HVDC links. In this paper, OPF problem of integrated AC–DC power systems is first solved by genetic algorithm that is a heuristic algorithm based on evolutionary. The proposed method is tested on two test systems which are the modified 5-node test system and the modified WSCC 9-bus test system. In order to show effectiveness and efficiency of the proposed method, the obtained results are compared to that reported in the literature.     

Optimal power flow emulation of interchange brokerage systems usinglinear programming

The authors propose an interchange brokerage system based on an optimal power flow (OPF) solution using linear programming (LP). Interchange brokering schedules power imports and exports between interconnected electric utilities to maximize profits for all participating parties and enhances the security of power systems. The data required for interchange brokerage systems are the amount of power available for trading and the system incremental cost. An LP software package called STORM was used to solve the active and reactive OPF subproblems and the interchange brokerage systems. The steps required for the implementation and problems involved in loss minimization are considered. The development of LP theory for OPF and interchange brokerage systems and its limitations are discussed. The experimental results are included     

Optimal Power Flow using Glowworm Swarm Optimization

An important objective of the Optimal Power Flow (OPF) problem is to minimize the generation cost and keep the power outputs of generators, bus voltages, bus shunt reactors/capacitors and transformer tap settings in their secure limits. Solving this OPF problem using classical methods suffer from the disadvantages of highly limited capability to solve the practical large scale power system problems. To overcome the inherent limitations of conventional optimization techniques, Swarm Intelligence (SI) methods have been developed. However, the environmental concern, dictate the minimization of emissions of the thermal plants. Individually, if one objective is optimized, other objective is compromised. Hence, Multi-Objective Optimal Power Flow (MO-OPF) problem has been formulated in this paper. Swarm Intelligence methods, such as Particle Swarm Optimization (PSO) and Glowworm Swarm Optimization (GSO) have been used to solve the OPF problem with generation cost and emission minimizations as objective functions. The effectiveness of the proposed algorithms are tested on IEEE 30 bus and practical Indian 75 bus systems for cost minimization as objective function, and IEEE 30 bus test system for minimization of cost and emission as objectives. The results obtained from both the networks, the PSO and GSO are compared with each other based on different parameters.     

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program.     

Unit commitment taking into account reactive power

In this paper, the Voltage Magnitude Constrained OPF (VMC‐OPF) algorithm to determine the reactive power injection from compensating equipment to load bus is developed. By introducing the proposed VMC‐OPF to the real power related Unit Commitment (UC) [1], a novel daily UC method taking into account the reactive power to secure bus voltage magnitude is presented. The Transmission Access Charge (TAC) and Ancillary Services Charge (ASC) are included in the objective function for considering costs of using transmission network and supplying reactive power to maintain the voltage. Using the proposed UC, the difference between two schedules based on benefit maximization and cost minimization is also discussed. To ascertain the effectiveness of the proposed UC method, we demonstrate various simulation results for a model power system of IEEE‐118 bus system. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(3): 17–26, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20590     

Optimal power flow using differential evolution algorithm

This paper presents an evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution (DE) algorithm for optimal settings of OPF control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objective functions that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. In addition, non-smooth piecewise quadratic cost function has been considered. The simulation results of the proposed approach are compared to those reported in the literature. The results demonstrate the potential of the proposed approach and show its effectiveness and robustness to solve the OPF problem for the systems considered.     

Optimal power flow using differential evolution algorithm

This paper presents an efficient and reliable evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution algorithm for optimal settings of OPF problem control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objectives that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. The proposed approach results are compared with the results reported in the literature. The results show the effectiveness and robustness of the proposed approach.     

Optimal Power Flow Using an Extended Conic Quadratic Formulation

Recent research has shown that the load flow equations describing the steady-state conditions in a meshed network can be placed in extended conic quadratic (ECQ) format. This paper presents a study of the implementation of the new load flow equations format in an optimal power flow (OPF) program which accounts for control devices such as tap-changing transformers, phase-shifting transformers, and unified power flow controllers. The proposed OPF representation retains the advantages of the ECQ format: 1) it can be easily integrated within optimization routines that require the evaluation of second-order derivatives, 2) it can be efficiently solved for using primal-dual interior-point methods, and 3) it can make use of linear programming scaling techniques for improving numerical conditioning. The ECQ-OPF program is employed to solve the economic dispatch and active power loss minimization problems. Numerical testing is used to validate the proposed approach by comparing against solution methods and results of standard test systems.      

发电市场预调度计划模型及算法的研究

结合中国发电市场的实际情况,根据最优潮流原理,以整个预调度周期内的市场购电费用（MPC）最小为目标,建立了预调度计划模型,并根据预调度计划的特点,将模型目标简化为各时段的市场清算电价（MCP0最小,同时设计了三段式预调度算法：用静态规划法求解整个顶调度计划周期内的优化问题,用优先级求解机组组合问题,用改进的Powell法求解最优潮流问题。算例结果表明,预调度模型和算法下的市场清算电价能跟踪系统负荷变化,且该模型算法具有复杂度低、结果最佳性较好的特点。     

含UPFC的灵活交流输电系统最优潮流控制

潮流计算和无功优化计算是电力系统非常重要的计算,两者都包括在电力系统最优潮流（OPF）问题中,灵活交流输电系统（FACTS）的出现需要对传统的潮流计算进行修正,利用遗传算法探讨了含统一潮流控制器（UPFC）的灵活交流输电系统最优潮注控制问题,计算机仿真表明,该方法可有效解决含UPFC的灵活交流输电最优潮流控制。     

Impact of Fault Level Constraints on the Economic Operation of Power Systems

The aim of this paper is to prove that fault levels may have a significant impact on the economic operation of modern power systems. First, we present a simple method for the incorporation of fault level constraints (FLCs) in the optimal power flow (OPF), the main optimization tool for the economic operation of power systems. The constraints imposed by fault levels are converted to simple nonlinear (inequality) constraints, described by variables of the conventional OPF. Most common OPF-solving engines already have the computational capacity to handle numerous nonlinear constraints, such as the ones described by the power balance equations on buses. Therefore, once FLCs are converted to nonlinear constraints described by OPF variables, they can be directly introduced to any optimization process performing the OPF. We applied this enhanced OPF on a simple 12-bus network. The results verified the significant impact fault levels have on the optimum operating point of the power system     

TCPST allocation using optimal power flow and Genetic Algorithms

This work presents an optimization model to allocate TCPST at congested transmission systems. The problem was resolved by the Genetic Algorithms (GA) together with an optimal power flow (OPF). The proposed strategy used the GA to make the allocation of the TCPST and the OPF to obtain the load flow solution and optimal adjustments of the phase shifter’s taps. The mathematical formulation of the methodology is based on installation’s costs of the equipment and total system overload minimization. In order to diminish the search field a methodology to elect the most favorable substations to the devices allocation was considered. This methodology was tested at a 291 bus system that is equivalent, in heavy load, to the electric network of the State of Paraná in Brazil.     

潮流不可解评估方法的比较

电力系统在线电压稳定监视与控制中,故障态潮流发散的情况经常出现。识别其是否确实为失稳故障、准确评估其不可解程度及其提供校正控制用的灵敏度信息是对不可解潮流解算技术的3个基本要求。最优乘子牛顿法、基于直接求解KKT条件的最优潮流法和新近提出的故障型连续潮流法是3个可以处理潮流不可解的技术。前两者提供了在功率注入空间某种距离最近的临界点,而故障型连续潮流法提供了故障参数空间最近的临界点。文中应用这3种方法对IEEE 118节点标准系统进行了计算,从识别的可靠性、不可解程度评估的准确性和灵敏度信息的合理性等方面对它们进行分析和比较,结果表明所得到的不可解程度评估和排序结果存在差异,都包含了控制灵敏度信息。     

Power loss minimization in distribution systems using multiple distributed generations

In this work, an efficient analytical method is proposed for optimally allocating distributed generations (DGs) in electrical distribution systems to minimize power losses. The proposed analytical method can be employed for obtaining the optimal combination of different DG types in a distribution system for loss minimization. The validity of the proposed method is demonstrated using two test systems with different configurations by comparing with the exact optimal solution obtained from the exhaustive optimal power flow (OPF) algorithm. The calculated results and the comprehensive comparisons with existing methods prove the superiority of the proposed method in terms of accuracy and calculation speed. The proposed loss minimization method can be a useful tool for any general DG allocation problem since it provides effective and fast loss evaluation taking into account other benefits. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Cost-based reactive power pricing with voltage security consideration in restructured power systems

In the restructuring power industry, voltage security has become a challenging problem since power systems tend to operate closer to security boundaries and as a consequence, the voltage instability, which is caused by insufficient reactive power supply, poses a serious threat to system security and reliability. Establishing an equitable and effective reactive power market with consideration of the voltage security problem is very important to provide a reliable restructured power system. Therefore, this paper proposes a cost-based reactive power pricing, which can integrate the reactive power cost minimization and the voltage security problem into the optimal power flow (OPF) problem, and the sequential quadratic programming (SQP) is employed to solve the optimization problem. The effectiveness of the proposed method is verified using a modified IEEE 14-bus system. A study on the effects of the voltage stability margin (VSM) requirement under normal condition and contingencies on the reactive power cost is also presented.     

基于二阶锥优化的含有载调压变压器主动配电网最优潮流

随着分布式电源接入,配电网变为具有一定可控性的主动配电网,其优化运行本质上为包含多种离散可调设备的最优潮流问题。因模型的非凸、非线性,该类问题的高效求解方法仍是研究的热点和难点。有载调压变压器(OLTC)是主动配电网的重要可调设备,其策略对系统运行特性,尤其是电压水平会产生显著影响,故研究含OLTC的主动配电网最优潮流及其高效求解方法是十分必要的。基于支路潮流模型,文中构建了含OLTC的主动配电网最优潮流模型,提出了一种基于分段线性化技术的OLTC精确线性化建模方法,并论证了二阶锥松弛法在求解所构建最优潮流模型上的适用性。基于修订的IEEE系统的算例分析验证了所提出OLTC建模方法的有效性及二阶锥松弛法在求解含OLTC的主动配电网最优潮流问题上的高效性。     

Fuzzy constraint enforcement and control action curtailment in anoptimal power flow

Conventional power system optimal power flow (OPF) solutions utilize standard optimization techniques. These techniques limit the practical value and scope of OPF applications. Realistic OPF solutions require special attention to the constraint enforcement and control action curtailment. From a practical point of view, an OPF does not need to find a rigid minimum solution. Certain trade-offs among: (1) minimizing of objective function; (2) satisfying constraints; and (3) moving control variables would be desirable. In this paper, a fuzzy set method is applied to the OPF problem to model these considerations. The method has been implemented in a successive linear programming OPF package. Test results based on the PG&E network (USA) are promising     

多故障暂态稳定约束最优潮流的轨迹灵敏度法

将暂态稳定约束最优潮流(transient stability constrained optimal power flow,TSC-OPF)计算过程分解为潮流、暂态稳定及轨迹灵敏度、降阶二次规划最优潮流3个子问题的交替求解。在迭代过程中,根据潮流和暂态稳定计算得到状态变量和代数变量时变轨迹;由此判断系统的稳定性,并计算失稳时刻状态变量和初始时刻代数变量对发电机有功和无功功率的轨迹灵敏度;据此将暂态稳定约束最优潮流问题转化以发电机有功和无功功率增量为独立变量的降阶二次规划最优潮流问题;求解这个二次规划模型得到发电机有功和无功功率增量。通过这种交替求解,最终能寻找到满足暂态稳定约束的最优潮流解。以此为基础,提出了不受故障类型和模式影响的多故障处理方法。新英格兰10机39节点和UK 20机100节点系统的计算结果表明,所提方法在计算精度和速度方面具有一定优势。     

Efficiency improvements in meta-heuristic algorithms to solve the optimal power flow problem

This paper presents three efficient approaches for solving the Optimal Power Flow (OPF) problem using the meta-heuristic algorithms. Mathematically, OPF is formulated as non-linear equality and inequality constrained optimization problem. The main drawback of meta-heuristic algorithm based OPF is the excessive execution time required due to the large number of load flows/power flows needed in the solution process. The proposed efficient approaches uses the concept of incremental power flow model based on sensitivities, and lower, upper bounds of objective function values. By using these approaches, the number of load flows/power flows to be performed are substantially, resulting in the solution speed up. The original advantages of meta-heuristic algorithms, such as ability to handle complex non-linearities, discontinuities in the objective function, discrete variables handling, and multi-objective optimization, are still available in the proposed efficient approaches. The proposed OPF formulation includes the active and reactive power generation limits, Valve Point Loading (VPL) effects and Prohibited Operating Zones (POZs) of generating units. The effectiveness of proposed approaches are examined on the IEEE 30, 118 and 300 bus test systems, and the simulation results confirm the efficiency and superiority of the proposed approaches over the other meta-heuristic algorithms. The proposed efficient approaches are generic enough to use with any type of meta-heuristic algorithm based OPF.