Interior point models for power system stability problems

In this paper, a detailed analysis of the use of optimization techniques in the study of voltage stability problems, leading to the incorporation of voltage stability criteria in traditional Optimal Power Flow (OPF) formulations is presented. Optimal power flow problems are highly nonlinear programming problems that are used to find the optimal control settings in electrical power systems. The relationship between the Lagrangian Multipliers of the OPF problem and the classification of the maximum loading point level of the system is given. Finally, the paper presents a sequential OPF technique to enhance voltage stability using reactive power and voltage rescheduling with no increase in real (active) generation cost.     

计及多重阻塞的电动汽车移动储能特性建模

为实现城市交通电力耦合系统在城市道路、充电设施、输电线路阻塞环境下的优化运行,提出了计及多重阻塞的动态交通电力流联合优化方法。首先,基于时空网络模型,提出了计及电动汽车移动、静止、充电、排队模式的队列时空网络模型,构建了适用于电动汽车的车辆调度模型,进而形成动态交通分配模型,以减少交通出行损失。其次,通过优化发电机组、储能等的出力和备用计划,计及城市电网安全、备用约束,构建了安全约束动态经济调度模型,以降低碳排放及发电成本。随后,形成多目标动态优化模型,并将其转换为混合整数凸二次规划问题。最后,在耦合IEEE-30、Sioux Falls系统中验证了所提模型的有效性。     

Chaotic artificial immune approach applied to economic dispatch of electric energy using thermal units

The economic dispatch problem (EDP) is an optimization problem useful in power systems operation. The objective of the EDP of electric power generation, whose characteristics are complex and highly non-linear, is to schedule the committed generating unit outputs so as to meet the required load demand at minimum operating cost while satisfying system constraints. Recently, as an alternative to the conventional mathematical approaches, modern heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution in EDPs. As special mechanism to avoid being trapped in local minimum, the ergodicity property of chaotic sequences has been used as optimization technique in EDPs. Based on the chaos theory, this paper discusses the design and validation of an optimization procedure based on a chaotic artificial immune network approach based on Zaslavsky’s map. The optimization approach based on chaotic artificial immune network is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. Simulation results and comparisons show that the chaotic artificial immune network approach is competitive in performance with other optimization approaches presented in literature and is also an attractive tool to be used on applications in the power systems field.     

带阀点效应水火联合调度问题的一种半定凸松弛求解法

水火联合调度问题是电力系统中一类复杂的优化问题。合理安排调度周期内的水火电出力,确定一个最优发电计划,可以带来巨大的经济效益。在实际系统中,汽轮机调汽阀开启时出现的拔丝现象会使机组耗量特性产生阀点效应。忽略阀点效应,在一定程度上降低求解的精度。本文考虑带阀点效应的水火联合调度问题。该问题非凸非光滑,且带有非线性约束,直接使用确定性全局优化方法求解是相当困难的。本文使用高效的半定规划求解此问题。首先用耗量特性函数的初始周期代替其余有限的周期,并对其进行二次拉格朗日插值拟合。再通过引进0-1变量,得到整个耗量特性函数的近似,进而把问题松弛为半定规划模型。最后,采用凸规划应用软件包CVX求解一个仿真算例,得到一个近似全局最优解。     

A multi-objective multi-population ant colony optimization for economic emission dispatch considering power system security

With increasing concern about global warming and haze, environmental issue has drawn more attention in daily optimization operation of electric power systems. Economic emission dispatch (EED), which aims at reducing the pollution by power generation, has been proposed as a multi-objective, non-convex and non-linear optimization problem. In a practical power system, the problem of EED becomes more complex due to conflict between the objectives of economy and emission, valve-point effect, prohibited operation zones of generating units, and security constraints of transmission networks. To solve this complex problem, an algorithm of a multi-objective multi-population ant colony optimization for continuous domain (MMACO_R) is proposed. MMACO_R reconstructs the pheromone structure of ant colony to extend the original single objective method to multi-objective area. Furthermore, to enhance the searching ability and overcome premature convergence, multi-population ant colony is also proposed, which contains ant populations with different searching scope and speed. In addition, a Gaussian function based niche search method is proposed to enhance distribution and accuracy of solutions on the Pareto optimal front. To verify the performance of MMACO_R in different multi-objective problems, benchmark tests have been conducted. Finally, the proposed algorithm is applied to solve EED based on a six-unit system, a ten-unit system and a standard IEEE 30-bus system. Simulation results demonstrate that MMACO_R is effective in solving economic emission dispatch in practical power systems.     

A smoothing SQP method for nonlinear programs with?stability constraints arising from power systems

This paper investigates a new class of optimization problems arising from power systems, known as nonlinear programs with stability constraints (NPSC), which is an extension of ordinary nonlinear programs. Since the stability constraint is described generally by eigenvalues or norm of Jacobian matrices of systems, this results in the semismooth property of NPSC problems. The optimal conditions of both NPSC and its smoothing problem are studied. A smoothing SQP algorithm is proposed for solving such optimization problem. The global convergence of algorithm is established. A numerical example from optimal power flow (OPF) is done. The computational results show efficiency of the new model and algorithm.     

Matrix minor reformulation and SOCP-based spatial branch-and-cut method for the AC optimal power flow problem

Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major computational challenge to today’s power industry for the real-time operation of large-scale power grids. In this paper, we propose a new technique for reformulation of the rank constraints using both principal and non-principal 2-by-2 minors of the involved Hermitian matrix variable and characterize all such minors into three types. We show the equivalence of these minor constraints to the physical constraints of voltage angle differences summing to zero over three- and four-cycles in the power network. We study second-order conic programming (SOCP) relaxations of this minor reformulation and propose strong cutting planes, convex envelopes, and bound tightening techniques to strengthen the resulting SOCP relaxations. We then propose an SOCP-based spatial branch-and-cut method to obtain the global optimum of AC OPF. Extensive computational experiments show that the proposed algorithm significantly outperforms the state-of-the-art SDP-based OPF solver and on a simple personal computer is able to obtain on average a \(0.71\%\) optimality gap in no more than 720 s for the most challenging power system instances in the literature.     

A semi-infinite programming algorithm for solving optimal power flow with transient stability constraints

This paper proposes a new algorithm for solving a type of complicated optimal power flow (OPF) problems in power systems, i.e., OPF problems with transient stability constraints (OTS). The OTS is converted into a semi-infinite programming (SIP) via some suitable function analysis. Then based on the KKT system of the reformulated SIP, a smoothing quasi-Newton algorithm is presented in which the numerical integration is used. The convergence of the algorithm is established. An OTS problem in power system is tested, which shows that the proposed algorithm is promising.     

Dynamic economic dispatch using Lbest-PSO with dynamically varying sub-swarms

Dynamic economic dispatch (DED) is one of the major planning problem in a power system. It is a non-linear optimization problem with various operational constraints, which includes the constraints of the generators operating characteristics and the system constraints. Its principal aim is to minimize the cost of power production of all the participating generators over a time horizon of 24 h, while satisfying the system constraints. This problem deals with non-convex characteristics if generation unit valve-point effects are taken into account. The paper intends to solve the DED problem with valve-point effects, using our modified form of Local-best variant of Particle Swarm Optimization (Lbest PSO) algorithm. We have tested our algorithm on 5-unit, 10-unit and 110-unit test system with non-smooth fuel cost functions to prove the effectiveness of the suggested method over different state of the art methods.     

Operation strategy optimization of desulfurization system based on data mining

Desulfurization systems in coal-fired power stations often suffer the problem of high operating costs caused by a rule-of-thumb control strategy, which implies great potential for optimization of the operation. Due to the complex desulfurization mechanism, frequently fluctuating unit load, and severe disturbance, it is challenging to determine the optimal operating parameters based on the traditional mechanistic models, and the operating parameters are closely related to the operational efficiency of the flue gas desulfurization system. In this paper, an operation strategy optimization method for the desulfurization process is proposed based on a data mining framework, which is able to determine online the optimal operating parameter settings from a large amount of historical data. First, Principal Component Analysis (PCA) is used to reduce data redundancy by mapping the data into a new vector space. Based on the new vector space, an enhanced fuzzy C-means clustering (Enhanced-FCM) is developed to cluster the historical data into groups sharing similar characteristics. Taking sulfur dioxide emission concentration as a constraint condition, the system is optimized with economic benefits and desulfurization efficiency as the objective function. When performing optimization, the group that current operating conditions belong to is determined first, then the operating parameters of the best performance are searched within the group and provided as the optimization results. The method is validated and tested based on the data from a wet flue gas desulfurization (WFGD) system of a 1000 MWe supercritical coal-fired power plant in China. The results indicate that the proposed operation strategy can appropriately obtain operating parameter settings at different conditions, and effectively reduce the desulfurization cost under the constraint of meeting emission requirements.     

A new multiobjective procedure for solving nonconvex environmental/economic power dispatch

In this article, an improved multiobjective chaotic interactive honey bee mating optimization (CIHBMO) is proposed to find the feasible optimal solution of the environmental/economic power dispatch problem with considering operational constraints of the generators. The three conflicting and noncommensurable: fuel cost, pollutant emissions, and system loss, should be minimized simultaneously while satisfying certain system constraints. To achieve a good design with different solutions in a multiobjective optimization problem, Pareto dominance concept is used to generate and sort the dominated and nondominated solutions. Also, fuzzy set theory is used to extract the best compromise solution. The propose method has been individually examined and applied to the standard Institute of Electrical and Electronics Engineers (IEEE) 30‐bus six generator, IEEE 180‐bus 14 generator and 40 generating unit (with valve point effect) test systems. The computational results reveal that the multiobjective CIHBMO algorithm has excellent convergence characteristics and is superior to other multiobjective optimization algorithms. Also, the result shows its great potential in handling the multiobjective problems in power systems. © 2014 Wiley Periodicals, Inc. Complexity 20: 47–62, 2014     

A class of optimal state-delay control problems

We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem–called an optimal state-delay control problem–that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control.     

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method.     

A distributionally robust optimization model for batch nonlinear switched time-delay system considering uncertain output measurements

In this paper, we consider a nonlinear switched time-delay (NSTD) system with unknown switching times and unknown system parameters, where the output measurement is uncertain. This system is the underling dynamical system for the batch process of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. The uncertain output measurement is regarded as a stochastic vector (whose components are stochastic variables) and the only information about its distribution is the first-order moment. The objective of this paper is to identify the unknown quantities of the NSTD system. For this, a distributionally robust optimization problem (a bi-level optimization problem) governed by the NSTD system is proposed, where the relative error under the environment of uncertain output measurements is involved in the cost functional. The bi-level optimization problem is transformed into a single-level optimization problem with non-smooth term through the application of duality theory in probability space. By applying the smoothing technique, the non-smooth term is approximated by a smooth term and the convergence of the approximation is established. Then, the gradients of the cost functional with respect to switching times and system parameters are derived. A hybrid optimization algorithm is developed to solve the transformed problem. Finally, we verify the obtained switching times and system parameters, as well as the effectiveness of the proposed algorithm, by solving this distributionally robust optimization problem.     

Solving nonconvex economic load dispatch problem using particle swarm optimization with time varying acceleration coefficients

This article presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve‐point effects, multi‐fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch (ELD) problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints. A particle swarm optimization with time varying acceleration coefficients is proposed to determine optimal ELD problem in this paper. The proposed methodology easily takes care of solving nonconvex ELD problems along with different constraints like transmission losses, dynamic operation constraints, and prohibited operating zones. The proposed approach has been implemented on the 3‐machines 6‐bus, IEEE 5‐machines 14‐bus, IEEE 6‐machines 30‐bus systems and 13 thermal units power system. The proposed technique is compared with solve the ELD problem with hybrid approach by using the valve‐point effect. The comparison results prove the capability of the proposed method give significant improvements in the generation cost for the ELD problem. © 2015 Wiley Periodicals, Inc. Complexity 21: 299–308, 2016     

CO2 emissions trading planning in combined heat and power production via multi-period stochastic optimization

The EU emissions trading scheme (ETS) taking effect in 2005 covers CO₂ emissions from specific large-scale industrial activities and combustion installations. A large number of existing and potential future combined heat and power (CHP) installations are subject to ETS and targeted for emissions reduction. CHP production is an important technology for efficient and clean provision of energy because of its superior carbon efficiency. The proper planning of emissions trading can help its potential into full play, making it become a true “winning technology” under ETS. Fuel mix or fuel switch will be the reasonable choices for fossil fuel based CHP producers to achieve their emissions targets at the lowest possible cost. In this paper we formulate CO₂ emissions trading planning of a CHP producer as a multi-period stochastic optimization problem and propose a stochastic simulation and coordination approach for considering the risk attitude of the producer, penalty for excessive emissions, and the confidence interval for emission estimates. In test runs with a realistic CHP production model, the proposed solution approach demonstrates good trading efficiency in terms of profit-to-turnover ratio. Considering the confidence interval for emission estimates can help the producer to reduce the transaction costs in emissions trading. Comparisons between fuel switch and fuel mix strategies show that fuel mix can provide good tradeoff between profit-making and emissions reduction.     

Efficient visit frequencies for polling tables: minimization of waiting cost

Polling systems have been used as a central model for the modeling and analysis of many communication systems. Examples include the Token Ring network and a communications switch. The common property of these systems is the need to efficiently share a single resource (server) amongN entities (stations). In spite of the massive research effort in this area, very little work has been devoted to the issue of how toefficiently operate these systems.In the present paper we deal with this problem, namely with how to efficiently allocate the server's attention among theN stations. We consider a framework in which a predetermined fixed visit order (polling table) is used to establish the order by which the server visits the stations, and we address the problem of how to construct an efficient (optimal) polling table. In selecting a polling table the objective is to minimize the mean waiting cost of the system, a weighted sum of the mean delays with arbitrary cost parameters. Since the optimization problem involved is very hard, we use an approximate approach. Using two independent analyses, based on a lower bound and on mean delay approximations, we derive very simple rules for the determination of efficient polling tables. The two rules are very similar and even coincide in most cases. Extensive numerical examination shows that the rules perform well and that in most cases the system operates very close to its optimal operation point.     

Interior point cutting plane method for optimal power flow

In this paper, an interior point cutting plane method (IPCPM)is applied to solve optimal power flow (OPF) problems. Comparedwith the simplex cutting plane method (SCPM), the IPCPM is simpler,and efficient because of its polynomial-time characteristic.Issues in implementing IPCPM for OPF problems are addressed,including (1) how to generate cutting planes without using thesimplex tableau, (2) how to identify the basis variables inIPCPM, and (3) how to generate mixed integer cutting planes.The calculation speed of the proposed algorithm is further enhancedby utilizing the sparsity features of the OPF formulation. Numericalsimulations on IEEE 14-300-bus test systems have shown thatthe proposed method is effective.     

Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems

This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods.     

Global optimization for optimal power flow over transmission networks

The optimal power flow (OPF) problem for power transmission networks is an NP-hard optimization problem with nonlinear constraints on complex bus voltages. The existing nonlinear solvers may fail in yielding a feasible point. Semi-definite relaxation (SDR) could provide the global solution only when the matrix solution of the relaxed semi-definite program (SDP) is of rank-one, which does not hold in general. Otherwise, the point found by SDR is infeasible. High-order SDR has recently been used to find the global solution, which leads to explosive growth of the matrix variable dimension and semi-definite constraints. Consequently, it is suitable only for OPF over very small networks with a few buses. In this paper, we follow our previously developed nonsmooth optimization approach to address this difficult OPF problem, which is an iterative process to generate a sequence of improved points that converge to a global solution in many cases. Each iteration calls an SDP of moderate dimension. Simulations are provided to demonstrate the efficiency of our approach.