Improved parameters for economic dispatch problems by teaching learning optimization

The solution of Economic Dispatch (ED) problems mainly depends on the modelling of thermal generators. The physical variations such as aging and ambient temperature affect the modelling parameters and are unavoidable. As these parameters are the backbone of ED solution, the periodical estimation of these characteristics coefficients is necessary for accurate dispatch. The process is formulated as an error minimization problem and a nature inspired algorithm namely Teaching Learning Based Optimization (TLBO) is proposed as an estimator. This work provides a frame work for the computation of coefficients for quadratic and cubic cost functions, valve point loading, piece-wise quadratic cost and emission functions. The effectiveness of TLBO is demonstrated on 5 standard test systems and a practical Indian utility system, involving varying degree of complexity. TLBO yields better results than benchmark Least Error Square (LES) method and other evolutionary algorithms. The economic deviation is also tested with existing systems.     

Analysis of FACTS devices on Security Constrained Unit Commitment problem

This paper focuses on solving Security Constrained Unit Commitment (SCUC) problem using ABC algorithm incorporating FACTS devices. The objective of the SCUC problem is to obtain the minimum operating cost simultaneously maintaining the security of the system. The SCUC problem is decomposed into Unit Commitment (UC), the master problem and Security-Constrained Economic Dispatch (SCED) as the sub-problem. The existing generation constraints, such as hourly power demand, system reserves, and minimum up/down time limits, ramp up/down limits are included in the SCUC problem formulation. The ability of FACTS devices to control the power flow through designated routes in transmission lines and thereby reducing the overloading of lines are studied. The solution of SCUC problem is also analyzed during a single line outage contingency. The SCUC is carried out incorporating FACTS devices such as SVC, TCSC, STATCOM, SSSC, UPFC and IPFC. The modeling of the FACTS devices within the power system network and finding a suitable location are discussed. The SCUC has been solved and validated on an IEEE 118-bus test system and a practical South Indian 86 bus utility.     

Fuel restricted short term economic dispatch using evolutionary programming for utility system

The objective of the paper is to minimize the production cost of the thermal power generation. An elegant approach is presented in order to obtain the equivalent cost function of the participating non-fuel restricted units and the Economic Dispatch Calculations (EDC) are carried out along with fuel restricted units. The Evolutionary Programming (EP) technique is used for real power optimization with fuel restricted units. The optimal solution is obtained neglecting losses. The Fast Decoupled Load Flow (FDLF) analysis is conducted to find the losses by substituting the generation values. Then the loss is participated among all generating units using participation factor method. The load flow is conducted again and the voltage limit violation is checked. The Algorithm is tested on IEEE 6-bus system IEEE 30-bus system and a 66-bus utility system. The results obtained by this new approach are compared with those obtained using classical method. It is observed that the proposed method is more reliable and efficient.     

考虑风险成本的含风电场的电力系统动态经济调度

在风电功率全额上网的基础上,考虑发电厂节能和减排,通过优化常规火电机组出力可实现动态经济调度。考虑风险成本的含风电场的经济调度数学模型是在考虑到火电发电成本、污染气体的排放量、风力发电成本、风险指标等因素下使系统的总成本最小化。对传统粒子群算法进行改进,并将改进后的算法用于求解考虑风险成本的含风电场的动态经济调度问题。仿真结果验证了该方法的可行性。     

Integrated Isolation Niche and Immune Genetic Algorithm for solving Bid-Based Dynamic Economic Dispatch

This paper presents a novel algorithm-Isolation Niche Immune Genetic Algorithm for solving power system Bid-Based Dynamic Economic Dispatch (INIGA–BDED). Economic Dispatch determines the electrical power to be generated by the committed generating units in a power system so that the generation cost can minimized, while simultaneously satisfying various load demands. The Bid-Based Dynamic Economic Dispatch model is proposed in order to maximize the social profit under a competitive electricity market environment. This model synthetically considers various constraints on ramp rates, transmission line capacity and emission constraints. The Isolation Niche Immune Genetic Algorithm was induced as a new solution for this model. With the introduction of niche technology, the immune genetic algorithm capability in dealing with multi-peak model function optimization was enhanced. This paper proposes the Niche based on the Isolation mechanism which is based on biological possesses. The proposed method effectively ensures diverse group solutions and also has a strong ability to guide evolution. Using the immune genetic algorithm itself is a very good and innovative method for multi-peak model function solutions. A new improved method for this algorithm is also presented in this paper. This research integrated these two methods to enhance the evolutionary capability in seeking a more optimal solution for solving nonlinear programming. The test results from this integrated method were very good.     

Secure and economic management of a power system in the presence of wind generation

Nowadays, large-scale integration of wind power is a challenge in terms of the minimization of the insecurity risk, that is, of the expected cost associated with the expected load not served. In fact, when there is an elevated proportion of wind power, the electrical power quality in the sense of continuity of supply may be low, since energy from wind power cannot be dispatched in the classical sense and its output varies as weather conditions change. However, continuity of supply may also be undermined by other uncertain factors, such as the occurrence of random events like line outages, generator failures or sudden demand variations. Assuming the insecurity risk as a part of the overall expected cost for a secure management of a deregulated power system, this paper proposes a DC formulation of an AC Economically correct Secure Economic Dispatch (EcSED), modified also for the introduction of uncertain Wind Power Generation (WPG) sources. Finally, simulations were carried out in order to investigate how the above overall expected cost changes, as a function of varying penetration levels and varying installation locations of a WPG plant.     

Iteration PSO with time varying acceleration coefficients for solving non-convex economic dispatch problems

This paper presents a novel heuristic algorithm for solving economic dispatch (ED) problems, by employing iteration particle swarm optimization with time varying acceleration coefficients (IPSO-TVAC) method. Due to the effect of valve-points and prohibited operation zones (POZs) in the generating units’ cost functions, ED problem is a non-linear and non-convex optimization problem. The problem even may be more complicated if transmission losses are taken into account. The effectiveness of the proposed method is examined and validated by carrying out extensive tests on three different test systems. Valve-point effects, POZs, ramp-rate constraints and transmission losses are modeled. Numerical results show that the IPSO-TVAC method has a good convergence property. Furthermore, the generation costs of the IPSO-TVAC method are lower than other optimization algorithms reported in recent literature.     

A fuzzified multi objective Interactive Honey Bee Mating Optimization for Environmental/Economic Power Dispatch with valve point effect

In this paper, an improved multi objective Interactive Honey Bee Mating Optimization (IHBMO) is proposed to find the feasible optimal solution of the Environmental/Economic Power Dispatch (EED) problem with considering operational constraints of the generators. The EED problem is an important issue in power industry with considered the production of environmental pollution caused by fossil fuel consumption such as dangerous gases and carbon monoxide. The EED problem is formulated as a nonlinear constrained multi objective optimization problem which is solved by multi objective IHBMO techniques that has a strong ability to find the most optimal results. The three conflicting and non-commensurable: fuel cost, pollutant emissions and system loss, should be minimized simultaneously while satisfying certain system constraints. For achieve a good design with different solutions in a multi objective optimization problem, Pareto dominance concept is used to generate and sort the dominated and non-dominated solutions. Also, fuzzy set theory is employed to extract the best compromise solution. The propose method has been individually examined and applied to the standard IEEE 30-bus 6-generator, IEEE 180-bus fourteen generator and 40 generating unit (with valve point effect) test systems. The effectiveness of the proposed approach is demonstrated by comparing its performance with other evolutionary multi-objective optimization algorithms such as NSGA, NPGA, SPEA, MOPSO, MODE and MOHBMO. The computational results reveal that the multi objective IHBMO algorithm has excellent convergence characteristics and is superior to other multi objective optimization algorithms. Also, the results confirm its great potential in handling the multi-objective problems in power systems.     

An enhanced Lagrangian neural network for the ELD problems with piecewise quadratic cost functions and nonlinear constraints

This paper presents a new Lagrangian artificial neural network (ANN) and its application to the power system economic load dispatch (ELD) problems with piecewise quadratic cost functions (PQCFs) and nonlinear constraints. By restructuring the dynamics of the modified Lagrangian ANN [IEEE ICNN, 1 (1996) 537], stable convergence characteristics are obtained even with the nonlinear constraints. The convergence speeds are enhanced by employing the momentum technique and providing a criteria for choosing the learning rate parameters. Instead of having one convex cost function for each unit, which is normally the case in typical ELD problem formulations, more realistic multiple quadratic cost functions are used to reflect the effects of valve point loadings and possible fuel changes. In addition, the B matrix approach is employed for more accurate estimation of the transmission losses than treating them as a constant, which necessitate the inclusion of a nonlinear equality constraint. The effectiveness of the proposed ANN applied to the ELD problem is demonstrated through extensive simulation tests.     

A recursive economic dispatch algorithm for assessing the costs ofthermal generator schedules

The authors develop an efficient, recursive algorithm for determining the economic power dispatch of thermal generators within the unit commitment environment. The algorithm uses the equal incremental fuel cost criterion as its basis. In the algorithm, the fuel cost functions of the thermal generators are modeled by quadratic polynomials and the transmission losses are discounted. A method for incorporating the operation limits of the online generators and limits due to ramping generators is developed. The algorithm is amenable to computer implementation using the artificial intelligence programming language Prolog. The performance, of the algorithm was demonstrated through its application to the evaluation of the costs of dispatching 13 thermal generators within a generator schedule in a 24-h schedule horizon     

求解非光滑燃料费用函数的基于进化规划的机组最优潮流

提出求解具有非光滑燃料费用函数的存在爬坡率限制的最优潮流方法。针对两次、阶梯形、联合循环机组的非光滑燃料费用函数,介绍一个基于进化规划的算法。在该算法中,为避免早熟,交叉操作随后代的数目非线性变化。介绍了所提出的进化算法应用于有线路约束的IEEE30节点系统和印度62节点系统的情况。以MVA为单位的线路潮流直接采用牛顿-拉夫逊法计算。算例证明所提出的进化算法简单,对求解具有非光滑燃料费用函数的存在很多约束的最优潮流问题有效。     

Load type impact on distribution system reconfiguration

An analysis establishing the significant impact of load type, and problem reformulation have been carried out for distribution reconfiguration problem. The process of changing one radial configuration to other using tie lines, as and when required, to meet a particular objective is called reconfiguration. Simulation study on a practical test system has been carried out to show the quantitative significance of load models in reconfiguration studies. A weighted sum of objective functions representing operational cost of the distribution system is investigated in such a scenario. The paper highlights the importance of considering voltage dependence of loads in reconfiguration problem. It is shown that if the loads are not modelled as voltage dependent and instead modelled as constant power, a system configuration may result yielding higher system intakes and higher financial losses.     

Equal embedded algorithm for economic load dispatch problem with transmission losses

This paper presents equal embedded algorithm (EEA) to solve the economic dispatch (ED) problem with quadratic and cubic fuel cost functions and transmission losses. The proposed algorithm involves selection of lambda values, then the expressions of output powers of generators are derived in terms of lambda by interpolation and finally optimal value of lambda is evaluated from the power balance equation by Muller method. The proposed method is implemented and tested by considering 3, 15 and 26 generators to solve the ED problem. Simulation results such as quality of solution, convergence characteristic and computation time of the proposed method are compared with some existing methods like genetic algorithm (GA), particle swarm optimization (PSO) and Lambda iterative method. It is observed from different case studies that the proposed EEA algorithm provides the qualitative solution with less computational time irrespective of the size of the system.     

Allocation of the cost of transmission losses using a radial equivalent network

This paper provides a procedure for the allocation of the cost of transmission losses that is based on deriving a radial network that is fully equivalent to the original one. This equivalence materializes in that voltage magnitudes and angles, and active and reactive power injections are identical for both networks. Once this radial equivalent network is available, the allocation of the cost of transmission losses to generators and demands can be performed in a straightforward manner. This equivalent network is derived solving a simple quadratic optimization problem whose solution can be obtained efficiently. A realistic case study including two load scenarios is analyzed. Results using the proposed technique are compared with those obtained using alternative allocation procedures.     

基于MO-APSO的含风电场电力系统动态环境经济调度

为综合考虑碳排放权交易对风火联供模式的影响,基于节能减排、发电效益、机组运行3个方面约束条件,引入碳排放权交易成本函数,构建了考虑发电成本、碳交易成本、环境成本的风火联供系统多目标动态环境经济调度(DEED)模型。提出一种多目标自适应粒子群优化(MO-APSO)算法求解该DEED问题。根据寻优过程中粒子当前的适应度函数值,对惯性权重及学习因子进行自适应修正,进一步改善早熟的缺陷,增强全局搜索能力。含风电场的10机电力系统仿真结果表明:所提方法能同时优化成本和排放这2个冲突的目标,且获得了比其他算法更为宽广和均匀的Pareto前沿,有效降低了联供系统的碳排放量及综合运行成本。     

Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches

The objective of the Economic Dispatch Problems (EDPs) of electric power generation is to schedule the committed generating units outputs so as to meet the required load demand at minimum operating cost while satisfying all units and system equality and inequality constraints. Recently, global optimization approaches inspired by swarm intelligence and evolutionary computation approaches have proven to be a potential alternative for the optimization of difficult EDPs. Particle swarm optimization (PSO) is a population-based stochastic algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Inspired by the swarm intelligence and probabilities theories, this work presents the use of combining of PSO, Gaussian probability distribution functions and/or chaotic sequences. In this context, this paper proposes improved PSO approaches for solving EDPs that takes into account nonlinear generator features such as ramp-rate limits and prohibited operating zones in the power system operation. The PSO and its variants are validated for two test systems consisting of 15 and 20 thermal generation units. The proposed combined method outperforms other modern metaheuristic optimization techniques reported in the recent literature in solving for the two constrained EDPs case studies.     

A zoom feature for a dynamic programming solution to economicdispatch including transmission losses

An iterative dynamic programming method for solving the economic dispatch problems of a system of thermal generating units including transmission line losses is presented along with a clear explanation of modifying generator cost functions during each iteration. A zoom feature is applied during the iterative process in order to converge to the economic dispatch solution with low computer time and storage requirements, Dynamic programming including a short-term load forecast is briefly discussed. A three-generator example is used to illustrate the method. Computer memory and time requirements are presented, along with results for a 15-unit system     

Optimum economic and emission dispatch using exchange market algorithm

In modern electric grid system, a decision maker (DM) has to operate the system with multiple aims in mind. Traditional electric system was not so complex and emphasis used to be given only in optimizing the cost of energy dispatch. However, recent regulations restrict the environmental emissions caused by the energy sources. Hence, optimum energy generation and dispatch is a very critical issue in modern grid system. When, viewed as an optimization problem complying with both economy and environmental restriction, it is a very challenging one. Researchers in the past have solved such problems as multi-objective Economic Load Dispatch (ELD) problem. This paper attempts to solve the same problem as an Optimum Active Power Dispatch (OAPD) problem using a very recently developed optimizer called ‘Exchange Market Algorithm’ (EMA). The problem is modelled as both single and multi-objective problem. The EMA algorithm proceeds for the global optima through two of its main phases; i.e. balance market phase and oscillated market phase, each having both exploitation and exploration. The superior search capability of EMA is successfully exploited in this paper to attain various objectives. Programs are developed in MATLAB and tested on standard IEEE 30 bus comprising of six thermal units. The results obtained using EMA are compared with other methods reported in consulted literature. Simulation results demonstrate the authority of EMA in terms of its computational efficiency and robustness.     

A security-constrained bid-clearing system for the New Zealandwholesale electricity market

This paper reports upon the mathematical models and implementation of the Scheduling, Pricing and Dispatch (SPD) application for the New Zealand Electricity Market (NZEM). SPD analyzes bids for energy offers, reserve offers and energy demands, and recognizes explicitly the effects on bid clearing due to transmission congestion, network losses, reserve requirements, and ramp rate limits. Advanced LP solution methods are utilized to solve the large-scale constrained optimization problem. Results on a 67-bus test system and the NZEM are included     

Active and reactive dispatch with minimum control movements

This paper proposes a new formulation of the combined Optimal Active and Reactive Dispatch (OARD) problem with Minimum Control Movements (MCM) for the voltage control devices. The main objective of the proposed model is to minimize the total power system operation cost which include fuel cost of generators and switching cost of equipments like tap transformers and shunt capacitors. Practical constraints such as maximum allowable number of switching operation in a day for tap changing transformers and switchable capacitors are taken into consideration. A penalty based approach has been formulated to tackle with the switching costs of adjustable equipments. The problem has been formulated as a nonlinear dynamic optimization problem with the presence of both continuous and discrete control variables and solved using Artificial Bee’s Colony (ABC) algorithm. The approach has been tested on IEEE 30 bus system and the simulation is carried out in MATLAB. In order to verify the effectiveness of the results obtained, both active and reactive power dispatch problems have been solved separately and compared with the proposed approach. Results demonstrate the effectiveness of the proposed approach.