Optimal power scheduling of thermal units considering emission constraint for GENCOs’ profit maximization

In this paper, authors propose a novel method to determine an optimal solution for profit based unit commitment (PBUC) problem considering emission constraint, under a deregulated environment. In a restructured power system, generation companies (GENCOs) schedule their units with the aim of maximizing their own profit by relaxing demand fulfillment constraints without any regard to social benefits. In the new structure, due to strict reflection of power price in market data, this factor should be considered as an important ingredient in decision-making process. In this paper a social-political based optimization algorithm called imperialist competitive algorithm (ICA) in combination with a novel meta-heuristic constraint handling technique is proposed. This method utilizes operation features of PBUC problem and a penalty factor approach to solve an emission constrained PBUC problem in order to maximize GENCOs profit. Effectiveness of presented method for solving non-convex optimization problem of thermal generators scheduling in a day-ahead deregulated electricity market is validated using several test systems consisting 10, 40 and 100 generation units.     

市场竞争条件下发电机组启停机计划优化研究

探讨市场竞争条件下的发电机组启停机计划问题有助于发电厂制定发电机组安全经济运行方案。文章以发电厂收益最大化为目标函数,考虑了无功和备用收益的影响,以机组本身的可用状态、发电功率限制、爬坡速率以及系统备用容量和电力市场交易等为约束条件,构造了市场竞争条件下发电机组启停机计划问题的数学模型,并提出了一种综合了二次规划、遗传算法、模拟退火算法的优点的混合优化方法进行解算。对某8机系统进行的算例分析表明:市场竞争条件下考虑了备用收入影响的发电厂启停机计划发生了一些变化;发电厂为了追求更大的收益更加注重生产成本问题;其通过竞争获得的发电功率直接影响发电机组启停计划及其功率分配;文中提出的混合优化算法较适用于求解市场条件下的启停机计划等优化问题。     

应用MAS解决基于利润的机组组合问题研究

电力系统引入放松管制的市场运行机制之后,形成一种基于利润的机组组合问题:①优化目标从费用最小转为利润最大;②各发电公司从自身利益出发,可以不完全满足中心调度的要求。针对以上特点,提出一种基于多Agent系统的解决方法。仿真结果表明,该方法能够适应解决现代电力系统机组组合问题的新需要,能够获得更大的经济效益。     

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     

Combined hydro-wind generation bids in a pool-based electricity market

Present regulatory trends are promoting the direct participation of wind energy in electricity markets. The final result of these markets sets the production scheduling for the operation time, including a power commitment from the wind generators. However, wind resources are uncertain, and the final power delivered usually differs from the initial power committed. This imbalance produces an overcost in the system, which must be paid by those who produce it, e.g., wind generators among others. As a result, wind farm revenue decreases, but it could increase by allowing wind farms to submit their bids to the markets together with a hydro generating unit, which may easily modify its production according to the expected imbalance. This paper presents a stochastic optimization technique that maximizes the joint profit of hydro and wind generators in a pool-based electricity market, taking into account the uncertainty of wind power prediction.     

Two-stage stochastic-robust model for the self-scheduling problem of an aggregator participating in energy and reserve markets

This paper addresses a two-stage stochastic-robust model for the day-ahead self-scheduling problem of an aggregator considering uncertainties. The aggregator, which integrates power and capacity of small-scale prosumers and fexible community-owned devices, trades electric energy in the day-ahead (DAM) and real-time energy markets (RTM), and trades reserve capacity and deployment in the reserve capacity (RCM) and reserve deployment markets (RDM). The ability of the aggregator providing reserve service is constrained by the regulations of reserve market rules, including minimum ofer/bid size and minimum delivery duration. A combination approach of stochastic programming (SP) and robust optimization (RO) is used to model diferent kinds of uncertainties, including those of market price, power/demand and reserve deployment. The risk management of the aggregator is considered through conditional value at risk (CVaR) and fuctuation intervals of the uncertain parameters. Case studies numerically show the economic revenue and the energy-reserve schedule of the aggregator with participation in diferent markets, reserve regulations, and risk preferences.     

Information Gap Decision Theory-Based Risk-Constrained Bidding Strategy of Price-Taker GenCo in Joint Energy and Reserve Markets

This paper presents an optimal bidding strategy for price-taker generation companies (GenCos), which participate in a day-ahead joint energy and reserve market. Moreover, this problem is formulated as a Mixed-Integer Quadratic Constrained Program (MIQCP) to maximize the profit. Also, the price uncertainties of energy and reserve markets prices have direct impacts on the expected profit and bidding curves. This optimization problem is modeled with utilization of information gap decision theory (IGDT) for optimizing robustness to failure—or opportunity to windfall—under uncertainty conditions. IGDT assesses the robustness/opportunity of bidding strategy in the face of price uncertainties to determine whether a decision is risk-averse or risk-taking. Correlations among the prices of energy and reserve markets are properly modeled based on the concept of weighted average squared error using a variance–covariance matrix. It is shown that the risk-averse decisions, as well as risk-taking decisions, will affect both expected profit and bidding curves. The proposed method is verified in simulation studies on a GenCo comprising 5-unit thermal that participates in a day-ahead joint energy and reserve markets. Also, the proposed model is applied to a 54-unit thermal GenCo of IEEE-118 bus to validate the computational effectiveness of the proposed model in large system.     

Effect of the accuracy of price forecasting on profit in a Price Based Unit Commitment

This paper discusses and quantifies the so-called loss of profit (i.e., the sub-optimality of profit) that can be expected in a Price Based Unit Commitment (PBUC), when incorrect price forecasts are used. For this purpose, a PBUC model has been developed and utilized, using Mixed Integer Linear Programming (MILP). Simulations are used to determine the relationship between the Mean Absolute Percentage Error (MAPE) of a certain price forecast and the loss of profit, for four different types of power plants. A Combined Cycle (CC) power plant and a pumped storage unit show highest sensitivity to incorrect forecasts. A price forecast with a MAPE of 15%, on average, yields 13.8% and 12.1% profit loss, respectively. A classic thermal power plant (coal fired) and cascade hydro unit are less affected by incorrect forecasts, with only 2.4% and 2.0% profit loss, respectively, at the same price forecast MAPE.     

Monte Carlo based unit commitment procedures for the deregulated market environment

The unit commitment problem, originally conceived in the framework of short term operation of vertically integrated utilities, needs a thorough re-examination in the light of the ongoing transition towards the open electricity market environment. In this work the problem is re-formulated to adapt unit commitment to the viewpoint of a generation company (GENCO) which is no longer bound to satisfy its load, but is willing to maximize its profits. Moreover, with reference to the present day situation in many countries, the presence of a GENCO (the former monopolist) which is in the position of exerting the market power, requires a careful analysis to be carried out considering the different perspectives of a price taker and of the price maker GENCO. Unit commitment is thus shown to lead to a couple of distinct, yet slightly different problems. The unavoidable uncertainties in load profile and price behaviour over the time period of interest are also taken into account by means of a Monte Carlo simulation. Both the forecasted loads and prices are handled as random variables with a normal multivariate distribution. The correlation between the random input variables corresponding to successive hours of the day was considered by carrying out a statistical analysis of actual load and price data. The whole procedure was tested making use of reasonable approximations of the actual data of the thermal generation units available to come actual GENCOs operating in Italy.     

GENCO's Risk-Based Maintenance Outage Scheduling

This paper presents a stochastic model for the optimal risk-based generation maintenance outage scheduling based on hourly price-based unit commitment in a generation company (GENCO). Such maintenance outage schedules will be submitted by GENCOs to the ISO for approval before implementation. The objective of a GENCO is to consider financial risks when scheduling its midterm maintenance outages. The GENCO also coordinates its proposed outage scheduling with short-term unit commitment for maximizing payoffs. The proposed model is a stochastic mixed integer linear program in which random hourly prices of energy, ancillary services, and fuel are modeled as scenarios in the Monte Carlo method. Financial risks associated with price uncertainty are considered by applying expected downside risks which are incorporated explicitly as constraints. This paper shows that GENCOs could decrease financial risks by adjusting expected payoffs. Illustrative examples show the calculation of GENCO's midterm generation maintenance schedule, risk level, hourly unit commitment, and hourly dispatch for bidding into energy and ancillary services markets.     

Hydrothermal self-scheduling problem in a day-ahead electricity market

This paper addresses the self-scheduling problem of determining the unit commitment status for power generation companies before submitting the hourly bids in a day-ahead market. The hydrothermal model is formulated as a deterministic optimization problem where expected profit is maximized using the 0/1 mixed-integer linear programming technique. This approach allows precise modelling of non-convex variable cost functions and non-linear start-up cost functions of thermal units, non-concave power-discharge characteristics of hydro units, ramp rate limits of thermal units and minimum up and down time constraints for both hydro and thermal units. Model incorporates long-term bilateral contracts with contracted power and price patterns, as well as forecasted market hourly prices for day-ahead auction. Solution is achieved using the homogeneous interior point method for linear programming as state of the art technique, with a branch and bound optimizer for integer programming. The effectiveness of the proposed model in optimizing the generation schedule is demonstrated through the case studies and their analysis.     

Thermal power generation scheduling by simulated competition

This paper presents a new method for solving the unit commitment problem by simulation of a competitive market where power is traded through a power exchange (PX). Procedures for bidding and market clearing are described. The market clearing process handles the spinning reserve requirements and power balance simultaneously. The method is used on a standard unit commitment problem with minimum up/down times, start-up costs and spinning reserve requirement taken into account. Comparisons with solutions provided by Lagrangian relaxation, genetic algorithms and Chao-an Li's unit decommitment procedure demonstrate the potential benefits of this new method. The motivation for this work was to design a competitive electricity market suitable for thermal generation scheduling. However, performance in simulations of the proposed market has been so good that it is presented here as a solving technique for the unit commitment problem     

Risk-constrained self-scheduling of a fuel and emission constrained power producer using rolling window procedure

This work addresses a relevant methodology for self-scheduling of a price-taker fuel and emission constrained power producer in day-ahead correlated energy, spinning reserve and fuel markets to achieve a trade-off between the expected profit and the risk versus different risk levels based on Markowitz’s seminal work in the area of portfolio selection. Here, a set of uncertainties including price forecasting errors and available fuel uncertainty are considered. The latter uncertainty arises because of uncertainties in being called for reserve deployment in the spinning reserve market and availability of power plant. To tackle the price forecasting errors, variances of energy, spinning reserve and fuel prices along with their covariances which are due to markets correlation are taken into account using relevant historical data. In order to tackle available fuel uncertainty, a framework for self-scheduling referred to as rolling window is proposed. This risk-constrained self-scheduling framework is therefore formulated and solved as a mixed-integer non-linear programming problem. Furthermore, numerical results for a case study are discussed.     

电力市场中市场力的评估与发电竞标策略

提出发电公司竞标价格函数，并构建了在不健全市场下发电公司的竞标模型，在这种竞标模型和竞标价格函数的基础上对市场力加以评估。市场力的评估主要针对供不应求而且具有价格限制的市场。当市场经常出现供不应求的局面时，具有装机容量非常大或市场中主要的市场垄断者或所在地理位置可容易地造成输电阻塞等特性的发电公司，可利用其对市场需求的准确预测，来行使市场力，控制市场价格，从而获取高额的利润。数字仿真结果表明，在市场供不应求和市场供求均衡等2种情况下发电公司实现利润最大化的竞标策略完全不相同，从另一方面看也证实了市场力的存在和表现。     

发电厂热备用容量的优化分配和成本分析

在竞争的发电市场环境下，备用作为一种重要的辅助服务，其成本分析是一个急待解决的问题，对发电厂热备用容量进行优化分配和成本分析，采用电能收益和备用容量收益总和最大化的目标函数。解算方法首先是根据发电厂总的发电负荷约束获得机组的经济组合，其次是将负荷在各机组间进行经济分配实现热备用容量的优化分配，热备用容量的成本采用其机会成本等值，方法简单，计算结果符合工程实际，研究结果表明，发电厂在计及备用收益和满足发电机组最低出力约束的条件下开机台数越多总收益也越大；在给定的时段和相应的电能电价下，备用容量成本随发电厂出力的增加而增加，在给定的时段和相应的发电出力下，备用容量成本随电价的增加而有较大的增加。     

电力市场中考虑机组启停约束的购电策略

在电力市场环境下,电网以最小化购电费用为目标,而发电公司以最大化售电收益为目标,如何寻找二者之间的市场成交点是一项复杂而重要的工作。制定发电计划时,机组的启停是必须考虑的问题。基于此,文中对电力市场中考虑机组启停约束的购电策略进行了研究,并建立了相应的数学模型,提出了机组报价对电网总购电费用灵敏度的概念,以及考虑机组启停约束的购电算法,得出的结论对制定发电计划有一定的指导意义。     

计及市场收益的含储能火电厂日前-日内两阶段优化调度方法

火电厂的市场收益主要包括电能收益与备用收益,机组容量的分配是影响市场收益的重要因素之一,因此提出考虑优化机组容量分配的日前-日内两阶段优化调度方法。分析储能参与电力调度的机理,量化储能可用备用容量,以减小机组爬坡频次、提高机组发电利用率为目标,建立含储能火电厂日前与日内两阶段优化调度模型。采用拉格朗日松弛法对模型进行处理,基于市场边际电价理论求解容量价格与电量价格,并计算火电厂总售电收益。在安装储能与否的两种场景中进行算例分析,结果表明,在火电厂侧安装储能可以有效提高机组发电利用率,增加火电厂收益。     

适用于不同电价机制的统一机组组合算法

现有电力市场中存在两种结算电价机制：按机组报价结算(一机一价)和按市场出清价格结算(统一电价)。不同市场之间的结算方式也有所不同,例如,双边交易中采用一机一价结算方式,而实时市场中采用边际电价结算方式。不同结算电价机制下,机组组合的目标函数不同,传统机组组合方法必须根据电价机制的不同进行调整。通过研究发现,两种结算方式下机组组合问题的最优条件具有类似的数学表达形式。基于这一统一的最优条件表达形式,提出了一种新的机组组合算法。与传统拉格朗日松弛法相比,新算法能够有效地求解两种电价机制下的机组组合问题。     

Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.     

Using immune genetic algorithm based hybrid techniques for short-term unit commitment problem

This paper presents a hybrid chaos search (CS), immune algorithm (IA)/genetic algorithm (GA), and fuzzy system (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shut-down schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve, and individual units. First, we combined the IA and GA, then we added the CS and the FS approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20, and 30 thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), standard genetic algorithm (SGA), traditional simulated annealing (TSA), and traditional Tabu search (TTS). A comparison with an immune genetic algorithm (IGA) combined with the CS and FS was carried out. The results show that the CS and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.