A new approach to security-constrained generation scheduling of large-scale power systems with a piecewise linear ramping model

This paper presents a new and efficient approach to determine security-constrained generation scheduling (SCGS) in large-scale power systems, taking into account dispatch, network, and security constraints in pre and post-contingency states. A novel ramp rate limit is also modeled as a piecewise linear function in the SCGS problem to reflect more practical characteristics of the generating units. Benders decomposition is applied to this constrained solution process to obtain an optimal SCGS problem based on mixed-integer nonlinear programming (MINLP). The formulation can be embedded in two stages. First, a MIP is formulated in the master problem to solve a unit commitment (UC) problem. This stage determines appropriate on/off states of the units. The second stage, the subproblem, is formulated as a NLP to solve a security-constrained economic dispatch (SCED) problem. This stage is used to determine the feasibility of the master problem solution. It provides information to formulate the benders cuts that connect both problems. The proposed approach is tested in the IEEE 118-bus system to show its effectiveness. The simulation results are more realistic and feasible, whilst assuring an acceptable computation time.     

Optimal power flow with expected security costs

This paper discusses the expected-security-cost optimal power flow (ESCOPF) problem. The objective of the problem is to minimize the expected total cost of system operation subject to power system constraints and expected security costs. The probabilities of operating in the pre-contingency operating state and the probabilities of operating in all possible post-contingency states are considered. In addition, the ESCOPF problem includes the cost of interrupting customer load and the cost of generator ramping, which may be necessary when a contingency occurs. The solution to the ESCOPF problem gives information regarding the marginal value of spinning reserve and the marginal value of interruptible load. A graphical tool is used to view the problem solution.     

Hydroelectric generation scheduling with an effective differentialdynamic programming algorithm

An effective multiplier method-based differential dynamic programming (DDP) algorithm for solving the hydroelectric generation scheduling problem (HSP) is presented. The algorithm is developed for solving a class of constrained dynamic optimization problems. It relaxes all constraints but the system dynamics by the multiplier method and adopts the DDP solution technique to solve the resultant unconstrained dynamic optimization problem. The authors formulate the HSP of the Taiwan power system and apply the algorithm to it. Results demonstrate the efficiency and optimality of the algorithm for this application. Computational results indicate that the growth of the algorithm's run time with respect to the problem size is moderate. CPU times of the testing cases are well within the Taiwan Power Company's desirable performance; less than 30 minutes on a VAX/780 mini-computer for a one-week scheduling     

Security-constrained optimal generation scheduling for GENCOs

This paper presents an approach for maximizing a GENCO's profit in a constrained power market. The proposed approach considers the Interior Point Method (IPM) and Benders decomposition for solving the security-constrained optimal generation scheduling (SC-GS) problem. The master problem represents the economic dispatch problem for a GENCO which intends to optimize its profit. The formulation of the master problem does not bear any transmission network constraints. The subproblem will be used by the same GENCO to check the viability of its proposed bidding strategy in the presence of transmission network constraints. In this case if the subproblem does not yield a certain level of financial return for the GENCO or if the subproblem results in an infeasible solution of the GENCO's proposed bidding strategy, the GENCO will modify its proposed solution according to the Benders cuts that stem out of the subproblem. The study shows a more flexible scheduling paradigm for a GENCO in a competitive arena. The proposed approach proves practical for modeling the impact of transmission congestion on a GENCO's expected profit in a competitive environment.     

Optimal scheduling of hydraulically coupled power plants with runoff prediction

This paper discusses an optimal short-range scheduling of multireservoir hydrothermal power systems considering runoff prediction. Using Prasad's rainfall-runoff model and the Kalman filter-based, second-order filtering technique, the hour-by-hour characteristic is estimated for a given short-range forecasted rainfall pattern. Unlike the usual hydroscheduling problem in which a single-reservoir operating condition is specified at the end of the scheduling period, various end point conditions are examined to deal with the predicted runoff characteristic and to avoid possible water spillages from reservoirs. Dynamic Programming Successive Approximations are applied successfully to obtain optimum operating strategies for many end point conditions at a time. A rapid convergence characteristic coupled with a simple computation algorithm makes the proposed method one of the attractive approaches for scheduling of complicated multireservoir hydrothermal systems considering runoff prediction.     

Allocation of fixed costs in distribution networks with distributed generation

In this paper, we propose a method for the allocation of fixed (capital and nonvariable operation and maintenance) costs at the medium voltage (MV) distribution level. The method is derived from the philosophy behind the widely used MW-mile methodology for transmission networks that bases fixed cost allocations on the "extent of use" that is derived from load flows. We calculate the "extent of use" by multiplying the total consumption or generation at a busbar by the marginal current variations, or power to current distribution factors (PIDFs) that an increment of active and reactive power consumed, or generated in the case of distributed generation, at each busbar, produces in each circuit. These PIDFs are analogous to power transfer distribution factors (PTDFs). Unlike traditional tariff designs that average fixed costs on a per kWh basis across all customers, the proposed method provides more cost-reflective price signals and helps eliminate possible cross-subsidies that deter profitable (in the case of competition) or cost-effective (in the case of a fully regulated industry) deployment of DG by directly accounting for use and location in the allocation of fixed costs. An application of this method for a rural radial distribution network is presented.     

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     

Electricity generation scheduling with large-scale wind farms using particle swarm optimization

Large-scale integration of wind power in the electricity system presents some planning and operational difficulties, which are mainly due to the intermittent and difficult nature of wind prediction process. Therefore it is considered as an unreliable energy source.     

Optimal security-constrained power scheduling by Benders decomposition

This paper presents a Benders decomposition approach to determine the optimal day-ahead power scheduling in a pool-organized power system, taking into account dispatch, network and security constraints. The study model considers the daily market and the technical constraints resolution as two different and consecutive processes. The daily market is solved in a first stage subject to economical criteria exclusively and then, the constraints solution algorithm is applied to this initial dispatch through the redispatching method. The Benders partitioning algorithm is applied to this constraints solution process to obtain an optimal secure power scheduling.     

Computation of power generation system production costs

This paper considers the problem of computing the expected value of generating system production costs. First, using a stochastic model for the frequency and duration of generation outage, it provides an efficient Monte Carlo procedure for the evaluation of the Baleriaux formula. Secondly, it points out the need for using a stochastic model for estimating production costs with time-dependent constraints via Monte Carlo. Lastly, it considers a model where the chronological load also has a random component and obtains an expression for expected production costs for this situation     

Daily generation scheduling optimization with transmissionconstraints: a new class of algorithms

The authors describe a novel class of algorithm dealing with the daily generation scheduling (DGS) problem. These algorithms have been designed by adding artificial constraints to the original optimization problem; handling these artificial constraints by using a dual approach; using an augmented Lagrangian technique rather than a standard Lagrangian relaxation technique; and applying the auxiliary problem principle which can cope with the nonseparable terms introduced by the augmented Lagrangian. To deal with the DGS optimization problem these algorithms are shown to be more effective than classical ones. They are well suited to solve this DGS problem taking into account transmission constraints     

Short-term thermal generation scheduling using improved immune algorithm

This paper proposes a new immune algorithm (NIA), which merges the fuzzy system (FS), the annealing immune (AI) method and the immune algorithm (IA) together, to resolve short-term thermal generation unit commitment (UC) problems. This proposed method differs from its counterparts in three main aspects, namely: (1) changing the crossover and mutation ratios from a fixed value to a variable value determined by the fuzzy system method, (2) using the memory cell and (3) adding the annealing immune operator. With these modifications, we can attain three major advantages with the NIA, i.e. (1) the NIA will not fall into a local optimal solution trap; (2) the NIA can quickly and correctly find a full set of global optimal solutions and (3) the NIA can achieve the most economic solution for unit commitment with ease. The UC determines the start-up and shut-down schedules for related generation units to meet the forecasted demand at a minimum cost while satisfying other constraints, such as each unit's generating limit. The NIA is applied to six cases with various numbers of thermal generation units over a 24-h period. The schedule generated by the NIA is compared with that by several other methods, including the dynamic programming (DP), the Lagrangian relaxation (LR), the standard genetic algorithm (GA), the traditional simulated annealing (SA) and the traditional Tabu search (TS). The comparisons verify the validity and superiority in accuracy for the proposed method.     

A new generation scheduling program at Ontario Hydro

The new daily generation scheduling model for the Ontario Hydro system is presented. The model is capable of considering the thermal and hydraulic systems together with system reserve requirement and transmission losses. The hydraulic system is considered in a detailed formulation that can handle river couplings in a complete manner. Inability to do this was a major weakness in the peak shaving technique used since early 1970s. A special network programming technique has been used to solve the problem. This method has proved to be very efficient from a computational point of view. Test results from application of the new technique are presented and compared to the peak shaving method. The user has estimated 1.4 million dollars per year of savings from the new computer package     

Optimal short-term scheduling for a large-scale cascaded hydrosystem

This paper describes a short term hydro generation optimization program that has been developed by the Hydro Electric Commission (HEC) to determine optimal generation schedules and to investigate export and import capabilities of the Tasmanian system under a proposed DC interconnection with mainland Australia. The optimal hydro scheduling problem is formulated as a large scale linear programming algorithm and is solved using a commercially-available linear programming package. The selected objective function requires minimization of the value of energy used by turbines and spilled during the study period. Alternative formulations of the objective function are also discussed. The system model incorporates the following elements: hydro station (turbine efficiency, turbine flow limits, penstock head losses, tailrace elevation and generator losses), hydro system (reservoirs and hydro network: active volume, spillway flow, flow between reservoirs and travel time), and other models including thermal plant and DC link. A valuable by-product of the linear programming solution is system and unit incremental costs which may be used for interchange scheduling and short-term generation dispatch     

Optimal short term hydro scheduling including security constraints

A method is presented for short-term production scheduling in a hydro system. The solution technique is based on iterative network linear programming and heuristic techniques. The method handles security constraints due to single branch and specified multiple contingencies. The postcontingency rescheduling capabilities are modeled explicitly in a DC optimal load flow. Using the rescheduling capabilities increases the transmission network utilization     

检修周期对发电成本经济性影响的分析

针对电厂机组采用不同检修周期对发电成本的影响进行了研究.通过对某机组的检修方案进行优化计算分析后发现,适当、合理地延长机组大修周期,可减少检修成本,降低发电成本.该研究成果可以在国产600 MW燃煤机组的检修工作中推广和应用,也可以为其他大型机组提供参考,对提高电力企业自身的市场竞争能力有实际指导作用.     

Interval type-2 fuzzy modeling of wind power generation in Genco's generation scheduling

Wind power is a promising source of electric power generation since it has tremendous environmental and social benefits. The generation scheduling (GS) problem encounters several uncertainties in terms of the system's parameters such as load, reserve and available wind power generation. The modeling of those uncertainties is an important issue in power system scheduling. A fuzzy based modeling approach can be used to develop the generation schedule under an uncertain environment.In this paper, the type-2 fuzzy membership function (MF) is implemented to model the linguistic uncertainty of type-1 MF of available wind power generation which stems from opinions of different experts. The proposed approach is applied to two test systems (six and twenty-six conventional generating units both with two wind farms) and the results of generation scheduling using both fuzzy modeling type-1, and type-2 are presented. These results demonstrate that the advantage of using the type-2 fuzzy to model the linguistic uncertainty of the type-1 MF. This paper demonstrates how unit scheduling in an uncertain environment of type-1 fuzzy MF modeling can be performed just by using a single type-2 fuzzy MF when all type-1 MF were in the footprint of uncertainty (FOU) of type-2 MF.     

Short-term hydrothermal generation scheduling model using a genetic algorithm

A new model to deal with the short-term generation scheduling problem for hydrothermal systems is proposed. Using genetic algorithms (GAs), the model handles simultaneously the subproblems of short-term hydrothermal coordination, unit commitment, and economic load dispatch. Considering a scheduling horizon period of a week, hourly generation schedules are obtained for each of both hydro and thermal units. Future cost curves of hydro generation, obtained from long and mid-term models, have been used to optimize the amount of hydro energy to be used during the week. In the genetic algorithm (GA) implementation, a new technique to represent candidate solutions is introduced, and a set of expert operators has been incorporated to improve the behavior of the algorithm. Results for a real system are presented and discussed.     

Influence of the Emissions Trading Scheme on generation scheduling

The paper investigates the effects of emissions constraints and Emissions Trading Scheme (ETS) on the generation scheduling outcome. ETS is a cap-and-trade market mechanism that has been introduced in European Union in order to facilitate CO₂ emissions management. This scheme gives generators certain amount of CO₂ allowances which they can use to cover emissions produced during energy generation. In a current setting, most of the allowances are given for free. However, under ETS generators also have an opportunity to buy and sell CO₂ allowances on the market. Since generation power outputs are bounded by the amount of CO₂ emissions that they are allowed to produce over time, it is becoming increasingly important for generating units to manage their allocations in the most profitable way and decide when and how much of permissions to spent to produce electricity. The method proposed here allows for modeling of this new limitation by including costs of buying and selling of CO₂ allowance in the generation scheduling procedure. It also introduces additional emissions constraints in the problem formulation. Although CO₂ permissions and energy are traded in separate markets, the proposed formulation permits analysis on how emission caps and emission market prices can influence market outcome. The method is illustrated on a 5-unit system. Given examples compare (i) a base-case when all generators have made a decision to use portions of their total free allocations that do not cause any shortfall during the investigated time period; (ii) two cases when the least expensive generators’ decisions on the amount of free allowances they are willing to use during the considered period are insufficient. In all cases generators also submit prices at which they expect to be able to “top-up” or sell allowances on the market, however, only in the second and third case the “buying” option becomes active and affects generation scheduling and total costs.In addition, the paper investigates how aggregation of emissions allowances of generators belonging to the same company can affect market clearing.