Optimal Short-term Scheduling Research Articles

Optimal short-term operation schedule of a hydropower plant in a competitive electricity market

This paper presents a dynamic programming model to solve the short-term scheduling problem of a hydropower plant that sells energy in a pool-based electricity market with the objective of maximizing the revenue. This is a nonlinear and non-concave problem subject to strong technical and strategic constraints, and in which discrete and continuous variables take part. The model described in this paper determines, in each hour of the planning horizon (typically from one day to one week), both the optimal number of units in operation (unit commitment) and the power to be generated by the committed units (generation dispatch). The power generated by each unit is considered as a nonlinear function of the actual water discharge and volume of the associated reservoir. The dependence of the units’ efficiency and operating limits with the available gross head is also accounted for in this model. The application of this model to a real hydropower plant demonstrates its capabilities in providing the operation schedule that maximizes the revenue of the hydro plant while satisfying several constraints of different classes. In addition, the use of this model as a supporting tool to estimate the economic feasibility of a hydropower plant development project is also analyzed in the paper.

A NEURAL NETWORK OPTIMIZER FOR SCHEDULING HYDROPOWER GENERATIONS

An approach based on neural network optimizer is proposed for determining the optimal short-term scheduling of multi-reservoir hydropower system. The proposed method is based on the Lagrange multiplier theory and search for solutions satisfying the necessary conditions of optimality in the state space. The equilibrium point of the network optimizer corresponds to the Lagrange solution of the problem and satisfies the Kuhn-Tucker condition for the problem. Here the main objective is to determine the optimal amounts of water to be released from each reservoir during each interval so as to minimize the overall energy shortages over the complete planning horizon. The method takes into account the water transportation delays between upstream and downstream reservoirs and a nonlinear hydropower generation function. An algorithm based on the proposed neural network optimizer has been developed and implemented on a multi-chain cascade of reservoir type hydropower system. Results so achieved have been compared with those obtained using conventional augmented Lagrange multiplier method. From the results, it is concluded that the proposed method is very effective in providing a good optimal solution along with constraint satisfaction.

Evolutionary techniques applied to the optimal short-term scheduling of the electrical energy production

This paper presents an evolutionary technique applied to the optimal short-term scheduling (24 h) of the electric energy production. The equations that define the problem lead to a non-convex non-linear programming problem with a high number of continuous and discrete variables. Consequently, the resolution of the problem based on combinatorial methods is rather hard. The required heuristics, introduced to assure the feasibility of the constraints, are analyzed, along with a brief description of the proposed genetic algorithm (GA). The GA is used to compute the optimal on/off status of thermal units and the fitness function is obtained by solving a quadratic programming problem by means of a standard non-linear Interior Point (IP) method. The results from real-world cases based on the Spanish power system are reported, which show the good performance of the proposed algorithm, taking into account the complexity and dimensionality of the problem. Finally, an IP algorithm is adapted to deal with discrete variables that appear in this problem and the obtained results are compared with that of the proposed GA.

Optimal Short-Term Scheduling of Multi-Purpose Batch Processes Considering Sequence-Dependent Constraints and Mixed Intermediate Storage Policies

A simple mathematical model for efficient short-term scheduling of non-sequential multi-product-multi-unit batch processes with unit- and sequence-dependent setup/changeover times and mixed intermediate storage policies is proposed. The scheduling objective is to minimize the makespan or the earliness of the completion of orders. When some of the sequence-dependent changeover times are relatively large compared to the processing times, a rigid formulation is provided to achieve optimality, which is seldom attended to in previous studies. Several intermediate storage policies for the batch processes are considered, including unlimited intermediate storage (UIS), no intermediate storage (NIS), finite intermediate storage (FIS), zero wait (ZW), and mixed intermediate storage (MIS). The problem is then formulated as a mixed-integer linear program (MILP). Two numerical examples are supplied to demonstrate the efficiency and the wide applicability of the proposed scheduling model in face of various different environments.

An MILP Continuous-Time Framework for Short-Term Scheduling of Multipurpose Batch Processes Under Different Operation Strategies

This work introduces a novel MILP continuous-time framework to the optimal short-term scheduling of non-sequential multipurpose batch processes with intermediate storage vessels. It is based on a problem representation that describes the batch sequence at any processing/storage unit by providing the full set of predecessors for every batch. Different operation modes can be considered by making minor changes in the problem model. The proposed framework can also handle sequence-dependent changeovers as well as multiple storage tanks available to receive material from one or several processing units. Three example problems involving up to fifteen batches and six processing tasks were successfully solved. Compared with previous work, a drastic reduction in both problem size and CPU time has been achieved.

Optimal Short-Term Scheduling of Multiproduct Single-Stage Batch Plants with Parallel Lines

The short-term scheduling of multiproduct single-stage batch plants with parallel lines involves the constraints concerning the release times and due dates of orders, as well as the sequence-dependent setup times and forbidden subsequences of production orders and the ready times of units. Taking the above constraints into consideration, this paper develops a short-term scheduling model for the multiproduct single-stage batch plants with parallel lines using the continuous-time domain representation and the notation of time slot. When the model is developed, the allocation of orders and units to time slots is represented by two sets of binary variables. The model is formulated as a mixed-integer linear programming (MILP) problem. It not only involves fewer binary variables than any other model based on the notation of time slot (Pinto, J. M.; Grossman, I. E. Ann. Oper. Res. 1998, 81, 433) but also can be used to optimize several types of objective functions. Based on the characteristics of the model and multiproduct single-stage batch plants, some heuristic rules are introduced. The rational employment of these heuristic rules can cut down the size of the model and has no effect on the optimality of the scheduling problem. A number of computational examples show that the optimal scheduling can be obtained by solving the MILP model in reasonable CPU time, especially when the scheduling problem involving several identical orders is considered.

Optimal short-term real power scheduling in a deregulated competitive market

Abstract A new approach using the Benders partition algorithm to determine the optimal short-term (one day) real power scheduling in a deregulated competitive market is presented in this paper. The ancillary services and the ramp rates for the generator outputs are considered. The problem is partitioned into two levels: the master level which determines the real power scheduling for multiple trading periods (48 or 24) considering the ramp rate constraints and the slave level which solves the feasibility of the DC optimal power flow with zero degree of freedom for the actual real power outputs. The simulation results for the IEEE 30-bus system show that the daily output pattern of each generator becomes smoother with the ramp rates taken into account.

Optimal Short-Term Scheduling of Maintenance and Production for Multipurpose Plants

The increased emphasis on the production of low-volume, high-value-added products has resulted in a renewed interest in multipurpose batch plants, which tend to be the most economical facilities for the production of small amounts of many different products. In such plants, the competition between the different products for the shared production resources gives rise to complex production scheduling problems. Amongst other factors, the profitability of a plant also depends on its availability which directly depends on the maintenance work carried out. In multipurpose plants, the integrated planning of production and maintenance so that these problems are solved simultaneously should result in increased profitability compared to the case where they are solved in isolation. This may be due, for example, to the ability to exploit equipment idle time or redundancy to perform preventive maintenance while having a minimal effect on production. We describe a mathematical model for simultaneously scheduling production and maintenance activities within a multipurpose plant, taking account of both production resources (e.g. equipment items) and maintenance resources (e.g., crews)

Optimal short-term scheduling for a large-scale cascaded hydro system

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sensitivity analysis of an optimal short term hydro-thermal schedule

The authors deal with the sensitivity analysis of an optimal short term hydro-thermal schedule. Methodological and practical aspects of the system economy loss (SEL) calculation caused by incorrect input data are investigated. It was shown and checked by numerical simulations that errors in the hydro plant characteristics can be studied through errors in the short term load forecasting. In a special case when differentiability conditions are satisfied (economic dispatching problem) analytical formulas for the SEL are developed. Some of the important results of sensitivity calculations concerning relevant errors in thermal cost coefficients, hydro plant characteristics, forecasted water inflows and forecasted system demands are presented. The critical input data have been selected and their tolerance margins established to preserve the beneficial effects of an optimal short term schedule. >

Optimum operation of a small autonomous system with unconventional energy sources

This paper presents a method for the determination of the optimum operation of a small autonomous system with both conventional and unconventional energy sources and storage battery. The system generation consists of diesel generators, wind turbine generators and photovoltaic panels. This is the generation mix of the Greek island of Cythnos; it may be applied to other small islands. A stochastic dynamic programming based algorithm is employed to determine the optimal short-term generation scheduling and battery storage policy which minimize the fuel consumption for the next 24-hour period. An application of the method to the power system of Cythnos is also presented.

Optimal short-term hydrothermal scheduling using decomposition approach and linear programming method

The operational planning problem of hydrothermal scheduling for the next day's demand in a power system is concerned with the determination of generation schedules for hydro and thermal plants to meet the daily system demand so that the total fuel cost of the thermal plants over the day is minimized subject to the operating constraints associated with the thermal and hydro plants as well as the network security constraints. This paper presents an effective algorithm which decomposes the problem into hydro and thermal subproblems and solves them alternatively. While the hydro subproblem is solved using a search procedure, the local variation method, the thermal subproblem is solved using the participation factors/Linear Programming method. The algorithm is very effective in enforcing security constraints and gives an optimal generation schedule which can be readily implemented for the next day. Results obtained from a 9-bus system and a 66-bus utility system demonstrate the effectiveness of the proposed algorithm.

Optimal hydro-termo scheduling on a personal computer

The purpose of optimal short-term scheduling is to maximize electrical energy production depending on the natural water inflows of a river, according to a daily load duration curve and the operation of thermal power plants with minimal oscillating load. Thermal power plants have a long start-up time and cannot follow changes in load demand so they are used to cover the constant part of the load, but peaks in load demand are covered by hydro units. A new mathematical model of a hydro plant chain was developed which used only two, instead of three, variables. The optimization algorithm used Newton's method which is applied on the exact L penalty function which allows a nonfeasible starting point so no phase I simplex or projection method is needed at the beginning. The mathematical model was implemented on a PC as a computer program using the FORTRAN 77 programming language and spreadsheet software. The program was applied to a hydro-chain on the river Drava. Preliminary results show that applying optimization techniques can greatly reduce costs of operating a hydro plant chain.

Short term generation scheduling in a small autonomous system with unconventional energy sources

The authors present a method for problem solving the short-term generation-scheduling problem in a small autonomous system with both conventional and unconventional energy sources and a storage battery. The system generation consists of diesel generators, wind turbine generators, and photovoltaic panels. This is the generation mix of the power system of the Greek island of Kythons, and may be applied to other Greek islands. A dynamic programming algorithm together with a standard unit commitment, is used to determine the optimal short-term scheduling, which minimizes the fuel consumption for a certain scheduling horizon, e.g., for the next 24 h.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal short-term scheduling of large-scale power systems

This paper is concerned with the long-standing problem of optimal unit commitment in an electric power system. We follow the traditional formulation of this problem which gives rise to a large-scale, dynamic, mixed-integer programming problem. We describe a solution methodology based on duality, Lagrangian relaxation, and nondifferentiable optimization that has two unique features. First, computational requirements typically grow only linearly with the number of generating units. Second, the duality gap decreases in relative terms as the number of units increases, and as a result our algorithm tends to actually perform better for problems of large size. This allows for the first time consistently reliable solution of large practical problems involving several hundreds of units within realistic time constraints. Aside from the unit commitment problem, this methodology is applicable to a broad class of large-scale dynamic scheduling and resource allocation problems involving integer variables.

Optimal short‐term hydro scheduling from the principle of progressive optimality

This paper presents an algorithm based on the principle of progressive optimality for determining the optimal short‐term scheduling of multireservoir power systems; the method takes into account water head variations, spilling, and time delays between upstream and downstream reservoirs. The method is computationally efficient and has minimal storage requirements. The convergence is monotonic and a global solution is reached. Contrary to dynamic programing, the state variables do not have to be discretized with this method. An example consisting of four hydroplants in series is solved, and the results are presented.