Large-scale Hydrothermal Power Systems Research Articles

Stochastic nonlinear model with individualized plants and demand elasticity for large-scale hydro-thermal power systems

Stochastic nonlinear model with individualized plants and demand elasticity for large-scale hydro-thermal power systems

The stochastic effects on the Brazilian Electrical Sector

The size and characteristics of the Brazilian Electrical Sector (BES) are unique. The system includes a large-scale hydrothermal power system with many hydroelectric plants and multiple owners. Due to the historical harnessing of natural resources, the National Interconnected System (NIS) was developed outside of the economic scale of the BES. The central components of the NIS enable energy generated in any part of Brazil to be consumed in distant regions, considering certain technical configurations. This interconnection results in a large-scale complex system and is controlled by robust computational models, used to support the planning and operation of the NIS. This study presents a different vision of the SEB, demonstrating the intrinsic relationship between hydrological stochasticity and the activities executed by the system, which is an important sector of the infrastructure in Brazil. The simulation of energy scenarios is crucial to the optimal manner to operate the sector and to supporting decisions about whether expansion is necessary, thus, avoiding unnecessary costs and/or losses. These scenarios are an imposing factor in the determination of the spot cost of electrical energy, given that the simulated quantities of water in the reservoirs are one of the determinants for the short-term energy price.

Optimal Scheduling of Hydrothermal System with Network and Ramping via SCE-UA Method

This paper describes a method for scheduling large-scale hydrothermal power systems based on the shuffled complex evolution (SCE-UA) method. A multi-reservoir cascaded hydro-electric system with a non-linear relationship between water discharge rate, net head and power generation is considered. The water transport delay between connected reservoirs is also taken into account. SCE-UA is a successfully proven method in global optimization for many situations. Benefiting from its unique global optimization strategies into the inverse procedure greatly enhances the performance of SCE-UA method since it can not only effectively locate the promising areas in the solution space for a global minimum but also avoid its wandering near the global minimum in the final stage of search. The efficiency of the SCE-UA method is analyzed in terms of the mean performance and computational time, in comparison with the particle swarm optimization (PSO) algorithm. The simulation results reveal that SCE-UA effectively overcomes the premature phenomenon and improves the global convergence and optimization searching capability. It is a relatively consistent, effective and efficient optimization method in solving the large scale hydrothermal scheduling problem.

Production planning under uncertainty: the case of hydrothermal systems

This paper formulates the hydrothermal production planning problem as a multi-stage stochastic programming model. This problem is usually solved using algorithms that are based on dynamic programming and nested Benders decomposition (NBD). The hydrothermal planning problem is remodelled as a capacitated production planning model with convex costs; then a vanishing effect property of the first period decision is derived. Based on this property, a special implementation scheme of the NBD algorithm is proposed, providing faster convergence and less computational effort. The NBD algorithm is implemented for a large-scale hydrothermal power system of the Pacific Northwest in the USA with 20 thermal plants and 21 thermal plants.

A Bolza problem in hydrothermal optimization

This paper studies the optimization of large-scale hydrothermal power systems. For the general problem with n hydro-plants, we present an algorithm using a particular strategy related to the Gauss–Southwell method of nonlinear optimization. The algorithm offers a constructive method for producing sequences of problems with one hydro-plant. For this simple problem we use Pontryagin’s minimum principle to prove a condition for the extremals of the functional. We set out our problem in terms of optimal control in continuous time, with the Bolza-type functional. Finally, we present one example employing a program developed with the “Mathematica” package and analyze the convergence of the algorithm.

Improving the B&B search for large-scale hydrothermal weekly scheduling problems

This paper presents an optimization based algorithm to solve the weekly scheduling problem of a large-scale hydrothermal power system, formulated as a mixed-integer linear programming model (MILP). The main drawback of the MILP approach is the high computational burden required to solve large-size problems. The proposed algorithm tackles this problem by providing an initial feasible and integer solution, which enhances the search of the Branch and Bound (B&B) over the space of feasible solutions, reducing the resolution time. A detailed representation of thermal, pumped storage, and hydroelectric units is considered, taking into account the net head dependence of hydro plants by means of an under-relaxed iterative process. The presented algorithm has been applied to real-scale study cases, obtaining satisfactory results in computational time and optimality.

Optimal scheduling of large-scale hydrothermal power systems using the Lagrangian relaxation technique

This paper describes a method for scheduling large-scale hydrothermal power systems based on the Lagrangian relaxation technique. Lagrangian multipliers are introduced to decompose the original problem into small independent subproblems one for each generating unit, which are solved through a three level calculation structure. Using this approach, a large-scale hydrothermal electric power system could be treated as a precise general problem that takes into account the following among other factors: (a) random load demand; (b) non-linear cost function of thermal production; (c) variations of water head in hydroelectric plants; (d) non-linear function of hydroelectric output; (e) a system of cascaded hydroelectric plants including regulation reservoirs with limited spillage capacity. An economic interpretation of the results is given and an illustrative application of the technique is presented.

Hydro-thermal, scheduling by tabu search and decomposition method

In this paper, an enhanced algorithm for hydro-thermal power system generation scheduling is presented. By applying the tabu search, a decomposition method and taking into account the nonlinearity of time-varying starting costs, an effective algorithm is proposed to increase the computing accuracy of the dynamic scheduling process. The proposed approach may start from any traditional scheduling method proposed earlier, and improve the sub-optimal solution by a neighborhood search method. In this regard, additional constraints can be added to the problem formulation which provides a fast scheduling or rescheduling solution to large scale hydro-thermal power systems. The results show that the proposed algorithm is both efficient and reliable.

Optimal generation scheduling for constrained multi-area hydrothermal power systems with cascaded reservoirs

The optimization problem in this paper is targeted at large-scale hydrothermal power systems. The thermal part of the system is a multi-area power pool with tie-line constraints, and the hydro part is a set of cascaded hydrostations. The objective is to minimize the operation cost of the thermal subsystem. This is an integer nonlinear optimization process with a large number of variables and constraints. In order to obtain the optimal solution in a reasonable time, we decompose the problem into thermal and hydro subproblems. The coordinator between these subproblems is the system Lagrange multiplier. For the thermal subproblem, in a multi-area power pool, it is necessary to coordinate the area generations for reducing the operation cost without violating tie limits. For the hydro subsystem, network flow concepts are adopted to coordinate water usage over the entire study time span, and the reduced gradient method is used to overcome the linear characteristic of the network flow method in order to obtain the optimal solution. In this study, load forecasting errors and forced outages of generating units are incorporated in system reliability requirements. Three case studies for the proposed method are presented.

An innovative approach to generations scheduling in large-scale hydro-thermal power systems with fuel constrained units

A methodology for short-term unit commitment is proposed. The development of the solution method is based on the Lagrangian relaxation approach. Thermal, fuel-constrained, and hydro units are modeled in the formulation of the problem, and restrictions on fuel and water utilization as well as limits on the storage levels of reservoirs are included. This procedure is especially applicable to systems whose unit commitment solution is sensitive to changes in the Lagrangian multipliers. In this regard, the method incorporates the following special features. First, a set of upper bounds is added to limit the excess in the spinning reserves at different periods during the search for a feasible suboptimal solution. Second, a revised economic dispatch algorithm is introduced in the final stage of the method. This algorithm identifies unnecessarily committed units in the generation schedule of a large power network and provides the solution for the economic allocation of system demand among the committed units.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Large-scale non-linear programming applied to operations planning

This paper presents solution methodologies used at the Swedish State Power Board for optimal operations planning. The electric power system involved can be classified as a large-scale hydrothermal power system with a dominating part of hydro energy resources. The solution methodologies employed for the planning process are based on non-linear programming techniques in combination with network flow programming. The network flow technique is especially effective for solving problems associated with the mathematical modelling of hydro energy resources. The optimal operations planning problem can be divided into several subproblems and in this paper we will address the important seasonal and weekly planning processes. The solution methodologies have been integrated in a production optimizer of an information system for optimal operations planning of hydro and thermal energy resources. The information system has been in use for the last three to four years for operational purposes.

Short-term resource scheduling in multi-area hydrothermal power systems

This paper describes the short-term resource scheduling problem in multi-area large-scale hydrothermal power systems. The description of the problem is comprehensive, providing information on important operating considerations and constraints which need to be modelled in practice. A rigorous and concise formulation of the problem is presented. The solution algorithm, which is based on Lagrangian relaxation, is described and its salient features are discussed. Numerical results and our experience with the solution algorithm are also presented.

A contribution to the midterm scheduling of large scale hydrothermal power systems

A concise mathematical model and nonlinear minimization algorithm were presented as a joint approach to set optimal midterm production targets for power systems with predominance of hydroelectric power generation. The algorithm uses the network structure of the problem and takes into account nondifferentiable points. The approach was successfully applied to the optimal midterm scheduling of a very large hydroelectric power system in southeastern Brazil. Further insight into the problem allowed the adoption of an optimization-simulation strategy which achieved a very good suboptimal solution with great savings in computer requirements. The main purpose of this research was to develop a working tool able to assist engineers in setting optimized midterm targets for the large power systems in Brazil, where more than 90% of the electric energy comes from hydraulic sources. >

Application of Decomposition Techniques to Short-Term Operation Planning of Hydrothermal Power System

This paper develops a realistic model for short-term operation planning of a large scale hydrothermal power system with a high share of hydro. This problem is a large scale mixed integer program. Benders' method is employed to decompose the problem with respect to integer and continuous variables. The master problem of this method contains only integer variables and considers the unit commitment of thermal plants. The subproblem includes only continuous variables and considers the economic dispatch problem. The special structure of master and subproblems are further exploited which results in considerable reductions in the size of the problem and computation time requirement.