Hydrothermal Dispatch Problem Research Articles

Moment-SOS relaxation of the medium term hydrothermal dispatch problem

This paper analyzes the application of moment-SOS (sum of squares) relaxation to solve the medium term hydrothermal dispatch (MTHD) problem for predominantly hydro systems. The optimal dispatch is formulated as a two stage stochastic programming problem, which is nonconvex due to constraints that represent hydro power production, and may have multiple solutions. The size and conditioning of the problem pose challenges to the use of the semidefinite programming (SDP) techniques that are discussed in the text. The size of the problem restricts this study to first order moment relaxations. Therefore, to improve the quality of relaxed solutions, additional meaningful constraints are introduced in the SDP problems. Subsequently, the problem re-scalded to achieve numerical stability in SDP relaxation. Results obtained for different test systems, most of them being partitions of the Brazilian hydroelectric system, indicate that the procedures used to improve the quality of SDP solutions are effective.

Electric and Energy Coupling for Long-Term Operation Considering Transmission Restrictions

The operation planning of the Brazilian power system is a great challenge due to its size of continental dimensions, large seasonal variations, and predominantly hydroelectric nature. Its operation requires careful planning to reconcile conflicting goals such as spill minimization during the rainy season, and minimization of generation deficits during the dry season, i.e., operation risk minimization. The optimization models for hydrothermal systems currently used to operate large systems do not include the electric network when determining the energy goals. This work aims at modeling a hydrothermal dispatch problem by means of genetic algorithms. The electrical constraints are included by an optimal power flow, which is solved monthly over the planning horizon. The fitness function is composed of criteria that look for using the reservoirs as much as possible during the rainy season, thus, minimizing spills and production costs and, at the same time, catering for the load and limits of energy exchange between the subsystems. The methodology was tested using the 33-bus system.

Impact of wind power in middle–termed hydrothermal dispatch

This paper describes a linear programming model and Monte Carlo simulation which solve a middle-termed hydrothermal dispatch problem for three different scenarios of wind power penetration. Transmission line effects are neglected. The fuel cost in thermal plants varies in each time period. The test system has two thermal and three hydroelectric plants that can continuously operate during the twelve-months planning term. Wind generation is modeled by using Weibull Distribution Functions particular to the Colombian system, while hydro-generation is modeled by Normal Distribution Functions. Results show costs reduction for the three scenarios of wind power penetration. The main contribution of this paper is to simultaneously introduce the stochastic effect of wind and hydrology in the hydrothermal dispatch.

Short-Term Hydrothermal Dispatch With River-Level and Routing Constraints

Recently, there has been a growing need to consider issues related to multiple uses of water-such as navigation, fishing, or recreation-in the operation planning of electrical power systems, specially in predominantly hydro systems. In short-term models, it is of particular importance to consider maximum/minimum values and ramp limits for the stream level of a river. However, in order to properly represent such constraints, it is also necessary to model in detail the river routing, i.e., the water wave propagation along the channels that connect reservoirs in cascade. This paper proposes a linear programming model to represent river stream-level constraints and river-routing effects in the short-term hydrothermal dispatch problem. Results show the high accuracy of the proposed approach to represent maximum hourly and daily river-level variations as well as the impacts of taking into account a detailed representation of river routing in the operation of hydrothermal systems.

A Four-Dimensional Model of Hydro Generation for the Short-Term Hydrothermal Dispatch Problem Considering Head and Spillage Effects

The generation of a hydroelectric plant is a nonlinear function of the turbined outflow, storage and sometimes also of the spillage. Other aspects, such as forbidden operating zones and individual turbine efficiency curves, are also important. Although for the self-scheduling of a hydro plant a precise integer modeling of the hydro power production function (HPF) is convenient, in the security constrained short-term hydrothermal dispatch problem for large-scale systems a strategy which best balances an accurate representation with an acceptable computational burden is required. In this paper, a detailed review of different approaches to model the HPF is presented, and a new four-dimensional piecewise linear model is proposed. This model takes into account the water head as a function of forebay and tailrace levels and considers spillage effects. Nonconcave regions of the HPF are approximated by using convexification and regression techniques. A major advantage of this approach is to consider the influence of storage, turbined outflow and spillage in a single function that can be used in a straightforward way, instead of deriving several curves for different heads. Numerical results show the applicability of this approach to the day-ahead network constrained short-term hydrothermal dispatch problem of the large Brazilian system.

Short-term hydro-thermal dispatch detailed model and solutions

An efficient method is described for the solution of the short-term hydro-thermal dispatch problem including optimal power flow (OPF) as the mathematical model of the thermal subsystem. This approach has the capability of taking into account the following effects: coupling of cascaded multichannel reservoirs, water time delays, reservoir head variations, load flow, and other constraints due to security and environmental considerations. The problem is decomposed into hydro and thermal subproblems which are then solved iteratively. An effective adjustment has been proposed to take into account the nonlinear relation between the two subproblems to speed up the convergence of the iterative process. In this adjustment, as well as in solving the thermal subproblem, equations of coordination and OPF are combined for better computational efficiency. On the basis of the proposed approach, four different methods, which differ in the degree of details in modeling the thermal system, have been tested and investigated. Numerical examples are included to demonstrate the advantages of the approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>