# New Algorithms for Optimal Hydropower Dispatch

**Project ID:** 5992

**Principal Investigator:** David Harpman

**Research Topic:** Improved Power Generation

**Funded Fiscal Years:**
2009

**Keywords:** *None*

## Research Question

At least every hour, Reclamation's powerplant operators determine the most economic combination of generator units to operate and their generation level. This is known as the economic dispatch problem. Substantial gains can be realized from even small improvements in dispatch efficiency. For example, increasing the generation efficiency at Glen Canyon Dam by 2 percent would yield over four million dollars (in 2004 dollars) annually. Recently, a number of new optimization algorithms have emerged including particle swarm optimization (PSO), ant colony optimization (ACO), extremal optimization (EO) and cross-entropy optimization (CEO). These methods are reportedly able to solve difficult constrained optimization problems, like the economic dispatch problem, quickly and successfully. We plan to review these algorithms, to apply some of them to an example economic dispatch problem, and to report on their performance.

## Need and Benefit

A typical Reclamation hydropower plant has several generator units. The operational characteristics of any given unit vary with the total amount of water released and the head. Identifying the most economic combination of generator units to operate and the level of their operation is known as the optimal economic dispatch problem.

In mathematical notation, this problem is typically specified as a mixed-integer constrained nonlinear optimization problem. Such problems may have multiple solution points (extrema) and are often very difficult to solve. Engineers and mathematicians have devoted countless hours of research to solving this class of problem. Sophisticated algorithms which aid the operator's dispatch decision are frequently embedded in a plant's supervisory control and data acquisition (SCADA) system.

The difficulty of solving the economic dispatch problem increases as the size of the problem becomes larger. For discrete or combinatorial problems, the problem size increases rapidly as the mesh size is decreased and the number of generation units in the problem increase.

Optimization problems have traditionally been addressed with a variety of calculus based methods. These approaches are taught to all engineers and economists. The reader is referred to the excellent reviews of this topic which can be found in Wood and Wollenberg (1996) and Rau (2003).

At the present, two calculus based optimization approaches are in the forefront of optimization technology. These are the sequential quadratic programming (SQQ) method, and, the generalized reduced gradient (GRG) method. Both of these methods are well described by Rau (2003).

Problems which have multiple local optima can often be solved by these and other calculus-based methods. However, there is no guarantee that the solution they identify is the global solution to the problem.

Since the advent of personal computers and the widespread availability of computing power, there has been extensive research on numeric techniques for solving optimization problems. A number of novel heuristic techniques have been identified. Many of these were devised for global optimization. Examples of these new technologies include PSO, simulated annealing (SA), genetic algorithms (GA), ACO, EO, and CEO. These new approaches are reportedly able to solve difficult constrained optimization problems more readily than traditional calculus-based algorithms and have a higher probability of identifying the global optima.

We plan to review these new optimization approaches in detail, identify the most promising ones, and to describe their implementation. We propose to apply one or more of these new optimization techniques to an illustrative hydropower dispatch problem. Finally, we will report on their relative suitability for solving the example problem and describe their solution performance.

## Contributing Partners

None

## Research Products

### Not Reviewed

The following documents were not reviewed. Statements made in these documents are those of the authors. The findings have not been verified.

**Scoping Report-- New Algorithms for Hydropower Optimization** (final, PDF,
477KB)

*By David Harpman*

*Report completed on November 15, 2011*

This information was last updated on November 27, 2014

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