Optimal Scheduling Strategy for Energy Consumption Minimization of Hydro-thermal Power Systems

A comparison analysis based method for computing the water consumption volume needed for electric energy production of optimal scheduling in hydro-thermal power systems is presented in this paper. The electric energy produced by hydroelectric plants and coal-fired plants is divided into 4 components: potential energy, kinetic energy, water-deep pressure energy and reservoir energy. A new and important concept, reservoir energy, is proposed, based on which is divided into a number of water bodies, for example 3 water bodies, and a reservoir is analyzed in a new way. This paper presents an optimal scheduling solution of electric energy production of hydro-thermal power systems based on multi-factors analytic method, in which some important factors, such as load demand, reservoir inflow , water consumption volume increment rate of hydroelectric plants or converted from coal-fired plants, and so on are given to model the objective function and the constraints. A study example with three simulation cases is carried out to illustrate flexibility, adaptability , applicability of the proposed method.


Introduction
Water is one of the important renewable energy sources and coal is a non-renewable energy source.For optimal scheduling of hydro-thermal power systems, it is the first thing that water must have much more priority to be used for electric energy production than coal so as to supply the demand load.It is an important study task how to minimize the sum of water consumption volume of the hydroelectric plant and water consumption volume converted from the coal-consumed volume of coal-fired plants in hydro-thermal power system dispatch.
In modeling electric energy production of hydroelectric plants, some pioneer did many significant works.For the portfolio management of a scandinavian power supplier, a linear stochastic model with hydraulic power plants under uncertain inflow and market price conditions is introduced [1].In [2], price uncertainty by scenarios and a model for maximizing risk-adjusted profit within an asset-liability framework is represented.A new multi-loop-cascaded governor, with which the perform-ance specifications and stability margins are improved significantly even in the presence of some uncertainties, is proposed to use for hydro turbine control [3] and some other stochastic programming models are proposed to represent the energy systems [4].However, with the achievements in recent liberalization of the electricity market, the discussion about improving the assumptions and considering further aspects of actual system operations is far from ending.Some works have done for the optimal scheduling solution of hydro-thermal power systems.There are many computational methods for the solution of some difficult optimization problem such as dynamic programming [5] [6], network flow [7][8][9], standard mixed integer programming methods [10][11][12], and modern heuristic algorithms [13] [14].Although dynamic programming is flexible and can handle the constraints better in a straightforward way, the "curse of dimensionality" still remains, and the main drawback of using dynamic programming for a realistic systems with multiple reservoirs J. K. WU and cascaded hydro plants still exists [14].Network flow would be the natural way to model hydro systems.Its main drawback, however, is its inability to deal with discontinuous operating regions and discrete operating states [15].Mixed integer programming is only suitable for small systems due to size limitations.Modern heuristic algorithms do not require such conditions that the objective function has to be differentiable and continuous, so these methods are considered as effective tools for non-linear optimization problems such as short-term scheduling of hydro systems.Particle swarm optimization (PSO) is one of the modern heuristic algorithms.
PSO has attracted great attention due to its features of easy implementation, robustness to control parameters and computation efficiency compared with other existing heuristic algorithms, and has been successfully applied to hydroelectric optimization scheduling problems [16][17][18][19][20].Some stochastic approaches are also used for the solution of the cascaded hydro plants problem [21][22].This paper presents a novel analysis method for modeling hydro-energy conversion and computing water consumption volume of optimal electric energy production in large-scale hydro-thermal power systems, taking some energy components, such as potential energy, kinetic energy, water-deep pressure energy and reservoir energy into consideration, and also taking some influence factors, such as load demand, reservoir in-flow, water consumption volume increment rate, and so on, into account.

Hydro-Energy Conversion
In a large-scale reservoir, if there is a hydro-mechanical-electric coupling system, with a shaft leading the reservoir water through penstock to a hydro turbine, the potential, kinetic and water-deep energy in water is harnessed by the HME coupling system and create electricity from it.For each HME system, the amount of electric energy transformed form hydro energy in reservoir depends on the forces applied on the water body in intake and tailrace of the pressure tunnel.In intake of the pressure tunnel, basing on the traditional analysis method, there is gravitational force corresponding to the potential energy, kinetic force corresponding to kinetic energy and pressure force corresponding to water-deep pressure energy.
In this paper, besides three traditional forces there are another three reservoir forces applied to the water body in intake if a reservoir is divided into three water bodies when modeling the hydroelectric energy of large-scale reservoir.These three reservoir forces applies to the water bode in intake of a pressure tunnel and do work in respective part, which is called 'reservoir energy' in this paper, as shown in Figure 1.For a unit in plant , the electric energy converted by a HME system in unit time(for example one second) may be expressed in a form of kilo-watt may be formulated in MWs: where The electric power of a generator is formu- where T is scheduling period of the hydroelectric plants.
For a unit time( one second), .
i ,

Water Consumption Volume Increment Rate
For a hydropower-driven generator, the variation of electric energy is obtained by differentiating Equation (1) with respect to : Water consumption volume increment rate is defined to be a ratio of the variation of the water consumption volume and the variation of electric power output of a hydropower-driven generator:

Coal Consumption Volume Increment Rate
For a thermal power-driven generator, the coal consumption volume is formulated as a quadratic function of electric power, as shown in the following form: where and is respectively coal consumption volume and electric power of a thermal power-driven generator; , , is respectively coefficient of coal consumption volume of a thermal power-driven generator.
The variation of coal consumption volume is obtained by differentiating Equation (25) with respect to : Coal consumption volume increment rate is defined to be a ratio of the variation of the coal consumption volume and the variation of electric power output of a thermal power-driven generator: Water is one of renewable energy, which is an energy source that can be replenished in a short period of time, and is mainly used for electric energy production.Coal is non-renewable energy, which is an energy source that may be used up and cannot be recreated in a short period of time.In order to make as possible as best use of renewable resource, water must be placed on more prior consideration for electric energy production than coal.
For this purpose, the objective of scheduling optimization of hydro-thermal power systems must minimize the water consumption volume consumed in electric energy production, including the water consumption volume consumed in hydro-electric plants and the water consumption volume exchanged from coal consumption volume consumed in coal-fired electric plants: where  The constraint conditions include: 1) Equality constraint for electric power of hydro-thermal power systems: at any time t , the sum of the electric power produced by hydro-driven generators and coal-fired generators must be hold to be equal to load-demanded power: where is load-demanded power at any time ) (t 2) Equality constraint for electric energy of hydro-thermal power systems: in the scheduling period T , the sum of the electric energy produced by hydro-driven generators and coal-fired generators must be hold to be equal to load-demanded energy: where is load-demanded energy in the scheduling period 3) Inequality constraint for active and reactive power of hydro-driven generators: where is respectively the lower and upper limited value of active and reactive power of hydro-driven generator in plant .i j 5) Inequality constraint for active and reactive power of coal-fired generators: where and where d coal consumption volume: for a whole, the coal consumption volume exchanged using water consumption volume of all hydro-driven generators is required to be greater than that consumed by all coal-fired generators:  is a coefficient exchanging water conn vol sumptio ume consumed in hydro-electric plants into coal consumption volume, and it is formulated: generators is required to be smaller than that consumed by all hydro-driven generators: , ,  ring high-water period, normal-water period, low water period, and flood period, saved-water level is required to be retained at a fixed value:   shown in Table 3.
Table 4 shows the electric energy production of hydro-thermal power systems and energy component of

Figure 1 .
Figure 1.Divided water bodies of a large-scale reservoir where and is respectively number of hydroelectric plants and hydro-driven generators in plant , and is respectively number of coal-fired electric plants and coal-fired generators, consumption volume consumed in coal-fired electric plants into water consumption volume, and it is formulated:


is average water consumption volume increment rate of all hydro-driven generators:

)
coal-fired generator l in plant k .6)Inequality constraint for generation flow: consu volume of coal-fired electric plant k in the scheduling period T .8) Inequality constraint for water consum e: r level t time anged from coal consumption volume of all coal-fired and H1 is for the remainder of the load, as shown in Table 3.With increases in the load, the coal-fired plants with smaller coal-water consumption volume are also gradually put into schedule for electric energy production till the load arrives at the sum of the rated install capacity of all hydroelectric and coal-fired plants, as

igure 2 .
Figure 2 and Figure 3.It is also seen that for small than about 7000MW of load, hydroelectr

Table 2
respectively.In the following section, three cases are given to illustrate the component and factor analytic method for optimal electric energy production of thermal power systems in one hour.