Multi-Objective Short-Term Hydro-Thermal Scheduling Using Meta-Heuristic Approaches

Multi-Objective Short-Term Hydro-Thermal Scheduling Using Meta-Heuristic Approaches

Moumita Pradhan (Dr. B. C. Roy Engineering College, India), Provas Kumar Roy (Kalyani Government Engineering College, India) and Tandra Pal (National Institute of Technology, Durgapur, India)
DOI: 10.4018/978-1-7998-3222-5.ch016


Every day humans face new challenges to survive in this world. It is a big challenge to utilize hydro and thermal generating unit properly. Researchers are trying to explore new techniques to improve scheduling of generating units. Environmental matter is a big issue to modern society. This chapter suggests a well-organized and effective approach using concept of grey wolf optimization (GWO) to deal with non-linear, multi-objective, short-term, hydro-thermal scheduling (MOHTS) problem. Moreover, authors have incorporated oppositional based learning (OBL) to enhance characteristics of GWO to achieve solution more consistently and accurately. To explore authenticity of our proposed algorithms, GWO and OGWO (oppositional based GWO) are applied to multi-chain cascade of 4-hydro and 3-thermal test system. Effective constraints like valve-point loading, water discharge, water storage, etc., are considered here. Statistical comparisons with other enlisted heuristic methods are done. The projected methods solve MOHTS problem quickly and efficiently.
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1. Introduction

Multi-objective short-term hydrothermal scheduling (MOHTS) is a vital organizing task in operation of the power system. Usually, hydro-thermal power system scheduling is more complex than thermal system scheduling. The bordering manufacture price of hydroelectric plants is insignificant, but one of the important problems is usage of available water. The cost of thermal generation is increased if they are present alone in the power system. However, the presence of large number of hydroelectric plants with a set of constraints coupled in proper time periods to maximize power generation from hydroelectric plants may decrease the cost. Economic load dispatch (ELD) is an optimization approach in the thermal power system which try to schedule power generation according to the load demand from the power plant. Conventionally, the hydrothermal power systems are worked in such a way that the total fuel cost is reduced with optimal power generation by both hydro and thermal power plant.

In our research work, we want to schedule the power generating units in such a way that’s why manufacturing cost is minimized. Load demand is circulated among generating units in ELD (Wood & Wollenberg, 1994; Happ, 1997; Chowdhury & Rahman, 1990; Liu & Cai, 2005) problem which will satisfy generation limit, prohibited operating zone, ramp rate, etc., considering transmission loss at every time interval such that the over-all cost is minimum. Fossil fuel produces various pollutants, like nitrogen oxides, carbon dioxide, sulfur oxides, etc., into the atmosphere at the time of generation of electricity from thermal power plant. The power companies have to assured standards concerning about the emission levels of pollutants for the strict government guidelines on ecological protection. As a responsible citizen, we must try to clean the air from different poisonous gasses. By European Clean Air Act Amendments of 1990 and similar acts by Japanese governments and others, show their concern by the management rules (Yalcinoz, Altun & Hasan, 2002). The awareness due to the increasing anxiety over contaminants, society bothers apposite and safe electric power must get in low price but in lower level of pollution. Newly, ELD problem has been incorporated by emission dispatch (CEED) problem (Roy, Ghoshal & Thakur, 2010a; Roy, Ghoshal & Thakur, 2010b; Zhang, Luh & Zhang, 1999); where many researchers consider emission as an additional constraint or second objective function with minimize the cost economy. For the instance of short-term hydro-thermal load managing, it is typically expected that the water volume entrances essential to encounter the load necessities and load demand are recognized through certainty. The several restrictions that cannot be disrupted HTS is a complicated decision-making process. Water discharge rate, hydraulic continuity restriction, lower and upper bounds of the reservoir volumes, water spillage, effective capacity limits of hydro plant etc., constraints makes the HTS problem as a complex optimization problem whose viable solution space is enormous.

Numerous optimization algorithms for mathematics are applied to the hydrothermal scheduling problem (Zhang, Luh & Zhang, 1999; Al-Agtash, 2001). Several classical methods, such as decomposition approach (DA) (Pereira & Pinto, 1983), dynamic programming (DP) (Yang & Chen, 1989), linear programming (LP) (Mohan, Kuppusamy & Khan, 1992), non-linear programming (Gul et al., 2019) and progressive optimality algorithm (Turgeon, 1981) have been deployed to solve the HTS problem. DP faces dimensionality problem in multi-dimensional search space. Other algorithms also have different kinds of obstacles like fall into local optima instead of the global optima in multi-dimensional search space, low convergence rate etc.

Key Terms in this Chapter

UP: Upstream hydro plants immediately upstairs the hydro reservoir.

: Maximum power output of thermal unit i.

poz: Number of prohibited operating zones.

T: Summation of the thermal units.

Qhjt: Water discharge rate of the j th hydro reservoir for time t interval.

: j th hydro reservoir’s initial storage volume.

ai,ßi,?i,?i,di: Coefficients for the emission of the i th thermal generator.

FCit: Sum of overall fuel costs of the i th thermal generator at t time.

: Prohibited operating zone’s lower limit for i th thermal unit.

: Final volume of j th hydro reservoir.

: Vectors of random in range[0,1].

: Previous volume of the j th hydro reservoir.

RES: Aggregation of reservoirs for hydro unit.

: Power generation coefficients of the j th hydro generator.

: Encircling behaviour representation for grey wolf.

P(n): Position vector of the prey.

Vhjt: Reservoir volume of the j th hydro plant at t time.

xhjt: Discharge rate of turbine at t time for the j th hydro reservoir.

?: From w th to j th reservoir’s water transport delay.

: Minimum value of the power output of i th thermal unit.

HT: Price penalty factor.

TTI: Accumulated time intervals.

FCE: Aggregation of fuel cost considering emission.

: Vector of GWO.

: Maximum and minimum water discharge rate.

ai,bi,ci,di,ei: Fuel cost coefficients for i th thermal generator.

T: Time schedule.

Ihjt: Inflow of the j th hydro reservoir.

FC: Aggregation of the burning cost of the thermal unit.

Phjt: Power generation at time t for the j th hydro generator.

: Upper prohibited operating zone limit for i th thermal generator.

: Position vector of grey wolf or search agents.

Dt: At time t aggregation of power demand.

WDr,t: At time t, water discharge rate of the r th hydro generator.

p: Population size.

: Previous hour’s power output of i th thermal unit.

: The smallest and the extreme volume of the j th hydro reservoir.

Pgit: Power generation of the i th thermal generator at time t.

: Coefficient vectors for GWO algorithm.

n: Current iteration number for GWO algorithm.

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