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A Modified Differential Evolution Algorithm for the Solution of a Large-Scale Unit Commitment Problem

  • Research Article - Electrical Engineering
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Abstract

The Unit Commitment (UC) problem is a nonlinear and complex optimization problem used to determine the start-up and shutdown scheduling of power-generating units to meet the forecasted load demand and spinning reserve over a specified time horizon so that the target of production cost minimization is achieved while satisfying various system and generator-based constraints. The increase in computational burden with the system size requires more efficient meta-heuristic approaches for solving the UC problem. This paper proposes a modified differential evolution (DE) approach for both discrete and real part of the UC problem. The infeasibility of the solutions is also handled by incorporating some repairing mechanisms in DE, which forcefully satisfy the system constraints and speed up the search process. The experimentation is carried out on various standard and large power systems, starting from the 10-unit base case and then going up to 100 units over a 24 -h time period. The obtained results indicate the effectiveness of the proposed approach as compared to the previous work reported in the literature.

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Abbreviations

N :

Number of units

\({P_i^{(t)}}\) :

Generated power for unit i at time t

\({Z_i^{(t)}}\) :

Binary variable used to represent the ON–OFF status of unit at hour t

\({a_i, b_i, c_i, e_i, f_i}\) :

Cost coefficients of i th unit (known)

\({{{\rm SC}}_i^{{{\rm (hot)}}}}\) :

Hot start cost of i th unit

CSH i :

Cold start hours of unit i

MDT i :

Minimum down time of the i th unit

\({P_{{{\rm SR}}}^{(t)}}\) :

Spinning reserve requirement at hour t

\({X_i^{({{\rm on}})}}\) :

Duration of i th unit being continuously on up to time t

I si :

The initial status of i th unit

X (t) :

Amount of violation in the spinning reserve

R (t) :

Excessive spinning reserve at hour t

PU(t) :

First unit in priority list at hour t

\({P_{({{\rm sum}})}^{(t)}}\) :

Sum of power generated by all committed units at time t

X j(min) :

Lower limit of the decision vectors

\({X_{r1}^{(G)}, X_{r2}^{( G )}, X_{r3}^{( G )}}\) :

Randomly chosen population vectors

\({C_{i,j}^{(G+1)}}\) :

Generated trial vector

\({X_i^{(G+1)}}\) :

Selected vector for the next generation

MUT:

Minimum up time

TC:

Total production cost

F :

Mutation factor

T :

Generation scheduling period in hours

\({{{\rm SC}}_i^{( t )}}\) :

Start-up cost of i th unit

\({F_i \big( {P_i^{(t)}}\big)}\) :

Operating fuel cost of i th unit at time t

P i(min) :

Minimum power generation limit of unit i

\({{{\rm SC}}_i^{({{\rm cold}})}}\) :

Cold start cost of i th unit

\({X_i^{( {{{\rm off}}})}}\) :

Duration of i th unit being continuously off up to time t

\({P_D^{(t)}}\) :

Known load demand at time t

P i(max) :

Maximum power generation limit of unit i at any time instant

MUT i :

Minimum up time of i th unit

FC i :

Full-load average production cost of i th unit

\({S_i^{(t)}}\) :

Status vector to represent the ON–OFF status of thermal units i at time t

\({P\_{{\rm list}^{(t)}}}\) :

Priority list of units at hour t

Q (t) :

Amount of deviation in the generated power at hour t

\({X_{j({{\rm max}} )}}\) :

Upper limit of the decision vectors rand Random number in the range 0-1

\({M_i^{(G+1)}}\) :

Mutant vector for the next generation

Cr:

User-defined crossover probability between 0 and 1

X M :

Mutation individual

MDT:

Minimum down time

CR:

Crossover probability

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Authors and Affiliations

  1. Electrical Engineering Department, University of Engineering and Technology, Taxila, 47050, Pakistan

    Nisma Saleem, Aftab Ahmad & Salman Zafar

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  1. Nisma Saleem
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  2. Aftab Ahmad
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  3. Salman Zafar
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Correspondence to Nisma Saleem.

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Saleem, N., Ahmad, A. & Zafar, S. A Modified Differential Evolution Algorithm for the Solution of a Large-Scale Unit Commitment Problem. Arab J Sci Eng 39, 8889–8900 (2014). https://doi.org/10.1007/s13369-014-1389-8

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  • DOI: https://doi.org/10.1007/s13369-014-1389-8

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