The Journal of the Institute of Internet, Broadcasting and Communication (한국인터넷방송통신학회논문지)

The Institute of Internet, Broadcasting and Communication (한국인터넷방송통신학회)
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Dynamic Economic Load Dispatch Problem Applying Valve-Point Balance and Swap Optimization Method

밸브지점 균형과 교환 최적화 방법을 적용한 동적경제급전문제

  • Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
  • 이상운 (강릉원주대학교 과학기술대학 멀티미디어공학과)
  • Received : 2015.08.28
  • Accepted : 2016.02.05
  • Published : 2016.02.29
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Abstract

This paper proposes a balance-swap method for the dynamic economic load dispatch problem. Based on the premise that all generators shall be operated at valve-points, the proposed algorithm initially sets the maximum generation power at $P_i{\leftarrow}P_i^{max}$. As for generator i with $_{max}c_i$, which is the maximum operating cost $c_i=\frac{F(P_i)-F(P_{iv_k})}{(P_i-P_{iv_k})}$ produced when the generation power of each generator is reduced to the valve-point $v_k$, the algorithm reduces i's generation power down to $P_{iv_k}$, the valve-point operating cost. When ${\Sigma}P_i-P_d$ > 0, it reduces the generation power of a generator with $_{max}c_i$ of $c_i=F(P_i)-F(P_i-1)$ to $P_i{\leftarrow}P_i-1$ so as to restore the equilibrium ${\Sigma}P_i=P_d$. The algorithm subsequently optimizes by employing an adult-step method in which power in the range of $_{min}\{_{max}(P_i-P_i^{min}),\;_{max}(P_i^{max}-P_i)\}$>${\alpha}{\geq}10$ is reduced by 10; a baby step method in which power in the range of 10>${\alpha}{\geq}1$ is reduced by 1; and a swap method for $_{max}[F(P_i)-F(P_i-{\alpha})]$>$_{min}[F(P_j+{\alpha})-F(P_j)]$, $i{\neq}j$ of $P_i=P_i{\pm}{\alpha}$, in which power is swapped to $P_i=P_i-{\alpha}$, $P_j=P_j+{\alpha}$. It finally executes minute swap process for ${\alpha}=\text{0.1, 0.01, 0.001, 0.0001}$. When applied to various experimental cases of the dynamic economic load dispatch problems, the proposed algorithm has proved to maximize economic benefits by significantly reducing the optimal operating cost of the extant Heuristic algorithm.

본 논문은 경제급전 최적화 문제에 균형-교환 방법을 제안하였다. 제안된 알고리즘은 모든 발전기를 가능한한 밸브지점으로 운영한다고 가정한다. 초기치로 최대 발전량 $P_i{\leftarrow}P_i^{max}$로 설정하고, 각 발전기의 밸브지점 $v_k$까지 발전량을 감소시켰을 때의 평균 발전단가 $c_i=\frac{F(P_i)-F(P_{iv_k})}{(P_i-P_{iv_k})}$가 최대가 되는 $_{max}c_i$ 발전기 i의 발전량을 밸브지점 발전단가 $P_{iv_k}$로 감소시켰으며, ${\Sigma}P_i-P_d$ > 0이면 $c_i=F(P_i)-F(p_i-1)$의 $_{max}c_i$ 발전기 발전량을 $P_i{\leftarrow}P_i-1$로 감소시켜 ${\Sigma}P_i=P_d$의 균형을 맞추었다. 다음으로, $_{min}\{_{max}(P_i-P_i^{min}),\;_{max}(P_i^{max}-P_i)\}$>${\alpha}{\geq}10$의 범위에 대해 "-10" 간격으로 감소시키는 성인걸음법으로, 10>${\alpha}{\geq}1$ 범위에 대해서는 "-1"의 아기걸음법으로, $P_i=P_i{\pm}{\alpha}$에 대한 $_{max}[F(P_i)-F(P_i-{\alpha})]$>$_{min}[F(P_j+{\alpha})-F(P_j)]$, $i{\neq}j$이면 $P_i=P_i-{\alpha}$, $P_j=P_j+{\alpha}$로 발전량을 교환하는 방법으로 최적화를 수행하였다. 다음으로 ${\alpha}=\text{0.1, 0.01, 0.001, 0.0001$에 대해 미세한 교환을 수행하였다. 동적 경제급전 문제의 시험 사례에 제안된 알고리즘을 적용한 결과 기존의 휴리스틱 알고리즘 최적화 발전비용을 크게 감소시켜 경제적인 이익을 극대화 시켰다.

Keywords

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