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Chapter 12: Unit Commitment by Evolving ... > IMPLEMENTATION OF THE PROPOSED METHO... - Pg. 209

Unit Commitment by Evolving Ant Colony Optimization Minimum up and down time constraints 1 , if T i , on < T i , up , 0 , = if T i , off < T i , down , 0 or 1 , otherwise U i , t (5) Startup cost HSC if T T i , off T i , cold + T i , down , i i , down ST i , t = CSC i if T i , off > T i , cold + T i , down (6) IMPLEMENTATION OF THE PROPOSED METHOD The implementation of EACO algorithm for solv- ing UC problem involves two phases. In the first phase, all possible states of the t th hour (using ex- haustive enumeration) that satisfy the load demand with spinning reserve constraints are found. For 10-unit system, a maximum of 256 eligible states are found in any hour by taking first two genera- tors as base units. i.e., first two generators are in `on' condition for 24 hours and only 256 feasible states (size of pheromone matrix) are available for remaining eight generators. From 20-unit case on- wards exhaustive enumeration is not possible. The base load units are always in switched on condition. In the remaining units for 20-unit case, the peak units are not considered for light load conditions to try the combinations. In that way, a maximum of 1024 feasible states are found in any hour for 20-unit case. For 40-unit case onwards the ant search space becomes large. To reduce the search space, some of the intermediate load units are also not considered to try the combinations. Which intermediate load units are not to be considered is decided based on the results of 10 and 20-unit systems. In this way, for 40-unit & 60-unit cases a maximum of 4096 feasible states are found in any hour. Because search grows space further, this method is applied up to 60 units only. Economic dispatch using Lagrangian multiplier method is carried out for all feasible states to calculate the optimal generator output and production cost for each hour and startup cost is added for production to get transition cost for each hour. This process is continued for the complete scheduling period of 24 hours to get total cost for each state of all feasible states which constitutes the Ant Search Space (ASS). The ASS which involves multi decision states is given in Figure 1. S t is the eligible state satisfy- ing load demand and spinning reserve at t th hour. Once the search space is identified, the second phase involves the artificial ants allowed to pass continuously through the ASS. Each ant starts its journey from the starting node (initial condition, i.e., 1 st hour), reaches the final node (24 th hour) to complete its tour. Whenever an ant reaches the final node, overall generation cost for 24 hours including start-up cost is calculated. For each transit stage (t to t+1 hour), the ant selects a state satisfying minimum uptime, mini- mum down time constraints etc. The generation cost together with start-up cost is calculated for all units which becomes transition cost. This process is continued till the time period becomes T (24 hours) and a tour is completed for that particular ant. Whenever a tour is completed by an individual ant and if the total generation cost is found is lesser than the minimum cost paths taken by the previous ants, the present cost path is captured. The procedure is continued for all the remaining ants available at the starting nodes, which enables to trace the optimal path. WORKING OF EACO The evolving ant colony search mechanism can be mainly divided into initialization, pseudo random probabilistic transition rule, fitness function and genetic algorithm, pheromone update rule. These steps are given below: 209