Abstract
In this article, an effective hybrid nodal ant colony optimization (NACO) and real coded clustered gravitational search algorithm (CGSA) is involved in producing a corrective/preventive contingency dispatch over a specified given period for wind integrated thermal power system. High wind penetration will affect the power system reliability. Hence, the reliability based security-constrained unit commitment (RSCUC) problem is proposed and solved using bi-level NACO-CGSA hybrid approach. The RSCUC problem comprises of reliability constrained unit commitment (RCUC) as the master problem and the sub problem as a security constrained economic dispatch (SCED). NACO solves master problem and the sub problem is solved by real coded CGSA. The objective of RSCUC problem model is to obtain the economical operating cost, while maintaining the system security. The proposed solution for the hourly scheduling of generating units is based on hybrid NACO-CGSA. Case studies with IEEE 118-bus test system are presented in detail.
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- \( {\text{AvgC}},{\text{Max}}_{\text{it}} \) :
-
Average minimum cost($) obtained in 10 simulations and Maximum number of iterations
- \( {\text{BF}}_{i,t} ,{\text{BF}}_{\text{i}}^{\hbox{max} } \) :
-
Flow through branch i at time t (MVA) and Maximum flow limits for branch I (MVA)
- \( {\text{C}}_{i} ({\text{P}}_{{({\text{i}},{\text{t}})}} ) \) :
-
Production cost ($) \( C_{i} (P_{(i,t)} ) = a + b^{*} P_{(i,t)} + c*P_{(i,t)}^{2} \)
- \( {\text{P}}_{{({\text{i}},{\text{t}})}} ,{\text{P}}_{{({\text{i}}\,{ \hbox{min} })}} \text{P}_{{{\text{i}}\hbox{max} }} \) :
-
Power level Minimum and Maximum power output of ith generator unit (MW)
- \( {\text{a}},{\text{b}},{\text{c}} \) :
-
Cost co-efficient of ith generator unit in ($/hr), ($/MWhr) and ($/MW2hr)
- \( {\text{D}}_{\text{t}} ,{\text{Fit}}_{\text{p}} \) :
-
Total system demand at time t and Fitness value of the solution p
- \( {\text{DR(i)}},{\text{UR(i)}} \) :
-
Ramp-down rate limit of ith generator unit and Ramp-up rate limit of ith generator unit
- \( {\text{G}}_{\text{ij}} {\text{B}}_{\text{ij}} \) :
-
Conductance and susceptance between bus i and bus j
- \( {\text{I}}_{(i,t)} {\text{L}}_{\text{gb}} \) :
-
Commitment state of ith unit at tth hour and Maximum total profit incurred till the current tour
- \( {\text{N}},{\text{N}}_{\text{ants,}} {\text{N}}_{\text{B}} \) :
-
Total number of generating units, Total number of ants and Number of busses
- \( {\text{N}}_{{{\text{B}} - 1}} ,{\text{N}}_{\text{PQ}} \) :
-
Number of buses excluding slack bus, Number of PQ bus,
- \( {\text{P}}_{\text{Gi,t,}} {\text{Q}}_{\text{Gi,t}} \) :
-
Active and reactive power generation at bus i at time t, respectively
- \( {\text{P}}_{\text{Di,t,}} {\text{Q}}_{\text{Di,t}} \) :
-
Minimum and maximum active power generation limit tor unit i
- \( { \Pr }_{\text{rs}}^{\text{k}} ({\text{st}}) \) :
-
Transition probability of kth ant from stage r to s
- \( {\text{Q}}_{\text{Gi}}^{ \hbox{min} } ,{\text{Q}}_{\text{Gi}}^{ \hbox{max} } \) :
-
Minimum and maximum reactive power generation limit for unit i
- \( {\text{R}}_{{({\text{i}},{\text{t}})}} ,{\text{SR}}_{\text{t}} \) :
-
System spinning reserve at tth hour (MW/hour) and Total system spinning reserve at time t
- \( {\text{SU}}_{\text{i}}^{\text{t}} ,{\text{SD}}_{\text{i}}^{\text{t}} \) :
-
Start up cost and shut down cost of unit i at time t,
- \( {\text{TS}},{\text{T}},{\text{TC}} \) :
-
Total number of stages, Dispatch period in hours and Total cost ($)
- \( {\text{T}}^{\text{on}} ({\text{i}}),{\text{T}}^{\text{off}} ,{\text{TC}} \) :
-
Minimum up-time of ith generator unit and Minimum down-time of ith generator unit
- \( {\text{V}}_{{{\text{i}},{\text{t}}}} ,{\text{V}}_{\text{pq}} \) :
-
Voltage magnitude of bus i at time t (pu) and Modified position of employed or onlooker bees
- \( {\text{V}}_{i}^{\hbox{min} } ,{\text{V}}_{i}^{\hbox{max} } \) :
-
Minimum and maximum voltage magnitude limit at bus i (pu)
- \( {\text{X}}^{\text{on}} ({\text{i}},{\text{t}}),{\text{X}}^{\text{off}} ({\text{I}},{\text{t}}) \) :
-
“ON” duration of ith generator unit till time t and “OFF” duration of ith generator unit till time t
- \( {\text{A}},{\text{B}},{\text{P}} \) :
-
Relative importance pheromone trail intensity and Relative importance of heuristic function
- \( {\text{P}},{\text{i}},{\text{t}} \) :
-
Evaporation factor, Index for generator unit and Index for time
- \( \uptau_{\text{rs}} ({\text{st}}),\Delta \tau_{\text{rs}} \) :
-
Heuristic function of stage (st) r to s and The updating co-efficient
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Banumalar, K., Manikandan, B.V., Chandrasekaran, K. (2016). Security Constrained Unit Commitment Problem Employing Artificial Computational Intelligence for Wind-Thermal Power System. In: Senthilkumar, M., Ramasamy, V., Sheen, S., Veeramani, C., Bonato, A., Batten, L. (eds) Computational Intelligence, Cyber Security and Computational Models. Advances in Intelligent Systems and Computing, vol 412. Springer, Singapore. https://doi.org/10.1007/978-981-10-0251-9_26
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