Modified radial movement optimization (MRMO) technique for estimating the parameters of fuel cost function in thermal power plants

Parameter estimation using a modified whale optimization algorithm for input‐output curves of thermal and hydro power plants

“…Based on the results presented in Tables , the following issues have been noted: The proposed CMWO algorithm has got the best estimation of models parameters (the least absolute errors of min (AES) index) for all thermal units (Sys3T, Sys2T, Sys13T, Sys5T) and a hydro one (Sys1H). There are some cases when algorithm CMWO gets the same values for min (AES) like algorithm MRMO (for model 1, Table ; and for model 2/unit 3, Table ) or algorithm IDE (model 4, Table ). In most cases, the values of statistical indexes mean (AES) , max (AES) , and SD (AES) resulted from CMWO algorithm are better than the ones got from competitor algorithms (see cases presented in Tables ). For model 4 (Table ), the values (errors) resulted from algorithm CMWO are very close to those of algorithm IDE, both for statistical indexes and calculation time.…”

“…For these units, model 4 is tested, for which five parameters should be estimated. Number of available data/observations for both units is O = 21. 13‐unit thermal system (Sys13T) : This system consists of 13 thermal units, the generated power ( P j ) and the actual values of the fuel cost ( F actual,j ) are taken from Vanithasri et al For these units, model 5 is tested, for which six parameters should be estimated. Number of observations for each unit is O = 8.…”

“…To determine the parameters limits, the values of reference vector X Ref were considered the best estimation X best obtained when running: MRMO algorithm from Vanithasri et al (for models 1, 2, and 5), IDE algorithm from Sayah and Hamouda (for model 3), CMWO algorithm (for models 4 and 6), and NR algorithm from El‐Hawary and Kumar (for models 8 and 9). In the case of model 7, vector X Ref has the actual values given in Durai et al…”

“…They consist of the values of model parameters related to the best estimation obtained by the algorithms mentioned (WO, MWO, CMWO), statistical indexes corresponding to the objective function AES ( min (AES) , mean (AES) , max (AES) , and SD (AES) ), and average calculation time (CPU). Also, Tables show the results obtained using other algorithms (for example: LES, PSO, ABC, CS, RMO, MRMO, and CSA for model 1; LES, PSO, ABC, CS, TLBO, RMO, MRMO, and CSA for model 2, etc).…”

“…To avoid derivative calculations and obtain good quality estimations for smooth and nonsmooth models, methods based on artificial intelligence can be used. Some of them are listed here: genetic algorithm (GA), particle swarm optimization (PSO), artificial bee colony (ABC), cuckoo search (CS) algorithm, teaching‐learning–based optimization (TLBO), radial movement optimization (RMO) technique, modified RMO (MRMO) algorithm, original differential evolution algorithm (DE), and improved differential evolution (IDE) algorithm …”