# Heat Transfer Search Algorithm for Combined Heat and Power Economic Dispatch

- 5 Downloads

## Abstract

This paper suggests heat transfer search (HTS) algorithm for solving complicated combined heat and power economic dispatch (CHPED) problem. The valve point effect, prohibited operating zones of conventional thermal generators and transmission loss are taken into consideration. The main objective of the CHPED problem is to minimize the total fuel cost for producing electricity and heat supplying to a load demand. HTS is a novel meta-heuristic optimization algorithm that is based on the law of thermodynamics and heat transfer. The efficiency of the suggested HTS algorithm has been confirmed on four test systems. Test results of the suggested HTS algorithm have been compared with those achieved by other evolutionary algorithms. It has been observed from the comparison that the suggested HTS algorithm has the ability to offer superior solution.

## Keywords

Heat transfer search algorithm Combined heat and power economic dispatch Prohibited operating zones Valve point effect## Abbreviations

- HTS
Heat transfer search

- CHPED
Combined heat and power economic dispatch

- PSO
Particle swarm optimization

- CPSO
Classical particle swarm optimization

- EP
Evolutionary programming

- GSO
Group search optimization

- OGSO
Opposition-based group search optimization

- OBL
Opposition-based learning

- PPS
Powell’s pattern search

- GA
Genetic algorithm

- HS
Harmony search

- CSA
Cuckoo search algorithm

- ECSA
Effective cuckoo search algorithm

- CSO
Civilized swarm optimization

- IAC
Improved ant colony algorithm

- TLBO
Teaching learning-based optimization

- OBTLBO
Opposition-based teaching learning-based optimization

- TVAC-PSO
Time-varying acceleration coefficients particle swarm optimization

- SARGA
Self adaptive real-coded genetic algorithm

- IGA-MU
Improved genetic algorithm with multiplier updating

- MBA
Mine blast algorithm

- FPA
Flower pollination algorithm

- GSA
Gravitational search algorithm

- KHA
Kill herd algorithm

- MPSO
Modified particle swarm optimization

## List of Symbols

- \(P_{{{\text{t}}i}}\)
Power output of

*i*th conventional thermal generator- \(P_{{{\text{t}}i}}^{\hbox{min} } ,\;P_{{{\text{t}}i}}^{\hbox{max} }\)
Minimum and maximum power generation limits of

*i*th conventional thermal generator- \(P_{{{\text{c}}i}} ,\;H_{{{\text{c}}i}}\)
Power output and heat output of

*i*th cogeneration unit- \(H_{{{\text{h}}i}}\)
Heat output of

*i*th heat-only unit- \(H_{{{\text{h}}i}}^{\hbox{min} } ,\;H_{{{\text{h}}i}}^{\hbox{max} }\)
Minimum and maximum heat production limits of the

*i*th heat-only unit- \(C_{\rm T}\)
Total production cost

- \(C_{{{\text{t}}i}} ,\;C_{{{\text{c}}i}} ,\;C_{{{\text{h}}i}}\)
Fuel cost characteristics of the conventional thermal generator, cogeneration unit and heat-only unit, respectively

- \(a_{i} ,b_{i} ,d_{i} ,e_{i} ,f_{i}\)
Cost coefficients of

*i*th conventional thermal generator- \(\alpha_{i} ,\beta_{i} ,\gamma_{i} ,\delta_{i} ,\varepsilon_{i} ,\xi_{i}\)
Cost coefficients of

*i*th cogeneration unit- \(\phi_{i} ,\eta_{i} ,\lambda_{i}\)
Cost coefficients of

*i*th heat-only unit- \(H_{\text{D}}\)
Heat demand

- \(P_{\text{D}}\)
Power demand

- \(P_{\text{L}}\)
Transmission loss

- \(N_{\text{t}} ,\;N_{\text{c}} ,\;N_{\text{h}}\)
Numbers of conventional thermal generators, cogeneration units and heat-only units, respectively

## References

- Abdelaziz AY, Ali ES, Abd Elazim SM (2016) Implementation of flower pollination algorithm for solving economic load dispatch problems in power systems. Energy 101:506–518CrossRefGoogle Scholar
- Adhvaryyu PK, Chattopadhyay PK, Bhattacharya A (2017) Dynamic optimal power flow of combined heat and power system with Valve-point effect using Krill Herd algorithm. Energy 127:756–767CrossRefGoogle Scholar
- Ali ES, Abd Elazim SM (2018) Mine blast algorithm for environmental economic load dispatch with valve point loading effect. Neural Comput Appl 30:261–270CrossRefGoogle Scholar
- Basu M (2010) Combined heat and power economic dispatch using differential evolution. Electr Power Compon Syst 38:996–1004CrossRefGoogle Scholar
- Basu M (2015a) Modified particle swarm optimization for non-smooth non-convex combined heat and power economic dispatch. Electr Power Compon Syst 43:2146–2155CrossRefGoogle Scholar
- Basu M (2015b) Combined heat and power economic dispatch using opposition-based group search optimization. Int J Electr Power Energy Syst 73:819–829CrossRefGoogle Scholar
- Basu M (2016) Group search optimization for combined heat and power economic dispatch. Int J Electr Power Energy Syst 78:138–147CrossRefGoogle Scholar
- Beigvand SD, Abdi H, Scala ML (2016) Combined heat and power economic dispatch problem using gravitational search algorithm. Electr Power Syst Res 133:160–172CrossRefGoogle Scholar
- Guo T, Henwood MI, van Ooijen M (1996) An algorithm for combined heat and power dispatch. IEEE Trans Power Syst 11(4):1778–1784CrossRefGoogle Scholar
- Hosseini SS, Jafarnejad A, Behrooz AH, Gandomi AH (2011) Combined heat and power economic dispatch by mesh adaptive direct search algorithm. Exp Syst Appl 38:6556–6564CrossRefGoogle Scholar
- Jubril AM, Adediji AO, Olaniyan OA (2012) Solving the combined heat and power dispatch problem: a semi-definite programming approach. Electr Power Compon Systems 40:1362–1376CrossRefGoogle Scholar
- Karami H, Sanjari MJ, Tavakoli A, Gharehpetian GB (2013) Optimal scheduling of residential energy system including combined heat and power system and storage device. Electr Power Compon Syst 41:765–781CrossRefGoogle Scholar
- Marty F, Serra S, Sochard S, Reneaume J (2017) Economic optimization of a combined heat and power plant: heat vs electricity. Energy Proc 116:138–151CrossRefGoogle Scholar
- Mohammadi-Ivatloo B, Moradi-Dalvand M, Rabiee A (2013) Combined heat and power economic dispatch problem solution using particle swarm optimization with time varying acceleration coefficients. Electr Power Syst Res 95:9–18CrossRefGoogle Scholar
- Narang N, Sharma E, Dhillon JS (2017) Combined heat and power economic dispatch using integrated civilized swarm optimization and Powell’s pattern search method. Appl Soft Comput 52:190–202CrossRefGoogle Scholar
- Nguyen TT, Vo DN, Dinh BH (2016) Cuckoo search algorithm for combined heat and power economic dispatch. Int J Electr Power Energy Syst 81:204–214CrossRefGoogle Scholar
- Nguyen TT, Nguyen TT, Vo DN (2017) An effective cuckoo search algorithm for large-scale combined heat and power economic dispatch problem. Neural Comput Appl. https://doi.org/10.1007/s00521-017-2941-8 CrossRefGoogle Scholar
- Patel VK, Savsani VJ (2015) Heat transfer search (HTS): a novel optimization algorithm. Inf Sci 324:217–246CrossRefGoogle Scholar
- Pereira-Neto A, Unsihuary C, Saavedra OR (2005) Efficient evolutionary strategy optimization procedure to solve the nonconvex economic dispatch problem with generator constraints. IEEE Proc Gen Trans Distrib 152(5):653–660CrossRefGoogle Scholar
- Ramesh V, Jayabaratchi T, Shrivastava N, Baska A (2009) A novel selective particle swarm optimization approach for combined heat and power economic dispatch. Electr Power Compon Syst 37:1231–1240CrossRefGoogle Scholar
- Rooijers FJ, van Amerongen RAM (1994) Static economic dispatch for co-generation systems. IEEE Trans Power Syst 9(3):1392–1398CrossRefGoogle Scholar
- Roy PK, Paul C, Sultana S (2014) Oppositional teaching learning based optimization approach for combined heat and power dispatch. Electr Power Energy Syst 57:392–403CrossRefGoogle Scholar
- Shaabani Y, Seifi AR, Kouhanjani MJ (2017) Stochastic multi-objective optimization of combined heat and power economic/emission dispatch. Energy 141:1892–1904CrossRefGoogle Scholar
- Song YH, Xuan YQ (1998) Combined heat and power economic dispatch using genetic algorithm based penalty function method. Electr Mach Power Syst 26(4):363–372CrossRefGoogle Scholar
- Song YH, Chou CS, Stonham TJ (1999) Combined heat and power dispatch by improved ant colony search algorithm. Electr Power Syst Res 52:115–121CrossRefGoogle Scholar
- Su CT, Chiang CL (2004) An incorporated algorithm for combined heat and power economic dispatch. Electr Power Syst Res 69(2–3):187–195CrossRefGoogle Scholar
- Subbaraj P, Rengaraj R, Salivahanan S (2009) Enhancement of combined heat and power economic dispatch using self adaptive real-coded genetic algorithm. Appl Energy 86:915–921CrossRefGoogle Scholar
- Vasebi A, Fesanghary M, Bathaee SMT (2007) Combined heat and power economic dispatch by harmony search algorithm. Electr Power Energy Syst 29:713–719CrossRefGoogle Scholar
- Walters DC, Sheble GB (1993) Genetic algorithm solution of economic dispatch with valve point loading. IEEE Trans Power Syst 8(3):1325–1332CrossRefGoogle Scholar
- Wong KP, Algie C (2002) Evolutionary programming approach for combined heat and power dispatch. Electr Power Syst Res 61:227–232CrossRefGoogle Scholar