Abstract
Decades before, researchers have only given emphasis on optimizing the cost of energy production from thermal generating units. In view of the massive global warming and environmental pollution issues, government regulations are being imposed on the utilities which restricts the generating companies to emit toxic gases like oxides of sulfur and nitrogen. Hence, it becomes utmost important to optimize environmental emissions together with the generating cost. Single-objective optimization optimizes only one objective at a time. Therefore, to comply with the government regulation, multi-objective optimization needs to be utilized to optimize two objectives at a same time. This work aims to solve a fuel-constrained economic emission dispatch (FCEED) problems with some standard load constraints for thermal generating units using multi-objective optimization. FCEED is highly nonlinear non-convex constrained optimization problem which tries to find the optimum generating schedule for committed generators such that the operating cost and environmental emissions are minimum for certain loading condition. Differential evolution (DE) is designed as the multi-objective optimization technique to solve the FCEED optimization problem. After comparison, the result shows that the consumption of fuel could be restricted by varying the output power of different generating units, for which the power system will be operated within its contractual constraints and fuel limitations. It is analyzed that to get the same power demand from the objective functions (level of emission and fuel cost), one can be increased and the other can be decreased. However, the penalty levied for failing to maintain the fuel contract could be compensated. Numerical findings have been examined for the various test systems and comparing the results to those obtained from the strength pareto the evolutionary algorithm 2.
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Abbreviations
- \(F_{im}\) :
-
Fuel delivered to thermal unit i in interval m
- \(F_{i}^{\min } ,F_{i}^{\max }\) :
-
Lower and upper fuel delivery limits of thermal unit i
- \(F_{D_m}\) :
-
Fuel delivered in interval m
- \(F_{\text{c}}\) :
-
Total cost of fuel
- \(F_{\text{e}}\) :
-
Total emission of fuel
- \({P}_{im}\) :
-
O/P power of thermal unit i in interval m
- \(P_{i}^{\min } ,P_{i}^{\max }\) :
-
Lower and upper generation limits of thermal unit i
- \(P_{D_m}\) :
-
Load demand in interval m
- \(t_{m}\) :
-
Duration of subinterval m.
- \(V_{im}\) :
-
Fuel storage of thermal unit i in interval m
- \(V_{i}^{\min } ,V_{i}^{\max }\) :
-
Lower and upper fuel storage limits of thermal unit i
- \(V_{i}^{0}\) :
-
Initial fuel storage of thermal unit i
- \(a_{i} ,b_{i} ,c_{i} ,d_{i} ,e_{i}\) :
-
Cost coefficients of ith thermal unit
- \(\alpha_{i} ,\beta_{i} ,\gamma_{i} ,\sigma_{i} ,\theta_{i}\) :
-
Emission coefficients of ith thermal unit
- \(\eta_{i} ,\delta_{i} ,\mu_{i}\) :
-
Fuel consumption coefficients of thermal unit i
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Jena, C., Rajan, A., Samal, S., Panda, B., Pradhan, A., Nanda, L. (2022). Intelligent Approach for Fuel-Constrained Economic Emission Dispatch Analysis Using Multi-objective Differential Evolution. In: Malik, H., Ahmad, M.W., Kothari, D. (eds) Intelligent Data Analytics for Power and Energy Systems. Lecture Notes in Electrical Engineering, vol 802. Springer, Singapore. https://doi.org/10.1007/978-981-16-6081-8_8
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