Abstract
Due to increased energy cost and limitations of fossil fuel energy sources, systems with higher efficiency such as combined heat and power (CHP) have become more popular. Optimal operation of the power system in the presence of CHP units which have non-linear and non-convex characteristics is getting more complicated. Difficulties of mentioned problem lead us to use heuristic and evolutionary methods. In this chapter, particle swarm optimization (PSO) is implemented in economic dispatch (ED) of CHP units. The main objective of ED problem is to obtain optimal output power and heat of each unit while the total generating cost is minimized and system operational constraints are satisfied. The results show the capability of this algorithm in solving CHP economic dispatch (CHPED) problem.
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Abbreviations
- \(C_{i} (P_{i}^{p} )\) :
-
Operation cost of ith power-only unit for producing \(P_{i}^{p}\) MW
- \(C_{j} (P_{j}^{c} ,H_{j}^{c} )\) :
-
Operation cost for jth co-generation unit for producing \(P_{j}^{c}\) MW electricity power and \(H_{j}^{c}\) MWth heat power
- \(C_{k} (P_{k}^{h} )\) :
-
Operation cost of heat-only unit while producing \(H_{k}^{h}\) MWth heat power
- \(N_{p}\), \(N_{c}\), \(N_{h}\):
-
Total number of power-only, CHP and heat-only units, respectively
- \(i\), \(j\), \(k\):
-
Indices for power-only, CHP and heat-only units, respectively
- \(\alpha_{i}\), \(\beta_{i}\), \(\gamma_{i}\):
-
Constant cost coefficients for ith power-only unit
- \(a_{j}\), \(b_{j}\), \(c_{j}\), \(d_{j}\), \(e_{j}\), \(f_{j}\):
-
Coefficients of cost function related to jth CHP unit
- \(a_{k}\), \(b_{k}\), \(c_{k}\):
-
Coefficients for calculating the operation cost of heat-only units
- \(P_{d}\), \(H_{d}\):
-
Electrical and heat power demands
- \(P_{loss}\) :
-
Power system transmission loss
- \(P_{i}^{p {\min} }\), \(P_{i}^{p {\max} }\):
-
Lower and upper generation limits for power-only units, respectively
- \(P_{j}^{c {\min} }\),\(H_{j}^{c {\min} }\), \(P_{j}^{c {\max} }\), \(H_{j}^{c {\max} }\):
-
Minimum and maximum electric and heat powers outputs for CHP units, respectively
- \(H_{k}^{h {\min} }\), \(H_{k}^{h {\max} }\):
-
Limits for heat-only units
- N :
-
Total number of decision variables in the problem
- \(\omega\) :
-
The inertia weight for PSO
- \(r_{1}^{n}\), \(r_{2}^{n}\):
-
Random numbers in the interval [0, 1]
- \(p_{{best_{i,n} }}^{iter - 1}\), \(g_{best,n}^{iter - 1}\):
-
Best position of ith particle in previous iteration and best position of entire swarm
- \(C_{1}\), \(C_{2}\):
-
Learning factors
- \(x_{n}^{ {\max} }\), \(x_{n}^{ {\min} }\):
-
Maximum and minimum limits of variables
- r :
-
Parameter to control the amount of change in velocity
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Sohrabi, F., Jabari, F., Pourghasem, P., Mohammadi-Ivatloo, B. (2020). Combined Heat and Power Economic Dispatch Using Particle Swarm Optimization. In: Pesaran Hajiabbas, M., Mohammadi-Ivatloo, B. (eds) Optimization of Power System Problems . Studies in Systems, Decision and Control, vol 262. Springer, Cham. https://doi.org/10.1007/978-3-030-34050-6_6
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