# IEEE 6-Units ELD Test System No.2

I. Introduction:

$$\bullet$$ This system consists of six thermal units and based on IEEE 30 bus system $$\rightarrow$$ please refer to our PF Library
$$\bullet$$ The load demand is 2.834 per unit (p.u.). Some researchers could evaluate their proposed optimization algorithms with different load demands as in [3].
$$\bullet$$ The fuel-cost function of this test system is modeled using the quadratic cost function as follows:

$$C_i\left(P_i\right) = a_i + b_i P_i + c_i P^2_i$$ .......... $$(1)$$

where $$a_i$$, $$b_i$$, and $$c_i$$ are the function coefficients and tabulated in Table 1.

$$\bullet$$ The network losses are modeled using Kron's loss formula as follows:

$$P_L = \sum_{i=1}^{n} \sum_{j=1}^{n} P_i B_{ij} P_j + \sum_{i=1}^{n} B_{0i} P_i + B_{00}$$ .......... $$(2)$$

where $$B_{ij}$$, $$B_{0i}$$, and $$B_{00}$$ are called loss coefficients (or just B-coefficients) and listed below:

$$B_{ij}=\begin{bmatrix} 0.02180 & 0.01070 & -0.00036 & -0.00110 & 0.00055 & 0.00330 \\ 0.01070 & 0.01704 & -0.00010 & -0.00179 & 0.00026 & 0.00280 \\ -0.00040 & -0.00010 & 0.02459 & -0.01328 & -0.01180 & -0.00790 \\ -0.00110 & -0.00179 & -0.01328 & 0.02650 & 0.00980 & 0.00450 \\ 0.00055 & 0.00026 & -0.01180 & 0.00980 & 0.02160 & -0.00010 \\ 0.00330 & 0.00280 & -0.00790 & 0.00450 & -0.00010 & 0.02978\end{bmatrix}$$

$$B_{0i} = 10^{-3} \times \left[0.010731,1.7704,-4.0645,3.8453,1.3832,5.5503\right]$$

$$B_{00} = 0.0014$$

$$\bullet$$ If the emission-rates are considered, then the following equation can be used to express these rates in the optimization problem:

$$E\left(\sum_{i=1}^n P_i\right) = \sum_{i=1}^n 10^{-2} \left(\alpha_i + \beta_i P_i + \gamma_i P^2_i \right) + \xi_i e^{\delta_i P_i}$$ .......... $$(3)$$

where $$\alpha_i$$, $$\beta_i$$, $$\gamma_i$$, $$\xi_i$$, and $$\delta_i$$ are the coefficients of the $$i$$th unit emission characteristics. Thus, Table 1 is expanded to Table 2 [4].

II. Files:

$$\bullet$$ System Data (Text Format) [Download]

III. References (Some selected papers that use this test system):

[1] M. A. Abido, “Environmental/Economic Power Dispatch Using Multiobjective Evolutionary Algorithms,” IEEE Trans. Power Syst., vol. 18, no. 4, pp. 1529–1537, Nov. 2003.
[2] R. T. F. A. King, H. C. S. Rughooputh, and K. Deb, “Evolutionary Multi-Objective Environmental/Economic Dispatch: Stochastic vs. Deterministic Approaches,” in Evolutionary Multi-Criterion Optimization (Third International Conference, EMO 2005, Guanajuato, Mexico, March 9-11, 2005. Proceedings), vol. 3410, C. A. C. Coello, A. H. Aguirre, and E. Zitzler, Eds. Springer Berlin Heidelberg, 2005, pp. 677–691.
[3] A. Bhattacharya and P. K. Chattopadhyay, “Application of Biogeography-based Optimization for Solving Multi-objective Economic Emission Load Dispatch Problems,” Electr. Power Components Syst., vol. 38, no. 3, pp. 340–365, Jan. 2010.
[4] S. Rajasomashekar and P. Aravindhababu, “Biogeography Based Optimization Technique for Best Compromise Solution of Economic Emission Dispatch,” Swarm Evol. Comput., vol. 7, pp. 47–57, Jun. 2012.