# IEEE 6-Units ELD Test System No.3

I. Introduction:

$$\bullet$$ This system consists of six thermal units and based on IEEE 30 bus system $$\rightarrow$$ please refer to our PF Library
$$\bullet$$ There load demands are selected as: 500 MW, 700 MW, and 900 MW. The researchers could evaluate their proposed optimization algorithms based on user-defined load demands.
$$\bullet$$ 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 transmission losses are modeled with the following relaxed formula:

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

where $$B_{ij}$$ is called a transmission-losses coefficient (or just B-coefficient) and given below:

$$B_{ij}=\begin{bmatrix} 0.002022 & -0.000286 & -0.000534 & -0.000565 & -0.000454 & -0.000103 \\ -0.000286 & 0.003243 & 0.000016 & -0.000307 & -0.000422 & -0.000147 \\ -0.000533 & 0.000016 & 0.002085 & 0.000831 & 0.000023 & -0.000270 \\ -0.000565 & -0.000307 & 0.000831 & 0.001129 & 0.000113 & -0.000295 \\ -0.000454 & -0.000422 & 0.000023 & 0.000113 & 0.000460 & -0.000153 \\ 0.000103 & -0.000147 & -0.000270 & -0.000295 & -0.000153 & 0.000898 \end{bmatrix}$$

$$\bullet$$ The NOx emission-rates are modeled in this design function as follows:

$$E_{NOx} = \sum_{i=1}^n \left(\alpha_i + \beta_i P_i + \gamma_i P^2_i \right)$$ .......... $$(3)$$

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

II. Files:

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

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

[1] H. C. S. Rughooputh and R. T. F. A. King, “Environmental/Economic Dispatch of Thermal Units Using an Elitist Multiobjective Evolutionary Algorithm,” in IEEE International Conference on Industrial Technology, 2003 (ICIT 2003), 2003, vol. 1, pp. 48–53.
[2] Y. Sonmez, “Multi-Objective Environmental/Economic Dispatch Solution with Penalty Factor Using Artificial Bee Colony Algorithm,” Sci. Res. Essays, vol. 6, no. 13, pp. 2824–2831, Jul. 2011.
[3] E. D. Manteaw and N. A. Odero, “Multi-Objective Environmental/Economic Dispatch Solution Using ABC_PSO Hybrid Algorithm,” Int. J. Sci. Res. Publ., vol. 2, no. 12, pp. 1–7, Dec. 2012.
[4] S. Arunachalam, R. Saranya, and N. Sangeetha, “Hybrid Artificial Bee Colony Algorithm and Simulated Annealing Algorithm for Combined Economic and Emission Dispatch Including Valve Point Effect,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8297 LNCS, no. PART 1, B. K. Panigrahi, P. N. Suganthan, S. Das, and S. S. Dash, Eds. Springer International Publishing, 2013, pp. 354–365.