# IEEE 13-Units ELD Test System

I. Introduction:

$$\bullet$$ This system contains thirteen generating units with a load demand of 1800 MW. Some researchers could evaluate their proposed optimization algorithms with different 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.

$$\bullet$$ If the valve-point loading effects are considered, then (1) becomes:

$$C_i\left(P_i\right) = a_i + b_i P_i + c_i P^2_i + \left|d_i \times \sin\left[e_i \times \left(P_i^{min} - P_i\right) \right]\right|$$ .......... $$(2)$$

where $$d_i$$ and $$e_i$$ are the coefficients of the valve-point loading effects. Thus, Table 1 is expanded to Table 2.

$$\bullet$$  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 2 is expanded to Table 3 [13].

II. Files:

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

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

[1] N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, “Evolutionary Programming Techniques for Economic Load Dispatch,” IEEE Trans. Evol. Comput., vol. 7, no. 1, pp. 83–94, Feb. 2003.
[2] T. A. A. Victoire and A. E. Jeyakumar, “Hybrid PSO-SQP for Economic Dispatch with Valve-Point Effect,” Electr. Power Syst. Res., vol. 71, no. 1, pp. 51–59, 2004.
[3] C.-L. Chiang, “Improved Genetic Algorithm for Power Economic Dispatch of Units With Valve-Point Effects and Multiple Fuels,” Power Syst. IEEE Trans., vol. 20, no. 4, pp. 1690–1699, Nov. 2005.
[4] C. H. Chen and S. N. Yeh, “Particle Swarm Optimization for Economic Power Dispatch with Valve-Point Effects,” in Transmission Distribution Conference and Exposition: Latin America, 2006. TDC ’06. IEEE/PES, 2006, pp. 1–5.
[5] L. dos Santos Coelho and V. C. Mariani, “Combining of Chaotic Differential Evolution and Quadratic Programming for Economic Dispatch Optimization with Valve-Point Effect,” IEEE Trans. Power Syst., vol. 21, no. 2, pp. 989–996, May 2006.
[6] C. C. Kuo, “A Novel Coding Scheme for Practical Economic Dispatch by Modified Particle Swarm Approach,” IEEE Trans. Power Syst., vol. 23, no. 4, pp. 1825–1835, Nov. 2008.
[7] L. dos S. Coelho and V. C. Mariani, “An Improved Harmony Search Algorithm for Power Economic Load Dispatch,” Energy Convers. Manag., vol. 50, no. 10, pp. 2522–2526, Jul. 2009.
[8] T. Niknam, “A New Fuzzy Adaptive Hybrid Particle Swarm Optimization Algorithm for Non-Linear, Non-Smooth and Non-Convex Economic Dispatch Problem,” Appl. Energy, vol. 87, no. 1, pp. 327–339, Jun. 2010.
[9] S. Duman, U. Güvenç, and N. Yörükeren, “Gravitational Search Algorithm for Economic Dispatch with Valve-Point Effects,” Int. Rev. Electr. Eng., vol. 5, no. 6, pp. 2890–2895, 2010.
[10] J. S. Alsumait, J. K. Sykulski, and A. K. Al-Othman, “A Hybrid GA-PS-SQP Method to Solve Power System Valve-Point Economic Dispatch Problems,” Appl. Energy, vol. 87, no. 5, pp. 1773–1781, Nov. 2010.
[11] S. Hemamalini and S. P. Simona, “Artificial Bee Colony Algorithm for Economic Load Dispatch Problem with Non-smooth Cost Functions,” Electr. Power Components Syst., vol. 38, no. 7, pp. 786–803, May 2010.
[12] T. Niknam, H. D. Mojarrad, and H. Z. Meymand, “A Novel Hybrid Particle Swarm Optimization for Economic Dispatch with Valve-Point Loading Effects,” Energy Convers. Manag., vol. 52, no. 4, pp. 1800–1809, Jan. 2011.
[13] 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.
[14] G. Xiong, D. Shi, and X. Duan, “Multi-Strategy Ensemble Biogeography-Based Optimization for Economic Dispatch Problems,” Appl. Energy, vol. 111, pp. 801–811, Jun. 2013.
[15] K. Zare and T. G. Bolandi, “Modified Iteration Particle Swarm Optimization Procedure for Economic Dispatch Solving with Non-Smooth and Non-Convex Fuel Cost Function,” in 3rd IET International Conference on Clean Energy and Technology (CEAT) 2014, 2014, pp. 1–6.
[16] R. Arul, G. Ravi, and S. Velusami, “An Improved Harmony Search Algorithm to Solve Economic Load Dispatch Problems with Generator Constraints,” Electr. Eng., vol. 96, no. 1, pp. 55–63, 2014.
[17] T. H. Khoa, P. M. Vasant, M. S. B. Singh, and V. N. Dieu, “Solving Economic Dispatch Problem with Valve-Point Effects Using Swarm-Based Mean-Variance Mapping Optimization (MVMO),” Cogent Eng., vol. 2, no. 1, pp. 1–18, Aug. 2015.