544 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 23, NO. 2, JUNE 2008 Noniterative Method to Approximate the Effective Load Carrying Capability of a Wind Plant Claudine D’Annunzio, Student Member, IEEE, and Surya Santoso, Senior Member, IEEE Abstract—The effective load carrying capability (ELCC) is con- sidered the preferred metric to evaluate the capacity value of added wind generation. However, the classical method of computing this metric requires substantial reliability modeling and an iterative process that is quite computationally intensive. Consequently, a noniterative method of estimating a wind plant’s ELCC is proposed in this paper. Inspired by Garver’s approximation and derived based on well-known reliability concepts, the proposed method provides an excellent approximation while requiring only mini- mal reliability modeling and no computationally-intensive itera- tive process. It computes ELCC estimates from a single function using only the wind plant’s multistate probabilistic representation and a graphically determined parameter that characterizes the ex- isting power system. After presenting the complete mathematical derivation of this function, the method is applied to compute the ELCC estimates of various wind plants at different penetration levels. It is shown that the resultant ELCC estimates only slightly overestimate the classically computed values by relative errors of 2.5% or less. Furthermore, the proposed method yields more ac- curate ELCC estimates than the capacity factor approximation, which is commonly used to approximate the ELCC of a wind plant. Index Terms—Approximation methods, capacity value, effective load carrying capability (ELCC), power generation planning, reli- ability, wind power generation. NOMENCLATURE C A,E,P Nameplate capacity for the additional generation; existing and potential systems [megawatt]. C j , p j Partial capacity outage states [megawatt] and corre- sponding individual probability. COPT Capacity outage probability table; P (X E >x) or P (X P >x). COIPT Capacity outage individual probability table; Table of C j and p j values of multistate unit. E Index for the existing system. ELCC Effective load carrying capability [percent]. k Number of partial capacity outage states. ΔL Amount of extra load that can be served by the addi- tional generation [megawatt]. L i Load demand condition [megawatt] of time duration t i [e.g., hour]. Manuscript received September 17, 2007; revised September 17, 2007. This work was supported in part by the National Science Foundation under Grant ECCS-0725548. Paper no. TEC-00092-2007. The authors are with the Department of Electrical and Computer Engineering, University of Texas at Austin, Austin TX 78712 USA (e-mail: dannunzi@ ece.utexas.edu; ssantoso@ieee.org). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEC.2008.918597 LOLE Loss-of-load expectation [days per year]. LOLP Loss-of-load probability. n Number of t i in the evaluation period [e.g., hours/ year]. P Index for the potential system. X E,P Discrete random variable representing the possible capacity outage states of the existing and potential systems [megawatt]. I. INTRODUCTION S EVERAL studies have identified the effective load carrying capability (ELCC) as being the preferred metric to evaluate the capacity value of wind generation [1]–[4]. Although accu- rate, this metric requires substantial reliability modeling and an iterative process that is computationally intensive. Conse- quently, interest has emerged in proposing simpler methods to approximate a wind plant’s ELCC. These simpler methods can be especially useful when performing preliminary investigation of wind generation expansions. The noniterative method pro- posed in this paper requires minimal reliability modeling and is less computationally intensive than the classical ELCC com- puting method. Various risk-based and time-period-based approximation methods have been proposed to estimate a wind plant’s ELCC [1]–[4]. Among the risk-based methods is Garver’s approxima- tion, a graphical method of estimating the ELCC of conventional generating units [5]. This approximation is mathematically de- rived using a two-state representation to model the additional conventional unit. Although modeling a generating unit as be- ing either fully ON or fully OFF is appropriate for conventional generation, it is not well suited for variable output generation. Therefore, the novel method introduced in this paper is adapted from Garver’s approximation but models the additional unit with a multistate representation. As for Garver’s approximation, the proposed method uses a graphically-determined parameter and is based on known reliability probabilistic concepts such as ca- pacity outage probability table (COPT), loss-of-load probability (LOLP), and loss-of load expectation (LOLE) [6]. Since the ELCC concept has been implemented in slightly different ways, we will start by defining the classical computing method used in this study. Then, we will derive the novel approx- imation method using known reliability probabilistic concepts. We will compare the classical and approximation methods by computing the ELCC of several wind plants at various penetra- tion levels. Finally, our ELCC estimates will be compared to the wind plant’s capacity factor, a current way of estimating the capacity value of wind generation [1]. 0885-8969/$25.00 © 2008 IEEE