The mixture of normals approximation technique for equivalent load duration curves

For applications such as capactiy expansion planning and screening studies of alternative expansion plans, there is a need for a fast, accurate, reliable and robust method to approximate the equivalent load duration curves (e.l.d.c.“s) for production costing. The concept of equivalent load, which is the sum of the customer load demand and the outage capacity of the generating blocks, plays a key role in probabilistic production costing. This paper describes a newly developed approximation technique based on mixtures of normal distributions. The mixtures of normals approximation (m.o.n.a.) for e.l.d.c.’s proceeds in three steps. First, the system load random variable is approximated by a mixture of normals distribution. Next, the approximation of the outage random variable of a group of one or more units by a mixture of normals distribution is obtained. Finally, these two approximations are combined to derive the m.o.n.a. of each e.l.d.c. The technique makes extensive use of the properties of mixtures of normal distributions. The construction of the m.o.n.a. for the system load random variable can be interpreted in terms of partitioning the load into various categories based on the load magnitudes. A salient feature of the m.o.n.a. technique is the simple recursive formula for convolving or “rolling in” and for deconvolving or “rolling out” the contribution of each generating block. The performance of the m.o.n.a. technique is analyzed in terms of its ability to fit the original load duration curve, its ability to fit the e.l.d.c.’s, its accuracy and robustness. Numerical results indicate that the m.o.n.a. technique is very robust, accurate and rapid. Comparison with conventional and cumulant-based techniques shows that the m.o.n.a. technique has excellent comparative computational performance on both well-behaved and pathological systems.