Energy sector planning using multiple-index pinch analysis

Abstract

Pinch analysis was initially developed as a methodology for optimizing energy efficiency in process plants. Applications of pinch analysis applications are based on common principles of using stream quantity and quality to determine optimal system targets. This initial targeting step identifies the pinch point, which then allows complex problems to be decomposed for the subsequent design of an optimal network using insights drawn from the targeting stage. One important class of pinch analysis problems is energy planning with footprint constraints, which began with the development of carbon emissions pinch analysis; in such problems, energy sources and demands are characterized by carbon footprint as the quality index. This methodology has been extended by using alternative quality indexes that measure different sustainability dimensions, such as water footprint, land footprint, emergy transformity, inoperability risk, energy return on investment and human fatalities. Pinch analysis variants still have the limitation of being able to use one quality index at a time, while previous attempts to develop pinch analysis methods using multiple indices have only been partially successful for special cases. In this work, a multiple-index pinch analysis method is developed by using an aggregate quality index, based on a weighted linear function of different quality indexes normally used in energy planning. The weights used to compute the aggregate index are determined via the analytic hierarchy process. A case study for Indian power sector is solved to illustrate how this approach allows multiple sustainability dimensions to be accounted for in energy planning.

Appendix: Analytic hierarchy process (AHP)

A brief overview of the computational aspects of AHP is given here. Details of the AHP framework are described extensively in the literature, and particularly in key reference books (Saaty 1980). The discussion below pertains to determination of weights of criteria, but the procedure is also applicable to quantifying scores for qualitative or subjective criteria. The methodology computes the weight vector (w) of n elements from pairwise comparisons summarized in a positive reciprocal square matrix A:

$${\mathbf{A}} = \left[ {\begin{array}{*{20}c} 1 & {a_{12} } & \cdots & {a_{1n} } \\ {\frac{1}{{a_{12} }}} & 1 & \cdots & {a_{2n} } \\ \vdots & \cdots & \ddots & {} \\ {\frac{1}{{a_{1n} }}} & {\frac{1}{{a_{2n} }}} & \cdots & 1 \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\frac{{w_{1} }}{{w_{2} }}} & {\frac{{w_{1} }}{{w_{2} }}} & \cdots & {\frac{{w_{1} }}{{w_{n} }}} \\ {\frac{{w_{2} }}{{w_{1} }}} & {\frac{{w_{2} }}{{w_{2} }}} & \cdots & {\frac{{w_{2} }}{{w_{n} }}} \\ \vdots & \cdots & \ddots & \vdots \\ {\frac{{w_{n} }}{{w_{1} }}} & {\frac{{w_{n} }}{{w_{2} }}} & \cdots & {\frac{{w_{n} }}{{w_{n} }}} \\ \end{array} } \right]$$

(1)

where

$$a_{ij} = \frac{1}{{a_{ji} }} = \frac{{w_{i} }}{{w_{j} }}.$$

(2)

In general, experts are asked to give n(n−1)/2 pairwise comparisons of criteria. Each ratio value (a _ij ) is based on a standard 9-point scale (Saaty 1980). Table 7 gives the 9-point scale for both criteria and alternatives. The relative weights (w) of the criteria are found using the normalized right eigenvector associated with the principal eigenvalue (λ _max) of A:

$${\mathbf{Aw}} = \, \lambda_{ \hbox{max} } {\mathbf{w}}$$

(3)

The weights are normalized so as to sum to unity:

$$\sum_{i} w_{i} = \, 1.$$

(4)

Table 7 AHP 9-point scale (Saaty 1980)

In the case of a perfectly consistent pairwise comparison matrix, λ _max is equal to n. Otherwise, the eigenvector method can also be used to measure a consistency index:

$${\text{CI }} = \left( {\lambda_{\hbox{max} } {-}n} \right)/\left( {n{-} \, 1} \right)$$

(5)

Other than the eigenvector approach described here, the weights can also be calculated using the simpler geometric mean method, which yields approximately the same results, but for which a consistency index cannot be calculated.