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SYSTEMATIC SENSITIVITY ANALYSIS
USING DESCRIBING FUNCTIONS

Fred C. Schweppe and James Gruhl

M.I.T. Energy Lab, Cambridge, Mass. 02139

1. INTRODUCTION

straightforward

This paper discusses simple, straight forward procedures for performing systematic sensitivity analysis on the input-output behavior of large mathematical models that are implemented as digital computer programs. The techniques were developed as part of an EPRI-funded study undertaken at the MIT Energy Laboratory, Model Assessment Group on the validation of the Baughman-Joskow "Regionalized Electricity Model" (REM); see, for example, reference 1. REM is used only as an example to give focus to the general ideas, and no conclusions or results about REM itself are given (these can be found in other documents such as in reference 2).

REM is a sophisticated computer program that simulates the dynamic behavior of portions of the U.S. energy supply/demand market with particular emphasis on the electric sector. For the sake of developing a simplified mathematical representation of REM de fine:

The elements of a and y can be generalized to cover series of discrete, or even continous, functions in time. The concepts of this paper, however, were developed and tested using the simple constant a and y as defined in Figure 1. The y are outputs in 1997 which is the terminal year for the base case simulation.

Once the inputs a and outputs y have been defined, any large computer model can be viewed simply as a nonlinear function f which translates the a into the y:

y = f (a)

(1.1)

a: vector of exogenous input parameters

y: vector of model outputs in 1997

This point of view is valid independent of whether the model is dynamic or static, a simulation or an optimization, deterministic or stochastic, etc.

To address the issue of sensitivity analysis of a model, define:

a base case input

Yo = f (a): base case output

Aa: input perturbation (e.g., uncertainty)

a=α +Aa: perturbed input

Y(Aα) = f(a +Aα): perturbed output

8y(Aα) = y(Aα) - Yo = f(αo +Aα) - f(α)

= output perturbation (e.g., uncertainty).