Aggregated Feasible Region of Heterogeneous Demand-Side Flexible Resources -- Part I: Theoretical Derivation of the Exact Model

TL;DR

This paper derives an exact mathematical model for the aggregated feasible region of heterogeneous demand-side resources using Fourier-Motzkin Elimination, providing a foundation for future approximation methods.

Contribution

It introduces a novel exact model for the aggregated feasible region of diverse demand resources, with a simplified computational approach based on FME.

Findings

The exact AFR model is derived using FME.

The number of constraints scales linearly with resources and exponentially with time intervals.

Computational complexity is significantly reduced compared to original FME.

Abstract

In the first part of the two-part series, the model to describe the exact aggregated feasible region (AFR) of multiple types of demand-side resources is derived. Based on a discrete-time unified individual model of heterogeneous resources, the calculation of AFR is, in fact, a feasible region projection problem. Therefore, the Fourier-Motzkin Elimination (FME) method is used for derivation. By analyzing the redundancy of all possible constraints in the FME process, the mathematical expression and calculation method for the exact AFR is proposed. The number of constraints is linear with the number of resources and is exponential with the number of time intervals, respectively. The computational complexity has been dramatically simplified compared with the original FME. However, the number of constraints in the model is still exponential and cannot be simplified anymore. Hence, In Part II of this paper, several approximation methods are proposed and analyzed in detail.