Trajectory-Independent Flexibility Envelopes of Energy-Constrained Systems with State-Dependent Losses

TL;DR

This paper introduces trajectory-independent energy bounds for energy-constrained systems with state-dependent losses, ensuring load constraints are always satisfied, unlike traditional trajectory-dependent bounds.

Contribution

It proposes novel TI energy envelope formulations that guarantee load constraint satisfaction for all feasible trajectories, improving flexibility management in energy systems.

Findings

Using TD envelopes can lead to temperature deviations of up to 3.8°C.

TI envelopes differ significantly from TD envelopes in poorly insulated buildings.

Proposed TI envelopes effectively ensure load constraints are always met.

Abstract

As non-dispatchable renewable power units become prominent in electric power grids, demand-side flexibility appears as a key element of future power systems' operation. Power and energy bounds are intuitive metrics to describe the flexibility of energy-constrained loads. However, to be used in operation, any power consumption trajectory fulfilling the power and energy bounds must necessarily fulfill the load's constraints. In this paper, we demonstrate that energy bounds defined as the minimum and maximum energy consumption potential of a load with state-dependent losses are Trajectory-Dependent (TD), i.e., for any energy value in the bounds a feasible power trajectory exists, but not all power trajectories enclosed in the energy envelopes satisfy the load's constraints. To guarantee the satisfaction of load constraints for all trajectories, we define Trajectory-Independent (TI) energy bounds. We present TI envelope formulations for individual loads, as well as physically coupled loads and assess the proposed formulations in a building heating system, a system with state-dependent losses. We find that using a TD envelope as energy bounds in operation may yield room temperature up to 3.8{\deg}C higher and 3.4{\deg}C lower than admissible. Overall, poorly insulated buildings observe a TI energy envelope that differs significantly from their TD envelope.