A Graphical Measure of Aggregate Flexibility for Energy-Constrained Distributed Resources

Abstract

We consider the problem of dispatching a fleet of heterogeneous energy storage units to provide grid support. Under the restriction that recharging is not possible during the time frame of interest, we develop an aggregate measure of fleet flexibility with an intuitive graphical interpretation. This analytical expression summarises the full set of demand traces that the fleet can satisfy, and can be used for immediate and straightforward determination of the feasibility of any service request. This representation therefore facilitates a wide range of capability assessments, such as flexibility comparisons between fleets or the determination of a fleet's ability to deliver ancillary services. Examples are shown of applications to fleet flexibility comparisons, signal feasibility assessment and the optimisation of ancillary service provision. NOMENCLATURE nTotal number of devices D i ith device N Set of all devices e i (t)Energy of the ith device at time t u i (t)Power output of the ith device at time t u(t) Vector of power outputs at time t, across all devices p i Maximum power rating of the ith devicē pVector of maximum power ratings, across all devices P Diagonal matrix of maximum power ratings, across all devices UpProduct set of power constraints, with vector of maximum powersp x i (t), z i (t) Time-to-go of the ith device at time t x(t), z(t) Vector of time-to-go values at time t, across all devices X State-space X(t) ). This work was supported by EPSRC studentship 1688672. P r (t)Reference at time t P r [t0,t)

Chance-Constrained Ancillary Service Specification for Heterogeneous Storage Devices

“…This property can be interpreted to mean that the capacity curve represents the full set of request profiles that a fleet can satisfy. As discussed in detail in [10], one can therefore use this curve to determine the maximum ancillary service capability of the fleet.…”

“…An alternative aggregate fleet representation was developed independently by Cruise and Zachary [11]. For an aggregate representation of this form to exist requires that the problem be restricted to one of discharge only, as was discussed in detail in [10]. This paper explores in greater depth how the E-p transform can be used to specify ancillary service capability.…”

“…Chance constraints are commonly applied to the dispatch of storage under uncertainty [12]- [14], and we utilise these to ensure that the probability of unsuccessful delivery of the procured service lies below a user-defined threshold. This involves a Monte Carlo simulation in which the E-p transform of [10] is used as a binary feasibility check on each drawn trace. We point out here that an alternative method for such a check would be a procedural simulation in time spanning the total duration of the delivery requirement.…”

Minimizing Unserved Energy Using Heterogeneous Storage Units

“…This paper builds directly on [9], which considered the dispatch policy that achieves maximal failure-time, and [10], which presented methods of capability assessments for a fleet of storage units. We here extend these results with the objective of maximising the contribution of energy storage to system adequacy.…”

“…• For comparison purposes, we define a peak-shaving policy that achieves the same minimal ENS by relying on perfect foresight. • We present an immediate means of determining the minimum ENS for a heterogeneous fleet using the E-p transform of [10]. • We provide a discrete time algorithm that implements a minimum ENS policy for time-resolved generation adequacy studies.…”