Towards price-based predictive control of a small-scale electricity network

ABSTRACT

With the increasing deployment of battery storage devices in residential electricity networks, it is essential that the charging and discharging of these devices be scheduled so as to avoid adverse impacts on the electricity distribution network. In this paper, we propose a non-cooperative, price-based hierarchical distributed optimisation approach that provably recovers the centralised, or cooperative, optimal performance from the point of view of the network operator. The distributed optimisation algorithm provides important insights into the appropriate design of contracts between an energy provider and their associated residential customers, who can themselves act as energy providers as well as consumers (e.g. due to rooftop solar photovoltaics and batteries) depending on the time of the day and on real-time prices. To make the presentation self-contained, and to highlight key properties of the price-based optimisation algorithm, the dual ascent method and its convergence properties are reviewed. The performance of the proposed price-based optimisation algorithm is validated on recent measurement taken from an Australian electricity distribution company, Ausgrid. In addition to analysing the results of the open loop solution, we investigate the effect of real-time prices in the closed loop using a model predictive control framework.

KEYWORDS:

• Distributed optimisation
• gradient ascent method
• smart grid battery scheduling
• real-time pricing

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The stepsize rule of Corollary 4.1 significantly reduces the average number of iterations in our numerical simulations.

2. The parameters chosen here are just for illustration. The value used for a can be scaled arbitrarily to obtain realistic energy prices.

3. We assume that the prediction horizon N and the maximal discharging rate ${\underset{\_}{u}}_i$, $i\in {\mathbb{N}}_{\mathcal{I}}$, are chosen such that the battery can always be discharged within the prediction horizon.

4. To obtain realistic energy prices, the numbers can be scaled arbitrarily in Figure 7 (left).

5. The number of time steps is chosen such that $x_i\left(0\right)=x_i\left(\mathcal{N}\right)=0$ for all $i\in {\mathbb{N}}_{\mathcal{I}}$. This is important to be able to calculate the overall savings of the individual systems. The simulation length $\mathcal{N}=387$ satisfying $x_i\left(\mathcal{N}\right)=0$ is found by simulating on a longer time interval.