Using Storage To Control Uncertainty in Power Systems Glyn Eggar Department of Actuarial Mathematics and Statistics Heriot-Watt University Energy Systems Week -April

Agenda Background5mins Part 1: Model Overview5-10mins Part 2: Solving the simplest case5-10mins Part 3: Extending the simplest case5-10mins Questions 2

Disclaimer 3

Motivation Can we use storage to control uncertainty in the electricity network? What sort of storage are we even talking about here? How much storage should we use? For a given level of storage how should we operate the management system? How do we quantify the benefits of using storage for this purpose? What are the costs of operating the storage facility? What are the alternative uses for the storage and what are the costs and benefits of these? 4

Assessing viability of use of storage Decide on type of storage mix under consideration For a given level of storage determine how to operate the system optimally Perform a cost- benefit analysis for this system with this level of storage Perform a cost- benefit analysis for alternative uses of this level of storage repeat for different levels of storage Decide on the optimal level of storage to use 5

Assessing viability of use of storage Decide on type of storage mix under consideration For a given level of storage determine how to operate the system optimally Perform a cost- benefit analysis for this system with this level of storage Perform a cost- benefit analysis for alternative uses of this level of storage repeat for different levels of storage Decide on the optimal level of storage to use 6

The Model 2 supply types, renewable and conventional, to meet demand Overgeneration-> store fills Undergeneration-> store empties Store has a maximum capacity, B, any excess is spilled 7

The Model(2) 8

The Model(3) 9

The Objective and Constraints Objective: Minimise (a) Expected energy ‘spilled’ from systemor (b) Total expected conventional generation used over a particular time horizon. Subject to: (c) The probability of ‘not meeting demand’ (i.e. having to resort to expensive fast ramping generation or importing) remaining sufficiently lowor (d)The expected cost from ‘not meeting demand’ limited to a particular level. OR (e) Minimise total system cost over a particular time horizon where the system cost is a function of the spilled energy and the costs arising from ‘not meeting demand’. 10

The ‘error’ process Key assumption and driver of ‘optimal’ control strategy ‘Ultimate’ wind prediction likely to be combination of periodic meteorological forecasts and mathematical time- series methods with correction based on real-time updates of power outputs Hard to know at this stage what the errors will look like, e.g. level of dependence over short and long timescales In general for setting strategies what is important is not ‘what you know now’ but ‘what you know you’ll know’ Can start the model analysis using simple (and unrealistic) assumption of I.I.D. errors 11

Summary of Model 12

The Simplest Case, T=1, k=1 13

Result 1 (T=1,k=1) 14

Result 1 (T=1,k=1) 15

Result 2 (T=1,k=1) 16

Result 2 (T=1,k=1) 17

Result 3 (T=1,k=1) 18

Agenda Background5mins Part 1: Model Overview5-10mins Part 2: Solving the simplest case5-10mins Part 3: Extending the simplest case5-10mins Questions 19

Extension 1, T>1 20

Extension 1, T>1 21

Extension 1, T>1 There can be a noticeable difference in performance between the T=1 and T=2 optimal solutions. 22

Extension 2, k<1 23

Extension 2, k<1 Example: T=1, B=20, k=0.8, Ɛ=0.5%, IID errors which take values Compare 3 strategies: (a) target point (b) do nothing (c) decrease by 1 24

Extension 2, k<1 25

Extension 3, ramp constraints 26

Summary We have developed a simple model to explore how storage can be used to manage uncertainty in power systems. In its simplest form there is a simple analytical solution for how to best control the system, given a particular risk appetite for avoiding high ‘importing’ or ‘fast ramping’ costs. We have explored how the nature of the problem and solution changes when we introduce further time-lags, storage inefficiencies and storage ramp constraints. 27

Thanks for listening. Any Questions ? 28