Using Storage To Control Uncertainty in Power Systems

Glyn EggarDepartment of Actuarial Mathematics and Statistics

Heriot-Watt UniversityEnergy Systems Week -April 2013

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Agenda

• Background 5mins• Part 1: Model Overview 5-

10mins• Part 2: Solving the simplest case 5-10mins• Part 3: Extending the simplest case 5-

10mins• Questions

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Disclaimer

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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?

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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

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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

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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

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The Model(2)

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The Model(3)

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The Objective and Constraints• Objective: Minimise

(a) Expected energy ‘spilled’ from system or(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’.

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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

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Summary of Model

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The Simplest Case, T=1, k=1

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Result 1 (T=1,k=1)

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Result 1 (T=1,k=1)

B

s0

0

u1e1

Ɛ

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Result 2 (T=1,k=1)

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Result 2 (T=1,k=1)

B

s0

0

u1*

e1

Ɛ

s1*

e1

u1' s1

'u2

'u2

*

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Result 3 (T=1,k=1)

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Agenda

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Extension 1, T>1

B

s0

0

u1e1s1

e2 u2?

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Extension 1, T>1

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Extension 1, T>1• There can be a noticeable difference in

performance between the T=1 and T=2 optimal solutions.

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Extension 2, k<1

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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

1 step ahead error -20 -10 -2 -1 1 2 10 20probability 0.5% 0.5% 9% 40% 40% 9% 0.5% 0.5%

20s0

0

u1

e110

-1v1 w10

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Extension 2, k<1

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Extension 3, ramp constraints

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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.

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Thanks for listening.

Any Questions

?

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