Risk-Constrained Multi-Stage (Renewable) Power...

Risk-Constrained Multi-Stage (Renewable) Power Investment

A. J. Conejo, 2015

President Obama's 2016 State of the Union Address

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“Now we’ve got to acceleratethe transition away from dirtyenergy. Rather than subsidizethe past, we should invest inthe future…”

1. Motivation & approach2. Problem description3. Case study4. Conclusions

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Contents

Power investor: seeks to determine the power capacity to bebuilt that maximizes its expected profit while controlling itsrisk of profit volatility.

Where to build?

When to build?

Which capacity to build?

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1. Motivation & approach

Market

Multi-stage

Uncertainty

Where to build (the network exist!)?

At nodes where construction is possible At nodes with the best (renewable)

investment conditions At nodes “well connected” to the system

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1. Motivation & approach

When to build (investment is necessarily multi-stage)?

It depends on: Demand growth uncertainty Fuel cost uncertainty Investment cost uncertainty

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1. Motivation & approach

Which capacity to build?

It depends on: Renewable production uncertainty Equipment failure rates

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1. Motivation & approach

How to solve this problem?

Stochastic model Complementarity model (we have a market!) Multi-stage model Risk-constrained model

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1. Motivation & approach

Increasing model complexity

Static, long-term deterministic, short-term stochastic Static, long-term stochastic, short-term stochastic Dynamic, long-term stochastic, short-term stochastic

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1. Motivation & approach

Uncertainty

Long-term (scenarios): from year to year Demand growth Investment cost Fuel cost

Short-term (operating conditions): within a year Renewable production + Demand level Equipment failure

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1. Motivation & approach

Static, ST stochastic, LT deterministic

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Static, ST stochastic, LT deterministic

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Static, ST stochastic, LT stochastic

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Dynamic, ST stochastic, LT stochastic

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Maximization of the wind investor profit

Control of the risk of profit volatility

Pool based electricity market:

The wind producer is paid the LMP of its node

Given transmission capacity (dc model)

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1. Motivation & approach

2. Problem description

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2. Problem description

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2. Problem description scenario

Operating condition

stage (year)

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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2. Problem description

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3-bus system:

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Two five-years periods

3. Case Study

3-bus system: Just investment cost uncertainty

Investment cost known in period 13 investment cost scenario realizations in period 2: high (H),

medium (M) and low (L)Risk-neutral (β=0) and risk-averse (β=1) solutions

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3. Case Study

Results3-bus system: investment cost uncertainty

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Scenario Risk-neutralPeriod 1 Period 2

Risk-aversePeriod 1 Period 2

H

114.3 MW

0

153.3 MW

0

M 39.0 MW 0

L 185.7 MW 146.7 MW

3. Case Study

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3-bus system: Just wind/demand uncertainty

3 wind/demand conditions in period 1: H, M and L3 wind/demand conditions in period 2 for each condition in

period 1: H, M and LRisk-neutral (β=0) and risk-averse (β=1) solutions

3. Case Study

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Results3-bus system: wind/demand uncertainty

Condition Risk-neutralPeriod 1 Period 2

Risk-aversePeriod 1 Period 2

HH, HM, HL

152.3 MW

108.3 MW

60.7 MW

108.3 MW

MH, MM, ML 0.8 MW 92.3 MW

LH, LM, LL 0 0

3. Case Study

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3-bus system: investment cost and wind/demand uncertaintyInvestment cost know for period 1Two scenario realizations of investment cost in period 2: M, L2 wind/demand conditions in period 1: H, L2 wind/demand conditions in period 2 for each condition in

period 1: H, LRisk-neutral (β=0) and risk-averse (β=1) solutions

3. Case Study

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Results3-bus system: investment cost and wind/demand uncertainty

Investment cost scenario

Demand/windcondition

Risk-neutralPeriod 1 Period 2

Risk-aversePeriod 1 Period 2

M HH, HL

67.2 MW

198.8 MW

130.0 MW

136.0 MW

M LH, LL 92.4 MW 78.7 MW

L HH, HL 232.8 MW 170.0 MW

L LH, LL 232.8 MW 170.0 MW

3. Case Study

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3-bus system: Investment cost and wind/demand uncertainty (efficient frontier)

3. Case Study

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IEEE 118-bus system:3 five-year periods32 wind/demand conditions and investment costs

scenarios2 potential locations of wind plantsRisk-neutral (β=0) and risk-averse (β=1) solutions

3. Case Study

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IEEE 118-bus system: resultsDifferent risk-aversion levels result in different

investment strategiesComputational issues:Intractable if MILP is solved directlyUsing Benders: around 20 h on a Linux-based server with

four processors clocking at 2.9 GHz and 250 GB of RAM(compatible with time requirements in investment studies)

3. Case Study

1. A risk-constrained multi-stage modeling is a must fordeciding renewable power investment

2. “Tractable” model for systems of realistic size viadecomposition

3. Different risk-aversion levels: different investmentstrategies

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4. Conclusions

• Baringo, L.; Conejo, A. J.; , "Risk-Constrained Multi-Stage WindPower Investment," Power Systems, IEEE Transactions on, vol.28, no. 1, pp.401-411, Feb. 2013

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Reading

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Notation: constants

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Notation: constants

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Notation: constants

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Notation: constants

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Notation: variables

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Notation: Indices and sets

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Notation: Indices and sets

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