# Reliability Assessment Unit Commitment with Uncertain Wind Power

• Jianhui Wang
• Jorge Valenzuela
• Audun Botterud
• Hrvoje Keko
• Ricardo Bessa
Chapter
Part of the Energy Systems book series (ENERGY)

## Abstract

This book chapter reports a study on the importance of modeling wind power uncertainty in the reliability assessment commitment procedure. The study compares, in terms of economic and reliability benefits, the deterministic and stochastic approaches to modeling wind power. The report describes the mathematical formulation of both approaches and gives numerical results on a 10-unit test system. It is found that scenario representation of wind power uncertainty in conjunction with a proper reserve margin to accommodate for wind power uncertainty may provide higher benefits to market participants.

### Keywords

Electricity market Wind power Unit commitment Stochastic optimization

### Indices

i

Index for wind unit, i = 1.. I

j

Index for thermal unit, j = 1.. J

k

Index for time period, k = 1.. 24

l

Index for generation block, thermal units, l = 1.. L

m

Index for reserve demand block, m = 1..M

s

Index for scenario, s = 1.. S

### Constants

a, b, c

Unit production cost function coefficients

α(s)

Operating reserve percentage, scenario s

WR(k)

Additional wind reserve, period k

D(k)

Cens

Cost of energy not served

CRrns,m

Cost of reserve not served, block m

Aj

Operating cost at minimum load, thermal unit j

MCl,j

Marginal cost (or bid), block l, thermal unit j

$$\overline{PT}_{j}$$

Capacity, thermal unit j

$$\underline{PT}_{j}$$

Minimum output, thermal unit j

$$\overline{\varDelta }_{{{\text{l}},{\text{j}}}}$$

Capacity, block l, thermal unit j

CCj

Cold start cost, thermal unit j

HCj

Hot start cost, thermal unit j

$${\mathbf{G}}(\cdot)$$

Generalized network constraints

$$T_{j}^{cold}$$

Time for cold start cost (in addition to minimum downtime), thermal unit j

$$T_{j}^{up}$$

Minimum up-time, thermal unit j

$$T_{j}^{up,0}$$

Minimum up-time, initial time step, thermal unit j

$$T_{j}^{dn}$$

Minimum down-time, thermal unit j

$$T_{j}^{dn,0}$$

Minimum down-time, initial time step, thermal unit j

SUj

Start-up ramp limit, thermal unit j

SDj

Shut-down ramp limit, thermal unit j

RLj

Ramping limit (up/down), thermal unit j

Wi(k)

Actual maximum wind generation, wind unit i, period k

$$PW_{i}^{f,s} (k)$$

Forecasted maximum generation, wind unit i, period k, scenario s

probs

Probability of occurrence, wind scenario s

### Variables

$$c_{j}^{p} (k)$$

Production cost, thermal unit j, period k

$$c_{j}^{u} (k)$$

Start-up cost, thermal unit j, period k

ptj(k)

Generation, thermal unit j, period k

$$\delta_{l,j} \left( k \right)$$

Generation, block l, thermal unit j, period k

$$\overline{pt}_{j} (k)$$

Maximum feasible generation, thermal unit j, period k

vj(k)

Binary on/off variable, thermal unit j, period k

$$pw_{i}^{s} \left( k \right)$$

Generation, wind unit i, period k, scenario s

$$cw_{i}^{s} \left( k \right)$$

Curtailed wind generation, wind unit i, period k, scenario s

$$ens^{s} (k)$$

Energy not served, period k, scenario s

$$rns_{m}^{s} (k)$$

Reserve curtailed, period k, scenario s

$$r^{s} (k)$$

Reserve requirement (spinning), scenario s, period k

## Notes

### Acknowledgments

The authors acknowledge the US Department of Energy, Office of Energy Efficiency and Renewable Energy through its Wind and Hydropower Technologies Program for funding the research presented in this paper. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (Argonne). Argonne, a US Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357.

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© Springer-Verlag Berlin Heidelberg 2013

## Authors and Affiliations

• Jianhui Wang
• 1
• Jorge Valenzuela
• 1
• 2
• Audun Botterud
• 1
• Hrvoje Keko
• 3
• 4
• Ricardo Bessa
• 3
• 4