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Measuring the price of security of supply. Andy Philpott The University of Auckland www.esc.auckland.ac.nz/epoc (joint work with Kailin Lee, Golbon Zakeri). From: Electricity Commission Reserve Energy Review, p44, November 2007. From Electricity Commission Presentation, October 2007.

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Measuring the price of security of supply

Measuring the price of security of supply

Andy Philpott

The University of Auckland

www.esc.auckland.ac.nz/epoc

(joint work with Kailin Lee, Golbon Zakeri)




Motivation
Motivation November 2007.

  • Minzone and energy margin

    • How much energy margin to hold for possible dry winters

    • Castalia Review of Security

    • Electricity Commission Reserve Energy Review (Nov 2007)

    • Energy margin depends on generators’ policies

  • Computational models for minimum expected cost

    • Stage and Larsson

    • RESOP (Read)

    • SDDP (Pereira) = DOASA (Guan,Philpott)

  • How should we compute energy margin?

  • How good is DOASA versus Stage and Larsson?


S stage y larsson aiee transactions power apparatus and systems august 1961
S. Stage, November 2007.Y. Larsson AIEE Transactions (Power Apparatus and Systems) August, 1961


Continuous model
Continuous model November 2007.


Discrete heuristic
Discrete heuristic November 2007.


Marginal water value at the state obtained by optimally releasing starting at state s and obtaining inflow i followed by j


Marginal water value is the average of endpoint marginal values of simulated trajectories

π releasing starting at state s and obtaining inflow i followed by j(100)=0

π(50)

π(m)=T

Marginal water value is the average of endpoint marginal values of simulated trajectories

π(70)


Test 1 versus sdp
Test 1 versus SDP releasing starting at state s and obtaining inflow i followed by j

Single reservoir with capacity 100MWh

Three thermal plants each capacity 3MW,

cost $45, $50, $100/MWh

One hydro plant capacity 3 MW

Demand is 8MW peak, 5 MW offpeak

Inflows are 1..8 MWh each with Pr=0.1

Inflow of 0 with Pr 0.2

52 peak hours and 52 offpeak hours


Test 2 sl versus doasa sddp
Test 2: SL versus DOASA (SDDP) releasing starting at state s and obtaining inflow i followed by j

  • 70 Historical inflow sequences (1934-2004)

  • Use 2005/2006 demand and cogeneration data

  • Geothermal capacity offered at zero cost

  • Wind capacities set at expected generation and zero cost

  • Thermal plant capacities and costs as in DOASA

  • 2005/2006 Minzone used (June 2005-May 2006)

  • DOASA assumes 10 (stagewise independent) random openings from 1995-2004.

  • Initial Marginal Water Value (SL)= 0


Doasa system

HAW releasing starting at state s and obtaining inflow i followed by j

MAN

TPO

DOASA system

demand

N

S

demand


Lower bound after 200 cuts
Lower bound after 200 cuts releasing starting at state s and obtaining inflow i followed by j

Takes about 8 hours on a standard Windows PC to converge

Upper Bound



Stage and larsson
Stage and Larsson sequences

SL Policy computed using same parameters

as DOASA

Cuts for SL recorded with slope b and intercept a.

Policy represented in DOASA by adding cuts of the form

ri parameters convert m3 to GWh for reservoir I


Thermal generation mwh
Thermal generation (MWh) sequences

SL: 4159 GWh

DOASA: 3741 GWh


2000 cost comparison
2000 cost comparison sequences

DOASA Thermal Fuel cost = $141 M

Stage-Larsson Thermal Fuel cost = $157 M


2001 cost comparison
2001 cost comparison sequences

DOASA Thermal Fuel cost = $207 M

Stage-Larsson Thermal Fuel cost = $297 M


So what
So what? sequences

  • Energy margin depends on generators’ policies

    • Analysis so far assumes policy is to minimize expected cost via a central planning model: risk aversion might alter the energy margin required.

    • What if we assume oligopoly model? Could compute the margin for result of Nash equilibrium policies (e.g. using Dublin)

  • If we adopt a central plan model then we must be aware of differences between Stage and Larsson, RESOP, and DOASA. These will give different recommendations for reserve.

  • This the first comparison made between DOASA models and heuristics. DOASA is better than I expected.


End sequences




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