Work supported in part byNSF Grants ECS 02 17836, DMI 00-85165
and SES 00-04315
Dynamics of Reserve Service PricesIn Power Networks
Sean MeynDepartment of ECEand the Coordinated Science Laboratory
Joint work with
Prof. I-K Cho, Dept. EconomicsM. Chen, Coordinated Science Lab, Urbana
What is the valueof improved transmission?More responsive ancillary service?
How does a centralized planneroptimize capacity?
Is there an efficient decentralized solution?
OREGON
NEVADA
MEXICO
SANFRANCISCO
LEGEND
COAL
GEOTHERMAL
HYDROELECTRIC
NUCLEAR
OIL/GAS
BIOMASS
MUNICIPAL SOLID WASTE (MSW)
SOLAR
WIND AREAS
California’s 25,000Mile Electron Highway
Variability in demand and operating conditionsare critical in determining allocations ...
Link at the California ISO website:
How do I tell whenI am going to be blacked out?
Dynamics and Congestion
Mission includes creation of efficient wholesale electric markets
"The California ISO determines a level of load reduction that is needed to maintain grid reliability ...
Please be advised that system conditions are dynamic and this information is subject to change without further notice!"
http://www.caiso.com
PG&E: "THERE ARE NO GRID CONSTRAINTS AT THIS TIME!"
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Forecast DemandForecast of the demand expected today. The procurement of energy resources for the day is based on this forecast
Actual DemandToday's actual system demand with historical trend
Revised Demand ForecastThe current forecast of the system demand expected throughout the remainder of the day.This forecast is updated hourly.
Available ResourcesThe current forecast of generating and import resources available to serve the demand for energy within the California ISO service area
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Glossary (paraphrased)Glossary (paraphrased)
Surplus/Shortfall This number represents the amount of capacity available tomeet the customer demand. If the number is negative, there is not enough capacity to meet the forecasted demand.
Ancillary Services The services other than scheduled energy which are required to maintain system reliability
Spinning/Non-Spinning Reserves The portion of generating capacity, controlled by the ISO, which is capable of being loaded in 10 minutes, and which is capable of running for at least two hours
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Glossary (paraphrased)Glossary (paraphrased)
Surplus/Shortfall This number represents the amount of capacity available tomeet the customer demand. If the number is negative, there is not enough capacity to meet the forecasted demand.
Ancillary Services The services other than scheduled energy which are required to maintain system reliability
Spinning/Non-Spinning Reserves The portion of generating capacity, controlled by the ISO, which is capable of being loaded in 10 minutes, and which is capable of running for at least two hours
Minimum Operating Reliability Criteria The sum of a) regulating reserve plus b) contingency reserve plus c) addtional reserve for interruptible imports plus d) additional reserve for on-demand obligations
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http://www.caiso.com
Emergency Notices
Generating reserves less than requirements
(Continuously recalculated. Between 6.0% & 7.0%)
Generating reserves less than 5.0%
Generating reserves less than largest contingency
(Continuously recalculated. Between 1.5% & 3.0%)
Generating Reserves
7.0%
6.0%
5.0%
4.0%
3.0%
2.0%
1.0%
0.0%
Stage 1EmergencyStage 1
Emergency
Stage 2EmergencyStage 2
Emergency
Stage 3EmergencyStage 3
Emergency
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Prices (Eur/MWh)
Volumes (MWh)
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Welcome to APX!
APX is the first electronic energy tradingplatform in continental Europe. The daily spotmarket has been operational since May 1999.The spot market enables distributors,producers, traders, brokers and industrialend-users to buy and sell electricity on aday-ahead basis.
The APX-index will be published daily around12h00 (GMT +01:00) to provide transparencyin the market. Prices can be used as abenchmark.
www.apx.nl
Main Page Market Results
D(t
t
) = demand - forecast
Centered demand:
Reserve options for servicesbased on forecast statistics
On-line capacity
Forecast
Actual demand
Revised forecast
Capacity planning
Excess capacity:
Power flow subject to peak and rate constraints:
K
Z(t)Z (t)a
Q(t) = Z(t) + Za(t) − D(t), t ≥ 0 .
−ζa− ≤ ddt
Za(t) ≤ ζa+ −ζ− ≤ ddt
Z(t) ≤ ζ+
One producer, one consumer model
Excess capacity: hedging policy
K
Z(t)Z (t)a
Q(t) = Z(t) + Za(t) − D(t)
q
t
Z (t) = 0
Downward trend:
Blackout
a
Z (t) = - ζ
q
-ddt
ζ +
ζ +
ζ a ++
- ζ -
One producer, one consumer model
Relaxations: instantaneous ramp-down rates:
Cost structure:
Control: design hedging points to minimize average-cost,
−∞ ≤ ddt
Z (t) ≤ ζ +, −∞ ≤ ddt
Za (t) ≤ ζa +.
c(X(t)) = c1Z(t) + c2Za(t) + c3|Q(t)|1{Q(t) < 0}
minEπ [c(Q(t))] .
X(t) =( Q(t)
Za(t)
)X(t) =
( Q(t)Za(t)
)Diffusion model & control
X(t) =( Q(t)
Za(t)
)X(t) =
( Q(t)Za(t)
)
Markov model:Markov model: Hedging-point policy:Hedging-point policy:
q̄2 q̄1
Ancillary serviceis ramped-up whenexcess capacity fallsbelow
Ancillary serviceis ramped-up whenexcess capacity fallsbelow q̄2
Diffusion model & control
X(t) =( Q(t)
Za(t)
)X(t) =
( Q(t)Za(t)
)
Markov model:Markov model: Hedging-point policy:Hedging-point policy:
q̄2 q̄1
γ0 = 2ζ++ζa+
σ2D, γ1 = 2
ζ+
σ2D.
Optimal parameters:Optimal parameters:
q̄∗2 =1
γ0log
c3c2
q̄∗1 − q̄∗2 =1
γ1log
c2c1
Markov model & control
Discrete Markov model:
q̄1 − q̄2q̄2
Average cost
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34
56
12
13
14
15
1617
18
18
20
22
24
Optimal hedging-pointsfor RBM:
q̄1 − q̄2 = 14.978
q̄2 = 2.996
E(k) i.i.d. Bernoulli.
Q(k + 1) − Q(k)= ζ(k) + ζa(k) + E(k + 1)
ζ(k), ζa(k) allocation increments.
Simulation
Line 1 Line 2
Line 3
E1D1
E2D2
E3D3
Gp1
Ga2 Ga3
Resource pooling from San Antonio to Houston?
Texas model
Line 1 Line 2
Line 3
single producer/consumer model
Assume Brownian demand, rate constraints as before
Provided there are no transmission constraints,
QA(t) =∑
Ei(t) − Di(t)
ZaA(t) =
=
=∑
Zai (t)
extraction - demand
aggregate ancillary
XA = (QA, ZaA) ≡
Aggregate model
Line 1 Line 2
Line 3Given demand and aggregate statefind the cheapest consistentnetwork configuration subject to transmission constraints
min
s.t.
∑(cpi z
pi + c
ai z
ai + c
boi q
−i )
qA =∑
(ei − di)zaA =
∑zai
0 =∑
(zpi + zai − ei)
q = e d−f = ∆p
f ∈ F
consistency
vector reserves
extraction = generation
power flow equations
transmission constraints
c̄(xA, d)Effective cost
Line 1 Line 2
Line 3
c̄(xA, d)
- 50- 50 - 40- 40 - 30- 30 - 20- 20 - 10- 10 00 1010 2020 3030 4040 505000
1010
2020
3030
4040
5050
1
2
3 4
zzaaAA
qqAA
XX++
xxAA
xxAA
xxAA xxAA
RRWhat do theseaggregate states sayabout the network?
Effective cost
qq11 == −−4646, q, q22 = 3= 3..05640564, q, q33 = 1= 122..94369436
gg11 == −−7711, g, gaa22 = 3= 333..05640564, g, gaa33 = 6= 6..94369436
ff11 == 1313, f, f22 == −−55,, ff33 == −−88
City 1 in blackout:City 1 in blackout:
Insufficient primary generation:Insufficient primary generation:
Transmission constraints binding:Transmission constraints binding:
Line 1 Line 2
Line 3
c̄(xA, d)
- 50- 50 - 40- 40 - 30- 30 - 20- 20 - 10- 10 00 1010 2020 3030 4040 505000
1010
2020
3030
4040
5050
zzaaAA
qqAA
1xxAA
Effective cost
xxAA
Line 1 Line 2
Line 3
- 50- 50 - 40- 40 - 30- 30 - 20- 20 - 10- 10 00 1010 2020 3030 4040 505000
1010
2020
3030
4040
5050
zzaaAA
qqAA
Will a competitivemarket supportsufficient reserves?
Dynamic Prices & Reserves
Line 1 Line 2
Line 3
- 50- 50 - 40- 40 - 30- 30 - 20- 20 - 10- 10 00 1010 2020 3030 4040 505000
1010
2020
3030
4040
5050
zzaaAA
qqAA
Prices
Reserves
Market prices risewith demand!
xxAA
q̄∗ = 1γ0
logc3p2
Dynamic Prices & Reserves
Sensitivity to transmission constraints?
Game among suppliers?
Design of financial contracts?
Policy structure as a function of ramp-rates
Workload formulation for model reduction
Solidarity between fluid, RBM,and other optimal MDP solutions
Future work:
Contributions:
3
16q̄1 − q̄2
q̄2
q̄ ∗2 =1
γ0log
c3c2
q̄ ∗1 − q̄ ∗2 =1
γ1log
c2c1
Conclusions & Extensions
3
16q̄1 − q̄2
q̄2
q̄ ∗2 =1
γ0log
c3c2
q̄ ∗1 − q̄ ∗2 =1
γ1log
c2c1
• M. Chen, C. Pandit, and S. Meyn. In search of sensitivity innetwork optimization. Queueing Systems, 2003
• I.-K. Cho and S. Meyn. Dynamics of ancillary service prices inpower distribution networks. CDC, 2003
• M. Chen, R. Dubrawski, and S. Meyn. Management of demanddriven production systems. IEEE TAC, 2004
References