![Page 1: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/1.jpg)
Presented at CERTS Review
STOCHASTIC INTERCHANGE SCHEDULING AN APPLICATION OF PROBABILISTIC REAL-TIME LMP FORECAST
Lang Tong and Yuting Ji School of Electrical and Computer Engineering Cornell University, Ithaca, NY
Acknowledgement:
Support in part by DoE (CERTS) and NSF
August 4, 2015
![Page 2: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/2.jpg)
Overview Objectives
Investigate the real-time LMP forecast problem by an operator
Develop probabilistic forecasting techniques and applications
Summary of results Real-time LMP models
Including energy only and energy-reserve markets Deterministic, probabilistic, and time varying contingencies
Forecast methods and applications A multiparametric program approach for ex ante LMP A Markov chain approach for ex ante and ex post LMPs Multi-area interchange scheduling under uncertainties
![Page 3: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/3.jpg)
Short-term LMP forecast
![Page 4: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/4.jpg)
Probabilistic forecast of real-time LMP Benefits
Valuable for generation and demand response decisions
Risk management
Congestion relief and operating cost reduction
Multi-area interchange scheduling under uncertainties
Examples: ERCOT, AEMO, ….
Short term LMP forecast by an operator Access to real-time data and network operating conditions
Access to internal LMP computation state
Ability to incorporate load/variable generation forecast models.
![Page 5: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/5.jpg)
Outline Introduction Real-time LMP forecast model and techniques
LMP forecast models for energy and reserve markets Forecast with probabilistic contingencies Numerical results
Stochastic inter-regional interchange scheduling The interchange scheduling problem and solutions Joint optimization, tie optimization, and coordinated transaction
scheduling Stochastic interchange scheduling via probabilistic forecast Simulation results
Conclusions and future work
![Page 6: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/6.jpg)
Ex ante real time LMP model
![Page 7: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/7.jpg)
Ex ante real time LMP model with co-optimization
![Page 8: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/8.jpg)
LMP forecast via MPLP
![Page 9: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/9.jpg)
Forecast of ex post LMP via Markov chain
![Page 10: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/10.jpg)
LMP forecast with probabilistic contingencies
![Page 11: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/11.jpg)
Numerical results: IEEE 118 bus system Quadratic cost function. Deterministic load. 3 stochastic generators (bus 42, 45 and 60).
5 transmission lines have limits (67, 68, 69, 89 and 90). 25 critical regions. 3 unique congestion patterns.
-30
-20
-10
0
-30
-20
-10
0-30
-25
-20
-15
-10
-5
0
Stochastic gen 1Stochastic gen 2
Sto
chas
tic g
en 3
![Page 12: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/12.jpg)
Sample forecast distribution
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Forecast probability
Obs
erve
d fre
quen
cy
σ=1.5σ0
perfect forecastσ=2σ0
![Page 13: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/13.jpg)
Outline Introduction Real-time LMP forecast model and techniques
LMP forecast models for energy and reserve markets Forecast with probabilistic contingencies Numerical results
Stochastic inter-regional interchange scheduling The inter-regional interchange problem The ideal, the practical, the practically optimal, and coordinated
transaction scheduling Stochastic interchange scheduling via probabilistic forecast Simulation results
Conclusions and future work
![Page 14: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/14.jpg)
Inter-regional interchange & the seams problem
ISOs schedule operations independently, trading power across seams: Stochastic and time varying price disparities between regions.
Under utilization of tie lines
Counter-intuitive flows
Estimated economic loss of $784 millions between NY & NE from 2006-2010.
![Page 15: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/15.jpg)
The ideal: joint optimization
Jointly optimal scheduling via decentralized optimization Extensively studied: Lagrange relaxation; decomposition techniques
Advantages and challenges:
achieve globally economic solution
rate of convergence, required information sharing, dealing with uncertainties, and the role of market participants.
![Page 16: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/16.jpg)
The practical: decoupled optimization
Each ISO has a simplified model of the neighboring area with a proxy bus
Market participants submit offers/bids for external transactions at proxy buses
Export/import quantity is scheduled ahead of time.
Each ISO schedules its own operations with fixed interchange.
FERC approves coordinated transaction scheduling (CTS) for PJM & NYISO, March 2014.
Estimated cost saving: 9M~26M per year.
Versions of CTS are being implemented for MISO-PJM, NYISO-ISONE
![Page 17: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/17.jpg)
(Deterministic) tie optimization (TO)
![Page 18: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/18.jpg)
A market perspective
![Page 19: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/19.jpg)
Tie optimization (TO) and equivalence
Surplus maximization
Cost minimization
![Page 20: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/20.jpg)
Stochastic tie optimization (STO) STO as a two stage stochastic program 1st stage: 2nd stage:
![Page 21: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/21.jpg)
Stochastic tie optimization (STO)
![Page 22: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/22.jpg)
Stochastic coordinated transaction scheduling (SCTS)
![Page 23: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/23.jpg)
Numerical results: 2 area 6 bus system
Deterministic load. All lines are identical with limit 100MW. A single wind generator.
![Page 24: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/24.jpg)
Discrete randomness
50 60 70 80 90 100
7800
8000
8200
8400
8600
8800
9000
9200
9400
Interchange (θ)
Exp
ecte
d ov
eral
l cos
t
Expected cost vs Interchange: P[w=30]=0.8, P[w=50]=0.2
50 60 70 80 90 100
7800
8000
8200
8400
8600
8800
9000
9200
9400
Interchange (θ)
Exp
ecte
d ov
eral
l cos
tExpected cost vs Interchange: P[w=30]=0.5, P[w=50]=0.5
50 60 70 80 90 100
7800
8000
8200
8400
8600
8800
9000
9200
9400
Interchange (θ)
Exp
ecte
d ov
eral
l cos
t
Expected cost vs Interchange: P[w=30]=0.2, P[w=50]=0.8
![Page 25: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/25.jpg)
50 60 70 80 90 10010
20
30
40
50
60
70
80
90
Interchange (θ)
Pric
e ( π
)Price vs Interchange: P[w~N(30,52)]=0.8, P[w~N(50,52)]=0.2
πATO(θ)
πASTO(θ)
πB(θ)
Continuous randomness
![Page 26: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/26.jpg)
Impact of uncertainty Assume that wind 𝑤𝑤~𝑁𝑁 40,𝜎𝜎2 . STO: capability to capture the uncertainty level 𝜎𝜎.
0 5 10 15 20 25 30 3585
85.5
86
86.5
87
87.5
88
88.5
89
Forecast standard deviation (σ)
Inte
rcha
nge
( θ)
Interchange vs Forecast uncertainty: w~N(40, σ2)
θTO(σ)
θSTO(σ)
![Page 27: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/27.jpg)
Contingency: transmission outage
50 60 70 80 90 10010
20
30
40
50
60
70
Interchange (θ)
Pric
e ( π
)
Price vs Interchange: (i)Wind: P[w~N(30,42)]=0.8, P[w~N(50,42)]=0.2(ii) Outage: P[l+45=100]=0.98, P[l+45=50]=0.02
πATO(θ)
πASTO(θ)
πB(θ)
![Page 28: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/28.jpg)
Example: 3+118 bus system
Area A: 3 bus system with constant cost 1 wind generator Pr[high wind]=Pr[low wind]=0.5
Area B: 118 bus system with quadratic cost 3 wind generators Pr[high wind]=Pr[low wind]=0.5
Two systems are connected with a single tie line. 150 200 250 300
35
36
37
38
39
40
41
42
43
Interchange (MW)
Pric
e
Price vs Interchange: area A (3 bus system) area B (IEEE 118 system)(i): P[wA=20]=0.5, P[wA=80]=0.5
(ii): P[wB=(30,60,20)]=0.5, P[wB=(90,100,50)]=0.5
πATO(θ)
πASTO(θ)
πBTO(θ)
πASTO(θ)
Q*TO
Q*STO
Counter intuitive Flow!
![Page 29: STOCHASTIC INTERCHANGE SCHEDULING€¦ · Access to real-time data and network operating conditions Access to internal LMP computation state Ability to incorporate load/variable generation](https://reader034.vdocuments.us/reader034/viewer/2022050301/5f6a5ef1462ec33b3b5dc036/html5/thumbnails/29.jpg)
Summary and future work Summary of results
Real-time LMP models Including energy only, energy-reserve markets & inter-regional interchange Deterministic, probabilistic, and time varying contingencies
Forecast methods and applications A multiparametric program approach for ex ante LMP A Markov chain approach for ex ante and ex post LMPs Multi-area interchange scheduling under uncertainties
Future work Addressing scalability issues of forecast Characterization of performance loss of decoupled optimization Performance evaluation in the presence of market participants