2.cm towards probabilistic risk-management in power system ... · background & motivation (1/2)...
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Towards probabilistic risk-management in powersystem operations
E. Karangelos and L. Wehenkel,{e.karangelos,l.wehenkel}@ulg.ac.be,
Institut Montefiore,Department of Electrical Engineering and Computer Science,
Universite de Liege,Liege, Belgium.
Background & motivation (1/2)
An on-going transition . . .
I from a thermal dominated generation system to low-inertia,intermittent & uncertain renewables;
I from an ageing physical power grid to a modern cyber-physical“smart” grid (advanced ICT, HPC, Big data, IoT, etc.);
I from a “passive” demand side to active electricity prosumers(demand response, electricity storage, micro-grids, etc.);
I from a (fairly) stable & predictable environment to more &more unforeseeable extreme events (the climate change);
→ already requires operating the power system within acomplex, dynamic & stochastic setting.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 2/ 18
Background & motivation (2/2)
An on-going transition . . .
I from today’s (∼ deterministic) N-1 practice;
– doing the job well under “average conditions” only?
I through probabilistic risk-assessment;
+ more informative by capturing uncertainty & variability inthreats and in their impact;
→ to probabilistic risk-management (i.e., assessment + control);
I the open question is how to take operational (andeventually planning) decisions while explicitly facing suchrisk.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 3/ 18
Background & motivation (2/2)
An on-going transition . . .
I from today’s (∼ deterministic) N-1 practice;
– doing the job well under “average conditions” only?
I through probabilistic risk-assessment;
+ more informative by capturing uncertainty & variability inthreats and in their impact;
→ to probabilistic risk-management (i.e., assessment + control);
I the open question is how to take operational (andeventually planning) decisions while explicitly facing suchrisk.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 3/ 18
1. Probabilistic risk-management for real-time systemoperation
E. Karangelos and L. Wehenkel, “Probabilistic reliabilitymanagement approach and criteria for power system real-timeoperation,” in 2016 Power Systems Computation Conference(PSCC), June 2016, pp. 1–9. [Online]. Available:http://hdl.handle.net/2268/193403
The Rt operation context
Horizon: 5’ ∼ 15’
Preventive Post-contingency Corrective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
uc ∈ Uc(u0)↓ •
u0 ∈ U0 • •↓ ↗ • ↗ •• πc(w0) • πb(w0) •x0 ↘ • ↘ •
• •xc •
xbc
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 4/ 18
Reliability mgmt approach & criterion (RMAC)
1. Discarding principle
2. Reliability target
3. Socio-economic function
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 5/ 18
Reliability mgmt approach & criterion (RMAC)
1. Discarding principle
I defines which part of the uncertainty space can be neglected;
I provided that its contribution to the risk is acceptably low;
→ in Rt operation adapt (dynamically) contingency list vsspatio-temporally variable probability & severity.
I choose Cc ⊂ C,I such that the residual risk implied by c /∈ Cc is negligible.
2. Reliability target
3. Socio-economic function
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 6/ 18
Reliability mgmt approach & criterion (RMAC)
1. Discarding principle
I defines which part of the uncertainty space can be neglected;
I provided that its contribution to the risk is acceptably low;
→ in Rt operation adapt (dynamically) contingency list vsspatio-temporally variable probability & severity.
I choose Cc ⊂ C,I such that the residual risk implied by c /∈ Cc is negligible.
2. Reliability target
3. Socio-economic function
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 6/ 18
Rt discarding principle
Preventive Post-contingency Corrective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
uc ∈ Uc(u0)↓ •
u0 ∈ U0 • •↓ ↗ • ↗ •• πc(w0) • πb(w0) •x0 ↘ ◦ ↘ •
◦ ◦xc ◦
xbc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
◦ RC\Cc (u) =∑
c∈C\Cc πc(w0) ·∑b∈B πb(w0) · S(xbc ,u,w0) ≤ ∆E .
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 7/ 18
Reliability mgmt approach & criterion (RMAC)
1. Discarding principle
2. Reliability target
I a context-specific notion of acceptable system trajectory;
I a maximum tolerance on the probability of unacceptabletrajectory (chance-constraint);
→ in Rt operation avoid instability, too large/long serviceinterruptions, etc. with a certain confidence.
3. Socio-economic function
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 8/ 18
Reliability mgmt approach & criterion (RMAC)
1. Discarding principle
2. Reliability target
I a context-specific notion of acceptable system trajectory;
I a maximum tolerance on the probability of unacceptabletrajectory (chance-constraint);
→ in Rt operation avoid instability, too large/long serviceinterruptions, etc. with a certain confidence.
3. Socio-economic function
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 8/ 18
Rt reliability target
Preventive Post-contingency Corrective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
uc ∈ Uc(u0)↓ •
u0 ∈ U0 • •↓ ↗ • ↗ •• πc(w0) • πb(w0) •x0 ↘ ◦ ↘ •
◦ ◦xc ◦
xbc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
• P{
(x0, xc , xbc )∈Xa|(c , b)∈C × B
}≥ (1− ε).
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 9/ 18
Reliability mgmt approach & criterion (RMAC)
1. Discarding principle
2. Reliability target
3. Socio-economic function
I blending TSO costs & the expected socio-economic impact tothe system users (e.g., cost of service interruptions);
I to be minimized when choosing amongst the set-of candidatedecisions complying with (1.) and (2.).
→ in Rt operation combine preventive control costs withexpectation of corrective control costs & ofsocio-economic severity of service interruptions.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 10/ 18
Rt socio-economic objective
Preventive Post-contingency Corrective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
uc ∈ Uc(u0)↓ •
u0 ∈ U0 • •↓ ↗ • ↗ •• πc(w0) • πb(w0) •x0 ↘ ◦ ↘ •
◦ ◦xc ◦
xbc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
minu∈U(x0)
{CP (x0, u0) +
∑c∈Cc πc(w0) · CC (xc , uc)
+∑
c,b∈C×B πc(w0) · πb(w0) · S(xbc ,u,w0)}.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 11/ 18
RMAC in the Rt Operation Context
Compact statement
minu∈U(x0)
{CP (x0, u0) +
∑c∈Cc
πc(w0) · CC (xc , uc)
+∑c∈Cc
πc(w0) ·∑b∈B
πb(w0) · S(xbc ,u,w0)
}(1)
s.t. P{
(x0, xc , xbc )∈Xa|(c, b)∈Cc × B
}≥ (1− ε) (2)
while
RC\Cc (u) ≤ ∆E . (3)
→ RMAC “tuning” via meta-parameters {Xa; ε; ∆E}.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 12/ 18
RMAC in the Rt Operation Context
Discarding principle
→ real-time contingency lists adaptable to exogenous conditions;
I a “classical” contingency analysis problem?
I approximate the risk of “discarded” contingency sub-set viaimportance sampling, data mining & bounding techniques?
Reliability target & socio-economic objective
→ choice of preventive vs preventive controls adaptable toimplied risks vs implementation costs;
I a (marginally) more complex variant of the classical SCOPFproblem;
I proof-of-concept algorithmic solution already achievable.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 13/ 18
2. Towards risk-management in look-ahead modeoperational planning?
The Operational planning context
uRt(t) ∈ URt (uP , uRt(t− 1), ξt)uP ∈ UP
ξt ∈ Ξt(ξt−1)
t1 t1 + Tt
tP
A “family” of practical problems
I e.g. w-1 maintenance requests, d-2 capacities for the market,t-1 reserve procurement;
I horizon start & length (t1;T ) “dictated” by the type ofdecision.
→ XXL multi-stage stochastic programming problems!
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 14/ 18
The Operational planning context
uRt(t) ∈ URt (uP , uRt(t− 1), ξt)uP ∈ UP
ξt ∈ Ξt(ξt−1)
t1 t1 + Tt
tP
Decision scope
I act in advance to facilitate the operation of the system inreal-time by choosing,uP ∈ UP : ∃uRt ∈ URt (uP , uRt(t − 1), ξt) ∀t ∈ [t1, t1 + T ];
I Nb.: in compliance with the doctrine of Rt operation (e.g.,N-1,RMAC,. . . ).
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 15/ 18
The Operational planning context
uRt(t) ∈ URt (uP , uRt(t− 1), ξt)uP ∈ UP
ξt ∈ Ξt(ξt−1)
t1 t1 + Tt
tP
Uncertainties (ξt ∈ Ξt(ξt−1))
I e.g., Res generation forecasts errors, weather, markets, etc.;
I spatially/temporally correlated continuous & discrete distros;
I resolved progressively;
I Nb.: define the informational state for Rt operation.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 16/ 18
Look-ahead mode RMAC
1. Discarding principle
I neglect those “planning scenarios” (e.g., forecast errors)whose contribution to the risk is acceptably low.
→ using proxy for Rt-decisions?
2. Reliability target
I ensure (with high enough probability) that the Rt operation“mission” (as per the N-1,RMAC,. . . ) is achievablethroughout the horizon;
→ using proxy for Rt-feasibility?
3. Socio-economic function
I blend cost of planning decisions with expectation ofRt-operation cost function over the planning horizon;
→ using proxy for Rt-costs?
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 17/ 18
Look-ahead mode RMAC
1. Discarding principle
I neglect those “planning scenarios” (e.g., forecast errors)whose contribution to the risk is acceptably low.
→ using proxy for Rt-decisions?
2. Reliability target
I ensure (with high enough probability) that the Rt operation“mission” (as per the N-1,RMAC,. . . ) is achievablethroughout the horizon;
→ using proxy for Rt-feasibility?
3. Socio-economic function
I blend cost of planning decisions with expectation ofRt-operation cost function over the planning horizon;
→ using proxy for Rt-costs?
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 17/ 18
Thank you for your attention!
AcknowledgmentThe research leading to these results has received funding from the EuropeanUnion Seventh Framework Programme (FP7/2007-2013) under grantagreement No 608540, project acronym GARPUR(www.garpur-project.eu/).
The scientific responsibility lies with the authors.
Karangelos & Wehenkel (ULg) Probabilistic risk-management in power system operations EPCC 2017, Wiesloch, Germany. 18/ 18
Supplementary slides
The Rt operation context
Horizon:
I the forthcoming 5’ ∼ 15’.
Uncertainties:
I occurrence of contingencies c ∈ C;
I behavior of post-contingency corrective controls b ∈ B.
→ weather (w0) dependent probabilities (πc(w0), πb(w0))respectively.
Decisions:
I apply preventive (pre-contingency) control u0 ∈ U0(x0) ?
I prepare post-contingency corrective controlsuc ∈ Uc (u0) ∀c ∈ C?
RMAC in the Rt Operation Context
1. Discarding Principle
→ adapt (dynamically) contingency list vs spatio-temporallyvariable probability & severity;
I choose Cc ⊂ C,
I such that the residual risk implied by c /∈ Cc is negligible.
RC\Cc (u) =∑
c∈C\Cc
πc(w0) ·∑b∈B
πb(w0) · S(xbc ,u,w0) ≤ ∆E .
∆E : discarding threshold (≥ 0),
S(xbc ,u,w0): socio-economic severity function.
RMAC in the Rt Operation Context
2. Reliability Target
→ avoid instability, too large/long service interruptions,etc. with a certain confidence.
P{
(x0, xc , xbc )∈Xa|(c , b)∈C × B
}≥ (1− ε).
Xa: “acceptable” system trajectories,
ε: tolerance level ∈ [0, 1],
X ε > 0 allows corrective control while managing the risk of itsfailure.
RMAC in the Rt Operation Context
3. Socio-economic objective
→ combine preventive control costs with expectation ofcorrective control costs & of socio-economic severity.
minu∈U(x0)
{CP (x0, u0) +
∑c∈C
πc(w0) · CC (xc , uc)
+∑
c,b∈C×Bπc(w0) · πb(w0) · S(xbc ,u,w0)
.
CP (x0, u0): preventive control cost function,
CC (xc , uc): corrective control cost function,
S(xbc ,u,w0): socio-economic severity function.
Demonstrative case studies (1/6)
Uncertainty
I single & common modedouble outages,
I failure of each elementarycorrective operation.
Variability
Case A: week 23 (summer),2509 MW.
Case B: week 46 (winter),2536 MW,+10% FOR,+15% voll.
Demonstrative case studies (2/6)
Benchmarking: preventive/corrective N-1
N-1 Operational Cost ($) N-1 Residual Risk ($)
Case A vs B
I Operational cost difference marginal (≈ 2.4%).
I Difference in residual risk more notable.
→ greater outage probabilities & value of lost load in case B.
Demonstrative case studies (3/6)
RMAC discarding
N-1 Residual Risk ($)
Case A Case B
Total = RC\CN−1(u) 162.11 282.55
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(A30,A34) 48.9 85.24
(A12-1,A13-1) 39.85 69.45
(A25-1,A25-2) 37.13 64.72
(A18,A20) 36.23 63.14
Other common mode outages 0 0
What if ∆E = $165?
I Need an extended sub-set in case B only (Cc ⊃ CN−1).
Demonstrative case studies (3/6)
RMAC discarding
N-1 Residual Risk ($)
Case A Case B
Total = RC\CN−1(u) 162.11 282.55
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(A30,A34) 48.9 85.24
(A12-1,A13-1) 39.85 69.45
(A25-1,A25-2) 37.13 64.72
(A18,A20) 36.23 63.14
Other common mode outages 0 0
What if ∆E = $165?
I Need an extended sub-set in case B only (Cc ⊃ CN−1).
Demonstrative case studies (3/6)
RMAC discarding
N-1 Residual Risk ($)
Case A Case B
Total = RC\CN−1(u) 162.11 282.55
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(A30,A34) 48.9 85.24
(A12-1,A13-1) 39.85 69.45
(A25-1,A25-2) 37.13 64.72
(A18,A20) 36.23 63.14
Other common mode outages 0 0
What if ∆E = $165?
X extended sub-set in case B only (Cc ⊃ CN−1).
Demonstrative case studies (4/6)
RMAC control
Case B (Cc ⊃ CN−1).
Preventive Cost vs ε ($) Exp. Corrective Cost vs ε ($)
ε ≤ 10−6: limited use corrective control, due to failure probabilityvs reliability target.
ε = 10−5: reduced preventive costs wrt ε = 10−6.
ε > 10−4: reliability target not binding.
Demonstrative case studies (5/6)
RMAC control
Case B (Cc ⊃ CN−1).
Contingency Classification
ε 0 10−6 10−5 10−4
Preventively Secured 41 40 39 35
Correctively Secured 0 1 1 4
Not Secured 0 0 1 2
ε = 0: blocks corrective control due to failure probability,
X unblocked through ε > 0,
ε↗ fewer low probability contingencies “covered” bypreventive/corrective controls.
Demonstrative case studies (6/6)
RMAC control
Case B (Cc ⊃ CN−1).
Socio-economic Cost vs ε ($) Expected Severity vs ε ($)
ε ∈ (0, 10−4]: operational costs savings at the expense ofadditional expected criticality.
ε > 10−4: socio-economic objective restrains further use ofcorrective control.