2.cm towards probabilistic risk-management in power system ... · background & motivation (1/2)...

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.


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

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


Reliability mgmt approach & criterion (RMAC)

1. Discarding principle

2. Reliability target

3. Socio-economic function




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.




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 .





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.



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).






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.


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)}.


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}.



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.


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!





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,. . . ).





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.


Look-ahead mode RMAC


I neglect those “planning scenarios” (e.g., forecast errors)whose contribution to the risk is acceptably low.

→ using proxy for Rt-decisions?


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?


I blend cost of planning decisions with expectation ofRt-operation cost function over the planning horizon;

→ using proxy for Rt-costs?


Thank you for your attention!

[email protected]

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.


www.garpur-project.eu/

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?


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.


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.


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.


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.


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).


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).


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.


RMAC control


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.


RMAC control


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.

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