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  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Synchronization-Aware and Algorithm-Efficient Chance Constrained Optimal Power Flow

    Russ Bent (LANL), Dan Bienstock (Columbia U) Misha Chertkov

    LANL/DOE:OE + LANL/DTRA & NMC/NSF:ECCS

    Nov 16, 2013, DC, NSF Workshop on Computing, Control and Signal Challenges

    in Future Power Systems Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Outline

    1 CC-OPF: Motivation & Pre-History Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    2 Towards AC CC-OPF Convex AC-OPF Synchronization-Constraint CC-OPF

    3 Summary & Path Forward Brief Summary Path Forward

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Reliability Measure & Optimization Under Uncertainty

    Instantons in Power Systems: MC, F. Pan, M. Stepanov (2010); MC, FP, MS, R. Baldick (2011); S.S. Baghsorkhi, I. Hiskens (2012)

    C

    N-1 violations

    Controllable resources - Dispatchable generation - DC line/ties, switching - Direct load control/Storage

    Stochastic resources - Wind/PV generation - Price-based DR - Dist. enery resources

    d d

    Control action in C modi�es the security boundary in S reducing the risk of failure below a threshold level.

    Instanton directions Security boundary

    P(d)=Joint probability distribution of forecast errors.

    Towards a GOOD fluctuations aware optimization/control

    Stochastic/uncontrollable participants (e.g. renewables) fluctuate

    Just the standard ”N-1”-security gives no guarantees under uncertainty

    First: given statistics of “errors” quantify Probabilistic Distance to Failure = instantons [how it started for us]

    Then, account for the probabilistic “errors” and modify existing optimization/control schemes = CC-OPF [in the center of today’s discussion]

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Chance Constrained Optimum Power Flow: Risk-Aware Network Control under Uncertainty

    D. Bienstock, MC, S. Harnett (Columbia/LANL) http://arxiv.org/abs/1209.5779

    Step one (distance to failure): compute the instantons to find the total probability of stochastic failure = Pfail Step two: if Pfail > threshold re-dispatch generation so that Pfail < threshold at minimum cost

    CC-OPF = make sure that generation is re-dispatched at minimum cost such that ∀failures : Pfailure (!!) < threshold (even better than steps one+two combined)

    Related, independent work

    E. Sjodin, D. F. Gayme and U. Topcu, Risk-Mitigated Optimal Power Flow for Wind Powered Grids, ACC 2012.

    L. Roald, F. Oldewurtel, T. Krause and G. Andersson, Analytical Reformulation of Security Constrained Optimal Power Flow with Probabilistic Constraints, Proceedings of the Grenoble PowerTech, Grenoble, France, June 2013.

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    http://arxiv.org/abs/1209.5779 https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Standard re-dispatch

    Constrained (thermal + generation limits) OPF DC-approximation :

    min p,θ

    c(p) (a quadratic)

    s.t.

    Bθ = p − d |βij(θi − θj)| ≤ uij for each line ij Pming ≤ pg ≤ Pmaxg for each generator g Notation:

    p = vector of generations ∈ Rn, d = vector of loads ∈ Rn

    B ∈ Rn×n

    (bus susceptance matrix = graph Laplacian weighted with βij)

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    How does OPF handle (renewable) fluctuations?

    Automatic frequency control: primary, secondary

    Generator output varies up or down proportionally to aggregate change

    Primary +secondary ⇒ modeled in a quasi-static way through affine control with rates α

    Experiment: Bonneville Power Administration data, Northwest US

    data on wind fluctuations at planned farms

    with standard OPF, 7 lines exceed limit ≥ 8% of the time

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Want to improve the standard OPF

    standard control [affine, possibly changing rates]

    aware of security (limits)

    not too conservative

    computationally practicable

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    OPF vs Chance Constrained-OPF Standard OPF (Dispatch for the mean forecast, not aware of fluctuations)

    minp c(p)︸︷︷︸ cost of generation

    ∣∣∣∣∣∣ Power Flow Eqs. (DC approx.) are SAT

    Generation limits are SAT Power Flow Thermal Limits are SAT

    Chance Constrained OPF (fluctuations aware dispatch)

    minp̄,α E [c(p̄, α)]

    ∣∣∣∣∣∣ Power Flow Eqs. are SAT for mean forecast

    Generation satisfies Chance Constraints Line Power Flows satisfy Chance Constraints

    Chance Constraints for Power Flows: ∀(i , j) ∈ E : Prob(|fij | > f maxij ) < εij . Interpretation: overload is allowed for �-fraction of “time”.

    p̄ - generation re-dispatch for beginning of the period; α - proportional (droop+AGC) rates for the period

    CC-OPF detailed formulation

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Chance Constrained OPF (fluctuations aware dispatch)

    minp̄,α E [c(p̄, α)]

    ∣∣∣∣∣∣ Power Flow Eqs. are SAT for mean forecast

    Generation satisfies Chance Constraints Line Power Flows satisfy Chance Constraints

    Chance Constraints for Power Flows : ∀(i , j) ∈ E : Prob(|fij | > f maxij ) < εij

    More Technical Details [it is NOT Monte Carlo]

    Assuming site-independent, Gaussian fluctuations enables explicit evaluation [formula] of chance constraints for given p̄, α

    The resulting (after averaging) dispatch problem is convex (conic)

    optimization

    Constraint violations are few/sparse. Cutting Plane method greatly speeds up optimization

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Back to motivating example

    BPA case

    standard OPF: cost 235603, 7 lines unsafe ≥ 8% of the time CC-OPF: cost 237297, every line safe ≥ 98% of the time run time = 9.5 seconds (one cutting plane!)

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summary & Path Forward

    Instantons = Probabilistic Measure of Uncertainty CC-OPF (DC, thermal limits)

    Back to motivating example

    BPA case

    standard OPF: cost 235603, 7 lines unsafe ≥ 8% of the time CC-OPF: cost 237297, every line safe ≥ 98% of the time run time = 9.5 seconds (one cutting plane!)

    Experiments with CC-OPF

    CC-OPF succeeds where standard OPF fails

    Cost of Reliability [CC-OPF saving over standard OPF]

    CC-OPF is not a naive fix. [Changes are nonlocal]

    Helps to provide better answers to many “standard” questions

    Michael (Misha) Chertkov – chertkov@lanl.gov https://sites.google.com/site/mchertkov

    https://sites.google.com/site/mchertkov

  • CC-OPF: Motivation & Pre-History Towards AC CC-OPF

    Summa