DCSC, 3mE Gather-and-broadcast frequency control in power systems Florian D¨ orfler Sergio Grammatico TU Delft – Power Web seminar Delft, The Netherlands, Nov 8, 2018 1 / 16
A few (of many) game changers in power system operation synchronous generator 2 / 16
A few (of many) game changers in power system operation synchronous generator ↝ power electronics 2 / 16
A few (of many) game changers in power system operation synchronous generator ↝ power electronics scaling 2 / 16
A few (of many) game changers in power system operation synchronous generator distributed generation generation ! ↝ power electronics transmission ! distribution ! scaling 2 / 16
A few (of many) game changers in power system operation synchronous generator distributed generation other paradigm shifts generation ! ↝ power electronics transmission ! distribution ! scaling 2 / 16
Conventional frequency control hierarchy 3. Tertiary control (offline) goal: optimize operation architecture: centralized & forecast strategy: scheduling (OPF) 2. Secondary control (slower) goal: maintain operating point architecture: centralized strategy: I-control (AGC) 1. Primary control (fast) goal: stabilization & load sharing architecture: decentralized strategy: P-control (droop) Is this top-to-bottom architecture based on bulk generation control Power System still appropriate in tomorrow’s grid? 3 / 16
Conventional frequency control hierarchy 3. Tertiary control (offline) goal: optimize operation architecture: centralized & forecast strategy: scheduling (OPF) 2. Secondary control (slower) goal: maintain operating point architecture: centralized strategy: I-control (AGC) 1. Primary control (fast) goal: stabilization & load sharing architecture: decentralized strategy: P-control (droop) Is this top-to-bottom architecture based on bulk generation control Power System still appropriate in tomorrow’s grid? 3 / 16
Outline Introduction & Motivation Overview of Distributed Architectures Gather-and-Broadcast Frequency Control Case study: IEEE 39 New England Power Grid Conclusions
Nonlinear differential-algebraic power system model ▸ generator swing θ i + D i ˙ θ i = P i + u i − ∑ B i,j sin ( θ i − θ j ) M i ¨ equations i ∈ G j ∈V ▸ frequency-responsive θ i = P i + u i − ∑ B i,j sin ( θ i − θ j ) D i ˙ loads & grid-forming inverters i ∈ F j ∈V ▸ load buses with 0 = P i + u i − ∑ B i,j sin ( θ i − θ j ) demand response i ∈ P j ∈V D i ˙ θ i is primary droop control (not focus today) u i ∈ U i = [ u i , u i ] is secondary control (can be U i = { 0 } ) ⇒ sync frequency ω sync ∼ ∑ i P i + u i = imbalance ⇒ ∃ synchronous equilibrium iff ∑ i P i + u i = 0 (load = generation) 4 / 16
Nonlinear differential-algebraic power system model ▸ generator swing θ i + D i ˙ θ i = P i + u i − ∑ B i,j sin ( θ i − θ j ) equations i ∈ G M i ¨ j ∈V ▸ frequency-responsive θ i = P i + u i − ∑ B i,j sin ( θ i − θ j ) D i ˙ loads & grid-forming inverters i ∈ F j ∈V 0 = P i + u i − ∑ B i,j sin ( θ i − θ j ) ▸ load buses with demand response i ∈ P j ∈V D i ˙ θ i is primary droop control (not focus today) u i ∈ U i = [ u i , u i ] is secondary control (can be U i = { 0 } ) ⇒ sync frequency ω sync ∼ ∑ i P i + u i = imbalance ⇒ ∃ synchronous equilibrium iff ∑ i P i + u i = 0 (load = generation) 4 / 16
Nonlinear differential-algebraic power system model ▸ generator swing θ i + D i ˙ θ i = P i + u i − ∑ B i,j sin ( θ i − θ j ) equations i ∈ G M i ¨ j ∈V ▸ frequency-responsive θ i = P i + u i − ∑ B i,j sin ( θ i − θ j ) D i ˙ loads & grid-forming inverters i ∈ F j ∈V 0 = P i + u i − ∑ B i,j sin ( θ i − θ j ) ▸ load buses with demand response i ∈ P j ∈V D i ˙ θ i is primary droop control (not focus today) u i ∈ U i = [ u i , u i ] is secondary control (can be U i = { 0 } ) ⇒ sync frequency ω sync ∼ ∑ i P i + u i = imbalance ⇒ ∃ synchronous equilibrium iff ∑ i P i + u i = 0 (load = generation) 4 / 16
Economically efficient secondary frequency regulation Problem I: frequency regulation Control { u i ∈ U i } i to balance load & generation: ∑ i P i + u i = 0 Problem II: optimal economic dispatch Control { u i ∈ U i } i to minimize the aggregate operational cost: u ∈ U ∑ i J i ( u i ) min s.t. ∑ i P i + u i = 0 5 / 16
Economically efficient secondary frequency regulation Problem I: frequency regulation Control { u i ∈ U i } i to balance load & generation: ∑ i P i + u i = 0 Problem II: optimal economic dispatch Control { u i ∈ U i } i to minimize the aggregate operational cost: u ∈ U ∑ i J i ( u i ) min s.t. ∑ i P i + u i = 0 5 / 16
Economically efficient secondary frequency regulation Problem I: frequency regulation Control { u i ∈ U i } i to balance load & generation: ∑ i P i + u i = 0 Problem II: optimal economic dispatch Control { u i ∈ U i } i to minimize the aggregate operational cost: u ∈ U ∑ i J i ( u i ) min s.t. ∑ i P i + u i = 0 � ⇒ identical marginal costs at optimality: J ′ j ) ∀ i,j i ( u ⋆ i ) = J ′ j ( u ⋆ 5 / 16
Economically efficient secondary frequency regulation Problem I: frequency regulation Control { u i ∈ U i } i to balance load & generation: ∑ i P i + u i = 0 Problem II: optimal economic dispatch Control { u i ∈ U i } i to minimize the aggregate operational cost: u ∈ U ∑ i J i ( u i ) min s.t. ∑ i P i + u i = 0 � ⇒ identical marginal costs at optimality: J ′ j ) ∀ i,j i ( u ⋆ i ) = J ′ j ( u ⋆ Standing assumptions −∑ i P i ∈ ∑ i U i = ∑ i [ u i , u i ] feasibility: { J i ∶ U i → R } i strictly convex & cont. differentiable regularity: 5 / 16
critical review of secondary control architectures
Centralized automatic generation control (AGC) integrate single measurement & broadcast λ = − ω i ∗ k ˙ u i = 1 λ A i � inverse optimal dispatch for J i ( u i ) = 1 2 A i u 2 i � few communication requirements (broadcast) Wood and Wollenberg. “Power Generation, Operation, and Control,” John Wiley & Sons, 1996. Machowski, Bialek, and Bumby. “Power System Dynamics,” John Wiley & Sons, 2008. 6 / 16
Centralized automatic generation control (AGC) integrate single measurement & broadcast λ = − ω i ∗ k ˙ u i = 1 λ A i � inverse optimal dispatch for J i ( u i ) = 1 2 A i u 2 i � few communication requirements (broadcast) � single authority & point of failure � ⇒ not suited for distributed gen Wood and Wollenberg. “Power Generation, Operation, and Control,” John Wiley & Sons, 1996. Machowski, Bialek, and Bumby. “Power System Dynamics,” John Wiley & Sons, 2008. 6 / 16
Decentralized frequency control integrate local measurement λ i = − ω i k i ˙ u i = λ i � nominal stability guarantee � no communication requirements M. Andreasson, D. Dimarogonas, H. Sandberg, and K. Johansson, “Distributed PI-control with applications to power systems frequency control,” in American Control Conference , 2014. C. Zhao, E. Mallada, and F. D¨ orfler, “Distributed frequency control for stability and economic dispatch in power networks,” in American Control Conference , 2015. 7 / 16
Decentralized frequency control integrate local measurement λ i = − ω i k i ˙ u i = λ i � nominal stability guarantee � no communication requirements � does not achieve economic efficiency � ∃ biased measurement � ⇒ instability M. Andreasson, D. Dimarogonas, H. Sandberg, and K. Johansson, “Distributed PI-control with applications to power systems frequency control,” in American Control Conference , 2014. C. Zhao, E. Mallada, and F. D¨ orfler, “Distributed frequency control for stability and economic dispatch in power networks,” in American Control Conference , 2015. 7 / 16
Distributed averaging frequency control integrate local measurement & average marginal costs λ i = − ω i + ∑ j w i,j ( J ′ i ( u i ) − J ′ j ( u j )) k i ˙ u i = λ i � stability & robustness certificates � asymptotically optimal dispatch J.W. Simpson-Porco, F. D¨ orfler, and F. Bullo, “Synchronization and power sharing for droop-controlled inverters in islanded microgrids,” in Automatica , 2013. N. Monshizadeh, C. De Persis, and J.W. Simpson-Porco, “The cost of dishonesty on optimal distributed frequency control of power networks,” 2016, Submitted. 8 / 16
Distributed averaging frequency control integrate local measurement & average marginal costs λ i = − ω i + ∑ j w i,j ( J ′ i ( u i ) − J ′ j ( u j )) k i ˙ u i = λ i � stability & robustness certificates � asymptotically optimal dispatch � high communication requirements & vulnerable to cheating � utility concern: “give power out of our hands” J.W. Simpson-Porco, F. D¨ orfler, and F. Bullo, “Synchronization and power sharing for droop-controlled inverters in islanded microgrids,” in Automatica , 2013. N. Monshizadeh, C. De Persis, and J.W. Simpson-Porco, “The cost of dishonesty on optimal distributed frequency control of power networks,” 2016, Submitted. 8 / 16
another (possibly better?) control protocol for distributed generation
Motivation: from social welfare to competitive markets Social welfare dispatch u ∈ U ∑ i J i ( u i ) min s.t. ∑ i P i + u i = 0 9 / 16
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