Problems Samples & Perspectives on Cyber-Physical Energy - - PowerPoint PPT Presentation

Problems Samples & Perspectives on Cyber-Physical Energy Networks

ETH D-INFK Seminar @ Oct 31 2016

Florian D¨

• rfler

@ETH for “Complex Systems Control”

system control

“Simple” control systems are well understood. “Complexity” can enter in many ways . . .

2 / 43

A “complex” distributed decision making system

. . .

physical interaction local subsystems and control sensing & comm.

local system local control local system local control

Such distributed systems include large-scale physical systems, engineered multi-agent systems, & their interconnection in cyber-physical systems.

3 / 43

Timely applications of distributed systems control

• ften the centralized perspective is simply not appropriate

robotic networks decision making social networks sensor networks self-organization pervasive computing traffic networks smart power grids

4 / 43

my main application of interest —– the power grid

Paradigm shifts in the operation of power networks

purpose of electric power grid: generate/transmit/distribute conventional operation: hierarchical & centralized things are changing . . .

IBM’s smart grid vision 5 / 43

Renewable/distributed/non-rotational generation on the rise

Source: Renewables 2014 Global Status Report

6 / 43

A few (of many) game changers . . .

synchronous generator

(ensure stable/robust op)

power electronics

(injects mostly garbage)

distributed generation

(not always coordinated)

transmission! distribution! generation!

scaling

(no sync through physics)

The results . . .

based ¡Schedule). ¡These ¡“market ¡induced” ¡effects ¡

low-inertia, over-voltages, etc.

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Many other paradigm shifts

1 controllable fossil fuel sources

⇒ stochastic renewable sources

2 generation follows load

⇒ controllable load follows generation

3 monopolistic energy markets

⇒ deregulated energy markets

4 . . . many technological advances 8 / 43

Summary: challenges & opportunities in tomorrow’s grid

www.offthegridnews.com

Public policy & environmental concerns:

1 increasing renewables & deregulation 2 more decentralization & uncertainty

⇒ increasing volatility & complexity Rapid technological and scientific advances:

1 re-instrumentation: sensors & actuators 2 complex & cyber-physical systems

⇒ cyber-coordination layer for smarter grids

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Exciting work @ intersection of domains & disciplines

. . . on scientific end

dynamics

stochastic disturbances large-scale & nonlinear low-inertia issues

• ptimization

nonlinear & relaxations massive computation stochastic programs

control

distributed & decentralized power electronics

economics

market mechanisms

• nline vs. offline

robust & stability certificates renewable modeling locational marginal prizing bidding & pooling remote real-time data networked

• ptimal

data-driven ancillary services prosumers load control distributed demand response complex networks mixed integer

power grid science

estimation privacy uncertainty CPS load models

& driven by very rapid technological advances

◮ power electronics ◮ battery storage systems ◮ plug-in electric vehicles ◮ real-time & wide-area phasor measurements ◮ communication ◮ wind turbine, PV, & solar manufacturing ◮ microgrid deployment ◮ energy-efficient buildings ◮ smart meters & household appliances ◮ . . .

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Problem samples today

coordination of distributed generation decentralized & optimal wide-area control

• nline power

flow optimization

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Outline

Introduction Basics of Power System Physics & Operation Coordination of Distributed Generation Decentralized Wide-Area Control Online Feedback Optimization Conclusions

energy is not packetized . . . two slides on the basics

Modeling: a power grid is a circuit

1 AC circuit with harmonic

waveforms Ei cos(θi + ωt)

2 active and reactive power flows 3 loads demanding constant

active and reactive power

4 sources: generators & inverters

inject power akin to physics/control

5 coupling via Kirchhoff & Ohm

Gij + i Bij i j Pi + i Qi i mech. torque electr. torque

injection = power flows ◮ active power: Pi =

• j BijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)

◮ reactive power: Qi = −

j BijEiEj cos(θi − θj) + GijEiEj sin(θi − θj)

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Power balance, frequency, & droop control

idealized power balance: generation = load + losses (does not hold due to unknown loads, renewables, & losses)

Hz

generation loads + losses 50 49 51 52 48

sync’d frequency ωsync ∼ imbalance droop control: control power injection ∝ frequency deviation Pi = Pref

i

− Di ˙ θi stabilizes grid & synchronizes frequencies: ˙ θi(t → ∞) = ωsync . . . but ωsync is wrong frequency

ωsync

˙ θ

P ref

1

P ref

2 13 / 43

Outline

Introduction Basics of Power System Physics & Operation Coordination of Distributed Generation Decentralized Wide-Area Control Online Feedback Optimization Conclusions

Conventional power systems control hierarchy

Power System

• 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 still appropriate in tomorrow’s grid?

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Plug’n’play architecture

flat hierarchy, distributed, no time-scale separations, & model-free

source # 1

… … …

Power System

source # n source # 2

Secondary Control Tertiary Control Primary Control

Transceiver

Secondary Control Tertiary Control Primary Control

Transceiver

Secondary Control Tertiary Control Primary Control

Transceiver

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approach from an optimal energy routing perspective

Energy management

as offline resource allocation & scheduling problem

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Energy management

as offline resource allocation & scheduling problem

minimize {cost of generation, losses, . . . } subject to physical constraints: equality constraints: power balance equations

• perational constraints:

inequality constraints: flow/injection/voltage constraints logic constraints: commit generators yes/no . . .

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A simple problem instance: optimal economic dispatch

dispatch generation: minui ∈ Ui

• i Ji(ui)
• generation cost

subject to

• i Pref

i

+ ui = 0

• load = generation

1 primal feasibility = imbalance:

i Pref i

+ ui = 0 ∼ ωsync (measurable)

2 identical marginal costs at optimality: J′

i (ui) = J′ j(uj) ∀i, j (consensus)

simple distributed optimization algorithm:

1 dual update on violation:

λ+ = λ + 1

k · ωsync

2 consensus on xi = J′

i (ui):

x+

i

= xi +

• j∈neighbors aijxj

⇒ altogether in real-time: ki ˙ λi = ˙ θi

• local dual update

−

• j∈neighborsaij
• J′

i (ui) − J′ i (ui)

• distributed consensus (comm-based)

⇒ inject ui(t) = λi(t)

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Plug’n’play architecture

power system physics: power flow & devices

• Di ˙

θi =P ref

i

− Pi − λi λi ˙ θi

• droop control:

trade off power injections & frequency

• r voltage

˙ θi Pi Pi =

• j BijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)

Qi = −

• j BijEiEj cos(θi − θj) + GijEiEj sin(θi − θj)

ki ˙ λi = ˙ θi −

• j∈neighbors

aij (J′

i(ui) − J′ i(ui))

• secondary &

tertiary control: integral errors & diffusive averaging

J′

i(ui)

. . .

J′

i(ui)

. . .

J′

k(uk)

J′

j(uj) 18 / 43

Plug’n’play architecture

similar control strategies for voltage magnitude

power system physics: power flow & devices

• Di ˙

θi =P ref

i

− Pi − λi τi ˙ Ei =−CiEi(Ei − E∗

i ) − Qi − ei

λi ˙ θi

• droop control:

trade off power injections & frequency

• r voltage

Qi Ei ˙ θi Pi ei Qi Pi =

• j BijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)

Qi = −

• j BijEiEj cos(θi − θj) + GijEiEj sin(θi − θj)

ki ˙ λi = ˙ θi −

• j∈neighbors

aij (J′

i(ui) − J′ i(ui))

κi ˙ ei = −

• j ⊆ neighbors

aij ·

• Qi

Qi − Qj Qj

• −εei
• secondary &

tertiary control: integral errors & diffusive averaging

J′

i(ui)

Qi/Qi

. . . . . .

J′

i(ui)

. . . . . .

J′

k(uk)

Qk/Qk Qj/Qj J′

j(uj)

Qj/Qj

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Experimental validation

in collaboration with Q. Shafiee & J.M. Guerrero @ Aalborg University

! "! #! $! %! &! "!! "&! #!! #&! $!! $&! %!! %&! &!!

Reactive Power Injections Time (s) Power (VAR)

! "! #! $! %! &! #!! %!! '!! (!! "!!! "#!!

A ctive Power Injection Time (s) Power (W)

! "! #! $! %! &! $!! $!& $"! $"& $#! $#& $$!

Voltage Magnitudes Time (s) Voltage (V)

! "! #! $! %! &! %'(& %'() %'(* %'(+ %'(' &! &!("

Voltage Frequency Time (s) Frequency (Hz)

DG DC Source LCL filter

DG

DG

DG Load 1 Load 2

Z

Z

Z

Z

Z

t = 22s: load # 2 unplugged t = 36s: load # 2 plugged back

$$ $$ $ $

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Under the hood: approaches & challenges

1 simple local control: proportional & integral feedback 2 distributed optimization via average consensus & diffusion 3 joint CPS stability & optimality certificates via passivity & Lyapunov

interesting extensions not shown today:

4 robustness to model uncertainties & CPS/comm issues 5 more general energy management tasks & constraints 6 transactive control: interaction with energy markets

• pen problems towards more complex specifications & logic constraints

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Outline

Introduction Basics of Power System Physics & Operation Coordination of Distributed Generation Decentralized Wide-Area Control Online Feedback Optimization Conclusions

Blackout of August 10, 1996

instability of the 0.25 Hz mode in the Western interconnected system

10 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 South Arizona SoCal NoCal PacNW Canada North Montana Utah

Source: http://certs.lbl.gov

0.25 Hz

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A few typical inter-area oscillations in Europe

0.5Hz 0.7Hz 0.22Hz 0.15Hz 0.33Hz 0.48Hz 0.8Hz 0.26Hz

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A closer look at some European incidents

0.5Hz

Myles et al., 1988

2/3/1982

Ding et al., 2007

0.7Hz

8/5/2005

0.26Hz

• f Denish grid

• f Denish grid

disconnection

• f Danish grid

5/29/2007 4/1/2007

AlAli et al., 2007

0.22Hz 0.15Hz

• '#''
• '#'&
• '#',
• '#'(

• '#''
• '#'&
• '#',
• '#'(

! !"#$%&'()' "#$%&'(&%)'*+,-..)$-/#! )0$%&! 1/2%&! 1.)#$! /3$)4%! -#! !!0!5678! $!5+8!

5/1/2005

! !

9/18/2010

AlAli et al., 2011

m d da g w a

Larrson et al., 2012 …

9/18/2010

lso due to transient events.

10/25/2011

0.33Hz 0.48Hz

Uhlen et al., 2008

• 20
• 10

8/14/2007

Wilson et al., 2008

0.8Hz

xx/xx/2007

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Remedies against electro-mechanical oscillations

conventional control

blue layer: interconnected generators fully decentralized control implemented locally

effective against local oscillations ineffective against inter-area oscillations

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Remedies against electro-mechanical oscillations

wide-area control (WAC)

blue layer: interconnected generators fully decentralized control implemented locally distributed wide-area control using remote signals

24 / 43

Setup & challenges in wide-area control design

power network dynamics

generator transmission line wide-area measurements (e.g. PMUs) remote control loops + + + channel noise local control loops

...

system noise FACTS

PSS & AVR

communication & processing

wide-area controller

1 performance objective

(e.g., critical modes) ?

2 signal selection

(sensors & actuators) ?

3 selection of control

channels (I/O pairs) ?

4 decentralized (structured)

control design ? Today:

1 performance metric: integral-quadratic performance index 2 simultaneously optimize control performance & architecture

⇒ fully decentralized & nearly optimal control architecture

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sparsity-promoting

• ptimal wide-area control

Optimal linear quadratic regulator (LQR)

model: linearized ODE dynamics ˙ x(t) = Ax(t) + Bu(t)

• ptimal static control with quadratic H2 - performance index:

minimize J(K) ∞ x(t)TQx(t) + u(t)TRu(t) dt subject to linear dynamics: ˙ x(t) = Ax(t) + Bu(t), linear control: u(t) = −Kx(t). (no structural constraints on K)

! " #

• local
• remote

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Sparsity-promoting optimal LQR

[Lin, Fardad, & Jovanovi´ c ’13]

simultaneously optimize performance & architecture

minimize ∞ x(t)TQx(t) + u(t)TRu(t) dt + γ · card(K) subject to linear dynamics: ˙ x(t) = Ax(t) + Bu(t), linear control: u(t) = −Kx(t). ⇒ for γ = 0: standard optimal control (typically not sparse) ⇒ for γ > 0: sparsity is promoted (problem is combinatorial) ⇒ card(K) convexified by weighted ℓ1-norm

• i,jwij|Kij|

27 / 43

Parameterized family of feedback gains

K(γ) = arg min

K

• J(K) + γ ·
• i,j wij|Kij|
• 28 / 43

case study: New England – New York

Case study: New England – New York test system

model features (242 states):

detailed generator models tuned local controllers ⇒ linearized model for design: ˙ x(t) = Ax(t) + Bu(t)

dominant inter-area modes in power spectral density

15 2 3 5 12 13 14 16 7 6 9 8 1 11 10 4 7 23 6 22 4 5 3 20 19 68 21 24 37 27 26 28 29 9 62 65 66 67 63 64 52 55 2 58 57 56 59 60 25 8 1 54 53 47 30 61 36 17 13 12 11 32 33 34 35 45 44 43 39 51 50 18 16 38 10 31 46 49 48 40 41 14 15 42

NETS NYPS AREA 3 AREA 4 AREA 5 29 / 43

Sparsity-promoting control architecture

γ = 0, card (K) = 1764 γ = 10−4, card (K) = 1746 γ = 0.00015, card (K) = 1603

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Sparsity-promoting control architecture

γ = 0.00023, card (K) = 1475 γ = 0.00031, card (K) = 1353 γ = 0.00041, card (K) = 1231

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Sparsity-promoting control architecture

γ = 0.00047, card (K) = 1106 γ = 0.00054, card (K) = 862 γ = 0.00063, card (K) = 733

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Sparsity-promoting control architecture

γ = 0.00095, card (K) = 609 γ = 0.0011, card (K) = 484 γ = 0.0015, card (K) = 353

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Sparsity-promoting control architecture

γ = 0.0060, card (K) = 191 γ = 0.0655, card (K) = 109 γ = 0.1, card (K) = 107

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Performance vs. sparsity

(J − Jc) /Jc card (K) /card (Kc)

10−4 10−3 10−2 10−1 0.5 1 1.5 2 2.5 3

γ percent

10−4 10−3 10−2 10−1 20 40 60 80 100

γ percent relative performance loss relative sparsity γ = 0.1 ⇒ 2.6 % relative performance loss 6.1 % non-zero elements in K ⇒ fully decentralized control is nearly optimal !

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Eye candy: time-domain simulations

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Under the hood: approaches & challenges

1 algebraic formulation via Gramian and Lyapunov equation 2 non-convexity in K: use homotopy path in γ & ADMM 3 element/block/row-sparsity by appropriate regularizations

angles remaining states element-wise penalty block-wise penalty row-wise penalty

important open problem: entire model is unknown ⇒ data-driven?

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Outline

Introduction Basics of Power System Physics & Operation Coordination of Distributed Generation Decentralized Wide-Area Control Online Feedback Optimization Conclusions

Time constants decreasing & volatility increasing . . .

⇒

real-time & adaptive power flow routing?

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Optimal power flow (OPF) control – in real-time feedback!

grid sensing grid actuation

Power distribution network

plant state x

power demands power generation

OPF

grid sensing grid actuation

Power distribution network

plant state x

power demands power generation

FEED BACK input disturbance

• utput

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Feedback optimization is robust, adaptive, . . . & hard

heavily nonlinear physics give rise to non-convex decision making tasks grid sensing grid actuation

Power distribution network

plant state x

power demands power generation

FEED BACK input disturbance

• utput

Recall the governing physical equations:

◮ active power: Pi =

• j BijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)

◮ reactive power: Qi = −

j BijEiEj cos(θi − θj) + GijEiEj sin(θi − θj)

36 / 43

. . . but physics are smooth!

The power flow manifold

grid equations can be written implicitly as F(x) = 0 set of all possible power flow solutions: P := {x | F(x) = 0} P is a regular submanifold embedded in R4n locally diffeomorphic to tangent plane (sparse linearization)

1 0.5 p2

• 0.5

0.5 q2 1 1.2 1 0.8 0.6 0.4 v 2

node 2 node 1

v1 = 1, θ1 = 0 y = 0.4 − 0.8j v2, θ2 p2, q2 p1, q1

v2

1 g − v1v2 cos(θ1 − θ2)g − v1v2 sin(θ1 − θ2)b = p1

−v2

1 b + v1v2 cos(θ1 − θ2)b − v1v2 sin(θ1 − θ2)g = q1

v2

2 g − v1v2 cos(θ2 − θ1)g − v1v2 sin(θ2 − θ1)b = p2

−v2

2 b + v1v2 cos(θ2 − θ1)b − v1v2 sin(θ2 − θ1)g = q2 37 / 43

Constrained manifold optimization problem

minimize J(x) subject to x ∈ P − → physically feasible input region g(x) ≤ 0 − → operational constraints first-order method in smooth & unconstrained case: follow the gradient “projected” on the manifold

• ur contribution: online

implementation, including constraints, & outsource retraction to the physics

power flow manifold linear approximant

x(t) Gradient of cost function Projected gradient x(t + 1) Retraction 38 / 43

Main idea of feedback manifold optimization

1 output: measure grid state 2 compute: project gradient on

tangent plane & constraints

3 input: actuate subset of

controllable states (injections) ≈ partial projected gradient feedback

Feedback disturbance input plant

• utput

Certificates: simple ideas work best! ⇒ non-actuated states follow, physics enforce retraction, & constraints are enforced ⇒ convergence to strict minima ⇒ cheap & distributable computation ⇒ scheme is robust & adaptive ⇒ appears to work also with inexact linearizations & saddle-point flows

39 / 43

Simple case study

$$$ $$ $

30 MW

scenario: generator # 1 ($$$) connects to larger utility grid generator #2 ($$) is back-up source generator #3 ($) is free solar source time-varying & volatile profiles for loads & solar ⇒ curtailment & saturation

40 / 43

41 / 43

Under the hood: approaches & challenges

1 convergence analysis of

projected dynamical systems on manifolds

2 nonlinear optimization

conditions & algorithms

3 feedback control of

differential-algebraic & nonlinear systems

• pen problems regarding

algorithms, CPS issues, logic, & complex specifications

42 / 43

Outline

Introduction Basics of Power System Physics & Operation Coordination of Distributed Generation Decentralized Wide-Area Control Online Feedback Optimization Conclusions

Conclusions

Summary: energy systems & power grid are a timely & challenging application three representative problems combining methodologies from control ∪ optimization ∪ distributed algorithms ∪ CPS issues many other rich problems at the intersection with econ & technology Opportunities for research of interest to D-INFK: in large-scale infrastructure networks, typically no exact & global model is available ⇒ data-driven & learning-based approaches more complex specifications than mere stability & convergence many open CPS & algorithmic issues in this problem domain ⇒ but results must come with stability, robustness, & safety certificates

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Acknowledgements: my team