Real-time Optimization for Power Distribution …...Real-time Optimization for Power Distribution...
Transcript of Real-time Optimization for Power Distribution …...Real-time Optimization for Power Distribution...
Real-time Optimization for Power Distribution SystemsAdrian Hauswirth
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 1
Agenda
Introduction
Facts and terminology everyone should know about
Tutorial in control & optimization
Transmission system operations
Active distribution grids
Research: combining control and optimization in a novel way
Conclusion
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 2
Electric Energy Supply
[BFE, Schweizerische Gesamtenergiestatistik 2015]
Swiss energy consumption by carrier (2015)
16,0%
34,7%25,0%
13,5%10,8%
Fossil fuels
Gasoline
Electricity
Natural Gas
Others
Power consumption
Electric energy consumption
Extra-HighVoltage
HighVoltage
Low Voltage
Transmission GridDistribution Grid
[Wikipedia, MBizon, 2010]
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 3
Electric Energy Supply
[BFE, Schweizerische Gesamtenergiestatistik 2015]
Swiss energy consumption by carrier (2015)
16,0%
34,7%25,0%
13,5%10,8%
Fossil fuels
Gasoline
Electricity
Natural Gas
Others
Power consumption
Electric energy consumption
Extra-HighVoltage
HighVoltage
Low Voltage
Transmission GridDistribution Grid
[Wikipedia, MBizon, 2010]
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 3
Electric Energy Supply
[BFE, Schweizerische Gesamtenergiestatistik 2015]
Swiss energy consumption by carrier (2015)
16,0%
34,7%25,0%
13,5%10,8%
Fossil fuels
Gasoline
Electricity
Natural Gas
Others
Power consumption
Electric energy consumption
Extra-HighVoltage
HighVoltage
Low Voltage
Transmission GridDistribution Grid
[Wikipedia, MBizon, 2010]
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 3
Agenda
Introduction
Facts and terminology everyone should know about
Tutorial in control & optimization
Transmission system operations
Active distribution grids
Research: combining control and optimization in a novel way
Conclusion
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 4
Fact 1:
Capacity 6= Flexibility
signs of inflexibility:• price volatility, negative market prices• significant renewable energy curtailment• balancing violations, frequency
excursions, etc.
increasing flexibility:• interconnected systems• fast generators, flexible loads, storage• market design, communication
infrastructure
Assumption 1
Enough capacity & flexibility such that demand can be met at all times.
[NREL, "Flexibility in 21st Century Power Systems," 2014]P L
Power
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 5
Fact 2:
supply 6= demand→ frequency deviation
50Hz 51Hz49Hz
Assumption 2
The power system is stabilized and operates in steady-state, i.e., at 50Hz.
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 6
Terminology
congestion→ cascading line failures(overloaded transmission lines)
under-/overvoltage→ voltage collapse
undervoltage
power demand
overvoltage
generationP L
Power
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 7
Agenda
Introduction
Facts and terminology everyone should know about
Tutorial in control & optimization
Transmission system operations
Active distribution grids
Research: combining control and optimization in a novel way
Conclusion
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 8
Primer in Control Engineering
Feedback actuate
observe
[Longchamp, 1995]
open-loop system (feedforward control):
Controller Systemr
u
y
closed-loop system (feedback control) :
Controller Systemr +
u
y
−
Feedback control can achieve:• no steady-state error, i.e., r(t) = y(t) for t→∞• stability: output y remains bounded (for bounded input r)• robustness: reduce influence of model uncertainties
r reference valueu control signaly output signal
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 9
Example: Frequency Control in Power Systems
supply 6= demand→ freq deviation
50Hz 51Hz49Hz
FrequencyControl
PowerSystem
50Hz +u
y
frequency measurement
−
49.935 Hz
50 Hz
50.065 Hz
1200MW
Power plant output Balancing service
15min5min0.5min
[swissgrid, 2010]
0
5000
10000
15000
20000
25000
30000
35000
2011 2012 2013 2014 2015leng
th o
f fre
quen
cy d
evia
tions
[s]
Frequency deviation ≥ 75 mHz[Elcom/swissgrid, 2010]
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 10
Steady-state AC power flow model
25
34
6
78
910
11
12 13
nodal voltagecurrent injectionpower injections
line impedanceline currentpower flow
Ohm’s Law Current Law
AC power
AC power flow equations
(all variables and parameters are -valued)P L
Power
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 11
Power system optimization
minimize φ(x)subject to x ∈ X
φ : Rn → R objective functionX ⊂ Rn constraint set
0
50
100
150
200
0 10 20 30 40 50 60 70 80 90 100
mar
gina
l cos
ts in
€/M
Wh
Capacity in GW
RenewablesNuclear energyLigniteHard coalNatural gasFuel oil
[Cludius et al., 2014]
(simple) Optimal Power Flow (OPF) problem
• minimize cost of generation
• respect generation capacity
• satisfy AC power flow laws
• no over-/under-voltage
• no congestion
minimize∑
k∈Ncostk(P G
k )
subject to P G + jQG = P L + jQL + diag(V )Y ∗V ∗
pk≤ P G
k ≤ pk, qk≤ QG
k ≤ qk ∀k ∈ N
vk ≤ Vk ≤ vk ∀k ∈ N|Pkl + jQkl| ≤ skl ∀{k, l} ∈ E
Y admittance matrix, P Gk , QG
k power generation,P Lk , QL
k load, {vk
, vk, . . .} nodal limits, skl line flow limit
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 12
Power system optimization
minimize φ(x)subject to x ∈ X
φ : Rn → R objective functionX ⊂ Rn constraint set
0
50
100
150
200
0 10 20 30 40 50 60 70 80 90 100
mar
gina
l cos
ts in
€/M
Wh
Capacity in GW
RenewablesNuclear energyLigniteHard coalNatural gasFuel oil
[Cludius et al., 2014]
(simple) Optimal Power Flow (OPF) problem
• minimize cost of generation
• respect generation capacity
• satisfy AC power flow laws
• no over-/under-voltage
• no congestion
minimize∑
k∈Ncostk(P G
k )
subject to P G + jQG = P L + jQL + diag(V )Y ∗V ∗
pk≤ P G
k ≤ pk, qk≤ QG
k ≤ qk ∀k ∈ N
vk ≤ Vk ≤ vk ∀k ∈ N|Pkl + jQkl| ≤ skl ∀{k, l} ∈ E
Y admittance matrix, P Gk , QG
k power generation,P Lk , QL
k load, {vk
, vk, . . .} nodal limits, skl line flow limit
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 12
Agenda
Introduction
Facts and terminology everyone should know about
Tutorial in control & optimization
Transmission system operations
Active distribution grids
Research: combining control and optimization in a novel way
Conclusion
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 13
Optimization and control in power system operations
Optimization Controller Systemr +
u
y
−
short-termplanning
D-14 . . . D-2(SC-OPF)
day-aheadscheduling
D-1(SC-OPF)
manualredispatch
low-level,automaticcontrollersdroop, AGCAVR, PSS
Dynamic PowerSystem Modelx = f(x, u, δ)
δ
u
x
Steady-state modelh(x, δ) = 0 (AC power flow)Optimization stage
generationsetpoints
stateestimation
prediction (load, generation, downtimes)
schedule
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 14
Optimization and control in power system operations
Optimization Controller Systemr +
u
y
−
short-termplanning
D-14 . . . D-2(SC-OPF)
day-aheadscheduling
D-1(SC-OPF)
manualredispatch
low-level,automaticcontrollersdroop, AGCAVR, PSS
Dynamic PowerSystem Modelx = f(x, u, δ)
δ
u
x
Steady-state modelh(x, δ) = 0 (AC power flow)Optimization stage
generationsetpoints
stateestimation
prediction (load, generation, downtimes)
schedule
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 14
National & international redispatch
• in case of unforseen congestion orvoltage problems
• (manually) dispatched on a15-minute timescale
1 588
2010
5 030
2011
7 160
2012
7 965
2013
8 453
2014
15 811
2015
Redispatch actions in the German transmission gridin hours
[Bundesnetzagentur, Monitoringbericht 2016]
371.9267.1
352.9227.6
154.8
secondary frequencycontrol reserves
104.267.4
156.1106.0
50.2
tertiary frequencycontrol reserves
27.068.3
33.026.732.6
reactive power
41.6164.8
113.3185.4
411.9
national & internat.redispatch
111.882.385.2
103.4110.9
primary frequencycontrol reserves
Cost of ancillary services of German TSOsin mio. Euros
2011 2012 2013 2014 2015[Bundesnetzagentur, Monitoringbericht 2016]
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 15
Agenda
Introduction
Facts and terminology everyone should know about
Tutorial in control & optimization
Transmission system operations
Active distribution grids
Research: combining control and optimization in a novel way
Conclusion
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 16
Traditional distribution grids
short-termplanning
day-aheadscheduling
manualredispatch
low-levelcontrol
TransmissionSystem
DistributionSystems
Steady-state model
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 17
Distribution grids with high renewable penetration
Challenges
• congestion (in urban grids)• under-/over-voltage (in rural grids)• hard to predict individual load/generation profiles
single PV plant
pow
er
time of day time of day
single residentialload profile
pow
er
Opportunities
• new degrees of freedom (flexibility!)• fast, inverter-based actuation• inexpensive, reliable communication
[IEEE 123 bus test feeder]P L
Power
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 18
The future of active distribution systems
short-termplanning
day-aheadscheduling
manualredispatch
low-levelcontrol
TransmissionSystem
optimization?smart charging,
load managementetc.
??local,
heuristiccontrol
DistributionSystems
Steady-state model
δprediction (load, distributed generation)
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 19
The future of active distribution systems
short-termplanning
day-aheadscheduling
manualredispatch
low-levelcontrol
TransmissionSystem
optimization?smart charging,
load managementetc.
??local,
heuristiccontrol
DistributionSystems
Steady-state model
δprediction (load, distributed generation)
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 19
Agenda
Introduction
Facts and terminology everyone should know about
Tutorial in control & optimization
Transmission system operations
Active distribution grids
Research: combining control and optimization in a novel way
Conclusion
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 20
Research: “feedback optimization”
Optimization problem
minimize f(u, y)subject to h(u, y) = 0
u ∈ Uy ∈ Y
feedbackoptimizer
staticsystem
h(u, y) = 0
actuateu
ymeasure
• no need to solve optimization problem numerically• algebraic system constraint enforced automatically• relies static system (or asymptotically stability with fast settling time)
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 21
The intuition behind feedback optimization
Update control variables
uk+1 = uk + ∆u ,
measurements adapt to
yk+1 ≈ yk + ∆y
where[∆u ∆y
]∈ kerDh(uk, yk).
Main Idea: Choose ∆u such that[∆u ∆y
]is a
descent direction that is feasible w.r.t. U and Y .
Optimization Problem
minimize f(u, y)subject to h(u, y) = 0
u ∈ Uy ∈ Y
feedbackoptimizer
staticsystem
h(u, y) = 0
actuateu
ymeasure
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 22
Related work
Dynamical systems that solve optimization problems:
• Isospectral flows on matricesApplications: sorting lists, computing eigenvalues, solve LPs[Brockett 1988], [Bloch 1990], [Helmke and Moore 1994]
• Arrow-Hurwicz-Uzawa flows for “soft-constrained” strongly-convex optimization problemsApplications: distributed consensus-based optimization[Arrow et al. 1958], [Kose 1956], [Feijer and Paganini 2010], [Cherukuri et al. 2016], [Simpson 2016]
• Projected dynamical systems for “hard-constrained” convex optimization problemsApplications: variational inequalities[Nagurney and Zhang 1996], [Heemels et al. 2000], [Cojocaru 2006]
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 23
Projected dynamical systems for feedback optimization
Feedback optimization with saturation:minimize f(u, y)
subject to h(u, y) = 0u ∈ Uy ∈ Y
feedbackoptimizer
static systemh(u, y) = 0
u
y
U
Projected dynamical systems:
Initial value problem:
x = ΠK (x, F (x)) , x(0) = x0
where ΠK(x, v) ∈ arg minw∈TxK
||v − w||.
F : Rn → Rn vector field, K ⊂ Rn closed domain, TxK tangent cone at x
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 24
Projected gradient descentTo find minimum on φ on a nonconvex K follow negative gradient vector field:
x = ΠK (x,−gradφ(x)) , x(0) = x0 .
• Does a solution trajectory exist? Is it unique? (yes, if K is convex, otherwise unknown)• Are solution trajectories (asymptotically) stable?• Do solution trajectories converge to a minimizer of φ?
Corollary [AH et al. 2016] (simplified)
Let x : [0,∞)→ K be a (Carathéodory-)solution of
x = ΠK (x,−gradφ(x)) x(0) = x0 .
Then, if φ has compact level sets on K sets x(t) will converge to a critical point x∗ of φ on K.Furthermore, if x∗ is asymptotically stable then it is a local minimizer of φ on K.A. Hauswirth, S. Bolognani, G. Hug, and F. Dörfler, “Projected gradient descent on Riemannian manifolds with applications to online power system optimization,” Allerton Conference, 2016
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 25
Tracking OPF solution despite intermittency
G1
G2 C1
C3 C2
W
S
Generator
Synchronous Condensor
Solar
Wind
G
C
S
W
0 2 4 6 8 10 12 14 16 18 20 22 240
100200300400
Time [hrs]
Aggregate Load & Available Renewable Power [MW]Load Solar Wind
Controller: Penalty + SaturationA. Hauswirth, S. Bolognani, F. Dörfler and G. Hug, “Online Optimization in Closed Loop onthe Power Flow Manifold,” Powertech Conference, 2017, accepted
Time [hrs]
0.95
1
1.05
1.1Bus voltages [p.u.]
0
0.5
1
Branch current magnitudes [p.u.]0.9
0 2 4 6 8 10 12 14 16 18 20 22 240
50100150200
Active power injection [MW]
Gen1 Gen2 Solar WindP L
Power
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 26
Further topics
• Distributed control/optimization: reduce information exchange to neighbor-to-neighborcommunication[Bolognani et al. 2013], [Dall’Annese and Simmonetto 2016], [Li et al. 2014], [Gan and Low 2016], ...
Further desirable properties:
• plug-and-play: no tuning required, distributed performance certificates
• privacy-preserving: no need to share private information
• incentive-compatible: individual, rational choices lead to social optimum
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 27
Agenda
Introduction
Facts and terminology everyone should know about
Tutorial in control & optimization
Transmission system operations
Active distribution grids
Research: combining control and optimization in a novel way
Conclusion
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 28
Summary
• Energy transition opens up new challenges in the operation of power systems at all gridlevels.
• Optimization and control theory are essential for a safe and reliable power supply.
• New methods are required to robustly stabilize & optimize power grids under largeuncertainty and in real-time.
• Feedback optimization is a new paradigm that tries to combine the advantages of bothworlds.
• Simulations look promising, but the math behind is still active research.
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 29
Thanks
Supervisors: Prof. Dr. Florian DörflerProf. Dr. Gabriela HugDr. Saverio Bolognani
Project students: Alessandro ZanardiJózsef Pázmány
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 30
Questions
Adrian HauswirthPhD student
ETH ZurichAutomatic Control LaboratoryPower Systems Laboratory
Phone +41 44 632 [email protected]
P LPower
Systems
Laboratory
AutomaticControl
Laboratory Adrian Hauswirth 2017-05-23 31