ABB Case Study: Optimal Control and...
Transcript of ABB Case Study: Optimal Control and...
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ABB Case Study: ABB Case Study: Optimal Control and AnalysisOptimal Control and Analysis
T. Geyer, M. T. Geyer, M. MorariMorari, , M. LarssonM. Larsson
Automatic Control LaboratoryAutomatic Control LaboratoryETH ZurichETH Zurich ABBABB
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1. Overview
2. Modeling
3. Optimal Control Problem
4. Sensitivity Analysis
5. Conclusions and Outlook
OutlineOutline
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1. Overview
2. Modeling
3. Optimal Control Problem
4. Sensitivity Analysis
5. Conclusions and Outlook
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ABB Case Study: ABB Case Study: OverviewOverview
Generator 1:Ø infinite bus
Generator 2:Ø internal controller (AVR)
Transformer:Ø internal controller (FSM)
Load:Ø aggregate dynamic load
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Collapse ScenarioCollapse Scenario
2. tap changer control
3. generator overexcitationlimiter activated
4. voltage collapse
1. load recovery
Line tripping (L3) at t=100s ...
... leads to voltage collapse.
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Why do we need Control?Why do we need Control?
Ø Power system designed for N-1 stability
Ø Power system collapse extremely expensive
Ø Time-constants rather small
Ø Power system operated closer to stability limit
because of• deregulation of energy market• environmental concerns• increase of electric power demand
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1. Overview
2. Modeling
3. Optimal Control Problem
4. Sensitivity Analysis
5. Conclusions and Outlook
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Generator 2: Generator 2: OverviewOverview
purpose:Ø generates limited power
assume:
Ø quasi-steady state behaviour
2 (static) components:
Ø automatic voltage regulator (AVR)
Ø synchronous machine
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Generator 2: Generator 2: ModelModel
Synchronous machine
static I/O-behaviour
generates elect.power
AVR saturating P-controller with input nonlinearity
controls terminalvoltage V2m
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Transformer: Transformer: OverviewOverview
purpose: Ø steps down voltageØ controls load-voltage V4m
by adjusting tap ratio 1:n
2 components:Ø transformerØ controller of tap ratio
manipulated variable:Ø voltage reference V4m,ref
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Transformer: Transformer: ControllerController
input nonlinearity:
logic:
finite state machine:
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Transformer: Transformer: EquationsEquations
transformer equations:
Ø nonlinear equationsØ relate V3, V4, I3, I4
depending on n
block diagram:
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purpose:Ø power consumption
assume: aggregate dynamic load Ø aggregate: distribution network with
various loads (motors, heating, lighting)Ø dynamic: self-restoring following a
disturbance
manipulated variable:Ø load shedding sL
Load: Load: OverviewOverview
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Load: Load: Self RestorationSelf RestorationFollowing a disturbance in the supply voltage, the active and reactive powersdrawn by the load are restored by internal controllers (like thermostats).
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Load: Load: ModelModelactive power:
reactive power:
whereand = load shedding (discrete manipulated var.)
output equations:
block diagram:
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Linear Linear SubmodelsSubmodels
generator 1:Ø infinite busØ supplies constant voltage V1 = 1.03
capacitor bank:Ø stabilizes power systemØ discrete manipulated variable
network: Ø algebraic equations at the buses
according to Kirchhoff’s laws
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Hybrid ModelHybrid ModelHybrid system:Ø saturationØ finite state machine with logicØ nonlinearitiesà pwa functionsØ discrete manipulated variables
Dimensions: Ø 2 ordinary diff. equationsØ 29 algebraic equations:
Ø11 linear, 18 nonlinear
Ø 3 states:Ø2 continuous, 1 discrete
Ø 3 manipulated variables:Ø1 continuous, 2 discrete
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Hybrid Model Hybrid Model ((ctdctd.).)
approximate by PWA functions
2 ODEs, 29 algebraic constraints saturation, FSM, logic
nonlinear DAE: discrete events:
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MLD FormulationMLD Formulation
where: auxiliary binary variablesauxiliary continuous variables
if problem is well-posed: for a given and the inequality
defines uniquely and .
… leads to 49 , 86 variables and 409 constraints
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1. Overview
2. Modeling
3. Optimal Control Problem
4. Sensitivity Analysis
5. Conclusions and Outlook
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Ø Control objectives: Ø stabilize V4m
Ø min. load shedding sL
Ø keep bus voltages withincertain limits V2m, V3m, V4m
ØManipulated variables:Ø ultc voltage reference: V4m,ref
Ø capacitor switching: sC
Ø load shedding: sL
Ø Fault:Ø line outage
Control ProblemControl Problem
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Model Predictive ControlModel Predictive Control
subject to
Ø MLD model:
Ø Soft constraints on bus voltages:
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Controller StructureController Structure
Controller of tap changer highly sensitive to
à Decompose MPC in cascaded controller
staticMPC
prediction model with as man. variable
• MPC sets tapping strategy
• Static controller chooses accordingly
• Mechanical wear results from tap changes
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Tuning of Cost FunctionTuning of Cost Function
choose such that:
Ø nominal control (no constraint violated):
allow ultc voltage reference and capacitor bank
Ø emergency control (constraints violated):
allow all controls including load-shedding
Penalty on u:
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Tuning of Cost Function (Tuning of Cost Function (ctdctd.).)Penalty on violation of soft constraints:
violation of i-th constraint
slack
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Preliminary ResultsPreliminary Results
fault
capacitor bankswitching
stop tapping
constraint violation
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Compensation for Output ErrorCompensation for Output Error
nonlinear DAE: discrete events:
filtered
… leads to reduced output error
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1. Overview
2. Modeling
3. Optimal Control Problem
4. Sensitivity Analysis
5. Conclusions and Outlook
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Nonlinear Hybrid MPCNonlinear Hybrid MPCQuestions:• Is the MPC cost function tuned properly?• How large is the max. tolerable approximation error?
à Simulate nonlinear hybrid MPC with exact model
Implementation:• branch on discrete inputs over prediction horizon• use bound techniques• Simulink (Modelica): used to simulate the model response
and to evaluate the cost function
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Nominal CaseNominal Caset=120s: cap. switching
t=180, 570s:constraint viol.predicted
no load shed.
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Parameter Uncertainty: P0 +0.5%Parameter Uncertainty: P0 +0.5%t=120s: cap. switching
no load shed.
small offset in bus voltages
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1. Overview
2. Modeling
3. Optimal Control Problem
4. Sensitivity Analysis
5. Conclusions and Outlook
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ConclusionsConclusions
Ø MPC cost function:• use cascaded control scheme,
• penalize tap changes,
• allow for short constraint violations and
• prediction horizon N=2 sufficient.
Ø Max. tolerable approximation error:• small parameter uncertainties lead to output offset,
• if P0 > +1%: nominal control moves can’t stabilize system,
• system parameters and structure are known very accurately (PMU)
except P0 (variations of up to 0.3% per minute)
à high accuracy for PWA approximation mandatory
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OutlookOutlookØ Reformulate MLD model using subdivided model
Ø Compensate for output error
Ø Reduce computational time
• search heuristics
• exploit model structure
Ø Large-scale power system
Ø Reachability analysis
Ø Controllability and observability
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Reformulation of MLD ModelReformulation of MLD Model
formulate as MLD modelapproximate by PWA functions with 4 real inputs
for all 16 combinations of discrete inputs
nonlinear DAE: discrete events:
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The endThe end
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Penalty on V4m,ref and P0 +0.5%Penalty on V4m,ref and P0 +0.5%t=120s: cap. switching
t=180s:constraint viol.predicted, but change in V4m,ref not effective
t=210s: load shed.
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Penalize all Constraint Viol. and P0 +0.5%Penalize all Constraint Viol. and P0 +0.5%constraint viol.for k=0 penalized, too
t=120s: cap. switching
t=840s:constraint viol.NOT predicted
t=870s:load shedding
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Static StateStatic State--EstimationEstimation
nonlinear DAE: discrete events:
… leads to reduced output error
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G
Instability: line outageInstability: line outage
old operating pointinstability
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G
Countermeasures: load sheddingCountermeasures: load shedding
old operating point
new operating point