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Bulk Power System Dynamics and Control V
David J Hill
City University of Hong Kong
(on leave from Sydney University)
Co-authors: Yi Guo, Mats Larsson, Youyi Wang
 Introduction
 Global Control Ideas
 Global Transient Stability and Voltage Regulation
 Emergency Voltage Control
 Conclusions
 Introduction
 Hybrid Models
 Control Elements
 Bifurcations and Global Control
 Optimal Coordination and Swarming
 Issues for Practical Implementation
Environmental limits
Load growth
All push the system harder
Mathematical Complexity
Stability margins reducing, ie more difficult
dynamics (nonlinearity)
Interconnection, ie larger-scale
More uncertainty
System structure changing
 No nominal operating point
 Less modelling data
Coordinated control with mixed signals,
costs and actions (heterogeneity)
Specific Features of Complexity
 Large-scale network structure
 Controls embedded, some with scope for tuning;
further design must allow for and enlist
 Hierarchical control structure
 Control actions largely determined and have diverse
timing, cost and priority
 Control goals are multi-objective with local and global
requirements which vary with operating state
 Control interacts with planning
Control Challenge
In general, we need a high-level version
of distributed adaptive control which
“swarms” around a complex system
attacking problems as they arise, but
keeping a meta-view so that other
problems are not ignored
ie. “reconfigurability” built in
Hybrid Models
• dynamic state variables x
• algebraic state variables ω
• parameters/controls l = (q, u, u)
Control Elements
Those existing controllers and their
tunable parameters which are free to
adjust for system-wide purposes
ui = U i ( xi , i , zi (k );q i ,i )
Bifurcations and Global Control
 Power systems have benefited from
bifurcation theory
 Most nonlinear control methodology
does not recognise bifurcations
Bifurcation Control
Avoiding the bifurcation
Eliminating the bifurcation
“Delaying” the bifurcation
Stabilisation through bifurcations
Can we control across boundaries?
What Can Modern Control Do?
 Robust control
 Adaptive control
 Nonlinear control
 Fuzzy control
 Neural control
A Strategy
Bifurcation boundaries define domains
of operation where dynamical behaviour
is qualitatively different
Design controllers for each region and
switch between them
u = ue  1u1   2u2
Optimal Coordination and Swarming
ui = U i ( xi ,  i , zi ( k );q i , i )
u = u e    i ui
• Nonlinear, multiple controls
• Swarming via i
• Optimal coordination via qi
Global Control
 Global view of nonlinear system
 State space segmentation into structurally stable
 Identification of regional controllers
• local models
• various control objectives
• different regional controller design approaches
 Combination and coordination of regional
controllers, e.g. scheduling, switching, hierarchical,
hybrid control
Control Algorithms
 Local tunable controllers, eg robust, adaptive
 Optimal control (hybrid systems)
 Staged optimisation
 Predictive control
 Speed-gradient and passivity
 Structure in HJ eqn, etc
 Introduction
 Dynamical Model
 Local Controllers
 Global Controller
Y Guo, DJHill and Y Wang, Global transient stability and voltage regulation for
power systems, IEEE Trans Power Systems, to appear.
 Transient stability and voltage regulation are required at different
stages of system operation
 Deal with the two problems separately, or employ a switching
strategy of two different controllers which causes a discontinuity
of system behaviour
 Aim to design global control law to co-ordinate the transient
stabilizer and voltage regulator, using heterogeneous control
 The global control objective is achieved with smooth and robust
responses with respect to different transient faults.
SMIB Power System Model
Local Controllers
 Transient controller:
 Voltage controller:
A Switching Controller
uf = {
uf 1
uf 2
t =t 0
t = ts
(t0 is the fault occuring time, ts is the switching time)
• The switching time is fixed;
• Not robust with respect to different faults.
Global Controller Design
 The fault sequence is NOT known beforehand
 The control law in each region is specified to be the usual type
developed from model-based (nonlinear) control techniques
 The global control law is the above weighted sum of local
controllers type, which achieves smooth transitions between the
transient period and post-transient period
 The controller is globally effective in the presence of different
uncertain faults; also the controller is robust with respect to
parameter uncertainties
Global Controller Design
 Operating region membership function:
Global Controller Design
 Global control law:
u f =  u f 1   V u f 2
 Advantages:
• Control action is determined by online measurement of
power frequency and voltage, which makes it unnecessary
to know the fault sequence beforehand
• The controller is globally effective in the presence of different
uncertain faults
• The controller inherits the properties of local controllers, i.e.,
it is robust with respect to parameter uncertainties
 Temporary fault + permanent fault:
Stage 1: The system is in a pre-fault steady state
Stage 2: A fault occurs at t=t0
Stage 3: The fault is removed by opening the breakers of the
faulted line at t=t1
Stage 4: The transmission lines are restored at t=t3
Stage 5: Another fault occurs at t=t4
Stage 6: The fault is removed by opening the breakers of the
faulted line at t=t5
Stage 7: The system is in a post-fault state
In the simulations, t0=0.1s, t1=0.25s, t3=1.4s, t4=2.1s, t5=2.25s;
 Introduction
 System Modelling
 Control Problem Formulation
 Tree Search Method
 Simulation Results
 Other Possibilities
M Larsson, DJHill and G Olsson, Emergency voltage control using
searching and predictive control, International J of Electrical Power and
Energy Systems, to appear.
Coordinated Control Scheme
(Popovic, Hill and Wu, presented in Santorini)
Provide voltage regulation
Provide security enhancement
Control actions
• reactive power compensation
• tap regulation
• load control
Traditionally, done one by one, trial and
Why coordination
• minimum overall effort / cost
• maximum control effect
• better voltage profile, ie. better quality of supply
• Combination of dissimilar controls
Optimal scheduling of control actions
 Actual control sequence accounts for
• combination of dissimilar controls
• different response speeds
• different dynamic characteristics
• priority
 Optimal scheduling by
• economic cost
• availability of controls
 When, how to take actions at each step?
Problem formulation
J ( p) :=  C ( xt , pt ),
pt  R m , xt  R m
t =1
subject to:
(i) controls capability constraints
 pt  pt
t = 1,2...N
(ii) stability constraints
S m arg in( pt )  Sm arg in ( pt 1 )  
Optimal Scheduling (=0.2)
Model Predictive Control approach
 Widespread in process control
 Multivariable, nonlinear allowed naturally
 Constraint handling
 Future behaviour predicted for many
candidate input sequences
 Optimal input sequence selected by
(constrained) optimization
Optimization by search
 All controls are switching actions
 Combinatorial optimization problem
 Organize control state space in tree structure
 Search tree for optimum
 Combinatorial explosion
 Search heuristics
 Similar problem as solved in chess
Numerical example
Simulation Example (Fig 17)
Complex System Features
Global Control
Possibilities for Power Systems
Complex System Features
Control over wide ranges of operating conditions
Nonlinearity, ie control “in the large”
High dimension, ie large-scale
Multiple steady-state solutions
Qualitatively different behavior under different operating
Lack of complete explicitly analytical description
Indices flag proximity to problems, ie bifurcations
‘Elements’ of control physically based
Accommodate different control objectives
Optimal coordination required
Global Control
 Global view of nonlinear system
 State space segmentation into structurally stable
 Identification of regional controllers
• local models
• various control objectives
 Optimal combination and coordination of regional
controllers, e.g. scheduling, switching, hierarchical,
hybrid control
 Swarming type adaptive control
Possibilities for Power Systems
 Power systems are increasing in complexity
 Security limits have huge financial implications
 Control-based expansion
 Modelling, analysis, control might all need to be redone
 Develop hybrid, global models and control
 Develop swarming type optimal hierarchical control of all
available devices
 Multi-level swarming, ie devices to system levels, according to
where problem is
 Adaptively group up the influential and available controls of
various types to attack a problem as and when it arises
 Project in HK considers power electronic controls.