1. GLOBAL HYBRID CONTROL OF POWER SYSTEMS Professor Peter P
GLOBAL HYBRID CONTROL OF POWER SYSTEMS Professor Peter P. Groumpos Graduate course Department of Electrical and Computer Engineering A SEMESTER
We discuss a promising approach to do control for general complex systems. I will only describe it in general terms. There are lots of more theoretical aspects.
The aim in this project is to further develop it for power systems.
Co-authors are in USA, Sweden and Singapore respectively, but all work was done while they were in Sydney.

2. OUTLINE Introduction Global Control Ideas
Global Transient Stability and Voltage Regulation
Emergency Voltage Control
Conclusions
After general ideas, look at two specific cases which are more recent work.
Say at outset that the term is just a simple way to capture the aims of:
Control in the large, cf global stability
Control over a large-scale system, cf global in a geographical sense

3. GLOBAL CONTROL IDEAS Introduction Hybrid Models Control Elements
Bifurcations and Global Control
Optimal Coordination and Swarming
Issues for Practical Implementation

4. Trends Environmental limits Load growth Deregulation
All push the system harder
Global control is a response to increasing complexity.

5. 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)

6. 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
These features apply to power systems and many others like chemical processes.

7. 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
Complexity has led to the use of AI methods, often ignoring models; we are here advocating getting the best of both in a framework.
One of the problems with applying modern control methods like adaptive, fuzzy or robust control to power systems is that they are established in a generic framework which is not sensitive to the structure of particular practical systems. Hence many practitioners get the impression that these methods, while sounding appealing at first, are really intellectual games. A more specific challenge is to blend these new ideas into the overall scheme of control which exists, ie excitation control, PSS, network regulators, eg tap-changers, security control. Typically, much of this is already trusted and we only need some new control modules and some overall co-ordination.

8. Hybrid Models dynamic state variables x algebraic state variables ω
parameters/controls l = (q, u, u)
Well-used to these models of DAD form.
x includes generator fluxes, continuous control and load dynamics
y includes network voltages, powers
Nonlinear discrete acting controls, eg tap changers, FACTS, give discrete part
Q represents tunable parameters
n represents (structured) uncertainty
u represents control variables which are yet to be designed

9. Control Elements
Those existing controllers and their tunable parameters which are free to adjust for system-wide purposes
Recall PSS where we design a dynamical feedback and keep some parameters tunable.
Could be any simple or complex controller.
Required to perform well inspite of uncertainty ni
Use qi to implement coordination.

10. Bifurcations and Global Control
Power systems have benefited from bifurcation theory
Most nonlinear control methodology does not recognise bifurcations
There is an enormous literature on nonlinear systems and control.
Most nonlinear control has only considered small systems and without bifurcations (effectively via assumptions).
Our control must work for large systems with lots of bifurcations!

11. Bifurcation Control Avoiding the bifurcation
Eliminating the bifurcation
“Delaying” the bifurcation
Stabilisation through bifurcations
Can we control across boundaries?
This is normal idea in power systems. Avoidance is possible with PQ control, ie keep a margin from instability.
Possible to eliminate or at least delay the bifurcation with nonlinear actions.
Stabilisation of bifurcated solutions, ie as pass through a surface, involves damping any unstable or oscillatory solutions that arise.
Stabilization of

12. What Can Modern Control Do?
Robust control
Adaptive control
Nonlinear control
Fuzzy control
Neural control
RC: For unstructured uncertainty only
AC: Requires stability of frozen systems
NC: In principle, but usual geometric methods have no sensitivity to structure in models.
FC: Does’t want models at all!
NC: Needs to be trained for all circumstances met; will not extrapolate to bifurcations

13. A Strategy
Bifurcation boundaries define domains of operation where dynamical behaviour is qualitatively different
Design controllers for each region and switch between them
A possible control strategy, accepting the boundaries, is to design controllers for each structurally stable region and switch between them in some way in a two-level structure.
Assuming the state-parameter space is partitioned into two domains, the control u takes this form: ue provides the new equilibrium manifold; μ1 and μ2 are functions of an indicator variable expressing the closeness to a particular region or control concern; and u1 and u2 are the local controllers. Has a weighted Sugeno type form used in fuzzy control.
Allows the controller to adjust the individual contributions of the local controllers according to the particular problem being faced at a given time. For instance when an instability occurs in a certain domain or in a certain variable type, eg voltage instability, the indicators driving the weighting functions will automatically adjust the control to emphasise the appropriate actions.

14. Optimal Coordination and Swarming
Nonlinear, multiple controls
Swarming via mi
Optimal coordination via qi
No major problem that the controllers are complex; they will be expressed in software code.
Also, at system-wide level, the controller complexity is related more to the number of parameters that need tuning.
This may involve simply tuning of free parameters, as in the PSS, or a more complicated scheduling exercise which allows for any control redundancy to use scaling and timing according to control costs, dynamic properties and priority - quite complicated for dynamical systems as it requires the solution of the optimal control problem.
When optimal coordination of many such controllers is considered, we can think of numerous controller elements in a complex system as swarming <cite>BON99</cite> to deal with problems as they arise.

15. Global Control Global view of nonlinear system
State space segmentation into structurally stable regions
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

16. Control Algorithms Local tunable controllers, eg robust, adaptive etc
Optimal control (hybrid systems)
Staged optimisation
Predictive control
Speed-gradient and passivity
Structure in HJ eqn, etc
There are enormous possibilities with this framework for constructing and analysing algorithms.

17. GLOBAL TRANSIENT STABILITY AND VOLTAGE REGULATION
Introduction
Dynamical Model
Local Controllers
Global Controller

18. Introduction
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 strategy
The global control objective is achieved with smooth and robust responses with respect to different transient faults.

19. SMIB Power System Model

20. Local Controllers
Transient controller:
Voltage controller:

21. A Switching Controller
(t0 is the fault occuring time, ts is the switching time)
Disadvantages:
The switching time is fixed;
Not robust with respect to different faults.

22. 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

24. Global Controller Design
Operating region membership function:
Z variable is the key to getting excitation to attend to the problems as they arise

25. Global Controller Design
Global control law:
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

26. Simulations 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; l=0.04.

28. We design smooth nonlinear feedback control law for the excitation system, such that the closed-loop power system is transiently stable when subjected to a severe disturbance, and restores the steady pre-fault voltage value after the disturbance.

29. EMERGENCY VOLTAGE CONTROL
Introduction
System Modelling
Control Problem Formulation
Tree Search Method
Simulation Results
Other Possibilities
Reference:
M Larsson, DJHill and G Olsson, Emergency voltage control using searching and predictive control, International J of Electrical Power and Energy Systems,

30. 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
FACTs
Traditionally, done one by one, trial and error
These are typically all switching type controls which must work with continuously acting ones.

31. Why coordination Difficulty minimum overall effort / cost
maximum control effect
better voltage profile, ie. better quality of supply
Difficulty
Combination of dissimilar controls

32. 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?

33. Problem formulation subject to: (i) controls capability constraints
(ii) stability constraints

34. Optimal Scheduling (=0.2)
We have studied this approach for a large system, ie NSW grid (Wu et al, IEEE Trans to appear).

35. 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
DDP emerged as an obvious way to deal with staging of the control. But it is just a way to do discrete optimal control. There are connections to other optimal control techniques like MPC, which have different tools.
MPC has developed to handle considerable complexity.

36. In contrast to normal MPC, we now have a specific set of basic control actions. There are moves in this direction mathematically, but here the actions are physical.
Also there are lots of combinations to check.

37. 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 computers!

38. Numerical example

39. Simulation Example (Fig 17)
Response with ESP, LMPC, ESPLO approximate predictors

40. CONCLUSIONS Complex System Features Global Control
Possibilities for Power Systems

41. 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 conditions
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
Of course optimal tuning is done in practice, eg all the PSS, but now asking for more, ie optimal staging of dissimilar controls.
This leads to concept of Global Control.
Use the term global here in both senses:
Large-scale, geographically, ie the globe
In the large or global stability, ie wrt to the state space
All the usual predictive, adaptive, neural methods break down when system moves across bifurcation boundaries.
Set up control actions for each region.
A picture can be use of the control actions ‘swarming’ on problems as they arise as detected by indicators.

42. Global Control Global view of nonlinear system
State space segmentation into structurally stable regions
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

43. 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.