View
51
Download
1
Category
Preview:
DESCRIPTION
Placing Controllers in a System. Overview of Class So Far…. General Introduction Deregulation Traditional approaches to control Static devices. Type of problems. Steady State Transient Stability Inter-Area Oscillations Subsynchronous Resonance Voltage Stability. Introduction to FACTS. - PowerPoint PPT Presentation
Citation preview
Placing Controllers in a System
Overview of Class So Far…
General Introduction Deregulation Traditional approaches to control Static devices
Type of problems
Steady State Transient Stability Inter-Area Oscillations Subsynchronous Resonance Voltage Stability
Introduction to FACTS
Detailed analysis of devices Thyristor controlled inductor SVC Statcom TCSC
System Modeling
Simplified models for use in system simulations and analysis Statcom TCSC (see Reference [1]) UPFC
Set up system equations to include FACTS devices
Get block diagrams or differential equations for device
Define device states Define device inputs Express device model in terms of existing
system states & device states Augment system equations
Use these devices to fix system problems!
OK, Say you work at an ISO & are in charge of ensuring system reliability. You've had 5 major blackouts in the last 3 years that have involved the propagation of problems from one part of the system to another. The utility members are convinced that the addition of a FACTS device or two will solve the problems & they even agree to pay!
Now what do you do? . . .
Brainstorming Activity: What things do you need to worry about? Break into groups of 2 or 3 Take 3 minutes & write down as many things as you
can No criticism allowed, Go for variety, Go for quantity not
quality
Questions:
Where do I put it? Controller Location What should it do? Controller Function
Things to consider:
More than one problem More than one system condition More than one mode More than one tool
Problems
Steady State Insure operating point is within acceptable limits
Interarea Oscillations Damp eigenvalues
Transient Stability Provide sufficient synchronizing and damping torque
Subsynchronous Resonance Avoid resonance frequencies
Voltage Stability Stabilize eigenvalues and avoid bifurcations
Interarea Oscillation Mitigation
Analysis Tools (Mostly Linear) Controllability and Observability Participations Sensitivities Power Oscillation Flows
Linearized System
x’ = Ax + Bu y = Cx + Du
Eigenvalues are i, i = 1, nstates Right Eigenvectors ri , R is matrix of ri's Left Eigenvectors (rows) i, L is matrix of i's L = R-1
Perform variable transformation to Jordan Form
x = Rz (Inverse transform z = Lx) Substituting into system equations . . .
Rz’ = AR z + B uy = CR z + Du
Multiply through by L = R-1
LRz’ = z’ = LAR z + LB u
y = CR z + Du
Controllability and Observability
Modal controllability matrix = LB tells how strongly connected the inputs (u's) are to
each of the modes Modal observability matrix = CR
tells how well we can measure or "see" each mode in the outputs (y's)
Participations
Connection strengths between modes and states
General participation pi hk = ri h lhk
link between ith (obs.) & kth (con.) states through mode h
Participation Factors pi h = ri h lh i link between mode h & state i
Eigenvalue Sensitivities
i’ = i/p
p some parameter of the system Tells how easily we can move an eigenvalue by
changing a parameter In general, i' = li A' ri
Sensitivities are also related to participations
pihk = h’ for p = aki (element of A) pih = h’ for p = akk (diagonal element)
u(t) x(t)
p
rest of system
xi
xk
Sensitivity with Controllers
The "Hybrid System"
The Power System
x’ = Ax + Bu y = Cx
assume no direct connection between y & y2
The controller transfer functionF(s,p) is the only place p shows up
Sensitivity for Hybrid System
i’ = i/p = li B {/p [F(s,p)]|s=i } C ri
related to the controllability and observability measures and to the controller transfer function (see Reference [5])
Uses of Sensitivities
Location of controllers Magnitude of ’ tells the displacement of the
eigenvalue if gain is equal to 1 Large magnitude indicates controller is a good
candidate for improving a mode Phase ’ of gives the direction of the
eigenvalue's displacement in the imaginary plane
Introduce devices likely to influence these characteristics
Simulations and Trial & Error
Tuning of a controller . . .
Adjust the phase compensation of the controller so that ’ has a phase of 180 degrees with controller in place
Adjust the gain of the controller to achieve the desired amount of damping
Power Oscillation Flows
Map where oscillations caused by a single eigenvalue appear in the system
n
x(t) ck ekt rk
k = 1
ck is the initial condition in Jordan Space
The idea is to choose ck's so that only one mode is perturbed, i.e. ci = 1 and ck= 0 for all k not equal i
then x(t) = ri eit
this solution can then be propagated through the system equations to find the power flow on key lines (or some other variable for that matter)
Placing a FACTS device using participations, sensitivities, etc.
Simple & Fast Detailed & More Accurate
Transient Stability and FACTS
Usually concerned with providing adequate damping and synchronizing torque
Often design using linear techniques and test with the nonlinear system
Nonlinear Methods
Normal forms of vector fields for extending the linear concepts to the nonlinear regions.
Second-order oscillations, participations, controllability & observability
Energy Methods
Lyapunov-based methods for determining stability indices
Tracking of energy exchanges during a disturbance
Control Strategy
Determine weak points in system Poorly damped oscillations Lack of synchronizing torque Large power swings Large energy exchanges Short critical clearing times Multi-machine instabilities
References
[1] Paserba, J. J., N. W. Miller, E. V. Larsen, and R. J. Piwko "A Thyristor Controlled Series Compensation Model for Power System Stability Analysis" IEEE Trans. on Power Delivery, Vol. 10?, (July 1994): 1471-1478.
[2] Chan, S. M. "Modal Controllability and Observability of Power-System Models" International Journal of Electric Power and Energy Systems, Vol. 6, No. 2, (April 1994): 83-89.
[3] Rouco, L., and F. L. Pagola "An Eigenvalue Sensitivity Approach to Location and Controller Design of Controllable Series Capacitors for Damping Power System Oscillations" IEEE-PES 1997 Winter Power Meeting, Paper No. PE-547-PWRS-0-01-1997.
[4] Ooi, B. T., M. Kazerani, R. Marceau, Z. Wolanski, F. D. Galiana, D. McGillis,
and G. Joos "Mid-Point SIting of FACTS Devices in Transimssion Lines" IEEE-PES 1997 Winter Power Meeting, Paper No. PE-292-PWRD-0-01-1997.
[5] Pagola, F. L., I. J. Perez-Arriaga, and G.C. Verghese "On Sensitivities, Residues, and Participations: Application to Oscillatory Stability Analysis and Control" IEEE Trans. on Power Systems, Vol. 4, No. 2, (February 1989): 278-285.
[6] Messina, A. R., J. M. Ramirez, and J. M. Canedo C. "An Investigation on the use of Power Systme Stabilizers for Damping Inter-Area Oscillations in Longitudinal Power Systems" IEEE-PES 1997 Winter Power Meeting, Paper No. PE-492-PWRS-0-01-1997.
[7] Zhou, E. Z. "Power Oscillation Flow Study of Electric Power Systems" International Journal of Electric Power and Energy Systems, Vol. 17, No. 2, (1995): 143-150.
Recommended