Waveform-Relaxation Based Iterative Real-Time
Playback Schemes for Testing of Wide Area Power
System Controllers
A M Kulkarni, K Salunkhe and M C Chandorkar
S P Panda and N Sankaranarayanan
Department of Electrical Engineering
Indian Institute of Technology
Mumbai, India, 400076
Email: [email protected]
Electrical Design Group
Nuclear Power Corporation of India Ltd
Mumbai, India, 400094
Email:[email protected]
Abstract—An alternative to real-time simulation for hardwarein-the-loop testing is proposed. This involves system simulation,
not necessarily done in real time, and real-time playback of the
simulated output to the controller under test. The time-stamped
controller output is stored and subsequently fed as an input to
the simulation. This whole process is done iteratively as in the
Waveform Relaxation method, till the waveforms converge. This
method can be used for testing multiple and dispersed controller
hardware and the associated communication equipment, e.g.,
wide-area measurement based control and system protection
schemes. It also has the potential to be an alternative to realtime simulators which are expensive when large systems have to
be simulated. The basic scheme and potential applications are
discussed in this paper.
Index Terms—Real-Time Simulation, Hardware in the Loop
Simulation, Waveform Relaxation Method, Wide Area Measurements Systems, Wide Area Control and Protection
I. I NTRODUCTION
Testing of protection and control equipment under various
simulated transient conditions is a necessary step before their
actual deployment in the field, i.e., their interface to high
power apparatus. This testing relies on digital simulators to
simulate power system transients in real-time with “Hardware
In the Loop” (HIL) [1] - see Fig.1. Real-Time Simulators
are available commercially and are widely used. However the
cost of a simulator is dependent on the maximum size of
the system that can be simulated on it. Moreover, if more
than one controller, relay or measurement system, placed at
geographically distant locations, are to be tested in situ with
the associated communication system, then HIL simulation is
infeasible. This situation may arise with centralized decision
and control schemes which use Wide Area Measurement
Systems (WAMS) [3], [4], wherein the performance of the
complete system is to be tested.
A WAMS scheme consists of Phasor Measurement Units
(PMUs) at various locations which are time sycnhronized with
each other using Global Positioning System (GPS) signals.
The PMUs convey time stamped measurements to a control
centre which may use the measurements for monitoring,
control or system protection schemes. WAMS are now be-
978-1-4244-6551-4/10/$26.00 ©2010 IEEE
ing deployed in various power systems. However WAMS
applications for system protection and control, e.g., Wide
Area Power System Stabilizers (WA-PSS) [5] and Controlled
System Separation schemes, require adequate testing so that
power system operators have the confidence to use them. The
infeasibility of HIL testing for wide area controllers is the
main motivation for this paper.
Non-Real-Time
Power System
Simulator
Real time
Power System
Simulator
Real Time Player
Controller
or
System
under
Relay
Decision
Test
Relay
Equipment
and operating
Time
Fig. 1.
HIL Simulation
Fig. 2.
Real-Time Playback
For testing equipment action which involves only one
discrete event (e.g. relay tripping), it is adequate to test the
equipment with real-time playback of transients which have
been simulated in non-real-time [2] - see Fig. 2. If a protection
system which uses remote measurements is to be tested with
its associated communication system, or the operation of
a relay in conjunction with other relays is to be verified,
then the relevant transient waveforms at different locations
can be played-back in a time-sychronized fashion, to the
geographically dispersed components of the protection system
[6] - see Fig. 3. Time synchronization can be achieved using
GPS signals. This feature is available in some commercial
relay test equipment.
If more than one discrete action of an equipment are
involved (e.g., tripping followed by auto-reclosure), then the
evolution of the system behaviour after any action has to be
k−1
(t)
c1
Non-Real Time Power System Simulator
Non−Real Time Power System Simulator
y
Time
Real Time Player
Time
Synchronized
Communication
Equipment
Relay
Real Time Player
Real Time Player
System
Relay
Controller
under
Synchronized
Communication
Equipment
Real Time Player
System
Controller
Test
Decision
and operating Time
Fig. 3.
Time Synchronized Real-Time Playback Testing
re-simulated, and the entire transient has to be replayed to
the equipment - see Fig. 4. This becomes infeasible if the
number of discrete actions is large. Also, if the equipment to be
tested delivers continuous feedback (as in a Wide-Area Power
System Stabilizer) to the system, such “open loop” playback
schemes are not meaningful.
Decision
and operating
Time (s)
Real Time Player
Relay
Fig. 4.
Decision
and operating
Time (s)
Discrete Multi-event Real-Time Playback
To overcome the infeasibility of HIL real-time simulation
and open loop real-time playback for testing of Wide-Area
control and system protection schemes, we propose the use
of Waveform-Relaxation (WR) [7] based iterative and timesynchronized real-time playback of simulated responses to
geographically dispersed components of the system. The basic
scheme is shown in Fig. 5 wherein the system under test
has two geographically dispersed controllers. The scheme can
be generalized to a larger number of such controllers. The
output of the controllers under test in the (k − 1) th iteration,
yck−1 (t), are fed as inputs to the non-real time power system
simulator. The simulation is performed using these inputs and
the simulated waveforms are played back in real time to the
controller to obtain the response for the new iteration, y ck (t).
under
Test
k
c1
Decision
and operating Time
Non-Real-Time
Power System
Simulator
k−1
(t)
c2
y
Fig. 5.
k
c2
y (t)
y (t)
Output Waveform
Output Waveform
Waveform Relaxation based Iterative Real-Time Playback
This is repeated till convergence is obtained. Note that if
ycl−1 (t) = ycl (t) for some l, then it is equivalent to “closing
the loop” in Fig. 5. Therefore if the WR iteration converges as
above, then the converged response of the tested equipment is
the same as the HIL response. In practice, the convergence of
the waveforms is only up to the specified tolerance, therefore
the equality given above is not strictly true. However, a small
enough convergence tolerance can be chosen by a user to get
the desired accuracy.
While this WR based scheme is uniquely suited for testing
Wide Area controllers, it may also be used as a cheap alternative to HIL real-time simulation in a more conventional setting
(no communication or geographical dispersion of equipment).
However, it is slower, requires repeated triggering of the
control equipment and may face convergence problems.
It should be noted that WR method was proposed as a
method of parallelizing the numerical integration of very
large systems (e.g., VLSI) [8], [9]. It was also attempted
for parallelizing transient stability simulations of large power
systems [10] in order to get overall speed-up. However, the
aim here is to use it for controller testing. The overall scheme
requires hardware interfaces and real-time playback. Therefore
the application proposed in this paper is distinct from the
earlier work on WR, and consequently the issues are unique
to this application.
In this paper we first give a brief description of WR method.
We also present examples to illustrate the use of the scheme as
an alternative to HIL simulation, as well its unique application
for testing Wide-Area controllers.
II. WAVEFORM R ELAXATION M ETHOD
The essence of the WR method [7], or rather the family
of WR algorithms, can be illustrated using a simple example. Consider the first-order two-dimensional differential
equations:
ẋ1 = f1 (x1 , x2 )
ẋ2 = f2 (x1 , x2 )
(1)
(2)
The basic idea of a WR algorithm is to fix the waveform x 2
in the time window [0, T ] and solve (1) as a one dimensional
differential equation. The solution thus obtained for x 1 , can
be substituted into (2) which will then reduce to another firstorder differential equation. Equation (1) is then re-solved using
the new solution for x 2 . This is done till x1 and x2 converge.
The algorithm can been seen as the analogue of the GaussSeidel technique for solving non-linear algebraic equations. A
Gauss-Jacobi variant of the algorithm can also be constructed.
However, unlike the problem of solving nonlinear algebraic
equations, the unknowns are waveforms rather than real variables. In this sense, the algorithms are techniques for timedomain de-coupling of differential equations. In general, for
large order systems, the system can be partitioned into two
or more sub-systems in many ways. In practice and for most
systems, the solution for the differential equations is obtained
numerically by discretization. The rate of convergence is
greatly affected by the choice of the sub-systems as well as
the numerical method used for discretization [7].
A. WR method for Hardware Testing
The application of the WR method for hardware testing can
be understood by considering an example.
Suppose we desire to test the controller of a generator excitation system, automatic voltage regulation of the generator
bus being one of its functions. The generator and exciter
(excluding the excitation controller which is to be tested), and
the rest of the power system are modeled in a power system
simulator as follows
ẋp = fp (xp , up , t)
yp = gp (xp )
xp denotes the states of the generator, exciter and the rest of
the power system, u p denotes the firing pulses for the thyristors
of the exciter, which are obtained from the Excitation System
Controller (ESC) and y p (t) denotes the variables which are
inputs to the ESC e.g., the three phase voltages at the generator
bus and field current.
The ESC is implemented on external electronic hardware.
The output of the ESC, y c (t) are the thyristor firing pulses.
If HIL testing is to be done, then y p (t) are obtained from a
real-time power system simulator and are fed to the ESC via
appropriate interface hardware. The firing pulses obtained at
the output of the ESC are fed back as inputs into the simulator.
However there is no delay in this process (the simulator and
controller are in a closed loop.)
On the other hand the WR method of hardware testing involves
the following steps:
1: Simulate the generator, exciter and the rest of the power
system (not necessarily in real-time) for an interval [0 T ].
In the first iteration, the firing pulse trains to the thyristors
of the exciter u 1p (t) = yc0 (t) are guessed.
2: The simulator gives the waveforms of the generator
voltages and other variables. The waveforms of variables
which are used as inputs to the ESC, y pk (t), are played
back in real-time to the ESC. The ESC produces pulse
trains for the thyristors of the exciter, y ck (t), which are
time stamped and stored.
3: The time stamped pulse trains for the thyristors are made
available to the power system simulator (Step 1) as inputs,
for evaluating its response for the next iteration,i.e.,
(t) = yck (t).
uk+1
p
The procedure is repeated till convergence is obtained. The
converged waveforms will be practically identical to those
obtained from HIL testing, as discussed in Section I.
The issues in the usage of WR based iterative real-time
playback for controller testing are somewhat different from
those encountered in typical applications of WR. We discuss
these issues below.
1) Partitioning of the dynamical system: In typical applications of WR method, like circuit simulation and
transient stability simulations [8]–[10], convergence of
the algorithm is determined by how the system differential equations are partitioned. In this application,
the controller under test is embodied in the external
electronic hardware. It accepts physical feedback signals
from the simulation (played back to it in real time) and
subsequently provides control inputs to the simulator.
2) Numerical Integration Algorithms: It is possible to
directly use a readily available non-real-time Power
System Simulator. Normally, the simulation algorithm,
i.e., the numerical integration method and the time step
for such a simulator will be geared towards achieving
a numerical stable and fast solution of the differential
equations. However, the simulation algorithm may need
to be changed or modified to optimize the overall
WR convergence time. On the other hand, there is no
flexibility to alter the digital algorithms of the equipment
under test merely to improve WR convergence; the
controller under test would have to be treated as a black
box. Therefore, no general statement or analysis relating
to the convergence properties can be presented without appropriate system identification of the controller.
Nonetheless, an idea of the viability of the scheme can
be obtained from the numerical experiments carried out
in the next section.
3) Selection of Time Interval: The time interval T could
be sub-divided to improve overall WR convergence.
If convergence is very slow for a given interval, then
the time interval can be reduced. Once the waveforms
are close to convergence in this smaller interval, the
interval can be increased. Depending on the extent of
convergence, the entire previous interval need not be
simulated again for further iterations. Even so, it defeats
the purpose of WR method if we sub-divide the time
Generator
x
xTCSC
Infinite bus
Xmax
s Tw
Generator
Slip
XTCSC
K
1 + s Tw
Xmin
Fig. 6.
SMIB system with a TCSC damping controller
2
1.5
1
Rotor Angle (rad)
interval into very small intervals.
4) Acceleration techniques like Sequential Over-Relaxation
[11] have been proposed. However, their efficacy for
power system applications need to be investigated further.
5) Automation of the Process: The controller which is
to be tested should allow for automated and repeated
testing and resetting. Direct manual set-point changes
in a controller during the testing are precluded because
it is difficult to ensure consistent timing of the manual
action for each iteration. This is not a major issue in
system protection schemes and stabilizing controllers,
but can be an issue, say if the controller being tested is
a regulator with manual set point adjustment and startup.
6) Synchronization: Synchronization of Real Time Playback is necessary for testing of geographically dispersed
multiple controllers. A method for implementing time
synchronization is the GPS system. The communication
channel between a centralized simulator and the real
time player in the field can be used to download the
playback waveforms at each iteration. This process can
be automated too.
0.5
0
III. E XAMPLES
To illustrate the method and bring out the relevant issues, we
present three examples in this section. The first example is an
illustration of how the method works. The second example
illustrates testing of a wide-area controller for which WR
method is uniquely suited. Subsequently, we ‘try out’ the
method for a conventional HVDC controller testing application
as well. We first present examples in which the controller,
measurement/communication delay and playback itself is simulated, i.e., the actual controller and playback hardware is not
used. However, in the last sub-section we also present the
laboratory implementation of the scheme wherein we interface
the non-real-time simulation with a real-time implementation
of a controller and playback.
0.5
initial waveform(no controller)
iteration 5
iteration 10
iteration 15
1
0
1
2
3
4
time(s)
5
6
7
8
Fig. 7. WR iterations for the SMIB system with a TCSC Damping Controller
number of iterations for convergence increases with an
increase in the controller gain (the limiter also comes into the
picture).
B. Wide Area Applications: WA-PSS
A. Single Machine System
Consider the Single-Machine Infinite Bus (SMIB) system
shown in Fig. 6. The transmission line connecting the machine
to the infinite bus is compensated using a Thyristor Controlled Series Compensator (TCSC) [12]. A damping controller
for the same is to be tested as given in the figure. The
system excluding the damping controller is simulated using
the Trapeziodal method (time step: 1ms), with the controller
also being discretized with the same algorithm. The controller
uses a remote signal (generator speed). Although controller
testing normally requires a detailed “EMTP” model of a power
system, a simplified low frequency model is used here for the
purpose of illustration.
The rotor angle waveforms at various WR iterations are
shown in Fig. 7. The disturbance is a three phase self-clearing
fault at the generator terminals. Convergence of the initial
part of the waveform (0 - 3 s) takes place quickly, however,
the tail of the waveform takes more time to converge. The
A WA-PSS is an application in which signals with
favourable properties for damping inter-area power swings,
are synthesized from wide area measurements. The measurement units are synchronized using GPS signals and the
measurements are communicated to the WA-PSS. One possible
objective of a WA-PSS is to selectively damp of critical interarea modes. To synthesize a signal which practically contains
only the modal speed of interest, we can utilize the following
expression:
ωm = q T ω
where ωm is the modal speed, ω are the measured speeds
of the generators and q denotes a vector containing the
left eigenvector components corresponding to the speed of
generators for this mode 1 . The complete wide area control
1 The eigenvector is obtained from the linearized model of the power system
for a given operating point. For major changes in the operating point or system
topology, the eigenvector would need to be re-calculated
Hardware to be tested
Real
Time
Player
Phasor
Measurement
Unit
Communication
Synchronized
and
Phasor
Measurement
Unit
Processing
Power
Real
Time
Player
Synchronized
Equipment
Central
Synchronized
System
Synchronized
Simulator
Real
Time
Player
Phasor
Measurement
Unit
To
Generator
Synthesized
Inter − area Slip
k−1
(t)
c
y
Excitation
Input
k
c
Wide area PSS
y (t)
Fig. 8.
Wide Area PSS testing
system, excluding the power apparatus, can be tested using
the WR based iterative scheme as shown in Fig. 8. Note that
if the same system (e.g. GPS) is used for synchronizing both
the real-time playback as well as the measurement units, a
test of the synchronization itself cannot be done. We carry
1
0
Modal Speed Deviation (rad/s)
1
2
3
4
C. HVDC Link
5
6
7
converged waveform
initial waveform (PSS disabled)
iteration 5
iteration 10
8
9
modulate the voltage reference of the exciters of the largest
power station in the region (which significantly participates in
this mode). Since the aim here is not to optimize the WAPSS design but to show the performance of the WR scheme,
we consider the simple controller structure in Fig. 6. A pure
transport delay of 50 ms is assumed to account for the WAMS
communication and processing delays.
Fig. 9 shows the modal speed signal as the iterations
progress. The initial waveform is the waveform obtained
without the WA-PSS - the disturbance being a fault in one
transmission line which is cleared in 60 ms. The iterations
practically converge in 10 iterations. Incidentally, the improved
damping with a WA-PSS is clearly seen.
0
2
4
6
Fig. 9.
8
10
time
12
14
16
18
20
Modal Speed Deviations
out the simulation of a large system - adapted from the Central
power grid of India ( 300 generators). This system has a
poorly damped swing mode of around 0.65 Hz between the
machines of the eastern and western parts of the grid. To
damp this mode, a WA-PSS is used which uses a modal speed
signal synthesized as shown previously. This signal is used to
We now evaluate the performance of the scheme for a
HVDC controller application.This is distinct and more complicated than the previous examples because the final output
of the controller are the thyristor firing pulses (which have
discrete levels). In general, a controller includes blocks like
synchronization blocks, limiters, a start up and shutdown
sequence, in addition to the current regulators and power
system stabilizers. This system is highly non-linear and it is
interesting to see how the proposed scheme behaves.
The system and controller is adapted from the demonstration
file (psbhvdc.mdl) of the SimPowerSystems Toolbox of
MATLAB/SIMULINK [13] - see Fig. 10. A complete description is available in the simulation file, but is summarized here
for convenience:
A 500 MW (250 kV, 2 kA) DC interconnection is used
to transmit power from a 315 kV, 5000 MVA, 60 Hz,
Fig. 10.
Block diagram of HVDC system [13]
AC network. The control system uses two main blocks: a
synchronized six-pulse generator and a PI Curent Regulator.
Voltages sent to the synchronization system are filtered by
2nd order band pass filters. The sequence of disturbances
and the corresponding converged transient waveforms have the
following features:
1) A step change in regulator set point is given at 0.3 s,
which is tracked quite well by the controller.
2) Subsequently, a DC side fault is given at 0.5 s. The fault
current increases to 5 kA and the Id current increases to
to 2 pu (4 kA) in 10 ms.
3) The fast regulator action lowers the current back to its
reference value of 1 pu.
4) At 0.55 s, the delay angle is forced by the protection system (not simulated) to reach 165 degrees. The rectifier
thus passes in inverter mode and sends the energy stored
in the line back to the 345 kV network. As a result, the
arc current producing the fault rapidly decreases. The
fault is cleared at 0.555 s when the fault current zero
crossing is reached.
5) At 0.57 s, the regulator is released and it starts to
regulate the DC current again. The steady-state 1 pu
current is reached at t = 0.75 s.
The waveforms as the WR iterations progress are shown in
Fig. 11. Note that:
1) At the first iteration, the thyristors of the rectifier are
blocked.
2) Set point changes in the controller are programmed to
occur in the given manner in each iteration.
Inspite of the inherent complexity of the problem (nonlinearities, switchings, faulted conditions), convergence is
obtained,which comes as a bit of a surprise. However the
number of iterations is quite large. Although a HIL real-time
simulation scheme is well suited for this application, the WR
iterative scheme may be explored as an alternative (inspite of
slow convergence), as it can give a substantial saving on the
cost of a simulator.
A similar exercise was carried out with both rectifier and
inverter modeled as twelve pulse converters (using the MATLAB demonstration file (psbhvdc12pulse.mdl). The controllers for the converters are more realistic with appropriate
startup and fault recovery features. The output of both rectifier
and inverter controllers were decoupled simultaneously and
the WR iterations were performed. The number of iterations
were large, as in the previous HVDC simulation; nonetheless
the iterations did converge. Note that the rectifier and inverter
controllers are at different geographical locations. Therefore in
situ testing of HVDC controllers along with their associated
communication system (before connection to the high power
apparatus), using the iterative approach, appears to be worth
exploring.
Note:
In the previous examples all the controllers are well tuned.
However, we also checked the performance of the method
when the controllers were faulty. For example,
1) Pulses to a thyristor valve in the HVDC Controller
missing
2) TCSC damping controller with the incorrect sign of the
gain.
It was verified that the WR method converged to the response
corresponding to the faulty controllers.
D. Laboratory Implementation of controller and playback
In the previous examples, the effect of playback and controller behaviour was simulated in non-real-time. Studies were
5
becomes comparable to the noise. This is an issue which needs
further investigation.
4
IV. OTHER A PPLICATIONS
Current (pu)
3
Rest of the
i = 84
2
converged
waveform
Idref
i = 42
1
Power System
i = 105
i = 63
i = 21
0
Boundary
nodes
fault
1
0
0.1
0.2
0.4
time (s)
0.3
0.5
0.6
0.7
0.8
Sub−network
Controller
Fig. 11. Simulated Current waveforms using the iterative scheme for the
HVDC system
Fig. 13.
also carried out using of real-time implementation of the
controller and playback along with automation of the entire
process of WR.
The MATLAB simulation of the power apparatus - running
in non-real-time on Linux platform - and the real-time playback and controller implementation using RTAI (Real-Time
Application Interface) on Linux, are run sequentially using two
computers interfaced with Peripheral Component Interconnect
(PCI) cards. The schematic is shown in Fig. 12
Partitioning of System at boundary nodes
Non−Real−Time Simulator
Entire power system
} excluding
sub−network
( Low frequency model )
Current phasors
at boundary nodes
U
Y
Instantaneous
to dynamic phasor
conversion
Voltage phasor
at boundary nodes
Convert
Phasor to
Instantaneous
y
k−1
(t)
s
u=y
Non-Real-time data
transfer(digital signals) via LAN
Real Time Player
k
s
y (t)
Real-time playback
PCI Card
Non-Real-time simulator
with Real-time player
(Analog signals)
PCI Card
Real − time Simulator
Real-time implementation of
Controller
( EMTP − detailed model )
HIL
Fig. 12.
Laboratory Implementation for Controller Testing
RTAI [14] is based on the Linux kernel, providing the ability
to make it fully pre-emptable. It is a real-time extension for
the Linux kernel - which allows us to write applications with
strict timing constraints (hard real-time) for Linux. RTAI offers
the same services of the Linux kernel core (device drivers,
networking etc), adding the features of an industrial real-time
operating system.
The performance of the WR algorithm using this system
was verified for the TCSC example. Some differences in
performance and the response (as compared to the MATLABsimulated controller implementation) were found due to numerical precision issues in A/D conversion and the superimposed noise in the transferred analog signal (which varies at
every iteration). This affects WR convergence for a TCSC
damping controller because the signal level of the playback
when the system comes near its equilibrium, is low and
}
Simulator
Sub−network
Control Equipment
Fig. 14.
Hybrid, Multi-Time Scale Real-Time and WR simulation
While the main motivation of using WR based iterative
real-time playback is the possibility of carrying out testing
of geographically dispersed controllers which use wide area
measurements, this approach shows promise of application
even in the conventional domain. Consider the problem of
testing a TCSC controller. The controller includes not only the
lower level reactance and firing angle controllers, but damping
and transient stability controllers as well. If the TCSC is
being utilised for stability improvement of inter-area angle
stability, it would be desirable to model the entire power
system. However, a typical real-time simulator would not be
able to handle the large number of elements involved. This
would necessitate creation of system equivalents at the chosen
“boundary nodes” - see Fig.13.
The development of this equivalent (and its validation)
would in itself be a challenging task. Therefore one can
use a multi-time scale hybrid approach. Detailed real-time
simulations of a small sub-network (“EMTP model”), can be
carried out with the controller hardware in the loop. These
simulations are used iteratively as inputs to the remaining
larger system (simulated in non-real-time using low frequency
models) whose outputs are the voltages at the boundary nodes.
This approach is shown in Fig. 14. The inputs to the rest of the
system simulation need to be converted to (dynamic) phasors
and down-sampled because the time-steps are larger for this
simulation. The main issue in this scheme is the choice of the
boundary nodes which will result in the quickest convergence
of the iterations.
V. C ONCLUSIONS
The use of a Waveform Relaxation based iterative real-time
playback scheme for controller and protection system testing
has been explored in this paper. This scheme is uniquely
suited for Wide Area control and protection schemes. The
results are encouraging and convergence could be attained
for the cases considered. The method is also tested for a
conventional application like HVDC controller testing. Inspite
of the inherent complexities like power electronic switching,
line faults, controller startup, synchronization etc., the method
does converge, but requires a large number of iterations.
Given the relatively low cost and the promise of easy implementation, this method can be explored as an alternative to
real-time HIL simulations, even in conventional applications.
Large scale system testing using a hybrid and multi-time scale
approach also is conceivable using a combination of realtime simulation and the proposed iterative approach. Further
research should be focussed on acceleration techniques to
improve convergence.
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