Use
of the phasor solution for transient stability analysis of multimachine
systems
G.
Sybille (Hydro-Québec)
Note:
Before starting the demo, open the Powergui block and notice that the 'Phasor
simulation' has been checked. The phasor solution is much faster
than the 'standard' detailed solution. In this solution method, the network
differential equations are replaced by a set of algebraic equations at
a fixed frequency, thus reducing dramatically the simulation time. This
allows transient stability studies of multimachine systems, as illustrated
below.
Circuit
Description
A 1000 MW hydraulic generation plant (machine M1) is
connected to a load center through a long 500 kV, 700 km transmission line.
The load center is modelled by a 5000 MW resistive load . The load is fed
by the remote 1000 MW plant and a local generation of 5000 MW (machine
M2). The system has been initialized so that the line carries 950 MW which
is close to its surge impedance loading (SIL = 977 MW) . In order to maintain
system stabilty after faults, the transmission line is shunt compensated
at its center by a 200-Mvar Static Var Compenstor (SVC). Notice that this
SVC model is a phasor model valid only for transient stabilty solution.
The SVC does not have a Power Oscillation Dampling (POD) unit. The two
machines are equiped with a Hydraulic Turbine and Governor (HTG), Excitation
system and Power System Stabilizer (PSS). These blocks are located
in the two 'Turbine and Regulator' subsystems.Two types of stabilizers
can be selected : a generic model using the acceleration power (Pa= difference
between mechanical power Pm and output electrical power Peo) and
a Multi-band stabilizer using the speed deviation (dw). The stabilizer
type can be selected by specifying a value (0=No PSS 1=Pa PSS
or 2= dw MB PSS) in the PSS constant block.
During this Demo you will apply faults on the 500 kV
system and observe the impact of the PSS and SVC on system stability.
Demonstration
1.
Load Flow and machine initialisation
In order to start the simulation in steady-state you
must first initialize the synchronous machines and regulators for the desired
load flow. Note that the system has already been initialized. If you are
familiar with the Load Flow procedure you can skip this item and
proceed to step 2. In the Powergui menu, select 'Load Flow and Machine
Initialization'. A new window appears. The machine M1 'Bus type' should
be already initialized as 'PV generator', indicating that the load flow
will be performed with the machine controlling its active power and its
terminal voltage. Machine M2 will be used as a swing bus for balancing
the power. Check that the following parameters are specified for M1 and
M2:
M1:
type = PV
Terminal voltage (Vrms) = 13800
Active Power = 950e6 |
M2:
type = Swing bus
Terminal voltage (Vrms) = 13800
Active power guess = 4000e6 |
Then press the 'Update Load Flow' button. Once the load
flow has been solved , the actual machine active and reactive powers, mechanical
powers and field voltages will be displayed. If you look in the the hydraulic
turbine and governor (HTG) and Excitation system contained in the two Regulator
subsystems, you will notice that the initial mechanical power and field
voltage have also been automatically initialized by the Load Flow. The
reference mechanical powers and reference voltages for the two machines
have also been updated in the two constant blocks connected at the HTG
and excitation system inputs: Pref1=0.95 pu (950 MW), Vref1=1pu; Pref2=0.8091
pu (4046 MW), Vref2=1 pu.
2.
Single-phase fault - Impact of PSS - No SVC
Open the SVC dialog box and notice that the SVC is set
to operate in 'Var control (fixed susceptance)' mode with Bref = 0. Setting
Bref to zero is equivalent to putting the SVC out of service. Verify also
that the two PSS (Pa type) are in service (value=1 in the PSS constant
block) Start the simulation and observe signals on the 'Machines' scope.
For this type of fault the system is stable without SVC. After fault clearing,
the 0.8 Hz oscillation is quickly damped. This oscillation mode is typical
of interarea oscillations in a large power system. First trace on the 'Machine'
scope shows the rotor angle difference d_theta1_2 between the two machines.
Power transfer is maximum when this angle reaches 90 degrees. This signal
is a good indication of system stability. If d_theta1_2 exceeds 90 degrees
for a too long period of time, the machines will loose synchronism and
the system goes unstable. Second trace shows the machine speeds. Notice
that machine 1 speed increases during the fault because during that period
its electrical power is lower than its mechanical power.
By simulating over a long period of time (50 seconds)
you will also notice that the machine speeds oscillate together at
a low frequency (0.025 Hz) after fault clearing. The two PSS (Pa type)
succeed to damp the 0.8 Hz mode but they are not efficient for damping
the 0.025 Hz mode. If you select instead the Multi-Band PSS (value=2
in the PSS constant block) you will notice that this stabilizer type succeeds
to damp both the 0.8 Hz mode and the 0.025 Hz mode.
You will now repeat the test with the two PSS out
of service (value=0 in the PSS constant block). Restart simulation. Notice
that the system is unstable without PSS. You can compare results
with and without PSS by double clicking on the 2nd blue block on the right
side. You can also compare the results obtained with the two solution methods
'Detailed' and 'Phasor' by double-clicking on the first blue block on the
right side.
Note: This system
is naturally unstable without PSS, even for small disturbances. For example,
if you remove the fault (by deselecting phase A in the Fault Breaker) and
apply a Pref step of 0.05 pu on machine 1, you will see the unstability
slowly building up after a few seconds.
3.
Three-phase fault - Impact of SVC - two PSS in service
You will now apply a 3-phase fault and observe the impact
of the SVC for stabilizing the network during a severe contingency. Put
the two PSS (Pa type) in service (value=1 in the PSS constant
block. Reprogram the 'Fault Breaker' block in order to apply a 3-phase-to-ground
fault. Verify that the SVC is in fixed susceptance mode with Bref = 0.
Start the simulation. By looking at the d_theta1_2 signal, you should observe
that the two machines quickly fall out of synchronism after fault clearing.
In order not to pursue unnecessary simulation, the Simulink 'Stop' block
is used to stop the simulation when the angle difference reaches 3*360degrees.
Now open the SVC block menu and change the SVC mode of
operation to 'Voltage regulation'. The SVC will now try to support the
voltage by injecting reactive power on the line when the voltage is lower
than the reference voltage (1.009 pu). The chosen SVC reference voltage
corresponds to the bus voltage with the SVC out of service. In steady state
the SVC will therefore be 'floating' and waiting for voltage compensation
when voltage departs from its reference set point.
Restart simulation and observe that the system is now stable
with a 3-phase fault. You can compare results with and without SVC by double
clicking on the 3rd blue block on the right side.