This example shows the use of the phasor solution for transient stability analysis of multi-machine systems. It analyzes transient stability of a two-machine transmission system with Power System Stabilizers (PSS) and Static Var Compensator (SVC).
Gilbert Sybille (Hydro-Quebec)
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 modeled 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 stability after faults, the transmission line is shunt compensated at its center by a 200-Mvar Static Var Compensator (SVC). Notice that this SVC model is a phasor model valid only for transient stability solution. The SVC does not have a Power Oscillation Damping (POD) unit. The two machines are equipped 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.
In this example we apply faults on the 500 kV system and observe the impact of the PSS and SVC on system stability.
Note: Before starting the example, open the Powergui block and notice that '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 multi-machine systems, as illustrated below.
Note that the system has already been initialized to start in steady-state. If you are familiar with the Load Flow procedure you can skip this item and proceed to step 2.
Open the mask of the M1 1000 MVA and M2 5000 MVA Synchronous Machine blocks:
In the Load Flow tab of machine M1, the 'Generator type' parameter is set to 'PV', indicating that the load flow will be performed with the machine controlling its active power and its terminal voltage. The 'Active power generation' parameter is set to 950e6 W and the terminal voltage is defined by the Load Flow Bus block labeled M1 and connected to the machine terminals.
The 'Generator type' parameter of machine M2 is set to 'swing', indicating that the machine will be used as a swing bus for balancing the power.
In the Powergui menu, select 'Load Flow'. A new window appears. A summary of the load flow settings is displayed in a table. Press the 'Compute' button to solve the load flow. The table now display the actual machine active and reactive powers.
Press the 'Apply' button to apply the load flow solution to the model.
Look in the hydraulic turbine and governor (HTG) and Excitation system contained in the two Regulator subsystems to note that the initial mechanical power and field voltage have 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 inter-area 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 instability 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.
 D.Jovcic, G.N.Pillai "Analytical Modeling of TCSC Dynamics" IEEE® Transactions on Power Delivery, vol 20, Issue 2, April 2005, pp. 1097-1104