Store 
| Products & Services | Solutions | Academia | Support | User Community | Company |
 |
Download Product Updates | | |  |
Get Pricing | | | |
Trial Software |
| Documentation → SimPowerSystems |
| Products & Services | Solutions | Academia | Support | User Community | Company |
|
Download Product Updates | | | |
Get Pricing | | | |
Trial Software |
| Documentation → SimPowerSystems |
| Contents | Index |
| Learn more about SimPowerSystems |
| On this page… |
|---|
Three-Phase Network with Electrical Machines |
In this section you
Learn how to simulate a three-phase power system containing electrical machines and other three-phase models
Perform a load flow study and initialize machines to start simulation in steady state by using the Load Flow and Machine Initialization option of the Powergui
Simulate the power system and observe its dynamic performance by using both the standard solution technique using a continuous solver and the phasor simulation method
You now use three types of machines of the Electrical Machines library: simplified synchronous machine, detailed synchronous machine, and asynchronous machine. You interconnect these machines with linear and nonlinear elements such as transformers, loads, and breakers to study the transient stability of an uninterruptible power supply using a diesel generator.
The two-machine system shown in this single line diagram is this section's main example:
Diesel Generator and Asynchronous Motor on Distribution Network
This system consists of a plant (bus B2), simulated by a 1 MW resistive load and a motor load (ASM) fed at 2400 V from a distribution 25 kV network through a 6 MVA, 25/2.4 kV transformer, and from an emergency synchronous generator/diesel engine unit (SM).
The 25 kV network is modeled by a simple R-L equivalent source (short-circuit level 1000 MVA, quality factor X/R = 10) and a 5 MW load. The asynchronous motor is rated 2250 HP, 2.4 kV, and the synchronous machine is rated 3.125 MVA, 2.4 kV.
Initially, the motor develops a mechanical power of 2000 HP and the diesel generator is in standby, delivering no active power. The synchronous machine therefore operates as a synchronous condenser generating only the reactive power required to regulate the 2400 V bus B2 voltage at 1.0 pu. At t = 0.1 s, a three-phase to ground fault occurs on the 25 kV system, causing the opening of the 25 kV circuit breaker at t = 0.2 s, and a sudden increase of the generator loading. During the transient period following the fault and islanding of the motor-generator system, the synchronous machine excitation system and the diesel speed governor react to maintain the voltage and speed at a constant value.
This system is modeled in a SimPowerSystems demo. Open the Demos library of powerlib and double-click the demo called Three-Phase Machines and Load Flow. A system named power_machines opens.
Power System of Diesel Generator and Asynchronous Motor on Distribution Network
The Synchronous Machine (SM) block uses standard parameters, whereas the Asynchronous Machine (ASM) block uses SI parameters.
The other three-phase elements such as the inductive voltage source, the Y grounded/Delta transformer, and the loads are standard blocks from the Electrical Source and Elements libraries of powerlib. If you open the dialog box of the Three-Phase Fault and Three-Phase Breaker blocks, you see how the switching times are specified. The Machine Measurement Demux block provided in the Machines library is used to demux the output signals of the SM and ASM machines.
The SM voltage and speed outputs are used as feedback inputs to a Simulink control system that contains the diesel engine and governor block as well as an excitation block. The excitation system is the standard block provided in the Machines library. The SM parameters as well as the diesel engine and governor models were taken from reference [1].
Diesel Engine and Governor System
If you simulate this system for the first time, you normally do not know what the initial conditions are for the SM and ASM to start in steady state.
These initial conditions are
SM block: Initial values of speed deviation (usually 0%), rotor angle, magnitudes and phases of currents in stator windings, and initial field voltage required to obtain the desired terminal voltage under the specified load flow
ASM block: Initial values of slip, rotor angle, magnitudes and phases of currents in stator windings
Open the dialog box of the Synchronous Machine and Asynchronous Machine blocks. All initial conditions should be set at 0, except for the initial SM field voltage and ASM slip, which are set at 1 pu. Open the three scopes monitoring the SM and ASM signals as well as the bus B2 voltage. Start the simulation and observe the first 100 ms before fault is applied.
As the simulation starts, note that the three ASM currents start from zero and contain a slowly decaying DC component. The machine speeds take a much longer time to stabilize because of the inertia of the motor/load and diesel/generator systems. In our example, the ASM even starts to rotate in the wrong direction because the motor starting torque is lower than the applied load torque. Stop the simulation.
To start the simulation in steady state with sinusoidal currents and constant speeds, all the machine states must be initialized properly. This is a difficult task to perform manually, even for a simple system. In the next section you learn how to use the Load Flow and Machine Initialization option of the Powergui block to perform a load flow and initialize the machines.
Double-click the Powergui block and click the Load Flow and Machine Initialization button. A new window appears. In the upper right window you have a list of the machines appearing in your system. Select the SM 3.125 MVA machine. Note that for the Bus Type, you have a menu allowing you to choose either PV Generator, PQ Generator, or Swing Generator.
For synchronous machines you normally specify the desired terminal voltage and the active power that you want to generate (positive power for generator mode) or absorb (negative power for motor mode). This is possible as long as you have a swing (or slack) bus that generates or absorbs the excess power required to balance the active powers throughout the network.
The swing bus can be either a voltage source or any other synchronous machine. If you do not have any voltage source in your system, you must declare one of the machines as a swing machine. In the next section, you perform a load flow with the 25 kV voltage source connected to bus B1, which is used as a swing bus.
In the Load Flow window, your SM Bus Type should already be initialized as P & V generator, indicating that the load flow is performed with the machine controlling its active power and terminal voltage. By default, the desired Terminal Voltage UAB is initialized at the nominal machine voltage (2400 Vrms). Keep it unchanged and set the Active Power to zero. The synchronous machine therefore absorbs or generates reactive power only to keep terminal voltage at 1 pu. Now select the ASM 2250 HP machine in the upper right window. The only parameter that is needed is the Mechanical power developed by the motor. Enter 2000*746 (2000 HP) and click the Update Circuit & Measurements button. You now perform the load flow with the following parameters.
SM | ||
Terminal Voltage | 2400 Vrms | |
Active Power | 0 kW | |
ASM | ||
Mechanical Power | 2000*746 W (2000 HP) | |
Click the Update Load Flow button. Once the load flow is solved, the three phasors of line-to-line machine voltages as well as currents are updated as shown on the next figure. Values are displayed both in SI units (volts RMS or amperes RMS) and in pu.
The SM active and reactive powers, mechanical power, and field voltage are displayed.
P | 0 W |
Q | 856 kvar or 856/3125 = 0.2739 pu |
Pmec | 844.2 W or 0.00027 pu, representing internal machine losses in stator windings |
Ef (field voltage) | 1.427 pu |
The ASM active and reactive powers absorbed by the motor, slip, and torque are also displayed.
P | 1.515 MW (0.9024 pu) |
Q | 615 kvar (0.3662 pu) |
Pmec | 1.492 MW (2000 HP) |
Slip | 0.006119 |
Torque | 7964 N.m (0.8944 pu) |
Close the Load Flow window.
The ASM torque value (7964 N.m) should already be entered in the Constant block connected at the ASM torque input. If you now open the SM and ASM dialog boxes you can see the updated initial conditions. If you open the load flow tool, you can see updated values of the measurement outputs. You can also click the Nonlinear button to obtain voltages and currents of the nonlinear blocks. For example, you should find that the magnitude of the Phase A voltage across the fault breaker (named Uc_3-Phase Fault/Breaker1) is 14.42 kV RMS, corresponding to a 24.98 kV RMS phase-to-phase voltage.
To start the simulation in steady state, the states of the Governor & Diesel Engine and the Excitation blocks should also be initialized according to the values calculated by the load flow. Open the Governor & Diesel Engine subsystem, which is inside the Diesel Engine Speed and Voltage Control subsystem. Notice that the initial mechanical power has been automatically set to 0.0002701 pu. Open the Excitation block and notice that the initial terminal voltage and field voltage have been set respectively to 1.0 and 1.427 pu.
Note that the load flow also initializes the Constant blocks connected at the reference inputs (wref and vref) of the Governor and Excitation blocks as well as the Constant block connected at the load torque input (Tm) of the Asynchronous Machine block.
Open the three scopes displaying the internal signals of synchronous and asynchronous machines and phase A voltage. Start the simulation. The simulation results are shown in the following figure.
Simulation Results
Observe that during the fault, the terminal voltage drops to about 0.2 pu, and the excitation voltage hits the limit of 6 pu. After fault clearing and islanding, the SM mechanical power quickly increases from its initial value of 0 pu to 1 pu and stabilizes at the final value of 0.82 pu required by the resistive and motor load (1.0 MW resistive load + 1.51 MW motor load = 2.51 MW = 2.51/3.125 = 0.80 pu). After 3 seconds the terminal voltage stabilizes close to its reference value of 1.0 pu. The motor speed temporarily decreases from 1789 rpm to 1635 rpm, then recovers close to its normal value after 2 seconds.
If you increase the fault duration to 12 cycles by changing the breaker opening time to 0.3 s, notice that the system collapses. The ASM speed slows down to zero after 2 seconds.
In this section you make a load flow with two synchronous machine types: a PV generator and a swing generator. In your power_machines window, delete the inductive source and replace it with the Simplified Synchronous Machine block in pu from the Machines library. Rename this machine SSM 1000MVA. Add two constant blocks at the Pm and E inputs of the Simplified Synchronous Machine. These two blocks, which are used to specify the mechanical power and the machine internal voltage, will be automatically initialized when you perform a new load flow. Save this new system in your working directory as power_machines2.mdl.Open the SSM 1000 MVA dialog box and enter the following parameters:
Connection type | 3-wire Y |
Pn(VA), Vn(Vrms), fn(Hz) | [1000e6 25e3 60] |
H(s), Kd(), p (), | [inf 0 2] |
R(pu), X(pu) | [0.1 1.0] |
Init. cond. | Leave all initial conditions at zero. |
As you specify an infinite inertia, the speed and therefore the frequency of the machine are kept constant. Notice how easily you can specify an inductive short-circuit level of 1000 MVA and a quality factor of 10 with the per unit system.
Also, connect at inputs 1 and 2 of the SSM block two Constant blocks specifying respectively the required mechanical power (Pmec) and its internal voltage (E). These two constants are updated automatically according to the load flow solution.
When there is no voltage source imposing a reference angle for voltages, you must choose one of the synchronous machines as a reference. In a load flow program, this reference is called the swing bus. The swing bus absorbs or generates the power needed to balance the active power generated by the other machines and the power dissipated in loads as well as losses in all elements.
Open the Powergui. In the Tools menu, select Load Flow and Machine Initialization. Change the SSM Bus Type to Swing Generator. Specify the load flow by entering the following parameters for the SM and ASM machines:
SM 1000 MVA: | |
Terminal voltage UAB | 2400 Vrms |
Active power | 0 W |
ASM 2250 HP: | |
Mechanical power | 1.492e+06 W (2000 HP) |
For the SSM swing machine you only have to specify the requested terminal voltage (magnitude and phase). The active power is unknown. However, you can specify an active power that is used as an initial guess and help load flow convergence. Respecify the following SSM parameters:
Terminal voltage | 24984 Vrms |
Phase of UAN voltage | 0 degrees |
Active power guess | 7.5e6 W |
Click the Update Load Flow button. Once the load flow is solved the following solution is displayed. Use the scroll bar of the left window to look at the solution for each of the three machines.
The active and reactive electrical powers, mechanical power, and internal voltage are displayed for the SSM block.
P=7.542 MW; Q=-147 kvar Pmec=7.547 MW (or 7.547/1000=0.007547 pu) Internal voltage E=1.0 pu
The active and reactive electrical powers, mechanical power, and field voltage of the SM block are
P=0 W; Q=856 kvar Pmec=844 W Vf=1.428 pu
The active and reactive powers absorbed by the motor, slip, and torque of the ASM block are also displayed.
P=1.515MW Q=615 kvar Pmec=1.492 MW (2000 HP) Slip=0.006119 Torque=7964 N.m
As expected, the solution obtained is exactly the same as the one obtained with the R-L voltage source. The active power delivered by the swing bus is 7.54 MW (6.0 MW resistive load + 1.51 MW motor load = 7.51 MW, the difference (0.03 MW) corresponding to losses in the transformer).
Restart the simulation. You should get the same waveforms as those shown in the figure called Simulation Results.
[1] Yeager, K.E., and J.R.Willis, "Modeling of Emergency Diesel Generators in an 800 Megawatt Nuclear Power Plant," IEEE® Transactions on Energy Conversion, Vol. 8, No. 3, September, 1993.
Up to now, you have simulated a relatively simple power system consisting of a maximum of three machines. If you increase complexity of your network by adding extra lines, loads, transformers, and machines, the required simulation time becomes longer and longer. Moreover, if you are interested in slow electromechanical oscillation modes (typically between 0.02 Hz and 2 Hz on large systems) you might have to simulate for several tens of seconds, implying simulation times of minutes and even hours. The conventional continuous or discrete solution method is therefore not practical for stability studies involving low-frequency oscillation modes. To allow such studies, you have to use the phasor technique (see Introducing the Phasor Simulation Method).
For a stability study, we are not interested in the fast oscillation modes resulting from the interaction of linear R, L, C elements and distributed parameter lines. These oscillation modes, which are usually located above the fundamental frequency of 50 Hz or 60 Hz, do not interfere with the slow machine modes and regulator time constants. In the phasor solution method, these fast modes are ignored by replacing the network's differential equations by a set of algebraic equations. The state-space model of the network is therefore replaced by a transfer function evaluated at the fundamental frequency and relating inputs (current injected by machines into the network) and outputs (voltages at machine terminals). The phasor solution method uses a reduced state-space model consisting of slow states of machines, turbines, and regulators, thus dramatically reducing the required simulation time. Continuous variable-step solvers are very efficient in solving this type of problem. Recommended solver is ode23tb with a maximum time step of one cycle of the fundamental frequency (1/60 s or 1/50 s).
Now apply the phasor solution method to the two-machine system you have just simulated with the conventional method. Open the power_machines demo.
Double-click the Powergui, click Configure Parameters, and in the Powergui block parameters dialog box set Simulation type to Phasor. You must also specify the fundamental frequency used to solve the algebraic network equations. A default value of 60 Hz should already be entered in the Phasor frequency field. Close the Powergui and notice that the word Phasors now appears on the Powergui icon, indicating that this new method can be used to simulate your circuit. To start the simulation in steady state, you must first repeat the load flow and machine initialization procedure explained in the previous section, Load Flow and Machine Initialization.
In the Configuration Parameters dialog box, specify a Max step size of 1/60 s (one cycle) and start the simulation.
Observe that simulation is now much faster. The results compare well with those obtained in the previous simulation. A comparison of synchronous machine and asynchronous machine signals is shown below.
Comparison of Results for Continuous and Phasor Simulation Methods
The phasor solution method is illustrated on more complex networks presented in the Demos library. These demos are identified as
Transient stability of two machines with power system stabilizers (PSS) and a static var compensator (SVC) (power_svc_pss model)
Performance of three power system stabilizers for interarea oscillations (power_PSS model)
The first demo illustrates the impact of PSS and use of a SVC to stabilize a two-machine system. The second demo compares the performance of three different types of power system stabilizers on a four-machine, two-area system.
The phasor solution method is also used for FACTS models available in the factslib library. Three case studies demonstrating phasor simulation are presented in Transient Stability of Power Systems Using Phasor Simulation.
 | Simulating Variable Speed Motor Control | Building and Customizing Nonlinear Models |  |
Learn more about Simulink through this collection of videos, articles, technical literature and the Getting Started with Simulink Guide.
| © 1984-2009- The MathWorks, Inc. - Site Help - Patents - Trademarks - Privacy Policy - Preventing Piracy - RSS |
