Instead of specifying the rotor inertia in kg*m2, you would generally give the inertia constant H defined as ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------H = kinetic energy stored in the rotor at synchronous speed in joules machine nominal power in VA 1 -- J w H = ------------------------Pnom The inertia constant is expressed in seconds. For large machines, this constant is around 3 to 5 seconds. An inertia constant of 3 seconds means that the energy stored in the rotating part could supply the nominal load during 3 seconds. For small machines, H is lower. For example, for a 3 HP motor, it can be between 0.5 and 0.7 seconds.
Example 1: Three-Phase Transformer
Consider, for example, a three-phase two-winding transformer. The following typical parameters could be provided by the manufacturer: Nominal power = 300 kVA total for three phases Nominal frequency = 60 Hz Winding 1: connected in wye, nominal voltage = 25 kV RMS line-to-line resistance 0.01 p.u., leakage reactance = 0.02 p.u. Winding 2: connected in delta, nominal voltage = 600 V RMS line-to-line resistance 0.01 p.u., leakage reactance = 0.02 p.u. Magnetizing losses at nominal voltage in % of nominal current: Resistive 1%, Inductive 1% The base values for each single phase transformer are first calculated: For winding 1: Base power Base voltage Base current Base impedance 300 kVA/3 = 100e3 VA/phase 25 kV/sqrt(3) = 14434 V RMS 100e3/14434 = 6.928 A RMS 14434/6.928 = 2083
Base resistance Base inductance For winding 2: Base power Base voltage Base current Base impedance Base resistance Base inductance
14434/6.928 = 2083 2083/(2*60)= 5.525 H
300 kVA/3 = 100e3 VA 600 V RMS 100e3/600 = 166.7 A RMS 600/166.7 = 3.60 600/166.7 = 3.60 3.60/(2*60) = 0.009549 H
The values of the winding resistances and leakage inductances expressed in SI units are therefore For winding 1: R1= 0.01 * 2083 = 20.83 ; L1= 0.02*5.525 = 0.1105 H For winding 2: R2= 0.01 * 3.60 = 0.0360 ; L2= 0.02*0.009549 = 0.191 mH For the magnetizing branch, magnetizing losses of 1% resistive and 1% inductive mean a magnetizing resistance Rm of 100 p.u. and a magnetizing inductance Lm of 100 p.u. Therefore, the values expressed in SI units referred to winding 1 are Rm = 100*2083 = 208.3 k Lm = 100*5.525 = 552.5 H

Figure 3-12: DC Motor Drive Using SimPowerSystems (power_dcdrive)
With a Manual Switch block, you can select both the reference speed and the load torque applied to the motor shaft in order to use either a constant value or a step function. Initially the reference speed is set to a constant value of 120 rad/s and the load torque is also maintained constant at 5 N.m. The DC motor represented by the DC Machine block is modeled in two separate parts: electrical and mechanical. To view the Simulink model of the DC motor, click the DC Machine block and use the Look under mask item in the model Edit menu.
The mechanical subsystem is
The armature circuit is represented by an RL circuit in series with a controlled voltage source, the value of which is KE. The field circuit is represented by an RL circuit.
The mechanical part is represented by Simulink blocks, which implement the following equation: d T m = J ------- + B + sgn ( ) T L dt Set the DC machine parameters to the desired values by using the dialog box of the DC Machine block. You implement the load torque-speed characteristic using a Simulink Math Function block. The motor used in this case study is a separately excited, 5 HP/240 V DC motor with the following parameters:

Ra La KE KT

0.mH 1.23 V/(rad/s) 1.23 N.m/A
A 10 mH inductor (Ls) is connected in series with the DC motor to smooth out the armature current. The constant excitation is implemented by the connection of a DC Voltage Source block to the field winding. The required trigger signal for the GTO thyristor is generated by a hysteresis current controller, which forces the motor current to follow the reference within +h/2 and h/2 limits (h is the hysteresis band). The current controller is a masked block that contains

2 Ia 1 Iref Relay

The speed control loop uses a proportional-integral controller, which is implemented by Simulink blocks.
Kp 1 wm 2 wref 1 s 1 Iref
Simulation of the DC Drive
Run the simulation by selecting Start from the Simulation menu in Simulink. Set the simulation parameters in the Simulation parameters dialog as follows.
Simulation time Solver Type Max Step Size Initial Step Size Relative Tolerance Absolute Tolerance Start Time: 0, Stop time: 1.2
Variable-step ode23tb (stiff/TR-BDF2) auto auto 1e-3 1e-3
The motor voltage, current waveforms, and motor speed are displayed on three axes of the scope connected to the variables Va, Ia, and.

Figure 3-20: Variable-Speed Field-Oriented Induction Motor Drive (power_acdrive)
The induction motor is modeled by an Asynchronous Machine block. The motor used in this case study is a 50 HP, 460 V, four-pole, 60 Hz motor having the following parameters:

Rs Lls Lm Rr Llr

0.087 0.8 mH 34.7 mH 0.228 0.8 mH
The reference speed and the load torque applied to the motor shaft can be both selected by a Manual Switch block in order to use either a constant value or a step function. Initially the reference speed is set a constant value of 120 rad/s and the load torque is also maintained constant at 0 N.m The current-controlled PWM inverter circuit is shown in Figure 3-20. The IGBT inverter is modeled by a Universal Bridge block in which the Power Electronic device and Port configuration options are selected as IGBT/Diode
and ABC as output terminals respectively. The DC link input voltage is represented by a 780 V DC voltage source. The current regulator, which consists of three hysteresis controllers, is built with Simulink blocks. The motor currents are provided by the measurement output of the Asynchronous Machine block.

2 Iabc

1 Pulses

1 Iabc*

The conversions between abc and dq reference frames are executed by the abc_to_dq0 Transformation and dq0_to_abc Transformation blocks of Figure 3-20.
id f(u) sin(u) 2 Iabc Mux f(u) iq 2/3 2/Id 2 Iq

1 Teta

cos(u)

abc_dq

3 Teta
cos(u) sin(u) Mux 2 Iq* 1 Id*
ia f(u) f(u) ib 1 ic Mux 1 Iabc

dq_abc

The rotor flux is calculated by the Flux_Calculation block of Figure 3-20.

34.7e3 0.1557s+1

1 Phir
The rotor flux position (e) is calculated by the Teta Calculation block of Figure 3-20.
1 Iq 2 Phir Mux 3 wr 2 Mux 34.7e3*u[1]/(u[2]*0.1557+1e3) s 1 Teta
The stator quadrature-axis current reference (iqs*) is calculated by the iqs*_Calculation block of Figure 3-20.

1 Te* 2 Phir

u[1]*0.341/(u[2]+1e3)

Xc Id 2 = acos cos ( ) ----------------------------- Vc 9.2 = acos cos ( 18 ) ---------------------------------- 18 = 16.9 213.3 Now verify the commutation angle by plotting the currents in two valves, showing for example current extinction in valve 1 and current buildup in valve 3 of one six-pulse bridge of the rectifier. Open the rectifier subsystem. Then open the upper bridge dialog box and select All voltages and currents for the Measurement parameter. Now copy the Multimeter block from the Measurements library into your case4 model. Double-click the Multimeter block. A window showing all the bridge voltages and currents appears. Select the following signals:

uSw1 iSw1 iSw3

Rectifier/Universal Bridge Rectifier/Universal Bridge Rectifier/Universal Bridge
The number of signals (3) is displayed in the multimeter icon. Using a Demux block, send the three multimeter output signals to a two-trace scope (Trace 1: uSw1 Trace 2: iSw1 and iSw3). Restart the simulation. The waveforms illustrating two cycles are shown in the following figure. The measured commutation angle is 14 steps of 50 s or 15.1 of a 60 Hz period. The resolution with a 50 s time step is 1.1; this angle compares reasonably well with the theoretical value.

2 uSw1 (V) 4

0.i Sw1 & Sw3 (A) 0.alphaR (deg) 10 0.5

= 15.1

0.505 0.51 0.515 0.52 0.525 0.53

0.515 Time (s)

Figure 3-29: Valve Voltage and Currents (Commutation from Valve 1 to Valve 3)
Finally, to validate the measurement at the inverter, plot the valve 1 voltage and current. Also plot the commutating voltage corresponding to the outgoing valve 1 to be extinguished and the filtered mean value of as shown in Figure 3-30. (The filter is low-pass with a time constant of 20 ms.) Verify also that the values of , , and add up to 180.
Figure 3-30: Current and Commutation Voltage of Valve 1 Showing
Response to a Step of Reference Current
At t = 0.6 s, a 0.2 p.u. step is applied to the reference current (decrease from 1 p.u. to 0.8 p.u.). At t = 0.75 s, another step is applied to set the reference back to 1 p.u. Observe the response of the current regulator. It stabilizes in approximately 0.1 s.
Figure 3-31: Response to a 0.2 p.u. Step of the Reference Current

DC Line Fault

Disconnect the Step Up & Down block in order to eliminate the step disturbance applied to the reference current. In the DC Fault and Forced Delay blocks of the power_hvdc12pulse model, change the multiplication factor of 100 to 1, so that a fault is now applied at t = 0.6 s. Open the FAULT scope to observe the fault current. Restart the simulation.

VdL (pu)

0.0.5 0.0.6 0.7 0.8 0.1.1 1.2 1.3

Id & Idref (pu)

0.5 0.6 0.7 0.8 0.1.1 1.2 1.3

alphaR (deg)

0.9 Time (s)

2 0.5 1.0.0.5 0.5 160

alphaI (deg)
0.0.6 0.7 0.8 0.1.1 1.2 1.3

ifalut DC (A)

0.5 0.6 0.7 0.8 0.9 time (s) 1 1.1 1.2 1.3
Figure 3-32: DC Line Fault on the Rectifier Side
At fault application (t = 0.6 s), the DC current increases to 2.3 p.u. and the DC voltage falls to zero at the rectifier. This DC voltage drop is seen by the Voltage Dependent Current Order Limiter (VDCOL), which reduces the reference current to 0.3 p.u. at the rectifier. A DC current still continues to circulate in the fault. Then, at t = 0.65 s, the rectifier firing angle is forced to 165 degrees when the signal applied to the ForcedAlpha input goes high. This signal would normally be provided by the protection system not simulated here. The rectifier now operates in inverter mode. The DC line voltage becomes negative and the energy stored in the line is returned to the AC network, causing rapid extinction of the fault current at its next zero crossing. Then is released at t = 0.7 s and the normal DC voltage and current recover in approximately 0.5 s.
AC Line-to-Ground Fault at the Rectifier
Now you modify the fault timings in order to apply a line-to-ground fault. In the DC Fault and Forced Delay blocks of power_hvdc12pulse, change the multiplication factor of 1 to 100, so that the DC fault is now eliminated. In the A-G Fault block, change the multiplication factor in the switching times to 1, so that a six-cycle line-to-ground fault is now applied at the rectifier. Restart the simulation.

RECTIFIER signals 2

1 0.0.6 0.7 0.8 0.1.1 1.2

Id & Id ref (pu)

0 0.5 0.6 0.7 0.8 0.1.1 1.2

Alpha (deg)

0 0.5 0.6 0.7 0.8 Time (s) INVERTER signals 2 0.1.1 1.2
0.5 0.6 0.7 0.8 Time (s) 0.1.1 1.2
Figure 3-33: Rectifier, Inverter Signals for an AC Line Fault on Rectifier Side

Vabc (pu)

0.0.1.5 0.5 0.6 0.7 0.8 0.1.1 1.2

Iabc (A)

50 0.5 0.6 0.7 0.8 Time (s) 0.1.1 1.2
Figure 3-34: Voltages and Currents on the 60 Hz Side for an AC Line Fault on the Rectifier Side
Notice the 120 Hz oscillations in the DC voltage and currents during the fault. When the fault is cleared at t = 0.7 s, the VDCOL operates and reduces the reference current to 0.3 p.u. The system recovers in approximately 0.4 s after fault clearing.

Limitations of Discretization with Nonlinear Models
There are a few limitations to discretizing nonlinear models.
Discretization of individual forced-commutated electronic devices is not allowed
Discretization of circuits containing forced-commutated power electronic devices (IGBT, GTO, or MOSFET) is permitted only with the Universal Bridge block. Discretization of circuits containing individual forced-commutated devices is not allowed. For example, an attempt to discretize the buck DC chopper circuit saved in the power_buckconv model produces a warning message:
Figure 4-5: A Circuit Containing Individual Forced Commutated Electronic Switches Cannot be Discretized
In this circuit, the opening of the GTO forces a quasi instantaneous conduction of the freewheeling diode. If the circuit was discretized, the diode would be fired with one step delay, and the inductive current chopping would produce large overvoltages. However, for conventional converter topologies as in the case of the Universal Bridge, the switch interactions are known in advance. For example, in a six-switch IGBT/Diode inverter (Figure 4-6 following), opening of IGBT1 causes instantaneous conduction of diode D2 in the same arm. As the circuit topology is predetermined, it is possible to force firing of the diode in the same step that the IGBT opens. You should use a continuous method if you prefer to use individual IGBT and Diode blocks to simulate a complete inverter.
Figure 4-6: IGBT Inverter Simulated by the Universal Bridge
Minimal load is required at machine terminals
When using electrical machines in discrete systems, you might have to use a small parasitic resistive load, connected at the machine terminals, in order to avoid numerical oscillations. Large sample times require larger loads. The minimum resistive load is proportional to the sample time. As a rule of thumb, remember that with a 25 s time step on a 60 Hz system, the minimum load is approximately 2.5% of the machine nominal power. For example, a 200 MVA synchronous machine in a power system discretized with a 50 s sample time requires approximately 5% of resistive load or 10 MW. If the sample time is reduced to 20 s, a resistive load of 4 MW should be sufficient.
Lon = 0 is used for diodes and thyristors in discrete circuits
Diodes and thyristors used in a discretized circuit must have a zero internal inductance. If you discretize a circuit containing diodes or thyristors with Lon > 0, SimPowerSystems prompts you with a warning indicating that Lon will be reset to zero.

Three-Phase Breaker Three-Phase Dynamic Load
Implement a three-phase circuit breaker opening at current zero crossing Implements a three-phase dynamic load with active power and reactive power as a function of voltage or controlled from an external input Implement a programmable phase-to-phase and phase-to-ground fault breaker system Implement a three-phase RL impedance with mutual coupling between phases and allow specification in the form of positive- and zero-sequence parameters Implement a three-phase parallel RLC branch Implement a three-phase parallel RLC load with selectable connection Implement a three-phase transmission line section with lumped parameters Implement a three-phase series RLC branch
Three-Phase Fault Three-Phase Mutual Inductance Z1-Z0 Three-Phase Parallel RLC Branch Three-Phase Parallel RLC Load Three-Phase PI Section Line Three-Phase Series RLC Branch
Three-Phase Series RLC Load Implement a three-phase series RLC load with selectable connection Three-Phase Transformer 12 Terminals Three-Phase Transformer (Two Windings) Three-Phase Transformer (Three Windings) Zigzag Phase-Shifting Transformer Implement three single-phase, two-winding transformers where all terminals are accessible Implement a three-phase transformer with two windings Implement a three-phase transformer with three windings Implement a zigzag phase-shifting transformer with secondary winding connection
Modeling with Phasor Elements
Static Var Compensator Implement a phasor model of a three-phase, three-wire static var compensator
Modeling Power Electronics Components
Diode GTO Ideal Switch IGBT MOSFET Three-Level Bridge Thyristor Universal Bridge Implement a diode model Implement a gate-turn-off (GTO) thyristor model Implement an ideal switch model Implement an insulated-gate-bipolar-transformer (IGBT) model Implement a metal-oxide-semiconductor-field-effect-transistor (MOSFET) model Implement a three-level neutral point clamped (NPC) power converter Implement a thyristor model Implement a universal three-phase bridge converter
Modeling Electrical Machines
Asynchronous Machine DC Machine Excitation System Generic Power System Stabilizer Hydraulic Turbine and Governor Model the dynamics of a three-phase asynchronous machine (induction machine) Model a separately excited DC machine. Provide an excitation system for the synchronous machine and regulate its terminal voltage in generating mode Provide a generic power system stabilizer for the synchronous machine and regulate its electrical power Model a hydraulic turbine and a proportional-integral-derivative governor system

Open the power_pwm demo. Note in the simulation parameters that a small relative tolerance is required because of the high switching rate of the inverter. Run the simulation and observe the machines speed and torque.
The first graph shows the machines speed going from 0 to 1725 rpm (1.0 p.u.). The second graph shows the electromagnetic torque developed by the machine. Because the stator is fed by a PWM inverter, a noisy torque is observed. However, this noise is not visible in the speed because it is filtered out by the machines inertia, but it can also be seen in the stator and rotor currents, which are observed next.
Finally, look at the output of the PWM inverter. Because nothing of interest can be seen at the simulation time scale, the graph concentrates on the last moments of the simulation.
[1] Krause, P.C., O. Wasynczuk, and S.D. Sudhoff, Analysis of Electric Machinery, IEEE Press, 1995. [2] Mohan, N., T.M. Undeland, and W.P. Robbins, Power Electronics: Converters, Applications, and Design, John Wiley & Sons, Inc., New York, 1995, Section 8.4.1.
Machine Measurement Demux, Powergui

Breaker

5Breaker
Implement a circuit breaker opening at the current zero crossing Elements The Breaker block implements a circuit breaker where the opening and closing times can be controlled either from an external Simulink signal (external control mode), or from an internal control timer (internal control mode). The arc extinction process is simulated by opening the breaker device when the current passes through 0 (first current zero crossing following the transition of the Simulink control input from 1 to 0). When the breaker is closed it behaves as a resistive circuit. It is represented by a resistance Ron. The Ron value can be set as small as necessary in order to be negligible compared with external components (typical value is 10 m). When the breaker is open it has an infinite resistance. If the Breaker block is set in external control mode, a Simulink input appears on the block icon. The control signal connected to the Simulink input must be either 0 or 1: 0 to open the breaker, 1 to close it. If the Breaker block is set in internal control mode, the switching times are specified in the dialog box of the block. If the breaker initial state is set to 1 (closed), SimPowerSystems automatically initializes all the states of the linear circuit and the Breaker block initial current so that the simulation starts in steady state. A series Rs-Cs snubber circuit is included in the model. It can be connected to the circuit breaker. If the Breaker block happens to be in series with an inductive circuit, an open circuit or a current source, you must use a snubber.

Breaker resistance Ron The internal breaker resistance, in ohms (). The Breaker resistance Ron parameter cannot be set to 0. Initial state The initial state of the breaker. A closed contact is displayed in the block icon when the Initial state parameter is set to 1, and an open contact is displayed when it is set to 0. Snubber resistance Rs The snubber resistance, in ohms (). Set the Snubber resistance Rs parameter to inf to eliminate the snubber from the model.
Snubber capacitance Cs The snubber capacitance, in farads (F). Set the Snubber capacitance Cs parameter to 0 to eliminate the snubber, or to inf to get a resistive snubber. Switching times Specifies the vector of switching times when using the Breaker block in internal control mode. At each switching time the Breaker block opens or closes depending on its initial state. For example, if the Initial state parameter is 0 (open), the breaker closes at the first switching time, opens at the second switching time, and so on. The Switching times parameter is not visible in the dialog box if the External control of switching times parameter is selected. External control of switching times If selected, adds a Simulink input to the Breaker block for external control of the switching times of the breaker. The switching times are defined by a logical signal (0 or 1) connected to the Simulink input. Measurements Select Branch voltage to measure the voltage across the Breaker block terminals. Select Branch current to measure the current flowing through the Breaker block. If the snubber device is connected to the breaker model, the measured current is the one flowing through the breaker contacts only. Select Branch voltage and current to measure the breaker voltage and the breaker current. Place a Multimeter block in your model to display the selected measurements during the simulation. In the Available Measurements list box of the Multimeter block, the measurement is identified by a label followed by the block name:
Measurement Label Ub: Ib:
Branch voltage Branch current

Limitations

When the block is connected in series with an inductor or another current source, you must add the snubber circuit. In most applications you can use a resistive snubber (Snubber capacitance parameter set to inf) with a large resistor value (Snubber resistance parameter set to 1e6 or so). Because of modeling constraints, the internal breaker inductance Ron cannot be set to 0. You must use a stiff integration algorithm to simulate circuits with the Breaker block. ode23tb or ode15s with default parameters usually gives the best simulation speed.

Simplified Synchronous Machine
5Simplified Synchronous Machine
Model the dynamics of a simplified three-phase synchronous machine Machines The Simplified Synchronous Machine block models both the electrical and mechanical characteristics of a simple synchronous machine. The electrical system for each phase consists of a voltage source in series with an RL impedance, which implements the internal impedance of the machine. The value of R can be zero but the value of L must be positive. The Simplified Synchronous Machine block implements the mechanical system described by
1 ( t ) = ------- ( Tm Te ) dt K d ( t ) 2H
( t ) = ( t ) + 0 where = Speed variation with respect to speed of operation H = Constant of inertia Tm = Mechanical torque Te = Electromagnetic torque Kd = Damping factor representing the effect of damper windings ( t ) = Mechanical speed of the rotor 0 = Speed of operation (1 p.u.) Although the parameters can be entered in either SI units or per unit in the dialog box, the internal calculations are done in per unit. The following block diagram illustrates how the mechanical part of the model is implemented. Notice that the model computes a deviation with respect to the speed of operation, and not the absolute speed itself.

Tm (p.u.) Te (p.u.)

1 1/2H 1/s

(p.u.)

The Kd damping coefficient simulates the effect of damper windings normally used in synchronous machines. When the machine is connected to an infinite network (zero impedance), the variation of machine power angle delta () resulting from a change of mechanical power (Pm) can be approximated by the following second-order transfer function: P m = ( s 2H ) ( s + 2 n s + n ) where Pm n s Pmax
Power angle delta: angle of internal voltage E with respect to terminal voltage, in radians Mechanical power in p.u. Frequency of electromechanical oscillations = s P max ( 2H ) in rad/s Damping ratio = ( K d 4 ) 2 ( s H P max ) Electrical frequency in rad/s Maximum power in p.u. transmitted through reactance X at terminal voltage Vt and internal voltage E. Pmax = V t E X (p.u.) where Vt, E, and X are in p.u. Inertia constant(s) Damping factor (p.u._of_torque / p.u._of_speed)
This approximate transfer function, which has been derived by assuming sin() = , is valid for small power angles ( < 30 degrees). It follows from the above expression that the Kd value required to obtain a given damping ratio is K d = 4 s H P max 2

The Surge Arrester block is modeled as a current source driven by the voltage appearing across its terminals. Therefore, it cannot be connected in series with an inductor or another current source. As the Surge Arrester block is highly nonlinear, a stiff integrator algorithm must be used to simulate the circuit. ode15s or ode23tb with default parameters usually gives the best simulation speed. For continuous simulation, in order to avoid an algebraic loop, the voltage applied to the nonlinear resistance is filtered by a first-order filter with a time constant of 0.01 microseconds. This very fast time constant does not significantly affect the result accuracy. When the Surge Arrester block is used in a discrete system, a time delay of one simulation step is used. This delay can cause numerical oscillations if the sample time is too large. The power_arrester demo illustrates the use of metal-oxide varistors (MOV) on a 735 kV series-compensated network. Only one phase of the network is represented. The capacitor connected in series with the line is protected by a 30 column arrester. At t = 0.03 seconds, a fault is applied at the load terminals.
The current increases in the series capacitor and produces an overvoltage that is limited by the Surge Arrester block. Then the fault is cleared at t = 0.1 seconds.
At fault application, the resulting overvoltage makes the MOV conduct. The waveforms displayed by Umov and Imov measurements as well as the V-I characteristic plotted by the X-Y scope are shown below:
Synchronized 6-Pulse Generator
5Synchronized 6-Pulse Generator
Implement a synchronized pulse generator to fire the thyristors of a six-pulse converter Extras/Control Block A discrete version of this block is available in the Extras/Discrete Control Blocks library.
The Synchronized 6-Pulse Generator block can be used to fire the six thyristors of a six-pulse converter. The output of the block is a vector of six pulses individually synchronized on the six thyristor voltages. The pulses are generated alpha degrees after the increasing zero crossings of the thyristor commutation voltages. The figures below display the synchronization of the six pulses for an alpha angle of 0 degrees. The pulses are generated exactly at the zero crossings of the three line-to-line synchronization voltages.

synchronization voltages

pulse 1

pulse 2

pulse 3

pulse 4

Number of bridge arms Set to 1 or 2 to get a single-phase converter (two or four switching devices). Set to 3 to get a three-phase converter connected in Graetz bridge configuration (six switching devices). Snubber resistance Rs The snubber resistance, in ohms (). Set the Snubber resistance Rs parameter to inf to eliminate the snubbers from the model. Snubber capacitance Cs The snubber capacitance, in farads (F). Set the Snubber capacitance Cs parameter to 0 to eliminate the snubbers, or to inf to get a resistive snubber.
In order to avoid numerical oscillations when your system is discretized, you need to specify Rs and Cs snubber values for diode and thyristor bridges. For forced-commutated devices (GTO, IGBT, or MOSFET), the bridge operates satisfactorily with purely resistive snubbers as long as firing pulses are sent to switching devices. If firing pulses to forced-commutated devices are blocked, only antiparallel diodes operate, and the bridge operates as a diode rectifier. In this condition appropriate values of Rs and Cs must also be used. When the system is discretized, use the following formulas to compute approximate values of Rs and Cs: Ts Rs > 2 -----Cs Pn Cs < -------------------------------------( 2f )Vn where P n = Nominal power of single or three phase converter (VA) Vn = Nominal line-to-line AC voltage (Vrms) f = Fundamental frequency (Hz) T s = Sample Time (s) These Rs and Cs values are derived from the following two criteria: - The snubber leakage current at fundamental frequency is less than 0.1% of nominal current when power electronic devices are not conducting. - The RC time constant of snubbers is higher than two times the sample time Ts. These Rs and Cs values that guarantee numerical stability of the discretized bridge can be different from actual values used in a physical circuit.
Power electronic device Select the type of power electronic device to use in the bridge. Ron Internal resistance of the selected device, in ohms (). Lon Internal inductance, in henries (H), for the diode or the thyristor device. When the bridge is discretized, the Lon parameter must be set to zero. Forward voltage Vf This parameter is available only when the selected Power electronic device is Diodes or Thyristors. Forward voltage, in volts (V), across the device when it is conducting. Forward voltages [Device Vf, Diode Vfd] This parameter is available when the selected Power electronic device is GTO/Diodes or IGBT/Diodes. Forward voltages, in volts (V), of the forced-commutated devices (GTO, MOSFET, or IGBT) and of the antiparallel diodes. [Tf (s) Tt (s)] Fall time Tf and tail time Tt, in seconds (s), for the GTO or the IGBT devices. Measurements Select Device voltages to measure the voltages across the six power electronic device terminals. Select Device currents to measure the currents flowing through the six power electronic devices. If antiparallel diodes are used, the measured current is the total current in the forced-commutated device (GTO, MOSFET, or IGBT) and in the antiparallel diode. A positive current therefore indicates a current flowing in the forced-commutated device and a negative current indicates a current flowing in the diode. If snubber devices are defined, the measured currents are the ones flowing through the power electronic devices only. Select UAB UBC UCA UDC voltages to measure the terminal voltages (AC and DC) of the Universal Bridge block.

Although this circuit contains a total of six inductors and capacitors, there are only four state variables. The names of the state variables are given by the first four lines of the states matrix. The last two lines are followed by an asterisk indicating that these two variables are a linear combination of the state variables. The dependencies can be viewed in the output file power_circ2ss.net.
The following capacitor voltages are dependent: Uc_b7_n12_0 = + Uc_b5_n11_0 - Uc_b6_n11_12 The following inductor currents are dependent: Il_b1_n1_2 = + Il_b2_n2_0
The A,B,C,D matrices contain the state-space model of the circuit without nonlinear elements (all switches open). The x0 vector contains the initial state values considering the switch Sw1 closed. The Asw, Bsw, Csw, and Dsw matrices
contain the state-space model of the circuit considering the closed switch Sw1. The x0sw vector contains the initial current in the closed switch.
A A = -4.0006e+0 --4992.2 Asw Asw = -80.999 -199.99 4.9947e+05 -5244.7 4.9922e+05 -5242.2
0 -499.25 04.9925e+05 -2 0
The system source frequencies are returned in the freq vector.

freq freq = 0

The corresponding steady-state complex outputs are returned in the (6-by-3) y matrix where each column corresponds to a different source frequency. For example, you can obtain the magnitude of the six voltage and current outputs at 60 Hz as follows:
abs(y(:,2)) ans = 0.0099987 199.42 0.99.808 2.0993 199.41 0.016519
The initial values of the four state variables are returned in the x0 vector. You must use this vector in the State-Space block to start the simulation in steady state.
x0 x0 = 2.3302 14.111 14.07 3.1391e-05
The initial values of switch currents are returned in x0sw. To start the simulation in steady state, you must use these values as initial currents for the nonlinear model simulating the switches.

x0sw x0sw = 0.16155 0

The Simulink diagram of the circuit shown in the following figure is available in the power_circ2ss_slk model. If no resistive switches had been used, the linear part of the circuit could have been simulated with the State-Space block of the Simulink/Continuous library. However, as resistive switches are used, the sfun_psbcontc S-function is used instead of the State-Space block. This S-function reevaluates the state-space matrices during simulation when the circuit topology is changing (after a switch is opened or closed). Appropriate inputs and outputs are used to connect the switch and saturable reactance models to the linear system. Notice that the status of each switch is fed back from the breaker to the S-function, after the inputs mentioned earlier. You can find the breaker and saturable_transformer blocks in the powerlib_models/Continuous library containing all the nonlinear continuous models used by SimPowerSystems. As the breaker model is vectorized, a single block is used to simulate the two switches Sw1 and Sw2. If you use the powerlib library to build your circuit, the same Simulink system is generated automatically by the power_analyze command. The powerlib version of this system is also available in the power_circ2ss_sps model and is shown below.