Model the Dynamics of Three-phase Round-rotor or Salient-pole Synchronous Machine - Simulink

4/12/2014 Model the dynamics of three-phase round-rotor or salient-pole synchronous machine - Simulink

http://www.mathworks.com/help/physmod/sps/powersys/ref/synchronousmachine.html 1/20

Synchronous MachineModel the dynamics of three-phase round-rotor or salient-pole synchronous machine

Library

Machines

Description

The Synchronous Machine block operates in generator or motor modes. The operating mode is dictated bythe sign of the mechanical power (positive for generator mode, negative for motor mode). The electrical partof the machine is represented by a sixth-order state-space model and the mechanical part is the same as inthe Simplified Synchronous Machine block.

The model takes into account the dynamics of the stator, field, and damper windings. The equivalent circuitof the model is represented in the rotor reference frame (qd frame). All rotor parameters and electricalquantities are viewed from the stator. They are identified by primed variables. The subscripts used aredefined as follows:

d,q: d and q axis quantity

R,s: Rotor and stator quantity

l,m: Leakage and magnetizing inductance

f,k: Field and damper winding quantity

The electrical model of the machine is

with the following equations.

( )



This model assumes currents flowing into the stator windings. The measured stator currents returned by theSynchronous Machine block (Ia, Ib, Ic, Id, Iq) are the currents flowing out of the machine.

Base Values, Transformation Ratio, and Rotor Parameters Referred to the Stator

The Synchronous Machine SI Fundamental block and the Synchronous Machine pu Fundamental block allowyou to specify the fundamental parameters of a synchronous machine. You enter field and damper windingsparameters (resistances, leakage inductances, and mutual inductances) in SI (Ω, H) or in pu. When youenter parameters in SI, the RL parameters of field and damper windings are not the actual field RL values ofthe machine but the RL values referred to the stator.

You can compute base values for stator and rotor windings when the parameters are specified in pu. Youcan also compute the Stator/Field transformation ratio and the field parameters referred to the stator from theactual field parameters (windings RL values, nominal field voltage, and nominal field current).

Stator Base ValuesThe stator base values are:

= base stator voltage = peak nominal line-to-neutral voltage (V)

= base stator current (A)

= base stator impedance (Ω)

= base angular frequency (rad/s)

= base stator inductance (H)

with

Pn = three-phase nominal power (VA)

Vn = nominal line-to-line voltage (Vrms)

V d

V q

V ′fd

V ′kd

V ′kq1

V ′kq2

= Rsi d +ddt φd −ωRφq

= Rsi q +ddt φq +ωRφd

= R′fdi ′fd +ddt φ

′fd

= R′kdi ′kd +ddt φ

′kd

= R′kq1i ′kq1 +ddt φ

′kq1

= R′kq2i ′kq2 +ddt φ

′kq2

φd

φq

φ′fd

φ′kd

φ′kq1

φ′kq2

= L di d + Lmd

(i ′fd + i ′kd

)

= L qi q + Lmqi ′kq

= L ′fdi ′fd + Lmd

(i d + i ′kd

)

= L ′kdi ′kd + Lmd

(i d + i ′fd

)

= L ′kq1i ′kq1 + Lmqi q

= L ′kq2i ′kq2 + Lmqi q

V sbase =V n

G2

G3

Isbase =Pn

G2

V nG3

Z sbase =V sbaseIsbase

=V n

2

Pn

ωbase = 2π f n

L sbase =Z sbaseωbase



fn = nominal frequency (Hz)

ifn = nominal field current producing nominal stator voltage at no load (A)

The stator parameters to specify in the Synchronous Machine SI Fundamental block are:

Rs = stator resistance per phase (Ω)

Ll = stator leakage inductance (H)

Lmd = direct-axis magnetizing inductance viewed from stator (H)

Lmq = quadrature-axis magnetizing inductance viewed from stator (H)

The stator parameters to enter in the Synchronous Machine pu Fundamental block are:

= stator resistance per phase (pu)

= stator leakage inductance (pu)

= direct-axis magnetizing inductance (pu)

= quadrature-axis magnetizing inductance (pu)

Stator/Field Transformation RatioThe following figure shows one phase of the stator winding coupled with the field winding.

Ns and Nf are, respectively, the equivalent number of sinusoidally distributed turns of the stator winding andof the field winding.

Rs , Ll = stator resistance and leakage inductance.

Rf , Llfd = field resistance and leakage inductance.

When the three stator windings are energized with a three-phase positive-sequence voltage and field windingis open, the stator magnetizing inductance is Lmd. However, when only one phase is energized and fieldwinding is open, the magnetizing inductance is 2/3 Lmd as shown in the figure.

At no load, when the field winding is rotating at nominal speed and bears the nominal field DC current ifn, theamplitude of AC voltage (peak value) induced on one phase of stator is Vsbase.

Rs_pu =Rs

Z sbase

L l_pu =L l

L sbase

Lmd_pu =LmdL sbase

Lmq_pu =LmqL sbase



The maximum mutual inductance between one stator winding and the field winding is obtained when the twowindings are aligned. It is given by:

from which we deduce the transformation ratio:

The transformation ratio can be also expressed as:

where Ifbase is the base field current, which is computed as explained below.

Field Base Values

= base field current (A)

= base field voltage (V)

= base field impedance (Ω)

= base field inductance (H)

The actual field parameters are:

Rf = field resistance (Ω)

Llfd = field leakage inductance (H)

The field parameters to enter in the Synchronous Machine pu Fundamental block menu are:

= field resistance (pu)

= field leakage inductance (pu)

Field Voltage, Current and RL Values Referred to the StatorThe field parameters to enter in the Synchronous Machine SI Fundamental block are the field resistance andleakage inductance referred to the stator (Rf′, Llfd′).

If the nominal field current ifn is known, the transformation ratio Ns/Nfis calculated using the same equationas for the stator/field transformation ratio.

L sfd =23 Lmd

N fN s

=V sbase

i fn ωbase

N sN f

= 23 Lmdi fn ωbaseV sbase

N sN f

= 23I fbaseIsbase

I fbase = i fn Lmd_pu

V fbase =PnI fbase

Z fbase =V fbaseI fbase

L fbase =Z fbaseωbase

R f_pu =R f

Z fbase

L lfd_pu =L l fdL fbase



According to Krause [1], the field voltage and current referred to the stator (Vf′, If′) are deduced from actualVf, If values as follows:

When the actual field resistance Rf and leakage inductances Llfd (seen from the rotor) are known, the valuesreferred to the stator are:

When the nominal field current is not known, and if the pu values of field resistance and leakage inductancesare known (Rf_pu, Llfd_pu), the corresponding SI values referred to the stator are computed as follows:

The same conversions are used for RL parameters of damper windings.

Field Voltage and Current for SI Fundamental Synchronous MachineWhen you specify the nominal field current, the signal applied to the Vf input corresponds to the actual fieldvoltage, as in real life. The field current returned by the measurement output also correspond to the actualfield current If.

Nominal field voltage producing nominal stator voltage at no load is given by:

When you do not specify the nominal field current, the signal applied to the Vf input corresponds to the actualfield voltage referred to the stator. In this case, the nominal field voltage referred to the stator producingnominal stator voltage at no load is:

The field current returned by the measurement output is the field current referred to the stator. The nominalfield current referred to the stator is:

Field Voltage and Current for PU Fundamental Synchronous MachineThe voltage applied at the Vf input of the Synchronous Machine pu Fundamental block is normalized withrespect to nominal field voltage so that a 1pu input produces a 1 pu stator voltage at no load. The If currentreturned by the measurement output of the block is also normalized with respect to nominal field current sothat a 1pu input produces If = 1pu.

V f ' =N sN f

V f

I f ' =23N fN s

I f

R f ' =32 R f

N sN f

2

L lfd ' =32 L lfd

N sN f

2

R f ' = R f_pu × Z sbase

L lfd ' = L lfd_pu × L sbase

V fn = R f × i fn

V fn ' =R f_puLmd_pu

V sbase =R f '

Lmd ωbaseV sbase

I fn ' =IsbaseLmd_pu

=IsbaseI fbase

i fn



Dialog Box and Parameters

In the powerlib library you can choose between three Synchronous Machine blocks to specify theparameters of the model. They simulate exactly the same synchronous machine model; the only differenceis the way that you enter the parameter units in the Parameters tab.

Configuration Tab

Preset modelProvides a set of predetermined electrical and mechanical parameters for various synchronous machineratings of power (kVA), phase-to-phase voltage (V), frequency (Hz), and rated speed (rpm).

Select one of the preset models to load the corresponding electrical and mechanical parameters in theentries of the dialog box. Select No if you do not want to use a preset model, or if you want to modifysome of the parameters of a preset model, as described below.

When you select a preset model, the electrical and mechanical parameters in the Parameters tab of thedialog box become nonmodifiable (unavailable). To start from a given preset model and then modifymachine parameters, do the following:



1. Select the preset model that you want to initialize the parameters.

2. Change the Preset model parameter value to No. This action does not change the machineparameters. By doing so, you just break the connection with the particular preset model.

3. Modify the machine parameters as you want, then click Apply.

Mechanical inputAllows you to select the mechanical power applied to the shaft or the rotor speed as a Simulink® input ofthe block, or to represent the machine shaft by a Simscape™ rotational mechanical port.

Select Mechanical power Pm to specify a mechanical power input, in W or in pu, and change labeling ofthe block input to Pm. The machine speed is determined by the machine Inertia J (or inertia constant H forthe pu machine) and by the difference between the mechanical torque Tm, resulting from the appliedmechanical power Pm, and the internal electromagnetic torque Te. The sign convention for the mechanicalpower is when the speed is positive, a positive mechanical power signal indicates generator mode and anegative signal indicates motor mode.

Select Speed w to specify a speed input, in rad/s or in pu, and change labeling of the block input to w. Themachine speed is imposed and the mechanical part of the model (inertia constant H) is ignored. Using thespeed as the mechanical input allows modeling a mechanical coupling between two machines.

The next figure indicates how to model a stiff shaft interconnection in a motor-generator set, where bothmachines are synchronous machines.

The speed output of machine 1 (motor) is connected to the speed input of machine 2 (generator). In thisfigure friction torque is ignored in machine 2. Therefore, its electromagnetic torque output Te correspondsto the mechanical torque Tm applied to the shaft of machine 1. The corresponding mechanical input powerof machine 1 is computed as Pm = Tm*w.The Kw factor takes into account speed units of both machines(pu or rad/s) and gear box ratio w2/w1. The KT factor takes into account torque units of both machines (puor N.m) and machine ratings. Also, as the inertia J2 is ignored in machine 2, J2 referred to machine 1speed must be added to machine 1 inertia J1.

Select Mechanical rotational port to add to the block a Simscape mechanical rotational port that allowsconnection of the machine shaft with another machine shaft or with other Simscape blocks havingmechanical rotational ports. The Simulink input representing the mechanical power Pm or the speed w ofthe machine is then removed from the block.

The next figure indicates how to connect an Ideal Torque Source block from the Simscape library to themachine shaft to represent the machine in motor mode, or in generator mode, when the rotor speed ispositive.



Rotor typeSpecify rotor type: Salient-pole or Round (cylindrical). This choice affects the number of rotor circuits inthe q-axis (damper windings).

Use signal names to identify bus labelsWhen this check box is selected, the measurement output uses the signal names to identify the buslabels. Select this option for applications that require bus signal labels to have only alphanumericcharacters.

When this check box is cleared, the measurement output uses the signal definition to identify the buslabels. The labels contain nonalphanumeric characters that are incompatible with some Simulinkapplications.

Parameters Tab for Synchronous Machine SI Fundamental



Nominal power, voltage, frequency, field currentThe total three-phase apparent power Pn (VA), RMS line-to-line voltage Vn (V), frequency fn (Hz), andfield current ifn (A).

The nominal field current is the current that produces nominal terminal voltage under no-load conditions.This model was developed with all quantities viewed from the stator, as explained in Krause [1]. Thenominal field current makes it possible to compute the transformation ratio of the machine, which allowsyou to apply the field voltage viewed from the rotor, as in real life. It also allows the field current, which isa variable in the output vector of the model, to be viewed from the rotor.

If the value of the nominal field current is not known, you must enter 0 or leave it blank. Since thetransformation ratio cannot be determined in this case, you have to apply the field voltage as viewed fromthe stator. The field current in the output vector is also viewed from the stator.

StatorThe resistance Rs (Ω), leakage inductance Lls (H), and d-axis and q-axis magnetizing inductances Lmd(H) and Lmq (H).



FieldThe field resistance Rf' (Ω) and leakage inductance Llfd' (H), both referred to the stator.

DampersThe d-axis resistance Rkd' (Ω) and leakage inductance Llkd' (H), the q-axis resistance Rkq1' (Ω) andleakage inductance Llkq1' (H), and (only if round rotor) the q-axis resistance Rkq2' (Ω) and leakageinductance Llkq2' (H). All of these values are referred to the stator.

Inertia, friction factor, pole pairsThe inertia coefficient J (kg.m2), friction factor F (N.m.s), and the number of pole pairs p. The frictiontorque Tf is proportional to the rotor speed ω (Tf = F.ω. Tf is expressed in N.m, F in N.m.s, and ω inrad/s).

Initial conditionsThe initial speed deviation Δω (% of nominal speed), electrical angle of the rotor Θe (degrees), line currentmagnitudes ia, ib, ic (A) and phase angles pha, phb, phc (degrees), and the initial field voltage Vf (V). Youcan compute these values automatically by using the Load Flow tool or the Machine Initialization tool ofthe Powergui block.

You can specify the initial field voltage in one of two ways. If you know the nominal field current (first line,last parameter), in the dialog box, enter the initial field voltage in volts DC referred to the rotor. Otherwise,enter a zero as the nominal field current, and specify the initial field voltage in volts DC referred to thestator. You can determine the nominal field voltage viewed from the stator by selecting the Display Vfdwhich produces a nominal Vt check box on the Advanced tab.

Simulate saturationSpecifies whether magnetic saturation of the rotor and stator iron is to be simulated or not.

[ifd; Vt]The no-load saturation curve parameters. Magnetic saturation of the stator and rotor iron is modeled by apiecewise linear relationship specifying points on the no-load saturation curve. The first row of this matrixcontains the values of field currents. The second row contains values of corresponding terminal voltages.The first point (first column of the matrix) must be different from [0,0]. This point corresponds to the pointwhere the effect of saturation begins.

You must select the Simulate saturation check box to simulate saturation. Selecting this check boxallows you to enter the matrix of parameters for simulating the saturation. If you do not want to modelsaturation in your simulation, do not select the Simulate saturation check box. In this case, therelationship between the ifd and Vt obtained is linear (no saturation).

Click Plot to view the no-load saturation curve.

Parameters Tab for Synchronous Machine pu Fundamental



Nominal power, line-to-line voltage, and frequencyTotal three-phase apparent power (VA), RMS line-to-line voltage (V), frequency (Hz), and field current (A).

This line is identical to the first line of the fundamental parameters in SI dialog box, except that you do notspecify a nominal field current. This value is not required here because we do not need the transformationratio. Since rotor quantities are viewed from the stator, they are converted to pu using the stator basequantities derived from the preceding three nominal parameters.

Stator; Field; DampersContain exactly the same parameters as in the previous dialog box, but they are expressed here in puinstead of SI units.

Inertia coefficient, friction factor, pole pairsThe inertia constant H (s), where H is the ratio of energy stored in the rotor at nominal speed over thenominal power of the machine, the friction factor F (pu torque/pu speed), and the number of pole pairs p.The friction torque Tf is proportional to the rotor speed ω (Tf=F.ω, where all quantities are expressed inpu).



Initial conditions; Simulate saturation; Saturation parametersThe same initial conditions and saturation parameters as in the SI units dialog box, but all values areexpressed in pu instead of SI units. For saturation, the nominal field current multiplied by the d-axismagnetizing inductance and nominal RMS line-to-line voltage are the base values for the field current andterminal voltage, respectively.

Parameters Tab for Synchronous Machine pu Standard

Nominal power, line-to-line voltage, and frequencyThe same parameters as in the pu Fundamental dialog box.

ReactancesThe d-axis synchronous reactance Xd, transient reactance Xd', and subtransient reactance Xd'', the q-axis



synchronous reactance Xq, transient reactance Xq' (only if round rotor), and subtransient reactance Xq'',and finally the leakage reactance Xl (all in pu).

d-axis time constants; q-axis time constant(s)Specify the time constants you supply for each axis: either open-circuit or short-circuit.

Time constantsThe d-axis and q-axis time constants (all in s). These values must be consistent with choices made onthe two previous lines: d-axis transient open-circuit (Tdo') or short-circuit (Td') time constant, d-axissubtransient open-circuit (Tdo'') or short-circuit (Td'') time constant, q-axis transient open-circuit (Tqo') orshort-circuit (Tq') time constant (only if round rotor), q-axis subtransient open-circuit (Tqo'') or short-circuit(Tq'') time constant.

Stator resistanceThe stator resistance Rs (pu).

Inertia coefficient, friction factor, pole pairs; Initial conditions; Simulate saturation; Saturationparameters

The same parameters as in the pu Fundamental dialog box.

Advanced Tab



Display nominal field current and voltage producing 1 pu stator voltageSelect to determine the nominal field current and voltage viewed from the stator. This parameter is visibleonly for the Synchronous Machine SI Fundamental block.

As an example, without saturation, a typical curve might be as in the following figure. ifn is 1087 A and Vnis 13800 V RMS line-to-line, which is also 11268 V peak line-to-neutral.



Saturation is modeled as a piecewise linear saturation curve by using two look-up tables implementingvariations of Lmd and Lmq magnetizing inductances.

The next figure illustrates the good fit graphically (the diamonds are the actual points entered in the dialogbox).

In this particular case, the following values are used:

ifn 1087 A

ifd [695.64, 774.7, 917.5, 1001.6, 1082.2, 1175.9, 1293.6, 1430.2, 1583.7] A

Vt [9660, 10623, 12243, 13063, 13757, 14437, 15180, 15890, 16567] V



Sample time (−1 for inherited)Specifies the sample time used by the block. To inherit the sample time specified in the Powergui block,set this parameter to −1.

Discrete solver modelSpecifies the integration method used by the block when the Solver type parameter of the Powergui blockis set to Discrete. The choices are: Trapezoidal non iterative, Trapezoidal iterative (alg. loop),and Forward Euler.

For more info on what method to use in your application, see Simulating Discretized ElectricalSystems.

Load Flow TabThe load flow parameters are used to define block parameters for use with the Load Flow tool of thePowergui block. These load flow parameters are used for model initialization only. They have no impact onthe block model and on the simulation performance.

The configuration of the Load Flow tab depends on the option selected for the Generator type parameter.

http://www.mathworks.com/help/physmod/sps/powersys/ug/simulating-discretized-electrical-systems.html



Generator typeSpecify the generator type of the machine.

Select swing to implement a generator controlling magnitude and phase angle of its terminal voltage. Thereference voltage magnitude and angle are specified by the Swing bus or PV bus voltage and Swingbus voltage angle parameters of the Load Flow Bus block connected to the machine terminals.

Select PV to implement a generator controlling its output active power P and voltage magnitude V. P isspecified by the Active power generation P parameter of the block. V is specified by the Swing bus orPV bus voltage parameter of the Load Flow Bus block connected to the machine terminals. You cancontrol the minimum and maximum reactive power generated by the block by using the Minimumreactive power Qmin and Maximum reactive power Qmax parameters.

Select PQ to implement a generator controlling its output active power P and reactive power Q. P and Qare specified by the Active power generation P and Reactive power generation Q parameters of theblock, respectively.

Active power generation PSpecify the active power that you want generated by the machine, in watts. When the machine operatesin motor mode, you specify a negative value. This parameter is available if you specify Generator type asPV or PQ.

Reactive power generation QSpecify the reactive power that you want generated by the machine, in vars. A negative value indicatesthat the reactive power is absorbed by the machine. This parameter is available only if you specifyGenerator type as PQ.

Minimum reactive power QminThis parameter is available only if you specify Generator type as PV. Indicates the minimum reactivepower that can be generated by the machine while keeping the terminal voltage at its reference value. Thisreference voltage is specified by the Swing bus or PV bus voltage parameter of the Load Flow Busblock connected to the machine terminals. The default value is -inf, which means that there is no lowerlimit on the reactive power output.

Maximum reactive power QmaxThis parameter is available only if you specify Generator type as PV. Indicates the maximum reactivepower that can be generated by the machine while keeping the terminal voltage at its reference value. Thisreference voltage is specified by the Swing bus or PV bus voltage parameter of the Load Flow Busblock connected to the machine terminals. The default value is inf, which means that there is no upperlimit on the reactive power output.

Inputs and Outputs

The units of inputs and outputs vary according to which dialog box you use to enter the block parameters. Ifthe fundamental parameters in SI units is used, the inputs and outputs are in SI units (except for dw in thevector of internal variables, which is always in pu, and angle Θ, which is always in rad). Otherwise, theinputs and outputs are in pu.

Pm

The first Simulink input is the mechanical power at the machine's shaft, in Watts or pu. In generatingmode, this input can be a positive constant or function or the output of a prime mover block (see theHydraulic Turbine and Governor or Steam Turbine and Governor blocks). In motoring mode, this input isusually a negative constant or function.



w

The alternative block input instead of Pm (depending on the value of the Mechanical input parameter) isthe machine speed, in rad/s.

Vf

The second Simulink input of the block is the field voltage. This voltage can be supplied by a voltageregulator in generator mode (see the Excitation System block). It is usually a constant in motor mode.

If you use the model in SI fundamental units, the field voltage Vf must be entered in volts DC if nominalfield current Ifn is specified, or in volts referred to stator if Ifn is not specified. To obtain the Vfd producingnominal voltage, select the Display nominal field current and voltage producing 1 pu stator voltagecheck box in the Advanced tab. If you use the model in pu Standard or in pu Fundamental units, Vf mustbe entered in pu (1 pu of field voltage producing 1 pu of terminal voltage at no load).

m

The Simulink output of the block is a vector containing measurement signals. You can demultiplex thesesignals by using the Bus Selector block provided in the Simulink library. Depending on the type of maskthat you use, the units are in SI or in pu.

Name Definition Units

ias Stator current is_a A or pu

ibs Stator current is_b A or pu

ics Stator current is_c A or pu

iq Stator current iq A or pu

id Stator current id A or pu

ifd Field current ifd A or pu

ikq Damper winding current ikq1 A or pu

Ikq2 Damper winding current ikq2 A or pu

ikd Damper winding current ikd A or pu

phimq Mutual flux phimq V.s or pu

phimd Mutual flux phimd V.s or pu

vq Stator voltage vq V or pu

vd Stator voltage vd V or pu

lmq Lmq saturated inductance H or pu

lmd Lmd saturated inductance H or pu

dtheta Rotor angle deviation d_theta rad

w Rotor speed wm rad/s

Pe Electrical power Pe VA or pu



dw Rotor speed deviation dw rad/s

theta Rotor mechanical angle theta rad

Te Electromagnetic torque Te N.m or pu

delta Load angle delta rad

Pe0 Output active power Peo VA or pu

Qe0 Output reactive power Qeo VAR or pu

Limitations

In Discrete systems, when you use Synchronous Machine blocks discretized with the trapezoidal noniterative solver or the forward Euler solver, you might have to use a small parasitic resistive load, connectedat the machine terminals, to avoid numerical oscillations. Large sample times require larger loads. Theminimum resistive load is proportional to the sample time. As a rule of thumb, remember that with a 25 μstime step on a 60 Hz system, the minimum load is approximately 2.5% of the machine nominal power. Forexample, a 200 MVA synchronous machine in a power system discretized with a 50 μs sample time requiresapproximately 5% of resistive load or 10 MW. If the sample time is reduced to 20 μs, a resistive load of 4MW should be sufficient.

However, if you discretize the Synchronous Machine block using the trapezoidal iterative (alg. loop) solver,you can use a negligible parasitic load (below 0.1% of nominal power) while preserving numerical stability.This iterative model producing an algebraic loop results in slower simulation speed.

Example 1

The power_SM_Fundamental example shows the use of the Synchronous Machine SI Fundamental block andthe Synchronous Machine pu Fundamental block to model a 555 MVA, 24 kV, 60 Hz, 3600 rpm synchronousgenerator. It shows how to specify SI and pu parameters. It also explains how to compute field and damperrotor winding parameters that are referred to the stator. In addition to the field winding, the round rotor of thismachine has three damper windings: one damper in the direct axis and two dampers in the quadrature axis.

Three circuits simulate the same synchronous machine:

Circuit 1: Fundamental parameters are specified in SI. The nominal field current is specified (ifn = 1300A).

Circuit 2: Fundamental parameters are specified in SI. The nominal field current is not specified (ifn = 0).

Circuit 3: Fundamental parameters are specified in pu.

Machine parameters are taken from an example in Kundur [3].

Look at the Model Properties/PreLoad Fcn callback section of the model to see machine specifications aswell as the computation of stator and field bases, RL rotor parameters referred to the stator, transformationratio, and nominal field voltage and current.

The machines initially operate in steady state at virtually no load (load = 0. 1 % of nominal power) withconstant field voltage and mechanical power. A phase-to-phase 6-cycle fault is applied at t = 0.1 sec. TheScope shows the comparison between line-to-line AB voltage, phase A stator current, and field current of thethree machines.

http://www.mathworks.com/help/physmod/sps/powersys/ref/rmvd_matlablink__9cb454edad5de85070c8f42db5b90409.html



To simulate the discrete model, select Discrete simulation type in the Configuration parameters of thePowergui block. The model is discretized with a sample time Ts = 50 μs. To obtain a stable model with sucha small load (0. 1 % of nominal power), select the Trapezoidal iterative (alg. Loop) discrete solver in theAdvanced tab of each Synchronous Machine block.

Example 2

The power_syncmachine example illustrates the use of the Synchronous Machine block in motor mode. Thesimulated system consists of an industrial grade synchronous motor (150 HP (112 kVA), 762 V) connectedto a network with a 10 MVA short-circuit level. The machine is initialized for an output electrical power of −50kW (negative value for motor mode), corresponding to a mechanical power of −48.9 kW. The correspondingvalues of mechanical power and field voltage are specified by the Pm Step block and in the Vf Constantblock. The Pm Step block applies a sudden increase of mechanical power from −48.9 kW to −60 kW at timet = 0.1 s.

Run the simulation.

After the load has increased from 48.9 kW to 60 kW at t = 0.1 s, the machine speed oscillates beforestabilizing to 1800 rpm. The load angle (angle between terminal voltage and internal voltage) increases from−21 degrees to −53 degrees.

References

[1] Krause, P.C., Analysis of Electric Machinery, McGraw-Hill, 1986, Section 12.5.

[2] Kamwa, I., et al., "Experience with Computer-Aided Graphical Analysis of Sudden-Short-CircuitOscillograms of Large Synchronous Machines," IEEE® Transactions on Energy Conversion, Vol. 10, No. 3,September 1995.

[3] Kundur, P., Power System Stability and Control, McGraw-Hill, 1994.

See Also

Excitation System, Hydraulic Turbine and Governor, Powergui, Simplified Synchronous Machine,Steam Turbine and Governor

http://www.mathworks.com/help/physmod/sps/powersys/ref/rmvd_matlablink__f2943f02f1bf5cddb5ab3ec225aaae5d.html

http://www.mathworks.com/help/physmod/sps/powersys/ref/excitationsystem.html

http://www.mathworks.com/help/physmod/sps/powersys/ref/hydraulicturbineandgovernor.html

http://www.mathworks.com/help/physmod/sps/powersys/ref/powergui.html

http://www.mathworks.com/help/physmod/sps/powersys/ref/simplifiedsynchronousmachine.html

http://www.mathworks.com/help/physmod/sps/powersys/ref/steamturbineandgovernor.html

Model the Dynamics of Three-phase Round-rotor or Salient-pole Synchronous Machine - Simulink

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