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Machines
The Synchronous Machine block operates in generator or motor modes. The operating mode is dictated by the sign of the mechanical power (positive for generator mode, negative for motor mode). The electrical part of the machine is represented by a sixth-order state-space model and the mechanical part is the same as in the Simplified Synchronous Machine block.
The model takes into account the dynamics of the stator, field, and damper windings. The equivalent circuit of the model is represented in the rotor reference frame (qd frame). All rotor parameters and electrical quantities are viewed from the stator. They are identified by primed variables. The subscripts used are defined 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 the Synchronous Machine block (Ia, Ib, Ic, Id, Iq) are the currents flowing out of the machine.
In the powerlib library you can choose between three Synchronous Machine blocks to specify the parameters of the model. They simulate exactly the same synchronous machine model; the only difference is the way that you enter the parameter units in the Parameters tab.
Provides a set of predetermined electrical and mechanical parameters for various synchronous machine ratings 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 the entries of the dialog box. Select No if you do not want to use a preset model, or if you want to modify some 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 the dialog box become nonmodifiable (unavailable). To start from a given preset model and then modify machine parameters, do the following:
Select the preset model that you want to initialize the parameters.
Change the Preset model parameter value to No. This action does not change the machine parameters. By doing so, you just break the connection with the particular preset model.
Modify the machine parameters as you want, then click Apply.
Allows you to select the mechanical power applied to the shaft or the rotor speed as a Simulink input of the 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 of the block input to Pm. The machine speed is determined by the machine Inertia J (or inertia constant H for the pu machine) and by the difference between the mechanical torque Tm, resulting from the applied mechanical power Pm, and the internal electromagnetic torque Te. The sign convention for the mechanical power is when the speed is positive, a positive mechanical power signal indicates generator mode and a negative 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. The machine speed is imposed and the mechanical part of the model (inertia constant H) is ignored. Using the speed 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 both machines are synchronous machines.
The speed output of machine 1 (motor) is connected to the speed input of machine 2 (generator). In this figure friction torque is ignored in machine 2. Therefore, its electromagnetic torque output Te corresponds to the mechanical torque Tm applied to the shaft of machine 1. The corresponding mechanical input power of 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 (pu or N.m) and machine ratings. Also, as the inertia J2 is ignored in machine 2, J2 referred to machine 1 speed must be added to machine 1 inertia J1.
Select Mechanical rotational port to add to the block a Simscape mechanical rotational port that allows connection of the machine shaft with other Simscape blocks having mechanical rotational ports. The Simulink input representing the mechanical power Pm or the speed w of the machine is then removed from the block.
The next figure indicates how to connect an Ideal Torque Source block from the Simscape library to the machine shaft to represent the machine in motor mode, or in generator mode, when the rotor speed is positive.
Specify rotor type: Salient-pole or Round (cylindrical). This choice affects the number of rotor circuits in the q-axis (damper windings).
Specifies the units of the electrical and mechanical parameters of the model.
The total three-phase apparent power Pn (VA), RMS line-to-line voltage Vn (V), frequency fn (Hz), and field 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. The nominal field current makes it possible to compute the transformation ratio of the machine, which allows you to apply the field voltage viewed from the rotor, as in real life. It also allows the field current, which is a variable in the output vector of the model, to be viewed from the rotor.
The transformation ratio (N) is defined as
Ns is the equivalent number of sinusoidally distributed turns in each stator phase winding. Nf is the equivalent number of sinusoidally distributed turns in the field winding.
This ratio is calculated as follows:
Ifbase is the base field current viewed from the rotor, and Isbase is the base stator current.
If the value of the nominal field current is not known, you must enter 0 or leave it blank. Since the transformation ratio cannot be determined in this case, you have to apply the field voltage as viewed from the stator. The field current in the output vector is also viewed from the stator.
The resistance Rs (Ω), leakage inductance Lls (H), and d-axis and q-axis magnetizing inductances Lmd (H) and Lmq (H).
The field resistance Rf' (Ω) and leakage inductance Llfd' (H), both referred to the stator.
The d-axis resistance Rkd' (Ω) and leakage inductance Llkd' (H), the q-axis resistance Rkq1' (Ω) and leakage inductance Llkq1' (H), and (only if round rotor) the q-axis resistance Rkq2' (Ω) and leakage inductance Llkq2' (H). All these values are referred to the stator.
The inertia coefficient J (kg.m2), friction factor F (N.m.s), and number of pole pairs p. The friction torque Tf is proportional to the rotor speed ω (Tf = F.ω, where Tf is expressed in N.m, F in N.m.s, and ω in rad/s).
The initial speed deviation Δω (% of nominal speed), electrical angle of the rotor Θe (degrees), line current magnitudes ia, ib, ic (A) and phase angles pha, phb, phc (degrees), and the initial field voltage Vf (V). You can compute these values automatically by using the Load Flow tool or the Machine Initialization tool of the 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 nominal field current, as previously described, and specify the initial field voltage in volts DC referred to the stator. You can determine the nominal field voltage viewed from the stator by selecting the Display Vfd which produces a nominal Vt check box on the Advanced tab.
Specifies whether magnetic saturation of rotor and stator iron is to be simulated or not.
The no-load saturation curve parameters. Magnetic saturation of stator and rotor iron is modeled by a nonlinear function (in this case a polynomial) using points on the no-load saturation curve. You must enter a 2-by-n matrix, where n is the number of points taken from the saturation curve. The first row of this matrix contains the values of field currents, while the second row contains values of corresponding terminal voltages. The first point (first column of the matrix) must correspond to the point where the effect of saturation begins.
You must select the Simulate saturation check box to simulate saturation. This check box allows you to enter the matrix of parameters for simulating the saturation. If you do not want to model saturation in your simulation, do not select the Simulate saturation check box. In this case the relationship between ifd and Vt obtained is linear (no saturation).
Total 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 not specify a nominal field current. This value is not required here because we do not need the transformation ratio. Since rotor quantities are viewed from the stator, they are converted to pu using the stator base quantities derived from the preceding three nominal parameters.
Contain exactly the same parameters as in the previous dialog box, but they are expressed here in pu instead of SI units.
The inertia constant H (s), where H is the ratio of energy stored in the rotor at nominal speed over the nominal 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 in pu).
The same initial conditions and saturation parameters as in the SI units dialog box, but all values are expressed in pu instead of SI units. For saturation, the nominal field current multiplied by the d-axis magnetizing inductance and nominal RMS line-to-line voltage are the base values for the field current and terminal voltage, respectively.
The same parameters as in the pu Fundamental dialog box.
The 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).
Specify the time constants you supply for each axis: either open-circuit or short-circuit.
The d-axis and q-axis time constants (all in s). These values must be consistent with choices made on the two previous lines: d-axis transient open-circuit (Tdo') or short-circuit (Td') time constant, d-axis subtransient open-circuit (Tdo'') or short-circuit (Td'') time constant, q-axis transient open-circuit (Tqo') or short-circuit (Tq') time constant (only if round rotor), q-axis subtransient open-circuit (Tqo'') or short-circuit (Tq'') time constant.
The stator resistance Rs (pu).
The same parameters as in the pu Fundamental dialog box.
Select to determine the nominal field voltage viewed from the stator. This parameter is visible only 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 Vn is 13800 V RMS line-to-line, which is also 11268 V peak line-to-neutral.
Saturation is modeled by fitting a polynomial to the curve corresponding to the matrix of points that you enter. The more points that you enter, the better the fit to the original curve.
The next figure illustrates the good fit graphically (the diamonds are the actual points entered in the dialog box).
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 |
Specifies the sample time used by the block. To inherit the sample time specified in the Powergui block, set this parameter to −1.
Specifies the integration method used by the block when the Solver type parameter of the Powergui block is set to Discrete. The choices are: Forward Euler (default), Trapezoidal non iterative, and Trapezoidal iterative (alg. loop).
For more info on what method to use in your application, see Simulating Discretized Electrical Systems.
The load flow parameters are used to define block parameters for use with the Load Flow tool of the Powergui block. These load flow parameters are used for model initialization only. They have no impact on the block model and on the simulation performance.
The configuration of the Load Flow tab depends on the option selected for the Generator type parameter.
Specify the generator type of the machine.
Select swing to implement a generator controlling magnitude and phase angle of its terminal voltage. The reference voltage magnitude and angle are specified by the Swing bus or PV bus voltage and Swing bus 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 is specified by the Active power generation P parameter of the block. V is specified by the Swing bus or PV bus voltage parameter of the Load Flow Bus block connected to the machine terminals. You can control the minimum and maximum reactive power generated by the block by using the Minimum reactive 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 Q are specified by the Active power generation P and Reactive power generation Q parameters of the block, respectively.
Specify the active power that you want generated by the machine, in watts. When the machine operates in motor mode, you specify a negative value. This parameter is available if you specify Generator type as PV or PQ.
Specify the reactive power that you want generated by the machine, in vars. A negative value indicates that the reactive power is absorbed by the machine. This parameter is available only if you specify Generator type as PQ.
This parameter is available only if you specify Generator type as PV. Indicates the minimum reactive power that can be generated by the machine while keeping the terminal voltage at its reference value. This reference voltage is specified by the Swing bus or PV bus voltage parameter of the Load Flow Bus block connected to the machine terminals. The default value is -inf, which means that there is no lower limit on the reactive power output.
This parameter is available only if you specify Generator type as PV. Indicates the maximum reactive power that can be generated by the machine while keeping the terminal voltage at its reference value. This reference voltage is specified by the Swing bus or PV bus voltage parameter of the Load Flow Bus block connected to the machine terminals. The default value is inf, which means that there is no upper limit on the reactive power output.
The units of inputs and outputs vary according to which dialog box you use to enter the block parameters. If the fundamental parameters in SI units is used, the inputs and outputs are in SI units (except for dw in the vector of internal variables, which is always in pu, and angle Θ, which is always in rad). Otherwise, the inputs and outputs are in pu.
The first Simulink input is the mechanical power at the machine's shaft, in Watts or pu. In generating mode, this input can be a positive constant or function or the output of a prime mover block (see the Hydraulic Turbine and Governor or Steam Turbine and Governor blocks). In motoring mode, this input is usually a negative constant or function.
The alternative block input instead of Pm (depending on the value of the Mechanical input parameter) is the machine speed, in rad/s.
The second Simulink input of the block is the field voltage. This voltage can be supplied by a voltage regulator 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 nominal field current Ifn is specified, or in volts referred to stator if Ifn is not specified. To obtain the Vfd producing nominal voltage, select the last check box of the dialog box. If you use the model in pu Standard or in pu Fundamental units, Vf must be entered in pu (1 pu of field voltage producing 1 pu of terminal voltage at no load).
The Simulink output of the block is a vector containing 22 signals. You can demultiplex these signals by using the Bus Selector block provided in the Simulink library.
Signal | Definition | Units |
|---|---|---|
1 | Stator current is_a | A or pu |
2 | Stator current is_b | A or pu |
3 | Stator current is_c | A or pu |
4 | Stator current is_q | A or pu |
5 | Stator current is_d | A or pu |
6 | Field current ifd | A or pu |
7 | Damper winding current ikq1 | A or pu |
8 | Damper winding current ikq2 | A or pu |
9 | Damper winding current ikd | A or pu |
10 | Mutual flux phimq | V.s or pu |
11 | Mutual flux phimd | V.s or pu |
12 | Stator voltage vq | V or pu |
13 | Stator voltage vd | V or pu |
14 | Rotor angle deviation d_theta | rad |
15 | Rotor speed wm | rad/s. |
16 | Electrical power Pe | VA or pu |
17 | Rotor speed deviation dw | rad/s |
18 | Rotor mechanical angle theta | rad |
19 | Electromagnetic torque Te | N.m or pu |
20 | Load angle delta | N.m or pu |
21 | Output active power Peo | rad |
22 | Output reactive power Qeo | rad |
When you use Synchronous Machine blocks in discrete systems, you might have to use a small parasitic resistive load, connected at the machine terminals, 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 μs 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 μs sample time requires approximately 5% of resistive load or 10 MW. If the sample time is reduced to 20 μs, a resistive load of 4 MW should be sufficient.
The power_syncmachine demo illustrates the use of the Synchronous Machine block in motor mode. The simulated system consists of an industrial grade synchronous motor (150 HP (112 kVA), 762 V) connected to a network with a 10 MVA short-circuit level. In order to start simulation in steady state, the machine is initialized using the Machine Initialization tool of the Powergui. The machine is initialized for an output electrical power of −50 kW (negative value for motor mode), corresponding to a mechanical power of −48.9 kW. The corresponding values of mechanical power and field voltage have been automatically entered into the Pm Step block and in the Vf Constant block. The Pm Step block has been programmed in order to apply a sudden increase of mechanical power from −48.9 kW to −60 kW at time t = 0.1 s.
Run the simulation and observe the RMS current, RMS voltage, speed, load angle δ, and output electrical power of the motor.
Since this is a four-pole machine, the nominal speed is 1800 rpm. The initial speed is 1800 rpm as prescribed. After the load has increased from 48.9 kW to 100 kW at t = 0.1 s, the machine speed oscillates before stabilizing to 1800 rpm. The load angle (angle between terminal voltage and internal voltage) increases from −21 degrees to −53 degrees.
[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-Circuit Oscillograms of Large Synchronous Machines," IEEE Transactions on Energy Conversion, Vol. 10, No. 3, September 1995.
Excitation System, Hydraulic Turbine and Governor, Powergui, Simplified Synchronous Machine, Steam Turbine and Governor
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