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# SSN Synchronous Machine Standard-PU (6 terminals)

# Library

ARTEMiS/SSN Machines

# Blocks

# Description

Implements a 3-phase synchronous machine with Standard Per-Unit parameters, modelled in the d-q rotor reference frame for use with the SSN solver. Stator windings are accessible on both side (+ and - for each phase) thus enabling the user to choose the winding connections (Wye or Delta) during the real-time simulation.

The model parameters are of the so-called Standard Per-Unit type and are based on machine open-circuit and short-circuit data. Canay inductance correction can also be used optionally. The model can have up to two q-axis dampers and 1 d-axis damper, resulting in a 6^{th} order model with all dampers.

# Mask

# Parameters

**Nominal power: **machine nominal power in Watts. (Pn)**Nominal voltage: **machine nominal RMS line-to-line voltage in Volts (Vn)

**machine nominal electric frequency in Hz (Fn)**

Nominal frequency:

Nominal frequency:

**machine nominal field currents in Amperes. This value is sometimes unspecified for synchronous machine with Standard Per-Unit parameters. Since this value is required by the internal SI-based model, the user must choose an appropriate one in this case. 5 times the Power/Voltage ratio is typical for large machines. (Ifldn)**

Nominal field current:

Nominal field current:

**Number of pair of poles:**the machine number of pair of poles. (pp)

**Base values**

Other model bases can be derived from the above base values.

Wbase=2*pi*Fn/pp base mechanical angular frequency

Zbase=Vn*Vn/Pn; base impedance

Lbase=Zb/(2*pi*Fn) base inductance

Tbase=Pnom/Wbase base torque

Ibase=Pnom/Vn/sqrt(3/2) base current

**Machine data parameters (all values in Per-Unit)**

Machine data for d- and q-axis according to the tests made, open circuit or short circuit, and the number of dampers on the q-axis (1 or 2). Typically, a Salient-type machine will have 1 q damper while a Round rotor machine will have 2.

Also, when the 1 q damper is selected, the prime value are required (Xq' Tq' or Tqo'). In SPS machine, primeprime ('') values are required by contrast. As this is just a definition issue, this has no effects on the model accuracy.

**Miscellaneous parameters**

**Inertia factor (H) (sec):** this parameters is used to compute the SI inertia in kg.m^2 for use in the mechanical part of the SSN-SM-Std-PU model and is NOT used internally as the model is inputted with the rotational speed.

**Field voltage (nominal):** This is the nominal field voltage in Volts that will give a 1 PU of stator voltage under no load conditions. It is computed and displayed for conversion purposes.

**Sample Time (s)**

**Delayed speed term**: with this option turned ON, the speed term of the machine equations is incorporated in the input term of the SSN state-space equations, resulting in symmetric nodal admittance and compatibility with the LDL^{T} factorization of SSN. The speed term includes a 1-step prediction to improve accuracy.

**Canay inductance correction**: this is a correction factor that consider the fact that flux linkage is not the same between all d-axis windings. It should be set ON if comparing with SPS Synchronous machine Std-PU R2018b and later as it automatically includes this inductance in these versions and only these versions[2].

**Backward Euler discretization**: check this to discretize the machine equations with the Backward Euler solver. By default, Trapezoidal discretization is used. The machine discretization can be different than the global SSN solver.

**Initial rotor angle:** the initial rotor angle of the machine. With nominal excitation, no load and at nominal rotational speed *f*, an angle of *x* degree will produce a phase A voltage that is equal to

Vn*cos(2*pi**f*+ pi/180**x*).

# Input and Output signals

**Simulink connection points**

**w_mec**: mechanical speed of the machine in Per-Unit. Typically, the speed will be computed from a separate mechanical model that will use this model electric torque (Te) as an input. A simple mechanical model is available in ARTEMiS/SSN/SSN rotating machines.

**V_field:** field winding input voltage in Per-Unit.

**meas**: measurements available, all in Per-Unit of their respective bases:

Iabc: ABC terminal currents in Per Unit.

Ifield: Filed terminal current in Per Unit

Vd Vq (V): stator dq voltage in Per Unit

Te (pu): Electric torque of the machine in Per-Unit

Note: other machines S.I. values are available inside the top-level mask of the Std-PU Synchronous Machine. They are listed here:

Peo(W): Total electric power generated by the machines in Watts.

Angle(rad): Electric angle of the rotor. The d-axis is aligned with phase A in this model. Therefore, at null load, the 0 angle corresponds to a null voltage of terminal A to ground, and with a negative slope.

Flux in air gap: phim_dq (Wb): This is the air gap in Wb.

saturation factor: this is the per-unit value global inductance. By definition, it has a value of 1 at the nominal operating point.

Id Iq (A): stator dq current in Amperes.

Load angle(deg): arctan(Vq/Vq)

*Note on Park referential and d-q values computed by the model: all SSN rotating machines internally use the following orthonormal Park transform, which is different from the classic North American one:*

**Physical Modeling connection points**

A+, B+, C+: normal ABC terminal phase connection points.

A-, B-, C-: other ends of the ABC+ windings. This is the side of windings that is normally connected together in Y configurations.

# Example

SSN_stdPU_synchronous_machine.slx is an example that compares several synchronous machine models: SPS SI, SPS Std-PU, SSN SI and this model (SSN Std-PU 6 terminals).

The simulated system consists on a synchronous machine, connected in floating Wye, running at fixed speed and starting with a small load. This load is actually required by the SPS reference model for stability. The SSN models don’t require this stabilization load but it is included for comparison purposes.

At some time during the simulation a RL load gets connected to the SM, then later on, a 3-phase-fault is applied to the machine terminals.

**Short-circuit validation**

The simulated system also includes a unitary test model (at the bottom-right of the Simulink model) to validate short-circuit parameters and zero-sequence currents. The following figure shows the short-circuit current.

The steady-state current measurement perfectly corresponds to the theoretical value of 1/Ld.

**Zero-sequence currents**

The same test case is now configured to check the zero-sequence current by applying a 1V source to phase A and with phase B and C open. The test result is shown below:

The machine stator resistance is 0.004 pu with a impedance base equal to Zb=Vn^2/Pn=76.1760 Ohms

The stator resistance is therefore equal to 0.3047 Ohms. The connections of the test also have 1 switch and 2 connecting resistances with resistance of 1 milliOhms each. We can therefore deduct the current going through the phase A and neutral:

Ineutral=1V/(0.3047+0.003)=3.25A , as measured by the test.

# References

[1] C. Dufour, “Highly stable rotating machine models using the state-space-nodal real-time solver”, COMPENG-2018 conference, Oct. 10-12, 2018, Florence, Italia.

[2] A. Moeini, I. Kamwa, P. Brunelle and G. Sybille, "Synchronous Machine Stability Model, an Update to IEEE Std 1110-2002 Data Translation Technique," 2018 IEEE Power & Energy Society General Meeting (PESGM), Portland, OR, 2018, pp. 1-5. doi: 10.1109/PESGM.2018.8586169

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