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# SSN Synchronous Machine

# Library

ARTEMiS/SSN Machines

# Blocks

# Description

Implements a 3-phase synchronous machine modelled in the d-q rotor reference frame for use with the SSN solver. Stator windings are connected in wye to an internal neutral point. The neutral point is connected to ground through a user-specified impedance or with an external impedance (model with Neutral terminal available). The model is 6th order for the round rotor type and 5th order for the salient rotor type.

Steady-state and differential saturation mode are supported using total flux in both dq axis for the round rotor and d-axis only for the salient type.

# Mask

# Parameters

**Nominal power, voltage, frequency, field current [ Pn(VA) Vn(Vrms) fn(Hz) ifn(A) ]:** nominal values for total power, line-line RMS voltage, frequency and field current

**Rotor type:** Salient (5ft order model)/Round (6th order model)

**Stator parameters [ Rs(ohm), Ll, Lmd, Lmq(H), Lcanay(H)]:** Stator resistance and leakage inductance, magnetization inductance for d-q axes. The Lcanay parameter is the Canay inductance correction that consider the fact that mutual flux couplings are not all equal on the d-axis. The parameter can be ignored or set to zero if unknown.

**Field parameters [ Rf'(ohm) Llfd'(H) ]:** Field resistance and leakage inductance (seen from the stator)

**Dampers parameters [ Rkd',Llkd' Rkq1',Llkq1' Rkq2' Llkq2' ] (R=ohm,L=H)**

**Pole pairs:** number of pair of poles

**Initial rotor angle (deg):** initial rotor electrical angle in degree. A null angle makes the back-EMF voltage maximum on phase A and would make the machine generate a waveform on phase A on no-load conditions.

**Initial currents Ifd Ia Ib Ic (A) (amplitude) Ia Ib Ic (deg)(angle )**

**Saturation:** Saturation is used if selected. By default, global saturation (or steady-state) saturation is used unless **Differential saturation** is selected.

The next figure shows the difference between global inductance and differential saturations when the machine is operated at its nominal saturation point.

**Differential saturation:** Differential saturation is used is selected.

**Open stator saturation curve: field current (pu) **The pu base is the nominal field current.

**Open stator saturation curve: phase-phase RMS voltage (pu) **The pu base is the nominal terminal voltage specified in the first parameter above.

When differential saturation is used, only 3 points (4 points with the 0,0 origin points) can be used to specify **Open stator saturation curve{ field current (pu), phase-phase RMS voltage (pu)}. **This is because a continuous function of order 3 is internally fitted to express the saturation characteristic and its derivative, the differential inductance, in this mode of the model. See [1] for a detailed explanation of saturation models.

**Plot saturation curves:** plot saturation curves.

**Zero sequence machine reactance (Ohms): (SM with internal neutral connection only) **sum of the machine zero-sequence reactance and the impedance used to connected the star common point to the ground

**Neutral grounding resistance (Ohms): (SM with internal neutral connection only) **values of the resistance, in series with** Zero sequence machine reactance**, connecting the machine stator star connection point to the ground.

**Sample Time (s):** sample time of the model in seconds.

**Computed stator-to-field coil winding turn ratio **(Ns_to_Nf) is found using the following formula:

Ns_on_Nf=Lmd*Ifn*(2*pi*fn)/Vn

where **Lmd** (d-axis mutual inductance),** Ifn** (nominal field current),** fn **(nominal electric frequency) and **Vn**(machine line-line RMS voltage). This turn ratio is sometimes useful when trying to convert commonly available stator referenced values to actual field referenced values.

**Delayed speed term:** when checked, the machine speed term is included with a delay in the state-space equations, and therefore is not include in the A state-space matrices but in B instead. This produces a model with a constant nodal admittance compatible with the SSN LDL^{T} factorization. See reference [1] for more details.

**Backward Euler discretization**: (model with External Neutral Terminal only): when checked, the SSN-SM equations are discretized with the Backward Euler method. This may help to obtain less oscillatory terminal voltages in some cases.

# Input and Output signals

**Simulink connection points**

**w_mec**: mechanical speed of the machine in rad/s. 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.

**meas**: measurements available:

flux: phid phiq phif phikd phikq phikq2 (Wb): fluxes of the machines used as states internally.

Iabc(A): ABC terminal currents in Amperes.

Ifield(A): Filed terminal current in Amperes

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

Te (N.m): Electric torque of the machine in N.m.

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.

Vd Vq (V): stator dq voltage in Volts

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**

Field: positive field winding terminal. The negative field terminal is implicitly connected to ground.

A,B,C: phase connection points.

Neutral: Neutral star connection point, only in the model with neutral terminal available. The model with explicit available Neutral terminal has an additional nodal connection node, will cause an increase in computational time and should be used only when required.

# Standard Per Unit Synchronous machine parameters

The demo model **SSN_stdPU_synchronous_machine** with Standard Per Unit parameters is available since ARTEMiS 7.5. The model compares the SSN and native SPS synchronous machine models. The model uses very recent and accurate Canay inductance determination [2].

# Example

SSN_SynchronousMachineFieldTerminal_withNeutral.mdl is an example that uses this SM model with a salient rotor. In the model, the machine filed terminal current is controlled by a thyristor rectifier. After the machine is brought to its nominal working point, a fault is made at the stator, followed by disconnection of both load and field feeding circuit. For the latter, a non-linear resistor is used to discharge the field current to 0 gradually after fault.

# 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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