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# power_AsynchronousMachineParams

Estimate electrical parameters of double cage asynchronous machine based on standard manufacturer specifications

## Syntax

power_AsynchronousMachineParams
params = power_AsynchronousMachineParams(spec)
params = power_AsynchronousMachineParams(spec, options)
[params, spec2] = power_AsynchronousMachineParams(spec, options)
[params, spec2, errors] = power_AsynchronousMachineParams(spec, options)

## Description

power_AsynchronousMachineParams opens a graphical user interface to compute the mask parameters required by the double-cage asynchronous machine block based on standard manufacturer specifications.

params = power_AsynchronousMachineParams(spec) computes the machine parameters from the input structure spec, which contains the manufacturer data. The solution is returned in the output structure params.

params = power_AsynchronousMachineParams(spec, options) lets you specify more options (display details, draw graphs, parameter units, and graph units) in the input structure options.

[params, spec2] = power_AsynchronousMachineParams(spec, options) returns the input manufacturer data along with some additional derived data (synchronous speed, number of pole pairs, nominal slip, starting torque, and so on) in the structure spec2.

[params, spec2, errors] = power_AsynchronousMachineParams(spec, options) returns the relative errors between the input manufacturer data and the equivalent data obtained with the computed parameters in the structure errors.

### Electrical Parameters of a Double-Cage Asynchronous Machine

The following figure shows the steady-state equivalent circuit of a double-cage asynchronous machine.

Rs, Lls, Rr1, Llr1, Rr2, Llr2, Lm are the seven electrical parameters of the machine. They form the fields of the params structure, as described in the Output Arguments section.

The power_AsynchronousMachineParams function computes the seven machine parameters by solving the nonlinear equations in the form f(x) = 0 with:

${f}_{1}\left(x\right)=\frac{{T}_{n}-T\left({s}_{n}\right)}{{T}_{n}}$

${f}_{2}\left(x\right)=\frac{{I}_{n}-I\left({s}_{n}\right)}{{I}_{n}}$

${f}_{3}\left(x\right)=\frac{pf-pf\left({s}_{n}\right)}{pf}$

${f}_{4}\left(x\right)=\frac{{I}_{st}-I\left(1\right)}{{I}_{st}}$

${f}_{5}\left(x\right)=\frac{{T}_{br}-T\left({s}_{br}\right)}{{T}_{br}}$

${f}_{6}\left(x\right)=\frac{{T}_{st}-T\left(1\right)}{{T}_{st}}$

where f = (f1, f2, f3, f4, f5, f6) and x = (Rs, Lm, Rr1, Llr1, Rr2, Llr2). The Lls parameter is obtained by assuming that the stator and outer cage leakage inductances are equal (Lls = Llr2). sn and sbr are the slip at nominal and breakdown torque, respectively. For details on the functions used in these equations, see [1].

Tn, In, pf, Ist, Ibr, Tst are the standard manufacturer specifications of the machine. They form the fields of the spec structure, as described in the Input Arguments section.

To solve these nonlinear equations, power_AsynchronousMachineParams is using the Optimization Toolbox™ function lsqnonlin. This function is based on a nonlinear least-squares algorithm and returns a solution x that minimizes f(x).

## Input Arguments

spec contains the manufacturer data in a structure with the following fields.

Field

Description

Vn

Nominal line-to-line rms voltage (V)

fn

Nominal frequency (Hz)

In

Nominal (full load) line current (A)

Tn

Ns, or p

You can either specify the Synchronous speed (rpm) or the pole pairs

Nn

Nominal (full load) mechanical speed (rpm)

Ist_In

Starting current to nominal current ratio

Tst_Tn

Starting torque to full load torque ratio

Tbr_Tn

Breakdown torque to full load torque ratio

pf

Nominal power factor (%)

options contains additional options to the function in a structure with the following fields.

Field

Description

DisplayDetails

If set to 1, displays detailed information (results, errors between the specified and the computed data) in the MATLAB® Command window. By default, this field is set to 0.

DrawGraphs

If set to 1, plots torque versus speed and stator current versus speed characteristics. By default, this field is set to 0.

units

Specifies the units of machine parameters in 'SI' or 'p.u.'. By default, this field is set to 'SI'.

graphUnits

Specifies the graph units in 'SI' or 'p.u.'. By default, this field is set to 'SI'.

## Output Arguments

params returns the machine parameters in a structure with the following fields.

Field

Description

Rs

Stator resistance (ohm or pu)

Lls

Stator leakage inductance (H or pu)

Rr1

Cage 1 (inner cage) resistance (ohm or pu)

Llr1

Cage 1 (inner cage) leakage inductance (H or pu)

Rr2

Cage 2 (outer cage) resistance (ohm or pu)

Llr2

Cage 2 (outer cage) leakage inductance (H or pu)

Lm

Magnetizing inductance (H or pu)

spec2 returns the input manufacturer data structure along with the following additional derived data fields.

Field

Description

cosphi

Nominal power factor (0-1)

Ns

Synchronous speed (rpm)

p

Number of pole pairs

we

Vin

Nominal phase voltage (V)

sn

Ist

Starting current (A)

Tst

Starting torque (N.m)

Tbr

Breakdown torque (N.m)

Pn

Nominal (full load) mechanical power (W)

errors returns the relative errors between the input manufacturer data and the equivalent data obtained with the computed parameters in a structure with the following fields.

Field

Description

In

Relative error with respect to specified nominal current (%)

Tn

Relative error with respect to specified nominal torque (%)

pf

Relative error with respect to specified nominal power factor (%)

Ist

Relative error with respect to specified starting current (%)

Ist_Iin

Relative error with respect to specified starting current to nominal current ratio (%)

Tst

Relative error with respect to specified starting torque (%)

Tst_Tn

Relative error with respect to specified starting torque to full load torque ratio (%)

Tbr

Relative error with respect to specified breakdown torque (%)

Tbr_Tn

Relative error with respect to specified breakdown torque to full load torque ratio (%)

maxError

Maximum relative error (maximum of above fields) (%)

## Dialog Box

power_AsynchronousMachineParams command opens a graphical user interface (GUI) that you can use to estimate parameters of the double-cage Asynchronous Machine block.

Specifications

Enter the manufacturer specifications. If you loaded a motor preset in the interface, the name of the MAT file is displayed in the upper section of the panel.

Compute Block Parameters

Compute the electrical parameters of the double-cage asynchronous machine and display the solution in the Block Parameters section. The button is grayed out when the block parameters have been estimated.

The button is reenabled when you enter new values in the Specifications section, to indicate that the displayed block parameters no longer correspond to the displayed specifications.

If the Display detailed results in the command window check box is selected, the errors between the specified manufacturer parameters and the obtained parameters are displayed in the command window. This allows you to check that the estimated RL machine parameters are satisfactory. For example, the errors obtained with the Baldor_2,2_kw_208_V.mat preset motor are shown below:

```Asynchronous machine parameter estimation results
-------------------------------------------------------------
Parameter        Specified       Obtained         Error (%)
---------        ---------       ---------        ---------
In (A)               8.3         8.26016           -0.48
Tn (N.m)           12.27         12.3656            0.78
Ist (A)           66.483         66.0075           -0.72
Ist/In ()           8.01         7.99106           -0.24
Tst (N.m)        43.3131         43.2625           -0.12
Tst/Tn ()           3.53         3.49861           -0.89
Tmax (N.m)       47.7303         47.9587            0.48
Tbr/Tn ()          3.89          3.87839           -0.30
pf (%)               87          86.4635           -0.62    ```
Block Parameters

This section displays the asynchronous machine block parameters corresponding to the given manufacturer specifications. These fields are empty the first time you open the interface, or when the function failed to find a solution. The block parameters are noneditable. They can be loaded in your Asynchronous Machine block by using the Apply to selected block button.

Apply to selected block

Open your model, select the machine you want to parametrize, then click the Apply to selected block button to load the displayed block parameters in the block. The block is grayed out when the Block Parameters fields are empty. The button is enabled when a valid solution is displayed in the Block Parameters section.

The button has no effect on a selected block that is not an Asynchronous Machine block.

File

Select New to clear the Block Parameters and Specifications sections. The Compute Block Parameters and Apply to selected block buttons are then disabled.

Select Open preset motor to load in the interface a given set of manufacturer specifications. The corresponding block parameters are also loaded when they are available in the preset file. If you do not have the Optimization Toolbox software installed you can still open these given preset data and load the corresponding machine parameters in your selected block.

Select Save preset motor to save the specifications displayed in the interface. The block parameters are also saved when available.

Options

If the Draw graph after computation option in the Compute Block Parameters submenu is selected, then when you click the Compute Block Parameters button the function displays the graphs of torque versus speed and stator current versus speed, corresponding to the block parameters. This option is not selected by default.

If the Display detailed results in the command window option in the Compute Block Parameters submenu is selected, then when you click the Compute Block Parameters button the function displays the errors between the specified manufacturer parameters and the obtained parameters are displayed in the command window. This option is selected by default.

If the Ask me before overwriting rotor type and preset model of selected block option in the Apply button submenu is selected, then when you click the Apply to selected block button it gives you a warning if you try to download double squirrel-cage parameters in a selected block that has a squirrel-cage or wound rotor, or if you try to overwrite a selected block using a preset model. This option is selected by default.

## Examples

Consider a three-phase 400V, 110 kW asynchronous machine with the following manufacturer specification:

Data

Values

Vn

400 V

fn

50 Hz

In

194 A

Tn

352 N.m

Nn

2982 rpm

Ist/In

7.6

Tst/Tn

2

Tbr/Tn

3

pf

86%

To obtain the electrical parameters (Rs, Lls, Lm, Rr1, Llr1, Rr2, Llr2) in per unit (pu) for the double cage asynchronous machine model based on this specification, enter the following commands in the MATLAB Command window:

```spec.Vn = 400;
spec.fn = 50;
spec.In = 194;
spec.Tn = 352;
spec.Ns = 3000;
spec.Nn = 2982;
spec.Ist_In = 7.6;
spec.Tst_Tn = 2;
spec.Tbr_Tn = 3;
spec.pf = 86;

options.DisplayDetails = 1;
options.units = 'p.u.';

[params,spec2,errors] = power_AsynchronousMachineParams(spec,options)```

You should get the following results:

```Asynchronous machine parameter estimation results
-------------------------------------------------------------
Parameter        Specified       Obtained         Error (%)
---------        ---------       ---------        ---------
In (A)               194         193.991           -0.00
Tn (N.m)             352         352.023            0.01
Ist (A)           1474.4         1474.35           -0.00
Ist/In ()            7.6          7.6001            0.00
Tst (N.m)            704           703.8           -0.03
Tst/Tn ()              2          1.9993           -0.03
Tmax (N.m)          1056            1056            0.00
Tbr/Tn ()             3          2.99981           -0.01
pf (%)               86          85.9949           -0.01

params =

Rs: 0.0303
Lls: 0.0506
Lm: 1.9066
Llr1: 0.0868
Rr1: 0.0056
Llr2: 0.0506
Rr2: 0.0762

spec2 =

fn: 50
In: 194
Tn: 352
Ns: 3000
Nn: 2982
Ist_In: 7.6000
Tst_Tn: 2
Tbr_Tn: 3
pf: 86
Vn: 400
p: 1
cosphi: 0.8600
we: 314.1593
Vin: 230.9401
sn: 0.0060
Ist: 1.4744e+003
Tst: 704
Tbr: 1056
Pn: 1.0992e+005

errors =

In: -0.0048
Tn: 0.0066
pf: -0.0059
Ist: -0.0035
Ist_In: 0.0013
Tst: -0.0284
Tst_Tn: -0.0349
Tbr: 2.1990e-004
Tbr_Tn: -0.0063
maxError: 0.0349```

To draw graphs of torque versus speed and stator current versus speed, enter the following commands:

```options.DrawGraphs = 1;
options.DisplayDetails = 0;
params = power_AsynchronousMachineParams(spec,options);```

The following figure shows the resulting graph:

## References

[1] Pedra, Joaquin, "On the Determination of Induction Motor Parameters From Manufacturer Data for Electromagnetic Transient Programs." IEEE® Transactions on Power Systems, vol.23, no.4, pp. 1709-1718, November 2008.