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.

R_s, L_ls, R_r1, L_lr1, R_r2, L_lr2, L_m 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:

$f_{1} (x) = \frac{T_{n} - T (s_{n})}{T_{n}}$

$f_{2} (x) = \frac{I_{n} - I (s_{n})}{I_{n}}$

$f_{3} (x) = \frac{p f - p f (s_{n})}{p f}$

$f_{4} (x) = \frac{I_{s t} - I (1)}{I_{s t}}$

$f_{5} (x) = \frac{T_{b r} - T (s_{b r})}{T_{b r}}$

$f_{6} (x) = \frac{T_{s t} - T (1)}{T_{s t}}$

where f = (f₁, f₂, f₃, f₄, f₅, f₆) and x = (R_s, L_m, R_r1, L_lr1, R_r2, L_lr2). The L_ls parameter is obtained by assuming that the stator and outer cage leakage inductances are equal (L_ls = L_lr2). s_n and s_br are the slip at nominal and breakdown torque, respectively. For details on the functions used in these equations, see [1].

T_n, I_n, pf, I_st, I_br, T_st are the standard manufacturer specifications of the machine. They form the fields of the spec structure, as described in the Input Arguments section.

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`	Nominal (full load) torque (N.m)
`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`	Nominal electrical angular speed (rad/s)
`Vin`	Nominal phase voltage (V)
`sn`	Nominal (full-load) slip
`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 user interface (UI) 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.

Save spec to MATLAB structure

Click Save spec to MATLAB structure to save the motor specifications in a MATLAB structure in the base workspace.

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.

Presets

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.

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, Number 4, 2008, pp. 1709–1718.