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

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

`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`.

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:

where *f* = (*f*_{1}, *f*_{2}, *f*_{3}, *f*_{4}, *f*_{5}, *f*_{6})
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.

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*).

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

Field | Description |
---|---|

| Nominal line-to-line rms voltage (V) |

| Nominal frequency (Hz) |

| Nominal (full load) line current (A) |

| Nominal (full load) torque (N.m) |

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

| Nominal (full load) mechanical speed (rpm) |

| Starting current to nominal current ratio |

| Starting torque to full load torque ratio |

| Breakdown torque to full load torque ratio |

| Nominal power factor (%) |

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

Field | Description |
---|---|

| If set to |

| If set to |

| Specifies the units of machine parameters in |

| Specifies the graph units in |

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

Field | Description |
---|---|

| Stator resistance (ohm or pu) |

| Stator leakage inductance (H or pu) |

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

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

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

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

| Magnetizing inductance (H or pu) |

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

Field | Description |
---|---|

| Nominal power factor (0-1) |

| Synchronous speed (rpm) |

| Number of pole pairs |

| Nominal electrical angular speed (rad/s) |

| Nominal phase voltage (V) |

| Nominal (full-load) slip |

| Starting current (A) |

| Starting torque (N.m) |

| Breakdown torque (N.m) |

| 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 |
---|---|

| Relative error with respect to specified nominal current (%) |

| Relative error with respect to specified nominal torque (%) |

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

| Relative error with respect to specified starting current (%) |

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

| Relative error with respect to specified starting torque (%) |

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

| Relative error with respect to specified breakdown torque (%) |

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

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

`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.

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

Data | Values |
---|---|

| 400 V |

| 50 Hz |

| 194 A |

| 352 N.m |

| 2982 rpm |

| 7.6 |

| 2 |

| 3 |

| 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:

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