TWI423047B - Method for estimating parameters of induction machine by time-varied parameters - Google Patents

Description

Method for solving induction machine parameters with time-varying parameters

The invention relates to a method for solving parameters of an induction machine, in particular to a method for solving parameters of an induction machine by time-varying parameter iteration.

The stator of the induction machine is a winding, and its rotor does not require a DC magnetic field circuit during operation. The rotor voltage induced by the relative motion between the stator and the rotor magnetic field is used to generate the rotor current; and the stator and the rotor magnetic field interact to generate an induced torque in the induction machine. Due to its simple structure and easy operation, the induction machine has become the most commonly used AC motor. The method and system design of the induction machine control are all assisted by the equivalent model and its parameters. The known techniques for obtaining related models and their parameters can be roughly divided into two categories: offline estimation and online real-time estimation: offline estimation can be obtained through standard methods such as DC test, no-load test and stall test; online real-time estimation The measurement can use the frequency spectrum to analyze its frequency response to estimate its parameters, use the structure of the reference model to estimate, or use numerical methods to identify the parameters of artificial intelligence. Each of the above methods has its own advantages and disadvantages and limitations, and most of them require expensive measuring equipment and wait for the speed of the induction machine to reach a steady state before all parameters are obtained.

In view of this, the main object of the present invention is to provide a method for solving the parameters of the induction machine, which is to find the equivalent circuit model and equivalent of the induction machine by the least square method and the optimum value search and calculation by the gradient method. Related parameters of the mechanical model. Moreover, setting a suitable set of initial values will aid in the convergence and efficiency of the iterative process, and another object of the present invention is to provide a preferred method of initial value setting.

For the above purposes, the method for solving the parameters of the induction machine proposed by the present invention comprises the following steps: first, a time-varying signal of voltage, current and rotational speed when the induction machine is started; secondly, calculating the induction machine is different. Resistance and reactance under slip; third, setting the objective function of a circuit parameter; fourth, setting the initial value of the equivalent circuit parameter of the induction machine, and repeating the iteration and correction by the gradient method, when the target When the value of the function converges to a permissible range value, the parameters of the equivalent circuit model of the induction machine can be calculated; fifth: according to the rotational speed signal obtained at step 1 and the equivalent circuit parameters obtained in step four, The dynamic simulation of the output torque of the induction machine, and calculate its output torque; Finally, according to the output torque and speed obtained in step 5, and set the objective function of a mechanical parameter, calculate the parameters of the equivalent mechanical model of the induction motor. In this way, the parameters of the equivalent circuit model of the induction machine can be solved: rotor resistance, stator resistance, rotor reactance, stator reactance and excitation reactance, and the parameters of the equivalent mechanical model: inertia and damping.

In order to further understand the present invention, the following detailed description is made in conjunction with the related embodiments and the drawings. Please refer to FIG. 1 , which is a flow chart of the method of the present invention, which mainly includes the following steps: taking a time series of measuring voltage v(n), measuring current I(n) and rotating speed w _r (n) at the start of the induction machine. The signal, the induction machine equivalent circuit can be obtained from the impedance versus the change in the rotational speed (step 110). Since the transient time constant of the induction machine is so short that the transient caused by the inductance will quickly fall to a negligible range at the beginning of the start, the characteristics of the voltage and current will be dominated by the steady-state impedance, and the steady state of the induction machine, etc. Refer to Figure 2 for the effective circuit model, where R _s is the stator resistance, R _r is the rotor resistance, X _m is the excitation reactance, X _s stator equivalent reactance, and X _r is the rotor equivalent reactance; s is the slip ratio, The time series initiated by the induction machine is defined as The primary side resistance and reactance of the calculation induction machine are respectively at different slip rates (step 120):

The invention adopts the least squares method to obtain the relevant circuit parameters, and the search for the optimum value is performed by the gradient method. The main principle of the gradient method is to use the gradient of the objective function as its search direction to deal with the minimization search of multivariable nonlinear functions. By a series of iterative processes, the set results can approach the actual value. Gradient refers to the first differentiation of the objective function. For the solution of the equivalent circuit parameters of the induction machine, the objective function can be set to (step 130).

E _R and E _X are functions with a minimum value, and at a minimum value, the gradient of each of the two functions is zero for each parameter. When a gradient other than 0 is obtained near the minimum value, the gradient can be set to the search direction of the optimal solution. In the present invention, R _s , R _{r are} used as the minimum value of searching E _R , and X _s , X _r , X _{m are used to} search for the minimum value of E _X , and an auxiliary equation can be established.

M = ( R _r / s ) ² + ( X _m + X _r ) ²

Then the error between the resistance and the reactance is

Then the gradient searching for the minimum values of E _R and E _X can be expressed as

The impedance parameter is modified by the above five equations to obtain the minimum value of the objective function, and the next state of each parameter is

Where η _Rs , η _Rr , η _Xs , η _Xr , and η _Xm are respectively corresponding to each circuit parameter acceleration factor; and the respective parameter values are corrected according to the above five equations, so that the objective function gradually converges.

Setting a preferred initial value will improve the efficiency of the cascade convergence of the gradient method. Therefore, the present invention provides a method for calculating the initial value of the equivalent circuit parameter of the induction machine as follows (step 140): Please refer to FIG. 3, which is possible when the induction machine is started. The resulting impedance corresponds to its slip rate, where the rotor speed often fails to reach the synchronous speed, and the present invention seeks an approximate initial value for this fact. When the slip ratio s =1, the impedance values are R (1) and X (1); when the slip ratio s = 0.5, the resistance value R (0.5); when approaching the synchronous speed, two close to 0 are obtained. The slip ratios s 1 and s 2 have corresponding reactance values of X ( s 1) and X ( s 2), respectively. At the beginning of the start, s is between 0.5 and 1. Since X _{m is} much larger than X _s and R _r and the resistance changes linearly, an approximate relationship R ( s ) ≒ R _s + R _r / s is obtained . The initial value of the available resistance is R _r ⁰ =0.5( R (0.5)- R (1)) and R _s ⁰ = R (1)- R _r ⁰ ; the reactance change is small at this time, and its value is about X. _The sum of _s and X _r , so set the initial value of X _s and X _r , ie X _s ⁰ = X _r ⁰ =0.5 X (1); the magnetizing reactance of the induction machine can be obtained at the no-load speed, when the induction machine arrives At synchronous speed, the reactance value is X (0) = X _s + X _m , but in practice, bringing the induction machine to synchronous speed will increase the complexity of the measurement. The present invention uses the extrapolation method without increasing the measurement. Accurate calculation results are achieved under complexity. When the induction machine approaches the synchronous speed, the reactance increases linearly. Therefore, it is possible to estimate the reactance at the synchronous speed by using several sampling values close to the synchronous speed. The exciting reactance value at the synchronous speed can be obtained according to the extrapolation method.

Through the above steps, the initial values of all the sensor circuit parameters can be calculated: R _s ⁰ , R _r ⁰ , X _s ⁰ , X _r ⁰ , X _m ⁰ .

The present invention calculates the torque of the induction machine by dynamic simulation. The parameters of the equivalent circuit of the induction machine can be obtained by the aforementioned steps, and under the stator reference architecture, the dynamic model of the three-phase induction machine can be expressed as

v _qs =( R _s + L _s p ) i _qs + L _m pi _qr

v _ds =( R _s + L _s p ) i _ds + L _m pi _dr

v _qr = L _m pi _qs -ω _r L _m i _ds +( R _r + L _r p ) i _qr -ω _r L _r i _dr

v _dr =ω _r L _m i _qs + L _m pi _ds +ω _r L _r i _qr +( R _r + L _r p ) i _dr

Where i _qs , i _ds is the stator current; i _qr , i _dr is the rotor current; v _qs , v _ds is the stator voltage; v _qr , v _dr is the rotor voltage; p is the differential factor ( L _r , L _m , L _s are the rotor inductance (X _r /w _s ), the magnetizing inductance (X _m /w _s ), and the stator inductance (X _s /w _s ), respectively. Therefore, the output torque can be further obtained (step 150).

T = 3 PL _m ( i _dr i _qs - i _qr i _ds )

Where P is the number of poles of the motor.

The inertia J and the viscous damping B are important parameters of the equivalent mechanical model of the induction machine, which jointly determine the relationship between the output torque and the rotational speed; that is, when the output torque and the rotational speed are known, Further inversely push the inertia and viscous damping. Assuming that the torque generated by the induction machine only causes the speed of the induction machine to change, and does not drive other mechanical loads, the corresponding speed corresponds to the following differential equation.

Expressed as discrete data:

J (ω _r ( n )-ω _r ( n -1)) + B ω _r ( n )= T ( n ), n=1, 2,...

When considering that the system is linear, where the inertia and viscous damping are constant, to obtain the most appropriate parameters, the objective function can be set to

When the objective function is the smallest, there is the most appropriate inertia J and viscous damping B , that is, the gradient of the upper inertia J and the viscous damping B is 0, so the inertia J and the viscous damping B can be obtained by (Step 160)

Through the above methods and steps, the parameters of the equivalent circuit model of the induction machine can be solved: rotor resistance, stator resistance, rotor reactance, stator reactance and excitation reactance, and parameters of the equivalent mechanical model: inertia and damping.

The above and other objects, features and advantages of the present invention will become more <RTIgt;

Assuming a three-phase, 4-pole, 0.5-horsepower, 60 Hz induction machine, please refer to Figure 4 for the measured curve data of voltage and current for the starting speed. At the beginning of the start-up, the voltage produces a slight voltage drop. As the speed rises, the voltage gradually returns to the normal value. At this time, due to the slip relationship, the potential of the rotor has not been established, resulting in a large current. When the speed is close to the rated speed, the current drops to a fairly small value. The phase of the impedance during the start-up phase varies between 30° and 70°. After the start and stability, the reactance is larger than the resistance. When the rated speed is approaching, the resistance is larger than the reactance.

Please refer to Figure 5 for the impedance at different slip rates. The resistance and reactance changes of the induction machine from standstill to rated speed confirm that the transient term has minimal effect on the start-up phase of the induction machine, and the steady-state term is sufficient to provide a simple and accurate enough accuracy. By using the equation for setting the initial value of the parameter of the induction machine provided by the invention, the initial value of the equivalent circuit parameter is obtained as R _r ⁰ = 0.5 ( R (0.5) - R (1)) = 8.68 Ω, R _s ⁰ = R (1) - R _r = 23.37 Ω, X _s ⁰ = X _r ⁰ = 0.5 X (1) = 13.52 Ω, and

The initial value is substituted into the gradient method to calculate the resistance and reactance of the induction machine. The results are shown in Table 1. The result of the convergence of the gradient method is shown: after 4000 iterations, the convergence result can be obtained, and the initial result can be found. The value setting has reached a result that is fairly close to the actual value, where the noise and nonlinear factors make the objective function unable to reach zero.

In this embodiment, the dynamic behavior of the system is simulated by the parameter results obtained above, and compared with actual values. For the simulation results, please refer to Figure 6, which shows the comparison of the currents, and the standard deviation of the current is 0.339. It can be found that the two are quite close; it can also be found that the transient will decay to a minimum value within one week, so the graph The current in 6 will show a steady state result. It is confirmed that the steady state term dominates the change in current. From the output torque and the rotational speed of the induction machine, the moment of inertia J and the viscous damping B are each 0.38 (g.m ² ) and 0.61 (mN.m/(rad/sec)). Figure 7 shows a comparison of the rotational speeds. The standard deviation of the rotational speed is 8.388, which is a relatively low value. It is confirmed that the parameters obtained by the method are quite in line with the actual situation.

While the present invention has been described above in terms of the preferred embodiments thereof, it is not intended to limit the invention, and the equivalent of the modification and retouching of the present invention is still within the spirit and scope of the present invention. Within the scope of patent protection of the present invention.

Step 110: Time-varying signals for measuring voltage, current, and speed at the start of the induction machine: v(n), i(n), w _r (n).

Step 120 calculates the resistance and reactance of the induction machine at different slip ratios: R(s), X(s).

Step 130 sets the objective function of the circuit parameters.

Step 140: setting an initial value of the equivalent circuit parameter of the induction machine, and calculating parameters of the equivalent circuit model by using a gradient method cyclic iteration: R _s , R _r , X _s , X _r , X _m .

Step 150: According to the start time change signal obtained in step 110, perform dynamic simulation of the induction machine and calculate its output torque: T(n).

Step 160 sets an objective function of a mechanical parameter and calculates a parameter of the equivalent mechanical model of the induction machine.

1 is a flow chart of a method for solving parameters of an induction machine according to the present invention.

Figure 2 shows the steady-state equivalent circuit of the induction machine.

Figure 3 is a graph of the impedance that may occur when the induction machine is started, corresponding to its slip rate, as a reference for the initial value setting.

4 is a measured data curve of the voltage and current of the induction machine in the starting phase with respect to the rotational speed of the embodiment.

FIG. 5 is a comparison of impedances of the induction machine of the present embodiment at different slip rates.

Fig. 6 is a comparison of the measured value of the current of the present embodiment with the simulation method of the present method.

Fig. 7 is a comparison of the actual measured value of the rotational speed of the present embodiment with the simulation solution of the present method.

Step 110: Time-varying signals for measuring voltage, current, and speed at the start of the induction machine: v(n), i(n), w _r (n).

Step 120 calculates the resistance and reactance of the induction machine at different slip ratios: R(s), X(s).

Step 130 sets the objective function of the circuit parameters.

Step 140: setting an initial value of the equivalent circuit parameter of the induction machine, and calculating parameters of the equivalent circuit model by using a gradient method cyclic iteration: R _s , R _r , X _s , X _r , X _m .

Step 150: According to the start time change signal obtained in step 110, perform dynamic simulation of the induction machine and calculate its output torque: T(n).

Step 160 sets an objective function of a mechanical parameter and calculates a parameter of the equivalent mechanical model of the induction machine.

Claims (7)

A method for solving the parameters of the induction machine comprises the following steps: Step 1: obtaining a time-varying signal for measuring voltage, current and speed at the start of the induction machine; Step 2: calculating the resistance and reactance of the induction machine at different slip rates; Step 3: Set the target function of a circuit parameter; Step 4: Set the initial value of the equivalent circuit parameter of the induction machine, and repeat the iteration and correction by the gradient method, when the value of the objective function converges to a allowable range value When the parameters of the equivalent circuit model of the induction machine are calculated, step 5: dynamic simulation of the output torque of the induction machine according to the rotational speed signal obtained at step 1 and the equivalent circuit parameters obtained in step 4 And calculating the output torque thereof; and step 6: calculating the equivalent mechanical model of the induction machine according to the output torque obtained in step 5 and the starting speed signal obtained in step 1, and setting an objective function of a mechanical parameter parameter. For example, the method for solving the parameters of the induction machine described in claim 1 wherein the parameters of the equivalent circuit model include: rotor resistance R _r , stator resistance R _s , rotor equivalent reactance X _r , stator equivalent reactance X _s , And the magnetizing reactance X _m . For the method for solving the parameters of the induction machine described in claim 1, the initial value of the equivalent circuit parameter of step 4 is set as follows: the initial value of the rotor resistance R _r ⁰ is 0.5 ( R (0.5)- R (1) ), the initial value of stator resistance R _s ⁰ is R (1)- R _r ⁰ , the initial value of rotor equivalent reactance X _r ⁰ is 0.5 X (1), and the initial value of stator equivalent reactance X _s ⁰ is 0.5 X (1) And the initial value of the excitation reactance X _m ⁰ is Each of the resistors and reactances is calculated in the step 2, and s ₁ and s ₂ respectively represent two slips close to 0 when the induction machine approaches the synchronous speed. For example, in the method for solving the parameters of the induction machine described in claim 2, the objective function in the step 3 is: Where s is the slip rate. For example, in the method for solving the parameters of the induction machine described in claim 1, the dynamic simulation of the output torque of the induction machine in step 5 is a stator reference architecture. For example, the method for solving the parameters of the induction machine described in claim 1 wherein the parameters of the equivalent mechanical model include: inertia J and damping B. For example, in the method for solving the parameters of the induction machine described in claim 1, the objective function in the step 6 is , Where T (n) is obtained in step 5 an output torque of the induction machine, and J, B and w _r, respectively, indicating that the inertia of the induction machine, the rotational speed and viscous dampers.