CN107894565A - A kind of asynchronous motor Identifying Dynamical Parameters method based on algebraic approach - Google Patents
A kind of asynchronous motor Identifying Dynamical Parameters method based on algebraic approach Download PDFInfo
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Abstract
The invention discloses a kind of method of the asynchronous motor Identifying Dynamical Parameters based on algebraic approach.Algebraic approach is a kind of discrimination method suitable for continuous system, has convergence good, identification result is accurate, and algorithm takes the advantages that short.This method determines the model to be identified of asynchronous motor first, the observable variable of corresponding parameter to be identified and asynchronous motor, then integral operation is carried out to the signal of observable variable, and influence of the state variable initial value to identification precision is eliminated by mathematic(al) manipulation.Simulation result shows that algorithm principle is reliable, and identification result is accurate.
Description
Technical Field
The invention relates to a method for identifying dynamic parameters of an asynchronous motor, in particular to an algebraic-method-based method for identifying dynamic parameters of an asynchronous motor.
Background
The asynchronous motor is a component of a power system, firstly, the asynchronous motor is used as a typical industrial load and has a large proportion of electricity consumption in the whole society, and secondly, with the development of renewable energy sources such as wind power and the like, the asynchronous motor has greater and greater contribution at a power generation end, so that the accurate identification of dynamic parameters of the asynchronous motor has important significance for the safe and stable operation of the power system.
The parameter identification of the asynchronous motor can be divided into two categories, namely frequency domain identification and time domain identification. The frequency domain identification method is based on the steady state analysis of the linear system and cannot reflect the dynamic process of the nonlinear system, so the frequency domain identification method has larger limitation.
At present, time domain identification methods include least square methods, model reference adaptive methods, genetic algorithms and the like. The least square method finds a group of optimal parameters to enable the square sum of errors of a measurement result and a calculation result to be minimum, but the least square method does not consider the influence of conditions such as noise and the like, so that the parameter values determined by the algorithm have the problems of multivalueness, deviation and the like.
The model reference self-adaptive method takes an actual asynchronous motor as a reference and takes a motor state equation as an adjustment model. The parameters of the tuning model are determined by observables of the motor.
Genetic algorithms are a new approach applied in recent years to the field of parameter identification of asynchronous motors. The method continuously updates the population through operations such as crossing, mutation and the like, and searches for the optimal solution of the parameters, and the method has the problems of low convergence speed and the like.
Disclosure of Invention
In order to solve the problems, the invention provides an algebraic-method-based asynchronous motor dynamic parameter identification method.
The technical scheme of the invention comprises the following steps:
1) determining a model to be identified of the asynchronous motor, corresponding parameters to be identified and observable variables of the asynchronous motor:
2) integral operation is carried out on the signal of the observable variable, the influence of the initial value of the state variable on the identification precision is eliminated through mathematical transformation, and the inertia time constant T of the rotor of the asynchronous motor is identifiedj：
3) Identifying the steady state reactance X of the rotor of the asynchronous motor, the transient state reactance X ' of the rotor and the time constant T ' of the rotor loop 'd0；
In the above technical solution, the step 1) determines the model to be identified of the asynchronous motor, the corresponding parameter to be identified, and the observable variable of the asynchronous motor. The interface equation of the asynchronous motor model and the network adopts the following formula:
wherein X' represents the rotor transient reactance of the asynchronous motor, Ex' represents the transient electromotive force of the x-axis component of the asynchronous motor, Ey' represents the transient electromotive force, U, of the y-axis component of the asynchronous motorxRepresenting the voltage, U, of the x-component of the asynchronous motoryRepresenting the voltage of the y-component of the asynchronous motor, IxRepresenting the x-component current of the asynchronous motor, IyRepresenting the asynchronous motor y-component current. The asynchronous motor is a three-order dynamic model and adopts the following formula:
where s denotes the rotor slip of the asynchronous motor, TMRepresenting mechanical torque, T, of an asynchronous motorERepresenting the electromagnetic torque of the asynchronous motor. Because the rotor speed is close to the synchronous speed under the normal operation condition, TEApproximately equal to the active power P. T isjDenotes the rotor inertia time constant, X denotes the rotor steady-state reactance, T'd0Representing the rotor loop time constant. The output of the asynchronous motor is active power and reactive power, and the following formula is adopted:
TE≈P＝-(Ex′Ix+Ey′Iy)
Q＝UyIx-UxIy
in the model of the asynchronous motor, the parameters to be identified of the asynchronous motor are the steady-state reactance X of the rotor, the transient-state reactance X' of the rotor and the inertia time constant T of the rotorjAnd a rotor circuit time constant T'd0. The observable variables of the asynchronous motor are slip s (t) and asynchronous motor voltage Ux(t)，Uy(t) asynchronous motor current Ix(t)，Iy(T), asynchronous motor power P (T), Q (T), asynchronous motor mechanical torque TM(t)。
Step 2) identifying the inertia time constant T of the rotor of the asynchronous motorjThe following formula is adopted:
in the above formula, T represents time, s (T) represents the slip ratio of the asynchronous motor rotor, TM(T) mechanical power of asynchronous motor, TE(t) represents the electromagnetic power of the asynchronous motor. The fractional integration rule is used for the left part of the equal sign of the above formula as follows:
therefore, the following holds:
the above equation can be rewritten as follows:
it can be seen that the disturbance of the initial values of the state variables is eliminated by mathematical transformation. The right side of the equal sign of the above formula is observable variable, so that the parameter T to be identified can be determined through the above formulaj. Furthermore, it can be concluded from the above formula: the parameter identified by the algebraic method is not a constant value but a function that varies with time.
Step 3) identifying the steady-state reactance X and the transient-state reactance X ' of the rotor of the asynchronous motor and the time constant T ' of a rotor loop 'd0The following formula is adopted:
in the above formula, t represents time, Ex' (t) denotes an electromotive force of an x-axis component of the asynchronous motor, Ey' (t) denotes the asynchronous motor y-axis component electromotive force, Ix(t) represents the x-axis component current of the asynchronous motor, IyAnd (t) represents the y-axis component current of the asynchronous motor. Due to Ex′(t)，Ey' (t) is an unobservable variable, so Ex′(t)，Ey' (t) is determined using the following formula:
Ey′(t)＝Uy(t)+X′Ix(t)
Ex′(t)＝Ux(t)-X′Iy(t)
wherein U isx(t) represents the asynchronous motor x-axis component voltage, Uy(t) represents the asynchronous motor y-component voltage, Ux(t) and Uy(t) are all observable variables. When E isx′(t)，Ey' (t) is expressed by the above formula, the following formula holds:
Y＝Aθ
wherein, it can be seen that the above formula is a set of linear non-homogeneous equations, comprising two linearly independent equations, three unknowns. The unknown parameter θ of the equation is determined using the following equation:
after determining theta, the steady state reactance X of the asynchronous motor rotor, the transient state reactance X ' of the rotor, and the time constant T ' of the rotor loop 'd0Determined using the following formula:
X′＝θ1
the invention has the beneficial effects that:
the invention aims to identify the dynamic parameters of the asynchronous motor by an algebraic method and provide an effective basis for the safe and stable operation of a power grid.
Drawings
FIG. 1 rotor inertia time constant TjIdentifying a result;
FIG. 2 rotor Loop time constant T'd0Identifying a result;
FIG. 3 shows the result of the steady-state reactance X identification of the rotor;
fig. 4 shows the rotor transient reactance X' identification.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
The method comprises the following steps:
1) determining a model to be identified of the asynchronous motor, corresponding parameters to be identified and observable variables of the asynchronous motor:
2) integral operation is carried out on the signal of the observable variable, the influence of the initial value of the state variable on the identification precision is eliminated through mathematical transformation, and the inertia time constant T of the rotor of the asynchronous motor is identifiedj：
3) Identifying the steady state reactance X of the rotor of the asynchronous motor, the transient state reactance X ' of the rotor and the time constant T ' of the rotor loop 'd0；
The step 1) determines a model to be identified, corresponding parameters to be identified and observable variables of the asynchronous motor, which are specifically described as follows:
the interface equation of the asynchronous motor model and the network adopts the following formula:
wherein X' represents the rotor transient reactance of the asynchronous motor, Ex' represents the transient electromotive force of the x-axis component of the asynchronous motor, Ey' represents the transient electromotive force, U, of the y-axis component of the asynchronous motorxRepresenting the voltage, U, of the x-component of the asynchronous motoryRepresenting the voltage of the y-component of the asynchronous motor, IxRepresenting the x-component current of the asynchronous motor, IyRepresenting the asynchronous motor y-component current. The asynchronous motor is a three-order dynamic model and adopts the following formula:
where s denotes the rotor slip of the asynchronous motor, TMRepresenting mechanical torque, T, of an asynchronous motorERepresenting the electromagnetic torque of the asynchronous motor. Because the rotor speed is close to the synchronous speed under the normal operation condition, TEApproximately equal to the active power P. T isjDenotes the rotor inertia time constant, X denotes the rotor steady-state reactance, T'd0Representing the rotor loop time constant. The output of the asynchronous motor is active power and reactive power, and the following formula is adopted:
TE≈P＝-(Ex′Ix+Ey′Iy)
Q＝UyIx-UxIy
in the model of the asynchronous motor, the parameters to be identified of the asynchronous motor are the steady-state reactance X of the rotor, the transient-state reactance X' of the rotor and the inertia time constant T of the rotorjAnd a rotor circuit time constant T'd0. The observable variables of the asynchronous motor are slip s (t) and asynchronous motor voltage Ux(t)，Uy(t) asynchronous motor current Ix(t)，Iy(T), asynchronous motor power P (T), Q (T), asynchronous motor mechanical torque TM(t)。
Step 2) identifying the inertia time constant T of the rotor of the asynchronous motorjThe details are as follows:
identification of inertia time constant T of asynchronous motor rotorjThe following formula is adopted:
in the above formula, T represents time, s (T) represents the slip ratio of the asynchronous motor rotor, TM(T) mechanical power of asynchronous motor, TE(t) represents the electromagnetic power of the asynchronous motor. The fractional integration rule is used for the left part of the equal sign of the above formula as follows:
therefore, the following holds:
the above equation can be rewritten as follows:
it can be seen that the disturbance of the initial values of the state variables is eliminated by mathematical transformation. The right side of the equal sign of the above formula is observable variable, so that the parameter T to be identified can be determined through the above formulaj. Furthermore, it can be concluded from the above formula: the parameter identified by the algebraic method is not a constant value but a function that varies with time.
Step 3) identifying the steady-state reactance X and the transient-state reactance X ' of the rotor of the asynchronous motor and the time constant T ' of a rotor loop 'd0The details are as follows:
identifying the steady state reactance X of the rotor of the asynchronous motor, the transient state reactance X ' of the rotor and the time constant T ' of the rotor loop 'd0The following formula is adopted:
in the above formula, t represents time, Ex' (t) denotes an electromotive force of an x-axis component of the asynchronous motor, Ey' (t) denotes the asynchronous motor y-axis component electromotive force, Ix(t) represents the x-axis component current of the asynchronous motor, IyAnd (t) represents the y-axis component current of the asynchronous motor. Due to Ex′(t)，Ey' (t) is an unobservable variable, so Ex′(t)，Ey' (t) is determined using the following formula:
Ey′(t)＝Uy(t)+X′Ix(t)
Ex′(t)＝Ux(t)-X′Iy(t)
wherein U isx(t) represents the asynchronous motor x-axis component voltage, Uy(t) represents the asynchronous motor y-component voltage, Ux(t) and Uy(t) are all observable variables. When E isx′(t)，Ey' (t) is expressed by the above formula, the following formula holds:
Y＝Aθ
wherein, it can be seen that the above formula is a set of linear non-homogeneous equations, comprising two linearly independent equations, three unknowns. The unknown parameter θ of the equation is determined using the following equation:
after determining theta, the steady state reactance X of the asynchronous motor rotor, the transient state reactance X ' of the rotor, and the time constant T ' of the rotor loop 'd0Determined using the following formula:
X′＝θ1
the method is adopted to carry out calculation on a 10-machine 39-node system, the node 4 is an asynchronous motor to be identified, and the actual values of the parameters to be identified are X-3.6791, X '-0.2960 and T'd0＝0.5760，TjThe active power injection variance at node 24 of 10s to 40s is white noise with 0.02, and the dynamic parameters of the asynchronous motor at node 4 are identified by an algebraic method, and the results are as follows:
FIG. 1 shows the rotor time constant T of an asynchronous motorjThe result of the identification. FIG. 2 is an asynchronous motor rotor circuit constant T'd0The result of the identification. Fig. 3 shows the result of identifying the steady-state reactance X of the rotor of the asynchronous motor. Fig. 4 shows the identification result of the transient reactance X' of the rotor of the asynchronous motor. As can be seen from fig. 1 to 4, the algebraically determined parameter value is not a constant value but a function that varies over time. However, the value of the function at each moment is very close to the true value, which shows that the method has good convergence and accurate identification result, and proves the effectiveness of the algebraic method.
The foregoing detailed description is intended to illustrate and not limit the invention, which is intended to be within the spirit and scope of the appended claims, and any changes and modifications that fall within the true spirit and scope of the invention are intended to be covered by the following claims.
Claims (4)
1. An algebraic-method-based asynchronous motor dynamic parameter identification method is characterized by comprising the following steps:
1) determining a model to be identified of the asynchronous motor, corresponding parameters to be identified and observable variables of the asynchronous motor:
2) integral operation is carried out on the signal of the observable variable, the influence of the initial value of the state variable on the identification precision is eliminated through mathematical transformation, and the inertia time constant T of the rotor of the asynchronous motor is identifiedj；
3) Identifying steady state reactance X of asynchronous motor rotorSub-transient reactance X ', rotor loop time constant T'd0。
2. An algebraic-based method of identifying dynamic parameters of an asynchronous motor as defined in claim 1, comprising: the method comprises the following steps of 1) determining a model to be identified of the asynchronous motor, corresponding parameters to be identified and observable variables of the asynchronous motor, wherein an equation of the asynchronous motor and a network interface adopts the following formula:
<mrow> <msub> <mi>I</mi> <mi>x</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mfrac> <mo>&lsqb;</mo> <mrow> <mo>(</mo> <msubsup> <mi>E</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> <mo>-</mo> <msub> <mi>U</mi> <mi>y</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>
<mrow> <msub> <mi>I</mi> <mi>y</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mfrac> <mo>&lsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <msubsup> <mi>E</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> <mo>-</mo> <msub> <mi>U</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>
wherein X 'represents the transient reactance of the rotor of the asynchronous motor, E'xRepresenting the transient electromotive force, E 'of the x-axis component of the asynchronous motor'yRepresenting the transient electromotive force, U, of the y-axis component of the asynchronous motorxRepresenting the x-axis component voltage of the asynchronous motor,Uyrepresenting the voltage of the y-component of the asynchronous motor, IxRepresenting the x-component current of the asynchronous motor, IyRepresenting the y-axis component current of the asynchronous motor; the asynchronous motor is a three-order dynamic model and adopts the following formula:
<mrow> <mfrac> <mrow> <mi>d</mi> <mi>s</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>T</mi> <mi>M</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>E</mi> </msub> </mrow> <msub> <mi>T</mi> <mi>j</mi> </msub> </mfrac> </mrow>
<mrow> <mfrac> <mrow> <msubsup> <mi>dE</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&lsqb;</mo> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <msub> <mi>I</mi> <mi>y</mi> </msub> <mo>+</mo> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mi>o</mi> </mrow> <mo>&prime;</mo> </msubsup> <msubsup> <mi>E</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> <mi>s</mi> <mo>-</mo> <msubsup> <mi>E</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> <mo>&rsqb;</mo> </mrow> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mi>o</mi> </mrow> <mo>&prime;</mo> </msubsup> </mfrac> </mrow>
<mrow> <mfrac> <mrow> <msubsup> <mi>dE</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&lsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> <mo>)</mo> </mrow> <msub> <mi>I</mi> <mi>x</mi> </msub> <mo>-</mo> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mi>o</mi> </mrow> <mo>&prime;</mo> </msubsup> <msubsup> <mi>E</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>E</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> </mrow> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mi>o</mi> </mrow> <mo>&prime;</mo> </msubsup> </mfrac> </mrow>
where s denotes the rotor slip of the asynchronous motor, TMRepresenting mechanical torque, T, of an asynchronous motorERepresenting the electromagnetic torque of the asynchronous motor; because the rotor speed is close to the synchronous speed under the normal operation condition, TEApproximately equal to the active power P; t isjDenotes the rotor inertia time constant, X denotes the rotor steady-state reactance, T'd0Representing the rotor loop time constant. The output of the asynchronous motor is active power and reactive power, and the following formula is adopted:
P＝-(E′xIx+E′yIy)
Q＝UyIx-UxIy
in the model of the asynchronous motor, the parameters to be identified of the asynchronous motor are the steady-state reactance X of the rotor, the transient-state reactance X' of the rotor and the inertia time constant T of the rotorjAnd a rotor circuit time constant T'd0. The observable variables of the asynchronous motor are slip s (t) and asynchronous motor voltage Ux(t)，Uy(t) asynchronous motor current Ix(t)，Iy(T), asynchronous motor power P (T), Q (T), asynchronous motor mechanical torque TM(t)。
3. An algebraic-based method of identifying dynamic parameters of an asynchronous motor as defined in claim 1, comprising: step 2) identifying the rotor inertia time constant T of the asynchronous motorjThe following formula is adopted:
<mrow> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>t</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mi>j</mi> </msub> </mfrac> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>t</mi> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>M</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>T</mi> <mi>E</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow>
in the above formula, T represents time, s (T) represents the slip ratio of the asynchronous motor rotor, TM(t) for asynchronous motorsMechanical torque, TE(t) represents an electromagnetic torque of the asynchronous motor; the fractional integration rule is used for the left part of the equal sign of the above formula as follows:
<mrow> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>t</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mi>t</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mo>|</mo> <mn>0</mn> <mi>t</mi> </msubsup> <mo>-</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mi>t</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow>
therefore, the following holds:
<mrow> <mi>t</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mi>j</mi> </msub> </mfrac> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>t</mi> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>M</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>E</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow>
the above equation can be rewritten as follows:
<mrow> <msub> <mi>T</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>t</mi> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>M</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>E</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow>
it can be seen that the interference of the initial value of the state variable is eliminated through mathematical transformation, and the right side of the equal sign of the formula is the observable variable, so that the parameter T to be identified is determined through the formulaj。
4. An algebraic-based method of identifying dynamic parameters of an asynchronous motor as defined in claim 1, comprising: the step 3) identifies asynchronous motorsThe steady-state reactance X of the mechanical rotor, the transient-state reactance X ' of the rotor and the time constant T ' of the rotor loop 'd0The following formula is adopted:
<mrow> <msubsup> <mi>tE</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msubsup> <mi>E</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> <msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>x</mi> </msub> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <mi>X</mi> <mo>-</mo> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mrow> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mn>0</mn> </mrow> <mo>&prime;</mo> </msubsup> </mfrac> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msub> <mi>tI</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msubsup> <mi>E</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mn>1</mn> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mn>0</mn> </mrow> <mo>&prime;</mo> </msubsup> </mfrac> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msubsup> <mi>E</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow>
<mrow> <msubsup> <mi>tE</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msubsup> <mi>E</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> <msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>x</mi> </msub> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mi>X</mi> <mo>-</mo> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mrow> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mn>0</mn> </mrow> <mo>&prime;</mo> </msubsup> </mfrac> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msub> <mi>tI</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msubsup> <mi>E</mi> <mi>x</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mn>1</mn> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mn>0</mn> </mrow> <mo>&prime;</mo> </msubsup> </mfrac> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msubsup> <mi>E</mi> <mi>y</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow>
in the above formula, t represents time, E'x(t) represents an asynchronous motor x-axis component electromotive force, E'y(t) represents the electromotive force of the y-axis component of the asynchronous motor, Ix(t) represents the x-axis component current of the asynchronous motor, Iy(t) represents the asynchronous motor y-axis component current; due to E'x(t)，E′y(t) is an unobservable variable, hence E'x(t)，E′y(t) is determined using the following formula:
E′y(t)＝Uy(t)+X′Ix(t)
E′x(t)＝Ux(t)-X′Iy(t)
wherein U isx(t) represents the asynchronous motor x-axis component voltage, Uy(t) represents the asynchronous motor y-component voltage, Ux(t) and Uy(t) are all observable variables. When E'x(t)，E′y(t) expressed by the above formula, the following formula holds:
Y＝Aθ
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>11</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>12</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>13</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>21</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>22</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>23</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&theta;</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&theta;</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
wherein, θ1＝X′，the unknown parameter θ of the equation is determined using the following equation:
<mrow> <mi>&theta;</mi> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msup> <mi>X</mi> <mi>T</mi> </msup> <mi>X</mi> <mi>d</mi> <mi>t</mi> <mo>&rsqb;</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </munderover> <msup> <mi>X</mi> <mi>T</mi> </msup> <mi>Y</mi> <mi>d</mi> <mi>t</mi> </mrow>
rotor steady state reactance X of asynchronous motor, rotor transient state reactance X ', rotor loop time constant T'd0Determined using the following formula:
X′＝θ1
<mrow> <msubsup> <mi>T</mi> <mrow> <mi>d</mi> <mn>0</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>&theta;</mi> <mn>2</mn> </msub> </mfrac> </mrow>
<mrow> <mi>X</mi> <mo>=</mo> <mfrac> <msub> <mi>&theta;</mi> <mn>3</mn> </msub> <msub> <mi>&theta;</mi> <mn>2</mn> </msub> </mfrac> <mo>.</mo> </mrow>
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