Induction motor group equivalent method considering critical stability characteristics

Abstract

The application relates to an equivalent method of an induction motor group considering critical stability characteristics, and belongs to the technical field of electric motors. The method comprises the following steps: S1, establishing an index representing the strength of the critical stability characteristics of the induction motor group; S2, combining a clustering analysis algorithm, and dividing the induction motor group into three groups with different stabilities; and S3, according to the basic principle of load equivalence of the induction motor group, solving the electrical parameters of the equivalent induction motor. The application has the beneficial effect that the induction motor group is reasonably grouped according to the critical stability characteristics of the induction motor, and the accuracy of the equivalent model of the induction motor group under different fault conditions is effectively improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electric motor, and relates to an induction motor group equivalence method considering critical stability characteristics, which effectively solves the problem that researchers do not consider the safe critical voltage and critical cut-off time of the induction motor in the equivalence of the induction motor group, and a more reliable induction motor group equivalence model is obtained. BACKGROUND

[0002] As the most common load type in the power system, the induction motor plays an important role in the operation analysis and stability control of the power system. Since the number of induction motors in the actual power system is large, it is impractical to model and analyze each induction motor. Therefore, the induction motor group in the power system is usually equivalent to a single or multiple motors for analysis.

[0003] At present, there are many related researches reported, but the equivalence methods of the induction motor group proposed by them ignore the influence of the safe critical voltage and critical cut-off time of the induction motor on the equivalent model. Therefore, how to consider the critical stability characteristics of the induction motor for the equivalence of the induction motor group so as to obtain a more reliable equivalent model is an urgent problem to be solved. SUMMARY

[0004] In view of this, the purpose of the application is to provide an induction motor group equivalence method considering critical stability characteristics.

[0005] To achieve the above purpose, the application provides the following technical scheme.

[0006] An induction motor group equivalence method considering critical stability characteristics, which specifically comprises the following steps:

[0007] S1: establishing an index representing the strength of the critical stability characteristics of the induction motor group;

[0008] S2: combining a clustering analysis algorithm, the induction motor group is divided into three groups with different stability;

[0009] S3: according to the basic principle of the load equivalence of the induction motor group, the electrical parameters of the equivalent induction motor are solved.

[0010] Optionally, in the step S1, the step of establishing the index is:

[0011] S11: the lower the safe critical voltage, the better the stability of the induction motor;

[0012] S12: the longer the critical cut-off time, the better the stability of the induction motor.

[0013] Optionally, in the step S2, the step of grouping the induction motor group by using clustering is:

[0014] S21: calculating the safe critical voltage and critical removal time of each induction motor;

[0015] S22: clustering the safe critical voltage and critical removal time of each induction motor in S21 by using clustering analysis algorithm;

[0016] S23: grouping for the first time according to the safe critical voltage, if the safe critical voltage value is lower than the clustering center value of the safe critical voltage in S22, then it is grouped into group a; otherwise, it goes to S24;

[0017] S24: grouping for the second time according to the critical removal time, if the critical removal time is longer than the clustering center value of the critical removal time in S22, then it is grouped into group b1; otherwise, it is grouped into group b2.

[0018] Optionally, in the step S3, the step of calculating the equivalent electrical parameters of the induction motor is:

[0019] S31: obtaining the equivalent circuit according to the equivalent circuit of the induction motor;

[0020]

[0021] The basic principle of the load equivalence of the induction motor is to keep the equivalent model and the original induction motor group having the same total active power P ∑0 and reactive power Q ∑0 , total electromagnetic power P ∑em , total rotor copper loss P ∑cur , total stator reactive loss Q ∑cus ; according to the grouping method of S2, an equivalence principle is added, that is, the safe critical voltage value and the critical removal time value of the equivalent induction motor are the K-means clustering center points of the original induction motor group;

[0022] wherein, U0 is the input voltage; I s is the stator current; I r is the rotor current; I m is the excitation current; s is the slip; R s , X s , X m , R r and X r are the stator resistance, the stator reactance, the excitation reactance, the rotor resistance and the rotor reactance respectively; Z s , Z r , Z m are the equivalent stator impedance, the equivalent rotor impedance and the equivalent excitation impedance respectively, and their expressions are shown in formula (2); C is the correction coefficient, and its expression is shown in formula (3);

[0023]

[0024]

[0025] In formula (1), if |Z s |<<|Z r |, take Z s / Z r = 0, formula (1) becomes:

[0026]

[0027] The expression of electromagnetic torque is obtained:

[0028]

[0029] In the formula, Ω s is the synchronous angular velocity, and its expression is:

[0030]

[0031] In the formula, p is the number of pole pairs; f is the system frequency, taking 50 or 60 Hz;

[0032] S32: Calculate the total active power P ∑0 and the total reactive power Q ∑0 , the total electromagnetic power P ∑em , the total rotor copper loss P ∑cur , the total stator reactive loss Q ∑cus of all induction motors;

[0033]

[0034] In the formula, n is the number of induction motors in the system;

[0035] S33: Calculate the total stator copper loss P ∑cus and the total stator current I ∑s ;

[0036] P ∑cus = P ∑0 -P ∑em (8)

[0037]

[0038] S34: Calculate the stator resistance R s and the stator reactance X s ;

[0039]

[0040]

[0041] S35: Calculate the equivalent impedance Z of the equivalent induction motor eq ;

[0042]

[0043] S36: Calculate the safe critical voltage U of each induction motor cri ;

[0044] First, take the derivative of dT with respect to s using equation (5) e , and set the derivative to zero to get the critical slip rate S cri :

[0045]

[0046] Second, substitute equation (13) into equation (5) to get

[0047]

[0048] The load torque model of an induction motor has three types. Take the constant torque load model as an example, its model is represented as:

[0049] T out (s) = T (15)

[0050] In the equation, T out is the load torque of the constant torque load model; T is a constant;

[0051] Finally, set equation (14) equal to equation (15) to get the safe critical voltage U cri of each induction motor:

[0052]

[0053] S37: Calculate the critical removal time t of each induction motor cri ;

[0054] The rotor motion equation of an induction motor is:

[0055]

[0056] In the equation, H is the time constant, whose value is determined by equation (18); T mec is the mechanical torque; U sag is the residual voltage value during the voltage sag;

[0057]

[0058] Integrate the electromagnetic torque-slip characteristic curve from slip rate S s to S c to get the critical removal time t of each induction motorcri ;

[0059]

[0060] S38: According to formula (5), (16) and (19), the electromagnetic torque T of the equivalent induction motor is calculated in combination with the K-means clustering algorithm equ , the safe critical voltage U cr and the critical cut-off time t cr ;

[0061] S39: According to formula (12) and the electromagnetic torque T of the equivalent model, the unknown parameters X equ , R m and X r of the equivalent model are calculated. r

[0062] The beneficial effects of the present application are that the induction motor group is reasonably grouped according to the critical stability characteristics of the induction motor, and the accuracy of the equivalent model of the induction motor group under different fault conditions is effectively improved.

[0063] Other advantages, objects and features of the present application will be set forth in part in the following specification taken in conjunction with the accompanying drawings, and in part will become apparent to those skilled in the art upon examination of the following specification and drawings. The objects and other advantages of the present application can be realized and attained by means of the instrumentalities and combinations pointed out in the following specification. BRIEF DESCRIPTION OF DRAWINGS

[0064] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred detailed description of the present application will be made below in conjunction with the drawings, wherein:

[0065] Figure 1 is a flowchart of the present application;

[0066] Figure 2 is a typical motor electromagnetic torque-slip and load torque-slip characteristic curve diagram;

[0067] Figure 3 is an induction motor group grouping flowchart;

[0068] Figure 4 is an equivalent circuit diagram of an induction motor;

[0069] Figure 5 is an IEEE-9 node system wiring diagram;

[0070] Figure 6 is a simulation result diagram. DETAILED DESCRIPTION

[0071] ​The present application is illustrated by way of example and not limitation in the figures of the accompanying drawings, in which like references indicate similar elements, and in which: BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Wherein, the figures are only used for example illustration, the representation is only schematic diagram, not real object figure, cannot be understood as the limitation to the present application; in order to better illustrate the embodiment of the present application, some components of the figure can be omitted, enlarged or reduced, and does not represent the size of actual product; for the person skilled in the art, some well-known structures and their description in the figure can be omitted.

[0073] The same or similar reference numerals in the figures of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it needs to be understood that if there are terms such as 'upper', 'lower', 'left', 'right', 'front', 'back' and the like indicating the orientation or positional relationship, it is based on the orientation or positional relationship shown in the figure, only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the figure are only used for example illustration, and cannot be understood as the limitation to the present application, for the person skilled in the art, the specific meaning of the above terms can be understood according to the specific situation.

[0074] As shown in Figure 1 , it is an equivalent method of induction motor group considering critical stability characteristics, including the following steps:

[0075] S1: establishing an index representing the strength of the critical stability characteristics of the induction motor group;

[0076] S2: combining the clustering analysis algorithm, the induction motor group is divided into three groups with different stability;

[0077] S3: according to the basic principle of load equivalence of induction motor group, the electrical parameters of equivalent induction motor are solved.

[0078] In step S1, the step of establishing the index is:

[0079] S11: the lower the safe critical voltage, the better the stability of the induction motor;

[0080] S12: the longer the critical cut-off time, the better the stability of the induction motor.

[0081] Taking the parameters of a typical induction motor as an example, its electromagnetic torque-slip and load torque-slip characteristic curves are as follows: Figure 2 As shown, when the induction motor operates at its rated voltage, the electromagnetic torque characteristic curve intersects the load torque characteristic curve at two points, A and B2, with corresponding slip rates S1 and S2, respectively. s and S c When a voltage sag occurs, the maximum electromagnetic torque T of the induction motor is... max The voltage will also decrease accordingly, and the electromagnetic torque-slip curve and the load torque-slip curve will gradually change from two intersection points to one intersection point, and finally there will be no intersection point. When the two curves have only one intersection point, the corresponding voltage is the safe critical voltage U of the induction motor. cr The lower the value, the stronger the stability of the induction motor. When the two curves do not intersect, the system's operating point jumps from A to A1. The system will move from point A1, deviating from the electromagnetic torque characteristic curve during the transient sag, towards point B1. If the voltage returns to normal before the system reaches point B1, the system can slowly recover stability and eventually stabilize at point A. Conversely, it becomes unstable. Therefore, the system from S... s Exercise to S c The time elapsed is the critical cut-off time t of the induction motor. cr .

[0082] like Figure 3 As shown, in step S2, the step of grouping the induction motor group using clustering is as follows:

[0083] S21: Calculate the safety critical voltage and critical cut-off time for each induction motor;

[0084] S22: Cluster the safety critical voltage value and critical cut-off time value of each induction motor in S21 using a clustering analysis algorithm;

[0085] S23: The first grouping is performed based on the level of the safety critical voltage. If the safety critical voltage value is lower than the cluster center value of the safety critical voltage in S22, it is divided into group a; otherwise, proceed to S24.

[0086] S24: Group the cells a second time based on the length of the critical resection time. If the critical resection time is longer than the cluster center value of the critical resection time in S22, the cells are divided into group b1; otherwise, they are divided into group b2.

[0087] In step S3, the steps for calculating the electrical parameters of the equivalent induction motor are as follows:

[0088] Where U0 is the input voltage; I s I is the stator current. r I is the rotor current; m is the excitation current; s is the slip; Rs , X s , X m , R r and X r are stator resistance, stator reactance, excitation reactance, rotor resistance and rotor reactance respectively.

[0089] The basic principle of induction motor load equivalence is that the equivalent model must have the same total active power P ∑0 and reactive power Q ∑0 , total electromagnetic power P ∑em , total rotor copper loss P ∑cur , total stator reactive loss Q ∑cus as the original induction motor group. According to the grouping method, an equivalent principle is added, that is, to ensure that the safe critical voltage value and critical removal time value of the equivalent induction motor are the K-means clustering center points of the original induction motor group.

[0090] Following the basic principle of equivalence and combining the equivalent circuit and power relationship of induction motor, the specific steps for calculating the equivalent model parameters of the induction motor group are as follows:

[0091] 1) According to the equivalent circuit of Figure 4 , the following can be obtained

[0092]

[0093] In the formula, Z s , Z r , Z m are the equivalent impedances of stator, rotor and excitation respectively, whose expressions are shown in formula (2); C is the correction coefficient, whose expression is shown in formula (3).

[0094]

[0095]

[0096] In order to simplify the calculation and analysis in practical application, in formula (1), because |Z s | << |Z r |, Z s / Z r = 0, formula (1) becomes:

[0097]

[0098] Combining the above contents, the expression of electromagnetic torque can be obtained:

[0099]

[0100] In the formula, Ω sis the synchronous angular velocity, whose expression is:

[0101]

[0102] where p is the pole pair number; f is the system frequency (50 or 60 Hz).

[0103] 2) Calculate the total active power Pabsorbed by all induction motors ∑0 and the total reactive power Q ∑0 , the total electromagnetic power P ∑em , the total rotor copper loss P ∑cur , the total stator reactive loss Q ∑cus .

[0104]

[0105] where n is the number of induction motors in the system.

[0106] 3) Calculate the total stator copper loss P ∑cus and the total stator current I ∑s .

[0107] P ∑cus = P ∑0 - P ∑em (8)

[0108]

[0109] 4) Calculate the stator resistance R s and the stator reactance X s .

[0110]

[0111]

[0112] 5) Calculate the equivalent impedance Z eq of the equivalent induction motor.

[0113]

[0114] 6) Calculate the safe critical voltage U cri of each induction motor.

[0115] First, take the derivative of s with respect to T e in equation (5) and set the derivative to zero to obtain the critical slip S cri :

[0116]

[0117] Second, substitute equation (13) into equation (5) to obtain

[0118]

[0119] There are three load torque models of induction motors. In this paper, the constant torque load model is taken as an example. Its model can be expressed as:

[0120] T out (s)=T (15)

[0121] where T out is the load torque of the constant torque load model; T is a constant.

[0122] Finally, by equating (14) and (15), the safe critical voltage U cri of each induction motor can be obtained as:

[0123]

[0124] 7) The critical switching-off time t cri of each induction motor is calculated.

[0125] The rotor motion equation of induction motor is:

[0126]

[0127] where H is the time constant, which can be determined by (18); T mec is the mechanical torque; U sag is the residual voltage during the voltage sag.

[0128]

[0129] Integrating the electromagnetic torque-slip characteristic curve of S s to S c , the critical switching-off time t cri of each induction motor is obtained.

[0130]

[0131] 8) According to (5), (16) and (19), combined with the K-means clustering algorithm, the equivalent induction motor's electromagnetic torque T equ , safe critical voltage U cr and critical switching-off time t cr are calculated.

[0132] 9) According to (12) and the equivalent induction motor's electromagnetic torque T equ , the equivalent model's unknown parameters X m , R r and X r are calculated.

[0133] Twelve typical induction motors with different parameters are taken as examples, and the parameters are shown in Table 1.

[0134] Table 1 Parameters of twelve typical induction motors with different parameters

[0135] Number [R s / pu]] X s / pu]] X m / pu]] [R r / pu]] X r / pu]] U cr / pu]] t cr / s]]> M1 0.031 0.100 3.200 0.018 0.180 0.386 1.103 M2 0.013 0.067 3.800 0.009 0.170 0.711 0.733 M3 0.033 0.076 2.400 0.048 0.062 0.663 0.705 M4 0.100 0.100 1.800 0.090 0.062 0.706 0.951 M5 0.056 0.087 2.400 0.053 0.082 0.588 0.620 M6 0.110 0.140 2.800 0.110 0.065 0.652 1.102 M7 0.110 0.120 2.000 0.110 0.130 0.468 0.684 M8 0.120 0.150 1.900 0.130 0.140 0.702 0.857 M9 0.530 0.830 1.900 0.036 0.680 0.721 1.328 M10 0.079 0.120 3.200 0.056 0.120 0.367 1.025 M11 0.250 0.088 3.200 0.160 0.170 0.520 0.792 M12 0.031 0.140 2.400 0.009 0.120 0.423 0.916

[0136] Table 2 is the equivalent induction motor parameters obtained by the method of the present application.

[0137] Table 2 Equivalent induction motor parameters

[0138] Number [R s / pu]] X s / pu]] X m / pu]] [R r / pu]] X r / pu]] U cr / pu]] t cr / s]]> Equivalent No. 1 machine 0.088 0.197 3.011 0.041 0.132 0.719 1.435 Equivalent No. 2 machine 0.105 0.252 2.195 0.066 0.155 0.517 1.916 Equivalent No. 3 machine 0.106 0.247 2.193 0.059 0.087 0.505 0.729

[0139] The simulation results are verified by taking an IEEE-9 node system as an example. Figure 5

[0140] The fault type is that a three-phase fault occurs at the line Bus5-Bus7 close to the Bus5 at 1s, and the fault is removed after 150ms.

[0141] The simulation results are that the voltage at the Bus5 in the two cases is compared, as shown in Table 2. It can be seen from the simulation results that the equivalent induction motor obtained by the method of the present application can well reflect the characteristics of the original induction motor group. Figure 6

[0142] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced equivalently without departing from the purpose and scope of the technical solutions, and they should be covered in the scope of the claims of the present application.​​

Claims

1. An induction motor group equivalent method taking into account the critical stability characteristic, characterized by: The method specifically comprises the following steps: S1: establishing an index representing the strength of the critical stability characteristics of the induction motor group; S2: combining a clustering analysis algorithm to divide the induction motor group into three groups with different stability; S3: solving the equivalent electrical parameters of the equivalent induction motor according to the basic principle of load equivalence of the induction motor group; In S1, the step of establishing the index is: S11: the lower the safe critical voltage, the better the stability of the induction motor; S12: the longer the critical cut-off time, the better the stability of the induction motor; In S2, the step of grouping the induction motor group by using clustering is: S21: calculating the safe critical voltage and the critical cut-off time of each induction motor; S22: using a clustering analysis algorithm to cluster the safe critical voltage and the critical cut-off time of each induction motor in S21; S23: performing the first grouping according to the high and low of the safe critical voltage, if the safe critical voltage is lower than the clustering center value of the safe critical voltage in S22, the induction motor is divided into group a; otherwise, S24 is entered; S24: performing the second grouping according to the length of the critical cut-off time, if the critical cut-off time is longer than the clustering center value of the critical cut-off time in S22, the induction motor is divided into group b1; otherwise, it is divided into group b2.

2. The induction motor group equivalence method considering critical stability characteristics according to claim 1, wherein, In S3, the step of calculating the equivalent electrical parameters of the equivalent induction motor is: S31: according to the equivalent circuit The basic principle of induction motor load equivalence is to keep the equivalent model having the same total active power P ∑0 and reactive power Q ∑0 , total electromagnetic power P ∑em , total rotor copper loss P ∑cur , total stator reactive loss Q ∑cus as the original induction motor group; according to the grouping method of S2, an equivalent principle is added, that is, to ensure that the safe critical voltage value and the critical removal time value of the equivalent induction motor are the K-means clustering center points of the original induction motor group; wherein U0 is the input voltage; I s is the stator current; I r is the rotor current; I m is the field current; s is the slip; R s , X s , X m , R r and X r are the stator resistance, the stator reactance, the field reactance, the rotor resistance and the rotor reactance, respectively; Z s , Z r , Z m are the stator equivalent impedance, the rotor equivalent impedance and the field equivalent impedance, respectively, whose expressions are shown in equation (2); C is the correction coefficient, whose expression is shown in equation (3); In formula (1), since |Z s | < |Z r |, take Z s = 0, formula (1) becomes: r = 0, formula (1) becomes: The expression of the electromagnetic torque is obtained: where Ω s is the synchronous angular velocity, which is expressed as In the formula, p is the number of pole pairs; f is the system frequency, which is 50 or 60 Hz; S32: Calculate total active power Pabsorbed by all induction motors ∑0 and reactive power Q ∑0 , total electromagnetic power P ∑em , total rotor copper losses P ∑cur , total stator reactive losses Q ∑cus ; In the formula, n is the number of induction motors in the system; S33: Calculate total stator copper loss P ∑cus and total stator current I ∑s ; S34: Calculate stator resistance R s and stator reactance X s ; S35: Calculate the equivalent impedance Z of the equivalent induction motor eq ; S36: Calculate the safe critical voltage U of each induction motor cri ; First, the derivative of s with respect to dT is taken using equation (5) e and set to zero to obtain the critical slip ratio s cri is: Secondly, formula (13) is brought into formula (5), and There are three kinds of load torque models of the induction motor, taking the constant torque load model as an example, the model is represented as: T out (s) = T (15) In the formula, T out is the constant torque load model load torque; T is a constant; Finally, let the equation (14) and (15) equal to each induction motor safety critical voltage U cri is: S37: Calculate the critical cut-off time t of each induction motor cri ; The rotor motion equation of the induction motor is: where H is a time constant whose value is determined by equation (18); T mec is the mechanical torque; U sag is the residual voltage during the sag; Integrating the electromagnetic torque-slip characteristic curve of each induction motor from S s to S c gives the critical cut-off time t cri of each induction motor. S38: Calculate the electromagnetic torque T of the equivalent induction motor according to formula (5), (16) and (19) in combination with K-means clustering algorithm equ , the safe critical voltage U cr and the critical cut-off time t cr ; S39: Calculate the unknown parameters X of the equivalent model according to formula (12) and the electromagnetic torque T of the equivalent induction motor equ . m , R r and X r .

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