CN115085152B - Method and system for calculating temporary drop critical elimination time of motor protector - Google Patents

Method and system for calculating temporary drop critical elimination time of motor protector Download PDF

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CN115085152B
CN115085152B CN202210775155.7A CN202210775155A CN115085152B CN 115085152 B CN115085152 B CN 115085152B CN 202210775155 A CN202210775155 A CN 202210775155A CN 115085152 B CN115085152 B CN 115085152B
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sag
voltage
phase
motor
representing
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CN115085152A (en
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陈伟
龙飞
裴喜平
李恒杰
林洁
魏占宏
魏祥林
张晓英
彭兆伟
刘升升
雷欢
张蕾
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Lanzhou University of Technology
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Lanzhou University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
    • H02H7/00—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions
    • H02H7/08—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions for dynamo-electric motors
    • H02H7/09—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions for dynamo-electric motors against over-voltage; against reduction of voltage; against phase interruption

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Abstract

The invention discloses a temporary drop critical elimination time calculation method and a temporary drop critical elimination time calculation system for a motor protector, wherein the method comprises the following steps: calculating slip of a stable balance point and slip of an unstable balance point of the load model; respectively calculating phase voltage sag ratios of the A phase, the B phase and the C phase when voltage sag occurs; if the phase voltage sag ratio of the phase A, the phase B and the phase C is uniform, the voltage sag is symmetrical; judging whether the voltage sag is an absolute safety voltage sag or not based on the voltage sag; if not, carrying out a first warning; calculating a first critical elimination time of the load model based on the stable balance point slip and the unstable balance point slip; if the sag time is longer than the first critical elimination time, performing a second warning, and judging whether the motor can automatically realize low voltage ride through; if not, cutting off the motor from the main circuit; according to the method, the motor can be rapidly and accurately protected according to the duration of the voltage sag and the load model.

Description

Method and system for calculating temporary drop critical elimination time of motor protector
Technical Field
The invention belongs to the technical field of electric energy quality protection of motor protectors, and particularly relates to a temporary boundary elimination time calculation method and system of a motor protector.
Background
The voltage sag is a voltage disturbance event that the root value of the power frequency voltage square at a certain point in the power system is suddenly reduced to 0.1p.u. to 0.9p.u., and the power frequency voltage square is restored to be normal after the power frequency voltage square is briefly lasting for 10ms to 1 min. The voltage disturbance event that the root value of the power frequency voltage side at a certain point in the power system suddenly drops to below 0.1p.u. is called voltage interruption, and is divided into short-time interruption and long-time interruption, the short-time interruption can be recovered to be normal after the voltage suddenly drops for 10 ms-1 min, and the long-time interruption cannot be automatically recovered. Whether a voltage dip (including an interruption) will cause the motor to shut down depends on the voltage survivor amplitude and duration.
Because the voltage amplitude is lower during the voltage interruption, except for the situations of shorter interruption time, smaller load and the like, the motor is stopped under most other situations, so the voltage sag and the voltage interruption are collectively called as the voltage sag for simplicity.
When voltage sag occurs at the stator end of the induction motor, if electromagnetic torque T during sag occurs e Curve and load torque T L The curve still has a stable equilibrium intersection, such a voltage dip is referred to as an absolute safe voltage dip (Absolutely safe voltage sag, abbreviated ASVS), otherwise as a Non-absolute safe voltage dip (Non-ASVS).
Under Non-ASVS, a motor protector software and hardware system for rapidly and relatively accurately judging whether a motor can realize low voltage ride through or not according to the duration of voltage sag and a load model and protecting the motor when the motor cannot pass through low voltage is lacking at present.
Some motor protectors already have an undervoltage (no-voltage) restart protection function. The motor industry standard JB/T10736-2007 "protector for Motor (abolished in 2017, temporary no alternative national standard) describes the undervoltage (loss of voltage) restarting function as follows: because of the main circuit undervoltage fault or voltage-losing stopping, a) if the voltage is recovered to be normal (the allowed restarting set value is higher than the allowed restarting set value) in the 'immediate restarting time', the protector can enable the motor to be immediately recovered to the running state before the motor stopping (without processes such as starting delay, voltage reduction and the like); b) If the voltage is recovered to be above the undervoltage (no-voltage) restarting set value within the set time of the delayed restarting delay time exceeding the instant restarting no-voltage time, the motor is started in a delayed mode according to the delayed restarting delay time (the same process as the normal starting), and the allowable error of the delay time is +/-10%; c) If the voltage is recovered after the 'delayed restart delay time', the motor is not restarted automatically. The error of the recovery voltage value is not more than +/-10%.
Drawbacks of undervoltage (no-voltage) restart protection techniques: whether the induction motor can re-accelerate successfully under Non-ASVS depends entirely on whether the duration of the voltage sag is less than a certain critical time (defined as the voltage sag critical elimination time in the present invention) which depends on the impedance parameters and load model of each motor, but the under-voltage (loss of voltage) restarting function is not differentially set for a specific motor and load model, but is a general protection which is performed in segments according to the duration of the under-voltage (loss of voltage) time (i.e., the speed interval after the motor is decelerated), i.e., "no matter the motor parameters, no matter how the load model is.
The following is a motor impedance parameter pair T e The effect of the curve is an illustration of the technical drawback of under-voltage (step-down) restart.
Due to motor impedance parameters determining T e Shape of curve, if T e The curve is at slip s epsilon s maxT ,1]Segment (note: s) maxT Slip at maximum electromagnetic torque, called critical slip), is steeper, in this interval T e The large segment of the curve is already at the load torque T L Under the curve (see fig. 2 of the drawings), it is assumed that the motor under-voltage (step-down) continues to return to normal when the voltage is near the "immediate restart step-down time The protector obviously cannot restore the motor to the running state before the motor stops, otherwise, the protector will react with the torque differential equationAgainst each other. Similarly, if T e Curve is s epsilon s maxT ,1]The segment is gentle, in this interval T e A considerable part of the curve is still located at T L On the curve, assuming that the voltage returns to normal when the motor under-voltage (voltage loss) continues to a small half time of the 'delayed restarting delay time', the motor can accelerate to the running state before the under-voltage (voltage loss) by the self force, and the motor does not need to be started in a delayed mode according to the 'delayed restarting delay time'.
Therefore, how to quickly and accurately protect the motor according to the duration of the voltage sag and the load model when the anti-interference device is not added and the non-absolute safety voltage sag occurs at the stator end of the induction motor is a problem to be solved by those skilled in the art.
Disclosure of Invention
In view of the above problems, the present invention provides a method and a system for calculating a sag critical elimination time of a motor protector, which at least solve some of the above technical problems, and the method can quickly and accurately protect a motor according to a voltage sag duration and a load model.
In one aspect, an embodiment of the present invention provides a method for calculating a temporary sag critical elimination time of a motor protector, including:
acquiring a motor impedance parameter and a load model;
constructing an electromagnetic torque three-coefficient model based on slip according to the motor impedance parameters;
according to the electromagnetic torque three-coefficient model, calculating the stable balance point slip and the unstable balance point slip of the load model by combining the load torque corresponding to the load model;
respectively obtaining phase voltage effective values of A phase, B phase and C phase of the motor when voltage sag occurs during the voltage sag period, and obtaining sag time of the voltage sag;
according to the phase voltage effective values of the A phase, the B phase and the C phase, respectively calculating the phase voltage sag ratio of the A phase, the B phase and the C phase;
if the phase voltage sag ratio of the phase A, the phase B and the phase C is uniform, the voltage sag is symmetrical; judging whether the voltage sag is an absolute safety voltage sag or not based on the voltage sag;
if the voltage sag is a non-absolute safety voltage sag, performing a first warning; calculating critical elimination time of the load model based on the stable balance point slip and the unstable balance point slip of the load model, and recording the critical elimination time as first critical elimination time;
If the sag time is less than the first critical elimination time, the motor is in a safe state;
if the sag time is longer than the first critical elimination time, performing a second warning and judging whether the motor can automatically realize low voltage ride through;
if the motor is unable to automatically achieve low voltage ride through, the motor is disconnected from the main circuit.
Further, the method further comprises the following steps:
if the phase voltage sag ratios corresponding to the phase A, the phase B and the phase C are inconsistent, the voltage sag is an asymmetric voltage sag; based on the above, positive sequence voltage sag ratio and negative sequence voltage sag ratio of the motor are calculated by combining the phase voltage sag ratios of the A phase, the B phase and the C phase;
based on the positive sequence voltage sag ratio and the negative sequence voltage sag ratio of the motor, combining the electromagnetic torque three-coefficient model to calculate the synthetic electromagnetic torque of the motor;
judging whether the voltage sag is an absolute safety voltage sag or not based on the synthesized electromagnetic torque of the motor;
if the voltage sag is not absolute safe voltage sag, performing a first warning, and calculating critical elimination time of the load model based on the stable balance point slip and the unstable balance point slip of the load model, and recording the critical elimination time as second critical elimination time;
If the sag time is less than the second critical elimination time, the motor is in a safe state;
if the sag time is longer than the second critical elimination time, performing a second warning and judging whether the motor can automatically realize low voltage ride through;
if the motor is unable to automatically achieve low voltage ride through, the motor is disconnected from the main circuit.
Further, determining whether the symmetrical voltage dip is an absolute safe voltage dip specifically includes:
judging whether a stable balance intersection point exists between an electromagnetic torque curve and a load torque curve in the voltage sag period;
if a stable balance intersection point exists, the voltage sag is an absolute safety voltage sag;
and if the stable balance intersection point does not exist, the voltage sag is a non-absolute safety voltage sag.
Further, determining whether the asymmetric voltage sag is an absolute safe voltage sag specifically includes:
judging whether a stable balance intersection point exists between the synthesized electromagnetic torque curve and the load torque curve;
if a stable balance intersection point exists, the voltage sag is an absolute safety voltage sag;
and if the stable balance intersection point does not exist, the voltage sag is a non-absolute safety voltage sag.
Further, the load model includes: a constant torque model, a constant power compound torque model and a fan pump compound torque model.
Further, the motor impedance parameter includes: stator resistor R 1 Leakage reactance X of stator 1 The rotor resistance R 'to the stator side' 2 And rotor leakage reactance X' 2 Exciting reactance X m 。
Further, the electromagnetic torque three-coefficient model is expressed as:
wherein T is e Representing electromagnetic torque; s represents slip; a, a 0 、a 1 And b 0 All represent coefficients.
Further, determining whether the motor is capable of automatically implementing low voltage ride through specifically includes: judging whether the sag time is smaller than the product of the correction coefficient and the critical elimination time or not;
if the voltage is smaller than the preset voltage, the motor can automatically realize low-voltage ride through;
if not, the motor can not automatically realize low voltage ride through.
In another aspect, an embodiment of the present invention provides a temporary sag critical elimination time calculation system of a motor protector, including: the system comprises an operation display unit, a signal acquisition processing unit, a protection calculation control unit, a control execution unit and a power supply module;
the operation display unit is used for acquiring the impedance parameters of the motor and the load model; and transmitting the acquired content to the protection calculation control unit;
The signal acquisition processing unit is used for acquiring phase voltage effective values of A phase, B phase and C phase of the motor during the voltage sag period and sag time of the voltage sag; and transmitting the acquired content to the protection calculation control unit;
the protection calculation control unit is used for calculating the phase voltage sag ratio of the phase A, the phase B and the phase C and judging whether the voltage sag is an absolute safety voltage sag or not based on the phase voltage sag ratio; the method is also used for calculating the critical elimination time of the load model, judging whether the motor is in a safe state or not and whether the motor can automatically realize low voltage ride through or not based on the critical elimination time; if the motor can not automatically realize low voltage ride through, a tripping instruction is sent out, and a judgment result is sent to the control execution unit;
the control execution unit is used for controlling the audible and visual alarm to finish warning operation; the motor is also used for executing a tripping instruction to cut off the motor from the main circuit;
the power module is used for providing power for the operation display unit, the signal acquisition processing unit, the protection calculation control unit and the control execution unit.
Further, the device also comprises a voltage detection module;
The voltage detection module comprises an external voltage transformer and an internal voltage detection unit;
the voltage detection module is used for detecting the working voltage of the motor and converting the working voltage of the motor into an analog voltage signal suitable for discrete acquisition by the signal acquisition processing unit.
Compared with the prior art, the temporary sag critical elimination time calculation method of the motor protector has the following beneficial effects: the motor can be protected rapidly and accurately according to the duration of the voltage sag and the load model.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
Fig. 1 (a) is a schematic diagram of a single-phase equivalent circuit of an induction motor according to IEEE recommendations provided in the related art.
Fig. 1 (b) is a simplified equivalent circuit schematic diagram based on the dyven theorem provided in the related art.
Fig. 2 (a) is a schematic diagram of a torque-slip characteristic curve corresponding to a continuous acceleration of a motor back to a stable equilibrium point during a non-absolute safety sag period provided by an embodiment of the present invention, wherein the voltage sag time is shorter.
Fig. 2 (b) is a schematic diagram of a torque-slip characteristic curve corresponding to a final shutdown of a motor with continuous deceleration during a non-absolute safety sag period provided by an embodiment of the present invention. .
Fig. 3 (a) is a positive sequence equivalent circuit diagram of the motor during asymmetric sag according to an embodiment of the present invention.
Fig. 3 (b) is a simplified positive-sequence equivalent circuit diagram based on the dyganan theorem provided by the embodiment of the invention.
Fig. 4 (a) is a diagram of a negative sequence equivalent circuit of a motor during an asymmetric sag according to an embodiment of the present invention.
Fig. 4 (b) is a simplified negative sequence equivalent circuit diagram based on the dyganan theorem provided by an embodiment of the present invention.
Fig. 5 is a flowchart of a method for calculating temporary sag threshold elimination time of a motor protector according to an embodiment of the present invention.
FIG. 6 is a schematic diagram showing comparison between critical cancellation time resolution values and actual measurement values of three load models during symmetric dip according to an embodiment of the present invention.
FIG. 7 is a schematic diagram showing comparison between critical cancellation time resolution values and actual measurement values of three load models during asymmetric sag according to an embodiment of the present invention.
Fig. 8 is a diagram of a temporary sag-elimination-time computing system frame of a motor protector according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of detecting a voltage state of a low-pass system of a motor protector according to an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
The embodiment of the invention provides a temporary sag critical elimination time calculation method of a motor protector, which is based on an induction motor five-parameter model recommended by IEEE (IEEE refers to American society of Electrical and electronic Engineers (Institute of Electrical and Electronics Engineers)), as shown in FIG. 1; since one motor corresponds to one set of impedance parameters (stator resistance R 1 And stator leakage reactance X 1 The rotor resistance R 'to the stator side' 2 And rotor leakage reactance X' 2 Exciting reactance X m ) The method comprises the steps of carrying out a first treatment on the surface of the Aiming at a specific load model, when a Non-absolute safety voltage sag (Non-ASVS) occurs at a motor stator end, one-to-one alarm and trip protection can be realized only by knowing the duration of the voltage sag, namely the embodiment of the invention can realize differential protection based on motor parameters and the load model.
The calculation method for the temporary sag critical elimination time of the motor protector provided by the embodiment of the invention can be divided into the following four aspects:
the method for constructing the three-coefficient model of the electromagnetic torque based on the slip comprises the following steps:
when the stator terminal phase voltage U 1,ph Is rated for phase voltage U 1N,ph In this case, the equivalent source voltage effective value U can be obtained according to the equivalent relationship between the networks at the left side of the two end points a and b in FIG. 1 (a) and FIG. 1 (b) 1,ph,eq Equivalent resistance R of Thevenin 1,eq And Thevenin equivalent reactance X 1,eq The following are provided:
wherein X is m Representing the excitation reactance; r is R 1 Representing the stator resistance; x is X 1 Representing stator leakage reactance;
then, the rotor phase current effective value I 'is calculated from the Thevenin equivalent circuit diagram in FIG. 1 (b)' 2,ph Expressed as:
wherein R 'is' 2 Representing rotor resistance; s represents slip; x'. 2 Representing rotor leakage reactance;
substituting (4) into an electromagnetic torque formula to obtain:
wherein T is e Representing electromagnetic torque [ N.m ]]；m 1 Representing the number of stator phases; omega s Representing synchronous angular velocity [ rad/sec ]]；
Based on equation (5), coefficient a is calculated 0 、a 1 And b 0 ：
Wherein U is 1,ph,eq Representing the effective value of the equivalent source voltage; r is R 1,eq Representing the equivalent resistance of thevenin; r's' 2 Representing rotor resistance; x is X 1,eq Representing the Thevenin equivalent reactance; x'. 2 Representing rotor leakage reactance; m is m 1 Representing the number of stator phases; omega s Representing synchronous angular velocity [ rad/sec ]]；
Based on formulas (5) - (8), the electromagnetic torque T based on slip s can be derived e Concise expression of the three-coefficient model:
wherein T is e Representing electromagnetic torque; s represents slip; a, a 0 、a 1 And b 0 All represent coefficients.
(II) a typical production mechanical load torque model:
(1) constant torque load model:
in the model, the load torque T L =constant, which can be noted as:
T L,ConT ＝T C (10)
wherein T is L,ConT Representing a constant torque load model load torque; t (T) C Represents a torque value, and T C Is a constant;
(2) constant power load model:
in this model, the load torqueThe constant power compound torque model with the friction force of the load torque (regarded as constant torque load) can be recorded as
Wherein T is L,ConP Representing a constant power load model load torque; p (P) c Represents active power, and P c Is a constant; omega m Representing mechanical angular velocity [ rad/sec ]]The method comprises the steps of carrying out a first treatment on the surface of the n represents the rotation speed [ r/min, abbreviated rpm ]]；ω s Representing synchronous angular velocity [ rad/sec ]]The method comprises the steps of carrying out a first treatment on the surface of the s represents slip;
(3) fan and pump load model:
in the case of the model of the present invention,the fan and pump compound torque model with static resistance torque (regarded as constant torque load) can be recorded as
Wherein T is L,Fan&Pump Representing the load torque of a fan and pump load model;k 1 、k 2 are all proportionality coefficients.
(III) definition of voltage sag threshold elimination time:
as shown in FIG. 2, T in the figure e Representing electromagnetic torque before voltage sag, T e,sag Representing electromagnetic torque during voltage sag, T L Load torque (constant torque for example) is indicated. Before the voltage dip, the electromagnetic torque curve (i.e., T e Corresponding curve, abbreviated as T e Curve) and load torque curve (i.e., T L Corresponding curve, abbreviated as T L Curve) has two equilibrium points, namely a stable equilibrium point S and an unstable equilibrium point U; wherein the slip corresponding to the stable equilibrium point S is called the stable equilibrium point slip S stab The method comprises the steps of carrying out a first treatment on the surface of the The slip corresponding to the unstable equilibrium point U is called the unstable equilibrium point slip s unst . Electromagnetic torque curve (i.e., T) when Non-absolute safe voltage sag (Non-ASVS) occurs at the motor stator end e,sag Corresponding curve, abbreviated as T e,sag Curve) and the load torque curve have no intersection point, there are two situations:
(1) If the duration of the dip is short, as shown in FIG. 2 (a), the motor jumps from point S to point C along T during the dip e The sag is eliminated when the curve runs to the point D, the motor jumps from the point D to the point E, and T is remained after recovery due to the short duration of the sag e >T L The motor may follow the T before the dip e The curve continuously accelerates along the E-S direction to return to the original stable equilibrium point S.
(2) If the dip is heldLonger duration, as shown in FIG. 2 (b), the motor jumps from point S to point C along T during the dip e The sag is eliminated when the curve runs to the point G, the motor jumps from the point G to the point H, and the sag has long duration and is recovered to be T e <T L The motor may follow the T before the dip e The curve continues to decelerate in the direction H.fwdarw.I until shutdown.
It can be seen that T is satisfied e ＝T L Is a critical point as long as the slip of the motor operating point at the moment of sag elimination is lower than the slip s corresponding to the unstable equilibrium point U unst The motor can re-accelerate and eventually return to the stable equilibrium point S, otherwise either at the unstable equilibrium point U or continue to slow down until shut down. Therefore, in the embodiment of the invention, the motor is controlled to be controlled from the point C (slip ratio is s in the Non-ASVS condition stab ) Along the sag period T e The curve is decelerated to the point F (slip s unst ) The time of (a) called the voltage sag threshold elimination time (Voltage sag critical removal time), is denoted as t VSCR . It can be seen that in the Non-ASVS case, as long as the sag time (i.e., the sag duration) is less than t VSCR The motor is also safe without additional protection, otherwise, an alarm and trip instruction should be sent for protection.
(IV) principle analysis of a voltage sag critical elimination time analysis algorithm:
the motor will be driven from point C in FIG. 2 (slip s stab ) Along the sag period T e Curve is F point (slip is s unst ) Operation, since the motor speed is subject to a torque equationConstraint, and left side of equation T e,sag Is an expression for s, so ω to the right m Also translated into an expression for s, using ω m =2n/60 and s= (n) s -n)/n s The above equation may be converted into:
wherein J represents a moment of inertia [ kg.m2 ]]；n s Represents synchronous rotation speed r/min]。
So long as the load torque T is applied L Also expressed as an expression for s, then by integrating the above equation, the voltage sag threshold cancellation time t can be obtained VSCR Is of the analytical formula:
the upper and lower integral limits in the above equation, i.e. the stable equilibrium point slip s stab And the slip s at the unstable equilibrium point unst (s stab ≤s unst ) The method can be obtained as follows:
note that when the induction motor is operating at a stable equilibrium point and an unstable equilibrium point, the drive and brake torque balance is satisfied, i.e
T e -T L ＝0 (15)
Obviously, T is e And T L Substituting the expression of s into the above expression to obtain s stab Sum s unst . The balance point slip ratio s of each of the constant torque, the constant power compound torque and the fan pump compound torque model is calculated respectively stab And the slip s at the unstable equilibrium point unst ：
(1) Constant torque model:
substituting the formulas (9) and (10) into the formula (15) includes
The upper left side molecule is a unitary quadratic polynomial, and two roots, namely balance point slip s, can be obtained by using a root-finding formula stab And the slip s at the unstable equilibrium point unst The method specifically comprises the following steps:
wherein s is stab,ConT Representing the stable balance point slip of the constant torque model; s is(s) unst,ConT Representing the slip of an unstable balance point of a constant torque model; root discriminant Δ= (b) 0 /T C -a 1 ) 2 -4a 0 ≥0。
(2) Constant power compound torque model:
substituting the formulas (9) and (11) into the formula (15) includes
Wherein:
(19) The left side molecule is a unitary cubic polynomial, and the root finding method is as follows:
given equation
s 3 +d 2 s 2 +d 1 s+d 0 ＝0 (20)
Let s=y-d 2 3, substituting the above formula to obtain
y 3 +u 0 s+w 0 ＝0 (21)
In the method, in the process of the invention,
let three roots of (21) be y 1 ,y 2 ,y 3 Root discriminant typeThen there is
In the method, in the process of the invention,
and then y is k (k=1, 2, 3) substitution s=y-d 2 And 3, obtaining three roots of the original course.
When delta>0, the original recipe has a real root and a pair of conjugate complex roots; when Δ=0, there are three real roots, two of which are equal; when delta<At 0, there are three unequal real roots. Obviously, the slip s at the stable equilibrium point stab The slip s of the unstable balance point is the minimum positive real root of the original equation unst Is the next smallest positive root of the original recipe.
(3) Fan pump type compound torque model: substituting the formulas (9) and (12) into the formula (15) includes
Wherein: e, e 3 ＝a 1 -2；
(25) The left side molecule of the formula is a unitary fourth-order polynomial, and the root-finding method is as follows:
given equation
s 4 +e 3 s 3 +e 2 s 2 +e 1 s+e 0 ＝0 (26)
Solving the equation first
Any real root x of (2) 0 When e 3 x 0 -2e 2 >At 0, the following two equations are solved:
when e 3 x 0 -2e 2 <At 0, the following two equations are solved:
likewise, the slip s at the stable equilibrium point stab The slip s of the unstable balance point is the minimum positive real root of the original equation unst Is the next smallest positive root of the original recipe.
According to the embodiment of the invention, the motor impedance parameter is obtained by obtaining the induction motor manufacturer data and a parameter identification method, and the electromagnetic torque T is established according to the impedance parameter e Slip s three-coefficient concise expression model (the existing disclosed models are all four-coefficient models); the embodiment of the invention also defines the voltage sag ratio K sag Establishing a relational model of positive and negative sequence voltage sag ratio, negative-positive sequence phase difference and voltage sag ratio of each phase for the asymmetric sag; the embodiment of the invention also depends on a torque differential equation during the sagT when Non-absolute safe voltage sag (Non-ASVS) is established VSCR Analytical algorithm, give t-based VSCR A sag time low voltage ride through determination method; give t VSCR The upper and lower limits of the integral in the analytical calculation are the stable and unstable balance point slip s stab Sum s unst For three typical typesProducing mechanical load torque T L A non-iterative algorithm of the model;
the following describes the calculation process of critical elimination time of three load models (namely a constant torque model, a constant power composite torque model and a fan pump composite torque model) during the non-absolute safe voltage sag period by means of two embodiments; in the following two embodiments, the subscript sag in the formula parameters indicates during a voltage sag.
Example 1: critical cancellation time t during a voltage sag when the symmetrical voltage sag is a non-absolute safe voltage sag VSCR The specific calculation method is as follows:
when the stator end generates symmetrical voltage sag, the effective value of the phase voltage in the sag period is set as U 1,sag,ph Equivalent source voltage effective value U 1,sag,ph,eq Coefficient b 0,sag Electromagnetic torque T based on slip s e,sag The concise expressions of the three-coefficient model are respectively:
the Thevenin equivalent resistance and reactance R in the above expression 1,eq 、X 1,eq Coefficient a 0 、a 1 As before the dip.
Definition of Voltage sag ratio
Wherein, K is more than or equal to 0 sag And (3) respectively comparing the formulas (30) - (32) with the formulas (1), (8) and (9)Obtaining the effective value U of the equivalent source voltage during the sag 1,sag,ph,eq Coefficient b 0,sag Electromagnetic torque T e,sag Proportional to the amount before dip:
U 1,sag,ph,eq ＝K sag U 1,ph,eq (34)
the respective t is calculated when the motor load is respectively a constant torque, a constant power compound torque and a fan pump compound torque model during the symmetrical sag VSCR 。
(1) Constant torque model:
substituting the electromagnetic torque (36) of the formula (10) and the symmetrical sag into the formula (14) can obtain the critical elimination time t of the constant torque model during the voltage sag VSCR,ConT Expressed as:
(2) Constant power compound torque model:
substituting the equation (11) and the equation (36) into the equation (14) can obtain the critical elimination time t of the constant-power compound torque model during the voltage sag period VSCR,ConP Expressed as:
wherein:
and s is i (i=1, 2, 3) is the zero point of the integral function denominator polynomial, i.e. the three roots of the following equation
s 3 +g 2 s 2 +g 1 s+g 0 ＝0 (39)
(3) Fan pump type compound torque model:
substituting the expression (12) and the expression (36) into the expression (14) can obtain the critical elimination time t of the fan pump compound torque model during the voltage sag period VSCR,Fan&Pump Expressed as:
in the formula, h 3 ＝a 1 -2＝e 3 ；
And s is i (i=1, 2,3, 4) is the zero point of the integral function denominator polynomial, i.e. the four roots of the following equation
s 4 +h 3 s 3 +h 2 s 2 +h 1 s+h 0 ＝0 (41)
Example 2: critical cancellation time t during voltage sag when asymmetric voltage sag is not an absolute safety voltage sag VSCR The specific calculation method is as follows:
1. when the asymmetric voltage sag occurs at the stator end, the related calculation formulas of positive sequence, negative sequence and zero sequence voltage sag ratio are required to be obtained firstly:
the effective values of positive, negative and zero sequence phase voltages of the stator during the asymmetric sag period are respectively U 1+,sag,ph 、U 1-,sag,ph And U 10,sag,ph Respectively defining positive sequence, negative sequence and zero sequence voltage sag ratio:
wherein K is sag+ ,K sag- ,K sag0 ∈[0,1]；K sag+ Representing a positive sequence voltage sag ratio; k (K) sag- Representing a negative sequence voltage sag ratio; k (K) sag0 Representing zero sequence voltage sag ratio;
because the voltage sag only relates to amplitude change, the phase angle is still unchanged (so that the phase difference of each phase is unchanged), and the phase voltage sag ratio of A, B, C phases is set to be K respectively sag,A (＝U 1A,sag,ph /U 1N,ph )、K sag,B (＝U 1B,sag,ph /U 1N,ph )、K sag,C (＝U 1C,sag,ph /U 1N,ph ) Then there is
Wherein K is sag,A Representing the phase voltage sag ratio of phase a; u (U) 1A,sag,ph Representing the phase voltage effective value of the phase A during the voltage sag period; u (U) 1N,ph Representing the nominal phase voltage; k (K) sag,B Representing the phase voltage sag ratio of phase B; u (U) 1B,sag,ph Representing the phase voltage effective value of the phase B during the voltage sag period; k (K) sag,C Representing the phase voltage sag ratio of phase C; u (U) 1C,sag,ph Representing the phase voltage effective value of the C phase during the voltage sag; subscript 1 denotes a stator end;representing positive sequence phase voltage of the stator end during the voltage sag period; />Representing the negative sequence phase voltage of the stator end during the voltage sag period; />Representing the zero sequence phase voltage of the stator end during the voltage sag; />Phase voltages representing phase a during a voltage sag; />Phase voltages representing phase B during a voltage sag; />Phase voltages representing phase C during a voltage sag;
wherein a=1.120 DEG is a unit vector operator,is the phase angle of phase a. Therefore, the calculation formulas of the positive sequence, the negative sequence and the zero sequence voltage sag ratio are respectively as follows
Respectively record negative sequence voltageAnd positive sequence voltage->Is +.>Zero sequence voltageAnd positive sequence voltage->Is +.>Then there is
2. Solving the expression of positive and negative sequence electromagnetic torque and synthesized electromagnetic torque:
the voltage of the stator of the induction motor is reduced asymmetrically, and the motor is actually switched from operation under symmetrical voltage to operation under asymmetrical voltage. If the stator winding of the induction motor is assembled into a Y shape without a neutral line, no zero sequence current is generated in the motor; when delta connection is formed, no zero sequence current exists in the line current, so that in normal conditions, only two components of positive sequence and negative sequence are needed to be analyzed.
Under the action of the asymmetric sag positive sequence voltage, the rotating magnetic field and the physical condition inside the induction motor are identical to those of the normal symmetric operation, so that the single-phase positive sequence equivalent circuit is shown in figure 3.
According to FIG. 3 (b), the positive phase current effective value of the rotor during the sag is set to be I' 2+,sag,ph Then the effective value U of the equivalent source positive sequence phase voltage 1+,sag,ph,eq Coefficient b 0+,sag Positive sequence electromagnetic torque T e+,sag The concise expressions of s are respectively
The Thevenin equivalent resistance and reactance R in the above expression 1,eq 、X 1,eq Coefficient a 0 、a 1 As before the dip.
Under the action of the asymmetric sag negative sequence voltage, a reverse rotating magnetic field is generated in the motor, and the rotating speed is-n s . Slip s of rotor to negative sequence magnetic field - Is that
Therefore, the equivalent resistance of the rotor after frequency reduction isThe single phase negative sequence equivalent circuit is shown in fig. 4.
According to FIG. 4 (b), the rotor negative sequence phase current effective value during the sag is set to be I' 2-,sag,ph Then the effective value U of the equivalent source negative sequence phase voltage 1-,sag,ph,eq Coefficient b 0-,sag Negative sequence electromagnetic torque T e-,sag The concise expressions of s are respectively
The Thevenin equivalent resistance and reactance R in the above expression 1,eq 、X 1,eq Coefficient a 0 、a 1 As before the dip.
Comparing the formulas (53) - (55) with the formulas (1), (8) and (9) respectively to obtain the effective value U of the equivalent source positive sequence phase voltage during the sag period 1+,sag,ph,eq Coefficient b 0+,sag Positive sequence electromagnetic torque T e+,sag Proportional to the amount before dip:
U 1+,sag,ph,eq ＝K sag+ U 1,ph,eq (60)
similarly, the effective value U of the equivalent source negative sequence phase voltage during the sag period can be obtained 1-,sag,ph,eq Coefficient b 0-,sag Negative sequence electromagnetic torque T e-,sag Proportional to the amount before dip:
U 1-,sag,ph,eq ＝K sag- U 1,ph,eq (63)
when positive and negative sequence voltages exist simultaneously, the resultant torque T is calculated because the positive sequence magnetic field and the negative sequence rotor current act and the negative sequence magnetic field and the positive sequence rotor current act without generating average torque e,sag In the case of using T as the main component e+,sag And T e-,sag Subtracting to obtain
In the method, in the process of the invention, N 3 ＝-4；/> N 0 ＝(4+2a 1 +a 0 )a 0 ；/>
3. calculating a motor load as constant torque, constant power compound torque and fan pump compound torque model T during asymmetric sag e,sag (s)-T L Expression of(s):
(1) Constant torque model:
substituting the equation (10) and the resultant electromagnetic torque (66) into T e,sag (s)-T L (s) have
(2) Constant power compound torque model:
substituting the formula (11) and the formula (66) into T e,sag (s)-T L (s) have
In the method, in the process of the invention,
(3) Fan pump type compound torque model:
substituting the formula (12) and the formula (66) into T e,sag (s)-T L (s) have
Wherein q is 5 ＝N 3 -2；
4. Calculating respective critical elimination time t for the motor load during the asymmetric sag for the constant torque, the constant power compound torque and the fan pump compound torque model respectively VSCR 。
(1) Constant torque model:
substituting the formula (67) into the formula (14) includes
Wherein s is i (i=1, 2,3, 4) is the zero point of the integral function denominator polynomial, i.e. the four roots of the following equation
(2) Constant power compound torque model:
substituting the formula (68) into the formula (14) includes
Wherein p is 4 ,p 3 ,p 2 ,p 1 ,p 0 The expression is described by the expression (68) and s i (i=1, 2,3,4, 5) is the zero point of the integral function denominator polynomial, i.e. the five roots of the following equation
s 5 +p 4 s 4 +p 3 s 3 +p 2 s 2 +p 1 s+p 0 ＝0 (73)
(3) Fan pump type compound torque model:
substituting the formula (89) into the formula (14) includes
Wherein q is 5 ,q 4 ,q 3 ,q 2 ,q 1 ,q 0 The expression is described by the expression (69), and s i (i=1, 2,3,4,5, 6) is the zero point of the integral function denominator polynomial, i.e. six roots of the following equation
s 6 +q 5 s 5 +q 4 s 4 +q 3 s 3 +q 2 s 2 +q 1 s+q 0 ＝0 (75)
Since the induction motor experiences an electromagnetic transient when a voltage dip occurs at the stator terminals, t is VSCR The resolved value does not coincide exactly with the actual value, t VSCR The analysis value needs to be multiplied by a correction coefficient k to reflect the transient process, and the correction coefficient k is determined according to the average value of the ratio of the actual value (or the simulation value) to the analysis value.
T when the symmetrical and asymmetrical voltage sags described in examples 1 and 2 are Non-ASVS VSCR By generalizing the calculation method of (2), t-based can be obtained as shown in FIG. 5 VSCR Is used for monitoring and protecting the program design flow chart of the low voltage ride through system.
In the above examples 1 and 2, t is established for Non-ASVS for three typical load models VSCR Specific calculation method only needs to know voltage sag ratio, sag time and T when sag of Non-ASVS property occurs e -s three coefficients, T L The model can finish the quick judgment of whether the motor can realize low voltage ride through; when the motor is judged to be unable to pass through the low voltage, the program sends out alarm and trip instructions in time. The invention can realize one-to-one differential accurate protection based on motor parameters and a load model, and overcomes the technical defect that the existing undervoltage (voltage loss) restarting protection technology only protects according to the indiscriminate undervoltage (voltage loss) time.
Effect experiments of examples 1 and 2:
to verify the present system t VSCR The accuracy of the analysis algorithm is verified by adopting a verification system consisting of a three-phase programmable voltage source, a certain induction motor, a mechanical load and a motor torque and rotation speed measuring instrument. The three-phase programmable voltage source can symmetrically reduce the positive sequence voltage amplitude to simulate a symmetrical sag, and can additionally apply negative sequence voltage with reduced amplitude to simulate an asymmetrical sag. Factory technical data and impedance parameters of a certain type of induction motor are shown in tables 1 and 2, respectively. The motor torque and rotation speed measuring instrument is used for displaying rotation speed n and electromagnetic torque T e 。
Table 1 factory technical data (f) of an induction motor N =50hz, delta connection
In the table: f represents the frequency [ Hz]The method comprises the steps of carrying out a first treatment on the surface of the Eta represents efficiency [%]The method comprises the steps of carrying out a first treatment on the surface of the cos phi represents the power factor; poles represents the number of poles;indicating the starting current multiple; />Representing a starting torque multiple; />Representing a maximum torque multiple; subscript: st represents start; max represents the maximum value.
Table 2 impedance parameters of certain induction motor
The motor is first run from idle, after which the mechanical load is applied at t=2 s after it has stabilized, and after the motor has reached a new stabilization point, a voltage dip is produced at t=3 s. Three typical torque model parameters for validation are shown in table 3.
Table 3 mechanical load torque model and parameters of induction motor for validation
1) Symmetric voltage sag verification and analysis
Taking a constant torque model as an example, the system t is verified by the verification system through experiments by describing that the symmetrical sag is reduced VSCR The process of the analytical algorithm is similar to the other two models. At a voltage sag ratio K belonging to a Non-absolute safety voltage sag (Non-ASVS) sag K in the range of values near the critical value, the second position after the decimal point is 5 or 0 sag The values are gradually reduced by 0.05 step, and each K is calculated by using the formula (37) sag T below VSCR . Then, the same K is used in the voltage sag ratio value range belonging to Non-ASVS near the critical value sag Step size down-regulating power supply amplitude parameter, and using verification system to define every K sag T below VSCR Actual measurement values. FIG. 6 gives t VSCR A comparison line graph of the analysis value and the measured value.
Analysis and conclusion: as can be seen from fig. 6, three models t VSCR The analysis values are respectively only in the voltage sag ratio K sag The error is higher than the measured value when the error is less than or equal to 0.25, 0.30 and 0.32, is lower than the measured value under the rest sag ratio, and reaches the maximum when the error is near the critical value, because the analysis algorithm does not account for the transient process, and the correction coefficient is multiplied when the actual protection is carried out: for constant torque of 0.72-1.83, the average value is 1.16; for constant power of 0.45-1.98, the average value is 1.07; for the fan pump class of 0.48-2.38, the average value is 1.19, and 1.1-1.2 is comprehensively taken. t is t VSCR The fact that the analytical value is lower than the measured value at most of the sag ratio indicates that t is symmetrically reduced VSCR The parsing algorithm is generally secure.
2) Asymmetric voltage sag verification and analysis
Taking a constant torque model as an example, the asymmetric sag is demonstrated by using the verification system to verify the system t through experiments VSCR And (5) analyzing the process of the algorithm. Without loss of generality, the voltage sag ratio of each phase can be set as follows: k (K) sag,A ＝0.9、K sag,B ＝0.4、K sag,C Varying from 0 to 1, from a highest K based on Non-ASVS with a second bit of 5 or 0 after the decimal point sag,C Starting the numerical value, and respectively calculating the corresponding positive and negative zero sequence voltage sag ratio K by using the steps (48) - (52) sag+ ,K sag- ,K sag0 Negative-positive order, zero-positive order phase differenceThe power supply amplitude phase angle parameter is set according to these calculated values. Each set of K is calculated using (70) sag+ ,K sag- Critical elimination time t at value VSCR Each set of K is then determined by a verification system sag+ ,K sag- ,K sag0 ,T at the value of VSCR Actual measurement values. Will K sag,C The values were gradually adjusted down in 0.05 steps and the above verification procedure was repeated, with the comparison of all analytical values and measured values plotted as a line graph in fig. 7.
Critical of constant power composite modelTime t of elimination VSCR Also adopts the mode of analytic calculation and experimental verification, K under Non-ASVS sag,C The comparison of the values was adjusted down by 0.05 each and the line graph is shown in fig. 7. Critical elimination time t of fan pump composite model VSCR Also adopts the mode of analytic calculation and experimental verification, K under Non-ASVS sag,C The comparison of the values at 0.1 down each time is shown in FIG. 7.
Analysis and conclusion: as can be seen from fig. 7, t VSCR The analysis value is lower than the actual measurement value under all sag ratios, which proves that the extracted t VSCR The algorithm is secure. The correction coefficient should be multiplied during actual protection: for constant torque of 1.48-1.93, the average value is 1.68; for constant power of 1.59-2.04, the average value is 1.84; for the fan pumps of 1.38-2.36, the average value is 1.79, and 1.7-1.8 are comprehensively taken.
The embodiment of the invention also provides a temporary sag critical elimination time calculation system of the motor protector, which comprises a voltage detection module (an external voltage transformer and an internal voltage detection unit), an operation display unit, a signal acquisition processing unit, a protection calculation control unit, a control execution unit and a power supply module; the system frame diagram is shown with reference to fig. 8; the schematic diagram of the scheme of the voltage detection unit and the external sensor circuit in the low voltage ride through system using the voltage transformer and the sampling resistor is shown in fig. 9.
The voltage detection unit is used for detecting the working voltage of the motor, and converting the working voltage of the motor into an analog voltage signal suitable for discrete acquisition by the signal acquisition processing unit through processing of a high voltage and high current detection circuit, an anti-aliasing filter and the like;
an operation display unit for acquiring motor manufacturer data (generally referred to as a technical data sheet, a factory inspection report, specifically referred to as rated power P) N [kW]Rated efficiency eta N Rated voltage U of stator 1N Rated stator current I 1N Rated power factorRated frequency f N Polar number pole, nominal rotational speed n N Rated torque T N Starting current multiple->Starting torque multiplier Maximum torque multiple->Moment of inertia J, etc.); then, the induction motor impedance parameter, i.e. the stator resistance R, is identified and obtained from the manufacturer data by using a parameter identification algorithm 1 Leakage reactance X of stator 1 The rotor resistance R 'to the stator side' 2 And rotor leakage reactance X' 2 Exciting reactance X m The method comprises the steps of carrying out a first treatment on the surface of the Wherein the identification process is completed by a protection calculation control unit (MCU); the operation display unit is also used for acquiring the load model and displaying alarm information.
The signal acquisition processing unit is used for acquiring phase voltage effective values of an A phase, a B phase and a C phase of the motor during the voltage sag period and the sag time of the voltage sag; and transmitting the acquired content to a protection calculation control unit; besides the basic functions, the chip used by the signal acquisition processing unit also has the functions of measuring the effective value of the voltage, measuring the time of the voltage sag and the like, and can be finished by adopting an ADE7880 chip of ADI company or an RN8302B chip of Rui-Nergy company.
The protection calculation control unit is used for calculating the phase voltage sag ratio of the phase A, the phase B and the phase C and judging whether the voltage sag is an absolute safety voltage sag or not based on the phase voltage sag ratio; the method is also used for calculating the critical elimination time of the load model, judging whether the motor is in a safe state or not and whether the motor can automatically realize low voltage ride through or not based on the critical elimination time; based on t VSCR Is characterized by comprising the steps of (1) sag time alarm and trip analysis processing: if the sag time t<t VSCR The motor is considered to be safe and does not send out an action command; if the sag time t VSCR ≤t<k·t VSCR (k is a correction coefficient), the motor is considered to be capable of achieving low voltage ride through, but a warning operation should be issuedInstructions (additional protection such as voltage compensation may be applied if conditional); if the sag time t is more than or equal to k.t VSCR Then consider T at this time e <T L Namely, the motor cannot be accelerated successfully by self force, so that a tripping instruction is sent out to cut off the motor from a main circuit; and sending the judgment result to a control execution unit; the protection calculation control unit (MCU) is responsible for reading data of the signal acquisition processing unit, alarm trip calculation, relay output start trip control and the like, and can adopt an intentional Semiconductor (ST) company to base onCortex TM The STM32F4 series micro controller of the M4 kernel mainly considers the computation performance, the running speed, the program FLASH and the memory capacity of the RAM of the MCU and various peripheral demands, and the STM32F4 series has the digital signal processor capacity with high performance, integrates a plurality of performances such as MCU, DSP, FPU and the like.
The control execution unit is used for controlling the audible and visual alarm circuit to finish audible and visual alarm or controlling the contactor to finish stopping control of the motor through the relay output; the output mode of the control execution unit is relay output, the isolation mode is relay isolation, and the electric shock protection is surge absorption, current limiting, voltage limiting and follow current. The digital quantity output by adopting a relay mode is critically dependent on the type selection of the relay, and the current scheme temporarily takes an economic and reliable domestic power relay as a preliminary type selection object, and can adopt a macro-transmission (HF) JQX-115F/005-1ZS3 type relay. The relay can basically meet the control output of most occasions, and in addition, the relay contacts are additionally limited in current and voltage, so that the influence of arcing possibly occurring in high power on the service life of the contacts is prevented. Besides, the relay can be replaced by an imported ohm dragon PCB relay or a solid state relay according to specific requirements.
The power module is used for providing power for the operation display unit, the signal acquisition processing unit, the protection calculation control unit and the control execution unit; the power supply module outputs DC power required by each subunit circuit in the system and can also output the DC power for other protection systems; the power module is used for converting input electric energy so as to provide stable electric power for all subunit circuits of the low-pass system. The embodiment of the invention adopts a DC power supply design, the input specification is DC 18-36V, the multi-path isolation and wide voltage input are mainly used as cores, and various protection circuits are used as assistance in combination with EMC. The isolation and voltage conversion mainly selects a DC/DC isolation conversion scheme with 18-36V wide voltage input, and adopts a DC/DC isolation converter meeting the equipment wide voltage input requirement for the main loop acquisition and core main control MCU, and selects an 18-36V ultra-wide input conversion module, wherein the isolation voltage is designed according to 3000V, so that the electrical isolation among all core circuits is ensured. The DC/DC back end is added with a linear voltage regulator (LDO), pi-type filtering and high-conduction magnetic beads according to specific design requirements, and high-frequency and low-frequency ripples, interference signals and the like are filtered.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.

Claims (7)

1. The method for calculating the temporary sag critical elimination time of the motor protector is characterized by comprising the following steps of:
acquiring a motor impedance parameter and a load model;
constructing an electromagnetic torque three-coefficient model based on slip according to the motor impedance parameters;
according to the electromagnetic torque three-coefficient model, calculating the stable balance point slip and the unstable balance point slip of the load model by combining the load torque corresponding to the load model;
respectively obtaining phase voltage effective values of A phase, B phase and C phase of the motor during voltage sag, and obtaining sag time of the voltage sag;
according to the phase voltage effective values of the A phase, the B phase and the C phase, respectively calculating the phase voltage sag ratio of the A phase, the B phase and the C phase when voltage sag occurs;
if the phase voltage sag ratio of the phase A, the phase B and the phase C is uniform, the voltage sag is symmetrical; judging whether the voltage sag is an absolute safety voltage sag or not based on the voltage sag;
if the voltage sag is a non-absolute safety voltage sag, performing a first warning; calculating critical elimination time of the load model based on the stable balance point slip and the unstable balance point slip of the load model, and recording the critical elimination time as first critical elimination time;
If the sag time is less than the first critical elimination time, the motor is in a safe state;
if the sag time is longer than the first critical elimination time, performing a second warning and judging whether the motor can automatically realize low voltage ride through;
if the motor cannot automatically realize low voltage ride through, cutting off the motor from a main circuit;
the motor impedance parameter includes a stator resistance;
the method for constructing the electromagnetic torque three-coefficient model based on the slip comprises the following steps:
when the stator terminal phase voltage U 1,ph Is rated for phase voltage U 1N,ph When the effective value U of the equivalent source voltage is obtained 1,ph,eq Equivalent resistance R of Thevenin 1,eq And Thevenin equivalent reactance X 1,eq The following are provided:
wherein X is m Representing the excitation reactance; r is R 1 Representing the stator resistance; x is X 1 Representing stator leakage reactance;
then, the rotor phase current effective value I 'is calculated' 2,ph Expressed as:
wherein R 'is' 2 Representing rotor resistance; s represents slip; x'. 2 Representing rotor leakage reactance;
substituting (4) into an electromagnetic torque formula to obtain:
wherein T is e Represents electromagnetic torque, and the unit is N.m; m is m 1 Representing the number of stator phases; omega s Represents a synchronous angular velocity in rad/sec;
based on equation (5), coefficient a is calculated 0 、a 1 And b 0 ：
Wherein U is 1,ph,eq Representing the effective value of the equivalent source voltage; r is R 1,eq Representing the equivalent resistance of thevenin; r's' 2 Representing rotor resistance; x is X 1,eq Representing the Thevenin equivalent reactance; x'. 2 Representing rotor leakage reactance; m is m 1 Representing the number of stator phases; omega s Represents a synchronous angular velocity in rad/sec;
based on formulas (5) - (8), the electromagnetic torque T based on slip s can be derived e Concise expression of the three-coefficient model:
wherein T is e Representing electromagnetic torque; s represents slip; a, a 0 、a 1 And b 0 All represent coefficients;
when a voltage dip occurs, the voltage dip ratio is expressed as:
wherein K is sag Representing a voltage sag ratio; u (U) 1,sag,ph Representing the phase voltage effective value during the sag; u (U) 1N,ph Representing the nominal phase voltage;
further comprises:
if the phase voltage sag ratios corresponding to the phase A, the phase B and the phase C are inconsistent, the voltage sag is an asymmetric voltage sag; based on the above, positive sequence voltage sag ratio and negative sequence voltage sag ratio of the motor are calculated by combining the phase voltage sag ratios of the A phase, the B phase and the C phase;
based on the positive sequence voltage sag ratio and the negative sequence voltage sag ratio of the motor, combining the electromagnetic torque three-coefficient model to calculate the synthetic electromagnetic torque of the motor;
judging whether the voltage sag is an absolute safety voltage sag or not based on the synthesized electromagnetic torque of the motor;
If the voltage sag is not absolute safe voltage sag, performing a first warning, and calculating critical elimination time of the load model based on the stable balance point slip and the unstable balance point slip of the load model, and recording the critical elimination time as second critical elimination time;
if the sag time is less than the second critical elimination time, the motor is in a safe state;
if the sag time is longer than the second critical elimination time, performing a second warning and judging whether the motor can automatically realize low voltage ride through;
if the motor cannot automatically realize low voltage ride through, cutting off the motor from a main circuit;
when the asymmetric voltage sag occurs at the stator end, the related calculation formulas of positive sequence, negative sequence and zero sequence voltage sag ratio are required to be obtained firstly:
the effective values of positive, negative and zero sequence phase voltages of the stator during the asymmetric sag period are respectively U 1+,sag,ph 、U 1-,sag,ph And U 10,sag,ph Respectively defining positive sequence, negative sequence and zero sequence voltage sag ratio:
wherein K is sag+ ,K sag- ,K sag0 ∈[0,1]；K sag+ Representing a positive sequence voltage sag ratio; k (K) sag- Representing a negative sequence voltage sag ratio; k (K) sag0 Representing zero sequence voltage sag ratio;
because the voltage sag only relates to the amplitude change, the phase angle is still unchanged, and the phase voltage sag ratio of A, B, C phases is set to be K respectively sag,A ＝U 1A,sag,ph /U 1N,ph 、K sag,B ＝U 1B,sag,ph /U 1N,ph 、K sag,C ＝U 1C,sag,ph /U 1N,ph Then there is
Wherein K is sag,A Representing the phase voltage sag ratio of phase a; u (U) 1A,sag,ph Representing the phase voltage effective value of the phase A during the voltage sag period; u (U) 1N,ph Representing the nominal phase voltage; k (K) sag,B Representing the phase voltage sag ratio of phase B; u (U) 1B,sag,ph Representing the phase voltage effective value of the phase B during the voltage sag period; k (K) sag,C Representing the phase voltage sag ratio of phase C; u (U) 1C,sag,ph Representing the phase voltage effective value of the C phase during the voltage sag; subscript 1 denotes a stator end;representing positive sequence phase voltage of the stator end during the voltage sag period; />Representing the negative sequence phase voltage of the stator end during the voltage sag period; />Representing the zero sequence phase voltage of the stator end during the voltage sag; />Phase voltages representing phase a during a voltage sag; />Phase voltages representing phase B during a voltage sag; />Phase voltages representing phase C during a voltage sag;
wherein a=1.120 DEG is a unit vector operator,is the phase angle of phase A; therefore, the calculation formulas of the positive sequence, the negative sequence and the zero sequence voltage sag ratio are respectively as follows:
respectively record negative sequence voltageAnd positive sequence voltage->Is +.>Zero sequence voltage->And positive sequence voltage->Is +.>Then there is
Solving the expression of positive and negative sequence electromagnetic torque and synthesized electromagnetic torque:
let the positive sequence phase current effective value of the rotor in the sag period be I' 2+,sag,ph Then the effective value U of the equivalent source positive sequence phase voltage 1+,sag,ph,eq Coefficient b 0+,sag Positive sequence electromagnetic torque T e+,sag The concise expressions of s are respectively
The Thevenin equivalent resistance and reactance R in the above expression 1,eq 、X 1,eq Coefficient a 0 、a 1 The same as before the dip;
under the action of the asymmetric sag negative sequence voltage, a reverse rotating magnetic field is generated in the motor, and the rotating speed is-n s The method comprises the steps of carrying out a first treatment on the surface of the Slip s of rotor to negative sequence magnetic field - Is that
Therefore, the equivalent resistance of the rotor after frequency reduction is R' 2 /(2-s)；
Let the effective value of the negative sequence phase current of the rotor in the sag period be I' 2-,sag,ph Then the effective value U of the equivalent source negative sequence phase voltage 1-,sag,ph,eq Coefficient b 0-,sag Negative sequence electromagnetic torque T e-,sag The concise expressions of s are respectively
The Thevenin equivalent resistance and reactance R in the above expression 1,eq 、X 1,eq Coefficient a 0 、a 1 The same as before the dip;
comparing the formulas (53) - (55) with the formulas (1), (8) and (9) respectively to obtain the effective value U of the equivalent source positive sequence phase voltage during the sag period 1+,sag,ph,eq Coefficient b 0+,sag Positive sequence electromagnetic torque T e+,sag Proportional to the amount before dip:
U 1+,sag,ph,eq ＝K sag+ U 1,ph,eq (60)
similarly, the effective value U of the equivalent source negative sequence phase voltage during the sag period can be obtained 1-,sag,ph,eq Coefficient b 0-,sag Negative sequence electromagnetic torque T e-,sag Proportional to the amount before dip:
U 1-,sag,ph,eq ＝K sag- U 1,ph,eq (63)
when positive and negative sequence voltages exist simultaneously, the resultant torque T is calculated because the positive sequence magnetic field and the negative sequence rotor current act and the negative sequence magnetic field and the positive sequence rotor current act without generating average torque e,sag In the case of using T as the main component e+,sag And T e-,sag Subtracting to obtain
In the method, in the process of the invention, N 3 ＝-4；N 0 ＝(4+2a 1 +a 0 )a 0 ；
if the voltage sag is an asymmetric voltage sag, judging whether the voltage sag is an absolute safety voltage sag or not, and specifically comprising the following steps:
judging whether a stable balance intersection point exists between the synthesized electromagnetic torque curve and the load torque curve;
if a stable balance intersection point exists, the voltage sag is an absolute safety voltage sag;
and if the stable balance intersection point does not exist, the voltage sag is a non-absolute safety voltage sag.
2. The method for calculating a sag threshold elimination time of a motor protector according to claim 1, wherein if a voltage sag is a symmetrical voltage sag, determining whether the voltage sag is an absolute safety voltage sag comprises:
judging whether a stable balance intersection point exists between an electromagnetic torque curve and a load torque curve in the voltage sag period;
if a stable balance intersection point exists, the voltage sag is an absolute safety voltage sag;
and if the stable balance intersection point does not exist, the voltage sag is a non-absolute safety voltage sag.
3. The method of calculating a sag threshold elimination time for a motor protector according to claim 1, wherein the load model comprises: a constant torque model, a constant power compound torque model and a fan pump compound torque model.
4. A method of calculating a sag threshold elimination time for a motor protector according to claim 1, wherein said motor impedance parameter comprises: stator resistor R 1 Leakage reactance X of stator 1 The rotor resistance R 'to the stator side' 2 And rotor leakage reactance X' 2 Exciting reactance X m 。
5. The method for calculating a temporary sag threshold elimination time of a motor protector according to claim 1, wherein determining whether the motor is capable of automatically achieving low voltage ride through comprises: judging whether the sag time is smaller than the product of the correction coefficient and the critical elimination time or not;
if the voltage is smaller than the preset voltage, the motor can automatically realize low-voltage ride through;
if not, the motor can not automatically realize low voltage ride through.
6. A system for calculating the sag threshold elimination time of a motor protector, wherein the method for calculating the sag threshold elimination time of the motor protector according to claim 1 comprises the following steps: the system comprises an operation display unit, a signal acquisition processing unit, a protection calculation control unit, a control execution unit and a power supply module;
the operation display unit is used for acquiring the impedance parameters of the motor and the load model; and transmitting the acquired content to the protection calculation control unit;
The signal acquisition processing unit is used for acquiring phase voltage effective values of A phase, B phase and C phase of the motor during the voltage sag period and sag time of the voltage sag; and transmitting the acquired content to the protection calculation control unit;
the protection calculation control unit is used for calculating the phase voltage sag ratio of the phase A, the phase B and the phase C and judging whether the voltage sag is an absolute safety voltage sag or not based on the phase voltage sag ratio; the method is also used for calculating the critical elimination time of the load model, judging whether the motor is in a safe state or not and whether the motor can automatically realize low voltage ride through or not based on the critical elimination time; if the motor can not automatically realize low voltage ride through, a tripping instruction is sent out, and a judgment result is sent to the control execution unit;
the control execution unit is used for controlling the audible and visual alarm to finish warning operation; the motor is also used for executing a tripping instruction to cut off the motor from the main circuit;
the power module is used for providing power for the operation display unit, the signal acquisition processing unit, the protection calculation control unit and the control execution unit.
7. The system for calculating a sag threshold elimination time for a motor protector of claim 6, further comprising a voltage detection module;
The voltage detection module comprises an external voltage transformer and an internal voltage detection unit;
the voltage detection module is used for detecting the working voltage of the motor and converting the working voltage of the motor into an analog voltage signal suitable for discrete acquisition by the signal acquisition processing unit.
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