CN107482617B - Rapid calculation method for characteristic coefficient of dynamic load model - Google Patents

Rapid calculation method for characteristic coefficient of dynamic load model Download PDF

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CN107482617B
CN107482617B CN201710554562.4A CN201710554562A CN107482617B CN 107482617 B CN107482617 B CN 107482617B CN 201710554562 A CN201710554562 A CN 201710554562A CN 107482617 B CN107482617 B CN 107482617B
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海世芳
孙士云
孙德娟
安德超
王杨
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Kunming University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention relates to a method for quickly calculating characteristic coefficients of a dynamic load model, and belongs to the technical field of power system stabilization and control. The method comprises the following steps: calculating the slip ratio; according to the relation between the slip ratio and the frequency and the voltage, a relational expression of active power and reactive power absorbed by the induction motor is obtained; respectively carrying out partial derivation on the frequency at the side of the stator according to the obtained active power and reactive power, and multiplying the partial derivation by the ratio of the initial frequency to the initial power to obtain a frequency characteristic coefficient expression; and respectively calculating partial derivatives of the power supply voltage according to the calculated active power and reactive power, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a voltage characteristic coefficient expression. The invention simplifies the complex calculation process, saves the calculation time and workload, and obtains the relatively simple relations between the active power, the reactive power, the slip ratio, the frequency and the voltage.

Description

Rapid calculation method for characteristic coefficient of dynamic load model
Technical Field
The invention relates to a method for quickly calculating characteristic coefficients of a dynamic load model, and belongs to the technical field of power system stabilization and control.
Background
With the gradual development and improvement of strategic engineering of 'west-east power transmission, south-north interconnection and national networking' in China, the realization of asynchronous interconnection between power grids of various provinces becomes a necessary development trend. Asynchronous interconnection can effectively reduce short circuit capacity, stop reactive power problems and improve the reliability of stable operation of the system, but the feed-in of a direct current system makes the operation mode of the system complicated, and the commutation failure of the direct current system easily causes direct current blocking faults. In some microgrid systems or small islands, if a fault occurs or a special impact load exists, the frequency characteristic and the voltage characteristic are simultaneously considered during load modeling, and the load dynamic characteristic of an actual system can be truly reflected.
With the advance of asynchronous networking, the power grid is larger and more complex, the dynamic voltage stability and the frequency stability of the power grid are more prominent, the influence of a load model on the simulation result of the power system is more and more sensitive, and particularly, the selection of the load model, the determination of parameters, the simulation of a power distribution network and the like have great influence on the stable calculation result of the networking system. Load modeling is a very complex problem: the load of the power system is formed by integrating a plurality of different electric equipment, and the electric system is various; the load composition and the load amount are changed along with time; lack of accurate data for load composition; many loads are non-linear. The accuracy of the model directly affects the simulation result and the decision scheme based on the simulation result, and the improper load model can lead the calculation result to be inconsistent with the actual situation, thereby forming the potential danger of the system or causing unnecessary waste. In the current load model, the frequency characteristic coefficient and the voltage characteristic coefficient usually adopt empirical values, and a more accurate model is urgently needed to be established.
The induction motor is also called as an asynchronous motor, is one of alternating current motors, and has the advantages of simple structure, convenient manufacture, use and maintenance, reliable operation, higher efficiency, lower price and the like. It is an important dynamic component in the load model because it has a large weight in the industrial load. The frequency characteristic coefficient and the voltage characteristic coefficient of the induction motor are rapidly calculated, and the method has good practical application significance.
Disclosure of Invention
The invention provides a method for quickly calculating a characteristic coefficient of a dynamic load model, which is used for quickly calculating a frequency characteristic coefficient and a voltage characteristic coefficient when an induction motor operates in a steady state.
The technical scheme of the invention is as follows: a fast calculation method of dynamic load model characteristic coefficient calculates slip ratio; according to the relation between the slip ratio and the frequency and the voltage, a relational expression of active power and reactive power absorbed by the induction motor is obtained; respectively carrying out partial derivation on the frequency at the side of the stator according to the obtained active power and reactive power, and multiplying the partial derivation by the ratio of the initial frequency to the initial power to obtain a frequency characteristic coefficient expression; and respectively calculating partial derivatives of the power supply voltage according to the calculated active power and reactive power, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a voltage characteristic coefficient expression.
The calculated slip S:
Figure BDA0001345331340000021
in the formula, p is a polar pair number; u is a power supply voltage; rrIs the rotor resistance; t isMIs a mechanical torque; l is1Is the sum of the stator inductance and the rotor inductance; f. ofsThe stator side frequency.
And solving a relational expression of active power and reactive power absorbed by the induction motor according to the relation between the slip ratio and the frequency and the voltage:
① active power P:
Figure BDA0001345331340000022
② reactive power Q:
Figure BDA0001345331340000023
in the formula, LμIs the inductance of the excitation loop.
And respectively carrying out partial derivation on the frequency at the side of the stator according to the obtained active power and reactive power, and multiplying the partial derivation by the ratio of the initial frequency to the initial power to obtain a frequency characteristic coefficient expression formula (4) - (5):
① characteristic coefficient of active power frequency pf：
Figure BDA0001345331340000024
② reactive power frequency characteristic coefficient qf：
Figure BDA0001345331340000025
In the formula (f)s0Operating an initial frequency for the system; p0Active power under initial operating conditions; q0Is the reactive power at the initial operating condition;
Figure BDA0001345331340000031
Figure BDA0001345331340000032
Figure BDA0001345331340000033
Figure BDA0001345331340000034
Figure BDA0001345331340000035
A4＝64π4TM 2L1 2fs 4；
A5＝p2Rr 2U4；
A6＝pRrU2。
and respectively calculating partial derivatives of the power supply voltage according to the calculated active power and reactive power, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a voltage characteristic coefficient expression formula (6) -7:
① characteristic coefficient of active power voltage pu：
Figure BDA0001345331340000036
② reactive power voltage characteristic coefficient qu：
Figure BDA0001345331340000037
In the formula of U0Operating an initial voltage for the system;
Figure BDA0001345331340000038
Figure BDA0001345331340000039
Figure BDA0001345331340000041
Figure BDA0001345331340000042
B4＝64π4TM 2L1 2fs 4；
Figure BDA0001345331340000043
B6＝pRrU2；
B7＝p2Rr 2U4；
Figure BDA0001345331340000044
Figure BDA0001345331340000045
Figure BDA0001345331340000046
Figure BDA0001345331340000047
C4＝64π4TM 2L1 2fs 4；
Figure BDA0001345331340000048
the invention has the beneficial effects that:
1. the induction motor is used as an important component of the dynamic load, and the equivalent circuit diagram of the induction motor is simplified, so that the complex calculation process is simplified, the calculation time and the workload are saved, and the relatively simple relation among the active power, the reactive power, the slip ratio, the frequency and the voltage is obtained.
2. The frequency characteristic coefficient and the voltage characteristic coefficient of the induction motor in steady-state operation are quickly calculated, the method is simple and easy to implement, the real-time operation state of the system is conveniently analyzed, and the stability of the system is judged. Has good practical application significance.
Drawings
FIG. 1 is a T-shaped equivalent circuit diagram of a motor;
fig. 2 is a Γ -shaped equivalent circuit diagram of the motor.
Detailed Description
Example 1: as shown in fig. 1-2, a method for rapidly calculating a characteristic coefficient of a dynamic load model calculates a slip ratio; according to the relation between the slip ratio and the frequency and the voltage, a relational expression of active power and reactive power absorbed by the induction motor is obtained; respectively carrying out partial derivation on the frequency at the side of the stator according to the obtained active power and reactive power, and multiplying the partial derivation by the ratio of the initial frequency to the initial power to obtain a frequency characteristic coefficient expression; and respectively calculating partial derivatives of the power supply voltage according to the calculated active power and reactive power, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a voltage characteristic coefficient expression.
Example 2: as shown in fig. 1-2, a method for rapidly calculating a characteristic coefficient of a dynamic load model calculates a slip ratio; according to the relation between the slip ratio and the frequency and the voltage, a relational expression of active power and reactive power absorbed by the induction motor is obtained; respectively carrying out partial derivation on the frequency at the side of the stator according to the obtained active power and reactive power, and multiplying the partial derivation by the ratio of the initial frequency to the initial power to obtain a frequency characteristic coefficient expression; and respectively calculating partial derivatives of the power supply voltage according to the calculated active power and reactive power, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a voltage characteristic coefficient expression.
The method for rapidly calculating the frequency characteristic coefficient and the voltage characteristic coefficient during the steady-state operation of the induction motor can be specifically carried out according to the following steps:
taking a three-phase four-pole squirrel-cage rotor asynchronous motor as an example, the motor is operated under the conditions that the rated power is 10kW, the rated voltage is 380V and the rated frequency is 50Hz, and the parameters are shown in Table 1.
TABLE 1 Induction Motor operating parameter settings
Figure BDA0001345331340000051
(1) Calculating slip
Calculating the slip S and the system frequency f of the motorsAnd the relational expression of the system voltage U:
Figure BDA0001345331340000052
in the formula, RrIs the rotor resistance; l is1Is the sum of the stator inductance and the rotor inductance; u is power voltage (when the rated initial voltage is adopted, the U is 380V); p is the number of pole pairs; t isMIs a mechanical torque; f. ofsIs the stator side frequency (at the rated initial frequency, f)sTaken as 50 Hz).
Calculating the initial slip S of the induction motor based on the induction motor parameter data in Table 10Comprises the following steps:
S0＝0.0406；
(2) calculating active and reactive power
And (3) solving a relational expression of active power and reactive power absorbed by the induction motor according to the relation between the slip ratio, the frequency and the voltage obtained in the step (1).
1) Active power
Figure BDA0001345331340000061
According to the induction motor parameter data in the table 1, the initial active power P absorbed by the induction motor is calculated0Comprises the following steps:
P0＝15708W；
2) reactive power
Figure BDA0001345331340000062
In the formula, LμIs the inductance of the excitation loop.
Calculating the initial reactive power Q absorbed by the induction motor according to the induction motor parameter data in Table 10Comprises the following steps:
Q0＝9387.4Var；
(3) calculating the active power frequency characteristic coefficient and the reactive power frequency characteristic coefficient
And (3) respectively solving partial derivatives of the active power and the reactive power obtained in the step (2) for the frequency at the stator side, and multiplying the partial derivatives by the ratio of the initial frequency to the initial power to obtain the formula (4) - (5), namely the solved frequency characteristic coefficient expression.
1) Characteristic coefficient of active power frequency
Figure BDA0001345331340000063
In the formula (I), the compound is shown in the specification,
Figure BDA0001345331340000064
Figure BDA0001345331340000065
Figure BDA0001345331340000071
Figure BDA0001345331340000072
A4＝64π4TM 2L1 2fs 4
A5＝p2Rr 2U4
A6＝pRrU2
2) characteristic coefficient of reactive power frequency
Figure BDA0001345331340000073
In the formula (I), the compound is shown in the specification,
Figure BDA0001345331340000074
(4) calculating an active power voltage characteristic coefficient and a reactive power voltage characteristic coefficient:
and (3) respectively solving partial derivatives of the active power and the reactive power obtained in the step (2) for the power supply voltage, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a formula (6) -a formula (7) which is the solved voltage characteristic coefficient expression.
1) Characteristic coefficient of active power voltage
Figure BDA0001345331340000075
In the formula (I), the compound is shown in the specification,
Figure BDA0001345331340000076
Figure BDA0001345331340000077
Figure BDA0001345331340000078
Figure BDA0001345331340000079
B4＝64π4TM 2L1 2fs 4；
Figure BDA0001345331340000081
B6＝pRrU2；
B7＝p2Rr 2U4；
2) characteristic coefficient of reactive power voltage
Figure BDA0001345331340000082
In the formula (I), the compound is shown in the specification,
Figure BDA0001345331340000083
Figure BDA0001345331340000084
Figure BDA0001345331340000085
Figure BDA0001345331340000086
C4＝64π4TM 2L1 2fs 4；
Figure BDA0001345331340000087
taking the induction motor load parameters shown in table 1 as an example, the rated frequency and rated voltage of the system are modified, and the frequency characteristic coefficient and voltage characteristic coefficient of the induction motor are calculated.
The results of calculating the frequency characteristic coefficient and the voltage characteristic coefficient of the induction motor rapidly when the frequency changes by 0.5Hz or the voltage changes by 0.1pu theoretically according to the parameter values in table 1 are shown in table 2.
TABLE 2 Power frequency characteristic coefficient and Voltage characteristic coefficient
Figure BDA0001345331340000088
The principle of the invention is as follows:
the induction motor generates a rotating magnetic field through three-phase current of a stator winding, and then generates induced electromotive force and induced current in a rotor winding by utilizing the principle of electromagnetic induction, and generates electromagnetic torque through the interaction of an air gap magnetic field and the rotor induced current so as to carry out energy conversion. The three-order induction motor model considering mechanical transient is used for quick calculation and deduction.
The relation between the active power and the reactive power and the slip and the frequency can be obtained through the T-shaped equivalent circuit, and the relation can be properly simplified as follows:
(1) simplifying the conditions
1) Reactance x of excitation loopμMuch greater than stator reactance xsσI.e. xμ＞＞xsσ(capacity of more than 40kW of asynchronous motor is satisfied)
2) Neglecting stator, rotor and excitation loop resistance
3) Assuming constant mechanical torque
Through the equivalent circuit diagram and the simplification conditions, the T-shaped equivalent circuit diagram shown in FIG. 1 can be simplified into the L-shaped equivalent circuit diagram shown in FIG. 2. (see the attached drawing)
The active power of the motor under the condition that the frequency of the external power supply is constant can be obtained by using the inverted L-shaped equivalent circuit diagram:
Figure BDA0001345331340000091
assuming constant mechanical torque, then
Figure BDA0001345331340000092
Wherein
Figure BDA0001345331340000093
x1＝xrσ+xsσ＝ωsL1(4)
ωs＝2πfs(5)
In the formula, S is the slip ratio of the motor, and P is the electromagnetic active power; rrIs the rotor resistance; x is the number ofrσIs the rotor reactance; x is the number ofsσIs a stator reactance; l is1Is the sum of the stator inductance and the rotor inductance; u is a power supply voltage; i is loop current; omegasIs the electrical angular velocity; f. ofsIs the stator side frequency; t iseIs an electromagnetic torque; t isMIs a mechanical torque; omegasIs the mechanical angular velocity; p is the number of pole pairs.
(2) Calculating the slip of the motor
And (3) carrying out simultaneous operation on the stable operation condition formulas (1) - (5) in the step (1) to obtain a one-dimensional quadratic equation about the slip ratio:
TM(2πfs)3L1 2S2-U2RrpS+TMRr 2(2πfs)＝0 (6)
solving the above equation, when the condition is satisfied:
(pU2Rr)2-4TM 2Rr 2L1 2(2πfs)4≥0 (7)
two solutions (S) are obtained for the slip of the induction motor1、S2) Are respectively:
Figure BDA0001345331340000101
Figure BDA0001345331340000102
considering the practical situation, when the induction motor is used as a motor, the value range of the slip ratio S is 0 < S < 1, so S in the expression is omitted1The slip S and the system frequency f of the induction motorsAnd the system voltage U is expressed as:
Figure BDA0001345331340000103
(3) calculating the active and reactive power of the motor
Substituting the slip expression obtained in the step (2) into the expression (1) to obtain a relational expression of the active power absorbed by the induction motor, wherein the relational expression is as follows:
Figure BDA0001345331340000104
as can be seen from the Γ -shaped equivalent circuit of the motor in fig. 2, the reactive power of the induction motor is divided into two parts, namely a stator loop, a rotor loop and an excitation loop after simplified conditions, and the obtained slip expression is substituted into a calculation formula of the reactive power:
Figure BDA0001345331340000105
wherein the content of the first and second substances,
xμ＝2πfsLμ(13)
in the formula, QsReactive power absorbed jointly for the stator and rotor circuits; qμThe reactive power absorbed by the excitation loop; x is the number ofμIs the reactance of the excitation loop; l isμIs the inductance of the excitation loop.
Obtaining the reactive power expression of the motor as follows:
Figure BDA0001345331340000111
(4) calculating the active power frequency characteristic coefficient and the reactive power frequency characteristic coefficient
The system frequency in the power expression is subjected to partial derivation and multiplied by the ratio of the initial frequency to the initial power, namely, the frequency characteristic coefficient calculation formulas of the active power and the reactive power are respectively shown as a formula (15) and a formula (16),
1) the active power frequency characteristic coefficient calculation formula is as follows:
Figure BDA0001345331340000112
in the formula, pfThe active power frequency characteristic coefficient; f. ofs0Operating an initial frequency for the system; p0Is the active power at the initial operating conditions.
2) Reactive power frequency characteristic coefficient calculation formula:
Figure BDA0001345331340000113
in the formula, qfThe characteristic coefficient of the reactive power frequency is obtained; q0Is the reactive power at the initial operating conditions.
And (4) respectively substituting the active power and the reactive power obtained in the step (3) into the frequency characteristic coefficient calculation formula to obtain an active power frequency characteristic coefficient expression formula (17) and a reactive power frequency characteristic coefficient expression formula (18) of the motor.
3) Characteristic coefficient of active power frequency of the motor:
Figure BDA0001345331340000114
in the formula (I), the compound is shown in the specification,
Figure BDA0001345331340000115
Figure BDA0001345331340000116
Figure BDA0001345331340000117
A4＝64π4TM 2L1 2fs 4
A5＝p2Rr 2U4
A6＝pRrU2
4) motor reactive power frequency characteristic coefficient
Figure BDA0001345331340000121
(5) Calculating the active power voltage characteristic coefficient and the reactive power voltage characteristic coefficient
The system voltage in the power expression is subjected to partial derivation and multiplied by the ratio of the initial voltage to the initial power, namely the voltage characteristic coefficient calculation formulas of the active power and the reactive power are respectively shown as a formula (19) and a formula (20),
1) active power voltage characteristic coefficient calculation formula
Figure BDA0001345331340000122
In the formula, puThe active power voltage characteristic coefficient; u shape0An initial voltage is run for the system.
2) Reactive power voltage characteristic coefficient calculation formula
Figure BDA0001345331340000123
In the formula, quIs made withoutAnd (4) a power voltage characteristic coefficient.
And (4) respectively bringing the active power and the reactive power obtained in the step (3) into a voltage characteristic coefficient calculation formula to obtain an active power voltage characteristic coefficient expression formula (21) and a reactive power voltage characteristic coefficient expression formula (22) of the motor.
3) Characteristic coefficient of active power voltage of motor
Figure BDA0001345331340000124
In the formula (I), the compound is shown in the specification,
Figure BDA0001345331340000125
Figure BDA0001345331340000131
Figure BDA0001345331340000132
B4＝64π4TM 2L1 2fs 4
Figure BDA0001345331340000133
B6＝pRrU2
B7＝p2Rr 2U4
4) voltage characteristic coefficient of reactive power of motor
Figure BDA0001345331340000134
In the formula (I), the compound is shown in the specification,
Figure BDA0001345331340000135
Figure BDA0001345331340000136
Figure BDA0001345331340000137
C4＝64π4TM 2L1 2fs 4
Figure BDA0001345331340000138
while the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (4)

1. A method for rapidly calculating the characteristic coefficient of a dynamic load model is characterized in that: calculating the slip ratio; according to the relation between the slip ratio and the frequency and the voltage, a relational expression of active power and reactive power absorbed by the induction motor is obtained; respectively carrying out partial derivation on the frequency at the side of the stator according to the obtained active power and reactive power, and multiplying the partial derivation by the ratio of the initial frequency to the initial power to obtain a frequency characteristic coefficient expression; respectively solving partial derivatives of the power supply voltage according to the obtained active power and reactive power, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a voltage characteristic coefficient expression;
the calculated slip S:
Figure FDA0002293310500000011
in the formula, p is a polar pair number; u is a power supply voltage; rrIs the rotor resistance; t isMIs a mechanical torque; l is1Is the sum of the stator inductance and the rotor inductance; f. ofsAs stator side frequencyAnd (4) rate.
2. The method for rapidly calculating the characteristic coefficient of the dynamic load model according to claim 1, wherein: and solving a relational expression of active power and reactive power absorbed by the induction motor according to the relation between the slip ratio and the frequency and the voltage:
① active power P:
Figure FDA0002293310500000012
② reactive power Q:
Figure FDA0002293310500000013
in the formula, LμIs the inductance of the excitation loop.
3. The method for rapidly calculating the characteristic coefficient of the dynamic load model according to claim 2, wherein: and respectively carrying out partial derivation on the frequency at the side of the stator according to the obtained active power and reactive power, and multiplying the partial derivation by the ratio of the initial frequency to the initial power to obtain a frequency characteristic coefficient expression formula (4) - (5):
① characteristic coefficient of active power frequency pf：
Figure FDA0002293310500000021
② reactive power frequency characteristic coefficient qf：
Figure FDA0002293310500000022
In the formula (f)s0Operating an initial frequency for the system; p0Active power under initial operating conditions; q0Is the reactive power at the initial operating condition;
Figure FDA0002293310500000023
Figure FDA0002293310500000024
Figure FDA0002293310500000025
Figure FDA0002293310500000026
Figure FDA0002293310500000027
A4＝64π4TM 2L1 2fs 4；
A5＝p2Rr 2U4；
A6＝pRrU2。
4. the method for rapidly calculating the characteristic coefficient of the dynamic load model according to claim 2, wherein: and respectively calculating partial derivatives of the power supply voltage according to the calculated active power and reactive power, and multiplying the partial derivatives by the ratio of the initial voltage to the initial power to obtain a voltage characteristic coefficient expression formula (6) -7:
① characteristic coefficient of active power voltage pu：
Figure FDA0002293310500000028
② reactive power voltage characteristic coefficient qu：
Figure FDA0002293310500000031
In the formula of U0Operating an initial voltage for the system;
Figure FDA0002293310500000032
Figure FDA0002293310500000033
Figure FDA0002293310500000034
Figure FDA0002293310500000035
B4＝64π4TM 2L1 2fs 4；
Figure FDA0002293310500000036
B6＝pRrU2；
B7＝p2Rr 2U4；
Figure FDA0002293310500000037
Figure FDA0002293310500000038
Figure FDA0002293310500000039
Figure FDA00022933105000000310
C4＝64π4TM 2L1 2fs 4；
Figure FDA00022933105000000311
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