CN114841005A - Method for evaluating equivalent inertia of asynchronous motor in inertia response stage - Google Patents
Method for evaluating equivalent inertia of asynchronous motor in inertia response stage Download PDFInfo
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- G06F30/20—Design optimisation, verification or simulation
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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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- G—PHYSICS
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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
- H02J2203/00—Indexing scheme relating to details of 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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
Abstract
The invention discloses an equivalent inertia evaluation method for an asynchronous motor in an inertia response stage, and relates to the technical field of inertia evaluation of power systems. In recent years, the power grid in China is gradually evolved into a power electronic power system with a high proportion, the inertia response of an asynchronous motor in the power system is researched, the effective inertia of the asynchronous motor under the inertia time scale and the supporting effect on system frequency adjustment are evaluated by the asynchronous motor, and the method has important significance for evaluating the inertia of the power electronic power system with the high proportion.
Description
Technical Field
The invention relates to the field of power system frequency stability, in particular to an equivalent inertia evaluation method for an asynchronous motor in an inertia response stage.
Background
In recent years, with the large investment of large-scale new energy, energy storage and direct-current transmission projects, the number and capacity of power electronic equipment of many power grids in China are rapidly increased, and the power grids are gradually evolving into power electronic power systems with high proportion. Compared with the conventional power system, the inertia of the system is insufficient, and the inertia of the load side gradually increases. The asynchronous machine is used as the main load of the power system, and the inertia of the asynchronous machine is not negligible. The existing research does not clearly analyze the frequency dynamic characteristics of the asynchronous motor from the mechanism and does not continuously evaluate the frequency supporting capability of the asynchronous motor under the inertial response time scale. The method provided by the invention is used for researching the inertia response of the asynchronous motor in the power system, evaluating the effective inertia of the asynchronous motor under the inertia time scale evaluation of the asynchronous motor and the supporting effect on the system frequency adjustment, and has important significance for the fields of the inertia evaluation of the power system and the frequency stability of the power system.
Therefore, the patent plans to establish an asynchronous motor model under electromechanical transient, deduce a transfer function of the asynchronous motor model, and analyze time-varying characteristics and influence factors of inertia of the asynchronous motor to a power grid. According to the idea of frequency supporting capacity of an inertia response stage, the frequency supporting capacity of the asynchronous motor to a system is evaluated, an evaluation model of equivalent inertia of the asynchronous motor is provided, the inertia supporting capacity of dynamic load is quantitatively embodied, and the frequency supporting capacity of the model and the dynamic characteristic of the asynchronous motor subjected to frequency disturbance are analyzed.
Disclosure of Invention
The invention provides an equivalent inertia evaluation method of an asynchronous motor in an inertia response stage, which aims to research the inertia response of the asynchronous motor in a power system and evaluate the effective inertia of the asynchronous motor under the inertia time scale and the supporting effect on system frequency adjustment. Firstly, a small-signal model of the asynchronous motor under the electromechanical transient state is established, and a transfer function related to the consumed power of the asynchronous motor and the system frequency deviation is deduced. Meanwhile, the effective inertia of the asynchronous motor to the power system is deduced, and the time-varying characteristic of inertia of the asynchronous motor to a power grid is analyzed. According to the thought of frequency supporting capacity in the inertia response stage, factors influencing the inertia frequency response of the asynchronous motor are analyzed. An equivalent inertia evaluation model of the asynchronous motor is provided, and inertia frequency supporting capacity of the dynamic load is represented quantitatively.
The invention adopts the following technical scheme for solving the technical problems:
an equivalent inertia evaluation method for an asynchronous motor in an inertia response stage. The method is characterized by comprising the following steps:
step 1: establishing a small signal model of the asynchronous motor under the electromechanical transient state;
step 2: constructing a transfer function between relevant frequency and electromagnetic power of the asynchronous motor;
and step 3: providing an equivalent inertia evaluation model of the asynchronous motor, and quantitatively embodying the frequency support capability;
further, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor are characterized in that: in the step 1, firstly, a relational expression of active power and mechanical power of an equivalent circuit under the electromechanical transient state of the asynchronous motor is solved. And solving the frequency supporting capacity of the asynchronous motor in the inertia response stage by using a small signal model, evaluating the inertia, and obtaining a frequency response transfer function and effective inertia of the response.
Further, the relation between the active power and the mechanical power of the asynchronous motor under the electromechanical transient state is characterized in that: the electromagnetic power P can be described by the equation of motion of the rotor of an asynchronous machine e And mechanical power P m The relationship between the two when power imbalance occurs. The relationship is as follows:
rotor equation:
active power:
mechanical power: p m ＝ω r k[α+(1-α)(1-s slip ) ρ ]
In the formula, H am Is the inertia constant of the asynchronous motor; omega r Is the angular velocity of the asynchronous motor rotor; delta P e Is the offset electromagnetic power of the asynchronous machine; delta P m Offset mechanical power for an asynchronous motor; r is s And x s Equivalent resistance and leakage reactance of the stator winding; r is r And x r Equivalent resistance and leakage reactance of the rotor winding; x is the number of m Mutual inductance of the stator and the rotor; s slip Is the slip ratio; k is a load factor; alpha is a constant moment part; ρ is an index relating to the mechanical characteristics of the load of the motor. In practical applications, k and ρ are time variables. In order to research the frequency supporting capacity in the inertia response process of the asynchronous motor, taking ρ ═ 2 and k ═ 1.85 as examples, a quadratic function form is adopted.
Slip ratio:
in the formula: omega is the angular velocity of the system; omega r The rotating speed of the asynchronous motor rotor.
Further, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor are characterized in that: in the step 1, when the system frequency is disturbed by a load and the variation range is small, the frequency supporting capability of the asynchronous motor in the inertia response stage is solved by using a small signal model and inertia evaluation is carried out. Carrying out linearization processing at an initial working point and converting the slip ratio s slip The variation amount of (2) is the system rotation speed omega and the asynchronous motor rotation speed omega r Is expressed by the amount of change in (c).
Slip ratio small signal model:
in the formula: omega r0 The initial value of the rotating speed of the asynchronous motor rotor is obtained; omega 0 Is the initial value of the system rotation speed.
Similarly, at the initial working point, the active power P e Is the slip ratio s for the variation amount of slip And the rotation speed omega of the asynchronous motor r Is expressed by the amount of change in (c).
Electromagnetic power small signal model: delta P e ＝f es Δs slip
Mechanical power small signal model: delta P m ＝f ms Δs slip +f mw Δω r
f ms ＝kω r0 ρ(1-α)(1-s slip0 ) ρ-1
f mw ＝k[α+(1-α)(1-s slip0 ) ρ ]
In the formula: f. of es At the initial operating point, the disturbance quantity Δ s slip Corresponding electromagnetic power Δ P e The slope value of (a); s slip0 Is the initial value of the slip ratio; f. of ms And f mw At the initial operating point, the disturbance quantity Δ s slip And Δ ω r Corresponding to the mechanical power DeltaP m The slope of (a).
At the initial operating point, the following relation can be obtained by performing linearization treatment:
2H am sΔω r ＝ΔP e -ΔP m
further, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor are characterized in that: in step 2, the input quantity Δ ω and the output quantity Δ P can be directly solved by the Meisen gain formula e The transfer function g(s).
Transfer function:
in the formula: k 1 、K 2 And K 3 Is the parameter quantity without s in the transfer function. According to the formula, the effective inertia of the asynchronous motor to the power system can be obtained in the following form:
effective inertia:
further, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor are characterized in that: in the step 3, firstly, a frequency response model of the asynchronous motor is constructed, and a response model of the load in a complex frequency domain is deduced. And solving a relational expression in a time domain by using a known deduced result and through pull type inverse transformation, and solving an equivalent inertia evaluation model of the asynchronous motor by considering the same frequency support capacity.
Further, the asynchronous motor frequency response model is characterized in that: equivalent aggregation of all generator rotor motion equations in the whole network is carried out to form a single machine model, equivalent fitting processing is carried out on a dynamic link of a prime motor-speed regulating System, the single machine model is used for representing the whole System, and a System Frequency Response (SFR) model is obtained. On the basis of an SFR model, the frequency response transfer function of the asynchronous motor is added, and the dynamic load of a certain node is equivalent to a single-machine model for analysis. An equivalent synchronous motor with the same frequency supporting capability is arranged to replace the original asynchronous motor.
Equivalent synchronous machine: g 2 (s)＝T m s
The inertia of the system:
in the formula: h g,i And S g,i Inertia time constant and capacity of the ith generator; n is the number of generators in the system; t is m The value of the equivalent inertia of the synchronous motor is equal to the finally-obtained equivalent inertia of the asynchronous motor.
When the system load fluctuates, the transfer function by the power system becomes the amount of change Δ f in frequency. Δ f passes through the synchronous motor and the asynchronous motor, and the electromagnetic power consumed by the system is as follows.
In the formula: delta f is the frequency variation of the step disturbance signal after passing through the transfer function of the power system; p ge Electromagnetic power consumed for the synchronous machine; p ae The electromagnetic power consumed by the asynchronous machine.
Further, the pull-type inverse transformation is used for solving a relational expression in a time domain, and is characterized in that: after the inverse laplace transform, the electromagnetic power of the motor after the load disturbance is specifically as follows.
Power of the synchronous motor:
asynchronous motor power:
in order to evaluate the frequency supporting capability of the inertia of the asynchronous motor, the equivalent inertia of the asynchronous motor needs to be calculated. In order to evaluate the frequency supporting capability of the inertia of the asynchronous motor, the equivalent inertia of the asynchronous motor needs to be calculated. In the inertia response time, when the synchronous motor and the asynchronous motor are disturbed by the same system frequency, the inertia of the asynchronous motor which has the same frequency support capability to the system can be equivalent to the inertia of the synchronous motor with the same characteristics.
The time domain integration is performed at the same inertia response time.
Equivalent inertia:
in the formula: t is t g Is the inertia response time.
When two motors with the same equivalent inertia are subjected to load disturbance with the same size of the system, the energy fed back by the two motors to the system is the same and the variation of the system frequency is the same before the intervention of primary frequency modulation under the inertia time scale.
Compared with the prior art, the technical scheme adopted by the paper has the following beneficial effects:
1. the invention provides a small signal model of an asynchronous motor, which is established when the system frequency is disturbed by a load and the change range is small. The model can reflect the mechanism of the asynchronous motor under the condition that the frequency has small disturbance, and provides a new idea for modeling of the asynchronous motor.
2. The invention provides an effective inertia evaluation method of an asynchronous motor, the model can effectively reflect the frequency supporting capacity of the asynchronous motor, and can effectively express the inertia time-varying characteristic of the asynchronous motor in the inertia response stage, thereby having important significance on the frequency safety of a power system.
3. The invention provides an equivalent inertia evaluation model of an asynchronous motor, which can effectively reflect the effective inertia of the asynchronous motor, can reasonably quantitatively evaluate the supporting capacity of the asynchronous motor to the system frequency, and has important significance for identifying the frequency recovery stabilization stage of a power system.
Drawings
FIG. 1 is a detailed flow chart of the method of the present invention
FIG. 2 is an equivalent circuit of an asynchronous motor in a mechanical transient state
FIG. 3 is an equivalent circuit of an asynchronous machine
FIG. 4 is a block diagram of a small signal model of an asynchronous motor
FIG. 5 is a system frequency response model considering asynchronous motor loading
FIG. 6 is a time curve of the variation of the system frequency
FIG. 7 is a time curve of the variation of the electromagnetic power of an asynchronous motor
FIG. 8 is the effective inertia curve of asynchronous motor in inertia response phase
FIG. 9 is a system frequency curve
FIG. 10 is a PSASP three-machine nine-node simulation model
FIG. 11 is a comparison of PSASP simulation and asynchronous machine frequency response model curves
FIG. 12 is a frequency plot of an asynchronous machine and a static load
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the present invention may be embodied in many different forms and should not be construed as 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 invention to those skilled in the art
The invention discloses an equivalent inertia evaluation method for an asynchronous motor in an inertia response stage. The method is characterized by comprising the following steps:
step 1: establishing a small signal model of the asynchronous motor under the electromechanical transient state;
step 2: constructing a transfer function between relevant frequency and electromagnetic power of the asynchronous motor;
and step 3: providing an equivalent inertia evaluation model of the asynchronous motor, and quantitatively embodying the frequency support capability;
further, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor are characterized in that: in the step 1, firstly, a relational expression of active power and mechanical power of an equivalent circuit under the electromechanical transient state of the asynchronous motor is solved. And solving the frequency supporting capacity of the asynchronous motor in the inertia response stage by using a small signal model, evaluating the inertia, and obtaining a frequency response transfer function and effective inertia of the response.
Further, the relation between the active power and the mechanical power under the electromechanical transient state of the asynchronous motor is characterized in that: the electromagnetic power P can be described by the equation of motion of the rotor of an asynchronous machine e And mechanical power P m The relationship between the two when power imbalance occurs. The relationship is as follows:
rotor equation:
active power:
mechanical power: p m ＝ω r k[α+(1-α)(1-s slip ) ρ ]
In the formula, H am Is the inertia constant of the asynchronous motor; omega r Is the angular velocity of the asynchronous motor rotor; delta P e Is the offset electromagnetic power of the asynchronous machine; delta P m Offset mechanical power for an asynchronous motor; r is s And x s Equivalent resistance and leakage reactance of the stator winding; r is r And x r Equivalent resistance and leakage reactance of the rotor winding; x is the number of m Mutual inductance of the stator and the rotor; s slip Is the slip ratio; k is a load factor; alpha is a constant moment part; ρ is an index relating to the mechanical characteristics of the load of the motor. In practical application, k and ρ are time variables, and in order to study the frequency support capability in the inertial response process of the asynchronous motor, ρ ═ 2 and k ═ 1.85 are taken as examples, and a quadratic function form is adopted.
Slip ratio:
in the formula: omega is the angular velocity of the system; omega r The rotating speed of the asynchronous motor rotor.
Furthermore, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor,the method is characterized in that: in the step 1, when the system frequency is disturbed by a load and the variation range is small, the frequency supporting capability of the asynchronous motor in the inertia response stage is solved by using a small signal model and inertia evaluation is carried out. Carrying out linearization processing at an initial working point and converting the slip ratio s slip The variation amount of (2) is the system rotation speed omega and the asynchronous motor rotation speed omega r Is expressed by the amount of change in (c).
Slip ratio small signal model:
in the formula: omega r0 The initial value of the rotating speed of the asynchronous motor rotor is obtained; omega 0 Is the initial value of the system rotation speed.
Similarly, at the initial working point, the active power P e Is the slip ratio s for the variation amount of slip And asynchronous motor speed omega r Is expressed by the amount of change in (c).
Electromagnetic power small signal model: delta P e ＝f es Δs slip
Mechanical power small signal model: delta P m ＝f ms Δs slip +f mw Δω r
f ms ＝kω r0 ρ(1-α)(1-s slip0 ) ρ-1
f mw ＝k[α+(1-α)(1-s slip0 ) ρ ]
In the formula: f. of es At the initial operating point, the disturbance quantity Δ s slip Corresponding electromagnetic power Δ P e The slope value of (a); s slip0 Is the initial value of the slip ratio; f. of ms And f mw At the initial operating point, the disturbance quantity Δ s slip And Δ ω r Corresponding to the mechanical power DeltaP m The slope of (a).
At the initial operating point, the following relation can be obtained by performing linearization treatment:
2H am sΔω r ＝ΔP e -ΔP m
further, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor are characterized in that: in step 2, the input quantity Δ ω and the output quantity Δ P can be directly solved by the Meisen gain formula e The transfer function g(s).
Transfer function:
in the formula: k 1 、K 2 And K 3 Is the parameter quantity without s in the transfer function. According to the formula, the effective inertia of the asynchronous motor to the power system can be obtained in the following form:
effective inertia:
further, the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor are characterized in that: in the step 3, firstly, a frequency response model of the asynchronous motor is constructed, and a response model of the load in a complex frequency domain is deduced. And solving a relational expression in a time domain by using a known deduced result and through pull type inverse transformation, and solving an equivalent inertia evaluation model of the asynchronous motor by considering the same frequency support capacity.
Further, the asynchronous motor frequency response model is characterized in that: equivalent aggregation of all generator rotor motion equations in the whole network is carried out to form a single machine model, equivalent fitting processing is carried out on a dynamic link of a prime motor-speed regulating System, the single machine model is used for representing the whole System, and a System Frequency Response (SFR) model is obtained. On the basis of an SFR model, the frequency response transfer function of the asynchronous motor is added, and the dynamic load of a certain node is equivalent to a single machine model for analysis. An equivalent synchronous motor with the same frequency supporting capability is arranged to replace the original asynchronous motor.
Equivalent synchronous machine: g 2 (s)＝T m s
The inertia of the system:
in the formula: h g,i And S g,i Inertia time constant and capacity of the ith generator; n is the number of generators in the system; t is m The value of the equivalent inertia of the synchronous motor is equal to the finally-obtained equivalent inertia of the asynchronous motor.
When the system load fluctuates, the transfer function by the power system becomes the amount of change Δ f in frequency. Δ f passes through the synchronous motor and the asynchronous motor, and the electromagnetic power consumed by the system is as follows.
In the formula: delta f is the frequency variation of the step disturbance signal after passing through the transfer function of the power system; p ge Electromagnetic power consumed for the synchronous machine; p ae The electromagnetic power consumed by the asynchronous machine.
Further, the pull-type inverse transformation is used for solving a relational expression in a time domain, and is characterized in that: after the inverse laplace transform, the electromagnetic power of the motor after the load disturbance is specifically as follows.
Power of the synchronous motor:
asynchronous motor power:
in order to evaluate the frequency supporting capability of the inertia of the asynchronous motor, the equivalent inertia of the asynchronous motor needs to be calculated. In order to evaluate the frequency supporting capability of the inertia of the asynchronous motor, the equivalent inertia of the asynchronous motor needs to be calculated. In the inertia response time, when the synchronous motor and the asynchronous motor are disturbed by the same system frequency, the inertia of the asynchronous motor which has the same frequency support capability to the system can be equivalent to the inertia of the synchronous motor with the same characteristics.
The time domain integration is performed at the same inertia response time.
Equivalent inertia:
in the formula: t is t g Is the inertia response time.
When two motors with the same equivalent inertia are subjected to load disturbance with the same size of the system, the energy fed back by the two motors to the system is the same and the variation of the system frequency is the same before the intervention of primary frequency modulation under the inertia time scale.
Example of the implementation
On an MATLAB/Simulink simulation platform, a system frequency model as shown in FIG. 3 is established, and in order to verify the effective inertia of the asynchronous motor and the change of the asynchronous motor after system frequency disturbance, the asynchronous motor needs to be connected into an equivalent power system. The parameters of the asynchronous motor are detailed in table 1 below. For convenience of calculation, all parameters of the model adopt per unit values. Meanwhile, in order to verify the frequency response curve of the actual power system, the frequency supporting capability of the asynchronous motor provided in the text is verified based on the WSCC9V7 model of the PSASP simulation platform.
TABLE 1 asynchronous machine parameters
Working condition 1: inertia verification and analysis
According to the above mentioned, M is 6.02s and D is 0.8 in the system model. In order to verify the frequency response process of the asynchronous motor, the system does not apply primary frequency modulation measures. The output quantity is the variation delta f of frequency and the variation delta P of asynchronous motor power e In steady state, Δ f should be 0 and Δ P e ＝0。
Simulation experiment, at the time of 10s, a step signal delta P is applied to the system fh 0.005p.u. By monitoring the variation delta f of the system frequency and the electromagnetic power deviation delta P of the asynchronous motor e To detect the effect of the asynchronous motor on the system frequency support. The results are shown in FIGS. 6 and 7.
Based on the above experiment, fig. 7 shows that when the system load increases and there is no external newly-connected power supply and no power supply added output, the system frequency decreases, and finally the system frequency stabilizes at 49.896 Hz. As can be seen from the graph of fig. 7, as the system frequency decreases, the electromagnetic power of the asynchronous motor decreases. Further, the system frequency is reduced, the electromagnetic power of the asynchronous motor is reduced, the load of the generator is reduced, the inertial response is provided for the system, and the adjustment of the system frequency is supported.
When the system has active power unbalance disturbance, each generator set instantaneously shares disturbance power according to inertia, and primary frequency modulation is carried out after 3s generallyAlready intervene, taking the inertia response time t in the text g Is 3 s. In the inertia response phase, the effective inertia of the asynchronous machine is shown in fig. 8. As can be seen from the image, the slip of the system responds first and the effective inertia is smaller as the frequency of the system decreases. Thereafter the kinetic energy stored on the rotor of the asynchronous machine is gradually released and the effective inertia of the asynchronous machine is gradually increased.
Working condition 2: equivalent inertia assessment
Based on the system parameters, the equivalent inertia T of the asynchronous motor can be deduced m Is 3.6204. The derivation calculation proves that the inertia of the asynchronous motor to the system is different from the inertia of the asynchronous motor. At time 0s, add a Δ P to the system fh Disturbance amount of 0.003p.u., observed at inertia response time t g 3s system frequency change.
As can be seen from the graph of fig. 9, the actual frequency variation curve of the asynchronous motor has the same trend as the frequency variation curve based on the synchronous motor with the equivalent inertia of the asynchronous motor. And the frequency variation is consistent under the same inertia time, at t g At 3s, the frequency change Δ f is 0.038 Hz. And the simulation result verifies the effectiveness of the equivalent inertia evaluation model.
Working condition 3: verification of complex examples
In order to verify the accuracy of the inertia response curve obtained in the simulation model, an example simulation system is built based on PSASP, and a five-order model is adopted for the generator. The asynchronous motor parameters adopt the data in table 1, and the total inertia of the three-motor system is calculated to obtain that M is 6.02. In steady state conditions, the system Δ f is 0 and Δ P e 0. At time t equal to 0, a Δ P is applied to the system load bus M1 e Observe the system load node M2 and M3 bus frequency changes as a disturbance of 0.02p.u. In order to verify the frequency response process of the asynchronous motor, the system does not apply primary frequency modulation measures.
Figure 11 compares the frequency curve of the PSASP system with the frequency curve obtained from the asynchronous machine frequency response model constructed above. It can be seen that the two model curve waveforms are substantially consistent with the frequency steady state deviation, and the accuracy of the model provided above is verified.
TABLE 2 points of the load frequency curves nadir
The loads carried by the power system of fig. 12 are static loads and asynchronous motor loads having the same power. Compared with the experiment, in order to better accord with the actual design, the system is additionally provided with a speed regulator, a voltage regulator and PSS equipment, and delta P is applied e 0.05p.u. of perturbation. As can be seen from the curves in table 2 and fig. 12, the asynchronous motor with inertia can more effectively prevent the frequency change, the nadir point of the system frequency curve is more backward, and the frequency change amount of the power system is significantly smaller than the static load, so that the system frequency change can be effectively prevented, and the power system frequency can be supported. Also due to the effect of inertia to resist frequency changes, system frequency recovery is slower than static load recovery without inertia.
The above embodiments are merely illustrative of the technical ideas of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like based on the technical ideas of the present invention should be included in the scope of the present invention.
Claims (8)
1. An equivalent inertia evaluation method for an asynchronous motor in an inertia response stage is characterized by comprising the following steps:
step 1: establishing a small signal model of the asynchronous motor under the electromechanical transient state;
step 2: constructing a transfer function between relevant frequency and electromagnetic power of the asynchronous motor;
and step 3: and providing an equivalent inertia evaluation model of the asynchronous motor, and quantitatively embodying the frequency support capability.
2. The effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor according to claim 1, wherein: in the step 1, firstly, a relation between active power and mechanical power of an equivalent circuit under the electromechanical transient state of the asynchronous motor is solved; and solving the frequency supporting capacity of the asynchronous motor in the inertia response stage by using a small signal model, evaluating the inertia, and obtaining a frequency response transfer function and effective inertia of the response.
3. The relation between active power and mechanical power in the electromechanical transient state of the asynchronous machine according to claim 2, characterized in that: the electromagnetic power P can be described by the equation of motion of the rotor of an asynchronous machine e And mechanical power P m The relationship between the two when power imbalance occurs is as follows:
rotor equation:
active power:
mechanical power: p m ＝ω r k[α+(1-α)(1-s slip ) ρ ]
In the formula, H am Is the inertia constant of the asynchronous motor; omega r Is the angular velocity of the asynchronous motor rotor; delta P e Is the offset electromagnetic power of the asynchronous machine; delta P m Offset mechanical power for an asynchronous motor; r is s And x s Equivalent resistance and leakage reactance of the stator winding; r is r And x r Equivalent resistance and leakage reactance of the rotor winding; x is the number of m Mutual inductance of the stator and the rotor; s slip Is the slip ratio; k is a load factor; alpha is a constant moment part; ρ is the index of the mechanical characteristic of the motor load, and in practical application, k and ρ are time variables
Slip ratio:
in the formula: omega is the angular velocity of the system; omega r The rotating speed of the asynchronous motor rotor.
4. The effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor according to claim 1, wherein: in the step 1, when the system frequency is disturbed by a load and has a small change range, the frequency supporting capacity of the asynchronous motor in the inertial response stage is solved by using a small signal model and inertia evaluation is carried out; carrying out linearization processing at an initial working point and converting the slip ratio s slip The variation amount of (2) is the system rotation speed omega and the asynchronous motor rotation speed omega r Is represented by a variation of (a);
slip ratio small signal model:
in the formula: omega r0 The initial value of the rotating speed of the asynchronous motor rotor is obtained; omega 0 The initial value of the system rotating speed is obtained;
similarly, at the initial working point, the active power P e Is the slip ratio s for the variation amount of slip And asynchronous motor speed omega r Is represented by a variation of (a);
electromagnetic power small signal model: delta P e ＝f es Δs slip
Mechanical power small signal model: delta P m ＝f ms Δs slip +f mw Δω r
f ms ＝kω r0 ρ(1-α)(1-s slip0 ) ρ-1
f mw ＝k[α+(1-α)(1-s slip0 ) ρ ]
In the formula: f. of es To be at the initial operating point, the disturbance quantity Δ s slip Corresponding electromagnetic power Δ P e The slope value of (a); s slip0 Is the initial value of the slip ratio; f. of ms And f mw At the initial operating point, the disturbance quantity Δ s slip And Δ ω r Corresponding to the mechanical power DeltaP m The slope of (a);
at the initial operating point, the following relation can be obtained by performing linearization treatment:
2H am sΔω r ＝ΔP e -ΔP m 。
5. the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor according to claim 1, wherein: in step 2, the input quantity Δ ω and the output quantity Δ P can be directly solved by the Meisen gain formula e The transfer function G(s);
transfer function:
in the formula: k 1 、K 2 And K 3 The parameter quantity of the transfer function without s is obtained; according to the formula, the effective inertia of the asynchronous motor to the power system can be obtained in the following form:
effective inertia:
6. the effective inertia analysis method and the equivalent inertia evaluation model of the asynchronous motor according to claim 1, wherein: in the step 3, firstly, an asynchronous motor frequency response model is constructed, and a response model of the load in a complex frequency domain is deduced; and solving a relational expression in a time domain by using a known deduced result and through pull type inverse transformation, and solving an equivalent inertia evaluation model of the asynchronous motor by considering the same frequency support capacity.
7. The asynchronous machine frequency response model of claim 6, wherein: equivalently aggregating all generator rotor motion equations in the whole network into a single machine model, simultaneously carrying out equivalent fitting treatment on a dynamic link of a prime motor-speed regulating System, and expressing the whole System by using the single machine model to obtain a System Frequency Response model (SFR); on the basis of an SFR model, a frequency response transfer function of an asynchronous motor is added, and the dynamic load equivalence of a certain node is taken as a single machine model for analysis; an equivalent synchronous motor with the same frequency supporting capacity is arranged to replace the original asynchronous motor;
equivalent synchronous machine: g 2 (s)＝T m s
The inertia of the system:
in the formula: h g,i And S g,i Inertia time constant and capacity of the ith generator; n is the number of generators in the system; t is m The equivalent inertia of the synchronous motor is equal to the finally obtained equivalent inertia of the asynchronous motor;
when the system load fluctuates, the transfer function of the power system is changed into the variable quantity delta f of the frequency, the delta f passes through the synchronous motor and the asynchronous motor, and the electromagnetic power consumed by the system is respectively as follows;
in the formula: delta f is the frequency variation of the step disturbance signal after passing through the transfer function of the power system; p ge Electromagnetic power consumed for the synchronous machine; p ae The electromagnetic power consumed by the asynchronous machine.
8. The inverse pull-type transform of claim 6, to solve the relation in time domain, wherein: after the laplace inverse transformation, the electromagnetic power of the motor after the load disturbance is specifically as follows;
power of the synchronous motor:
asynchronous motor power:
in order to evaluate the frequency supporting capacity of the inertia of the asynchronous motor, the equivalent inertia of the asynchronous motor needs to be solved; in order to evaluate the frequency supporting capacity of the inertia of the asynchronous motor, the equivalent inertia of the asynchronous motor needs to be solved; in the inertia response time, when the synchronous motor and the asynchronous motor are disturbed by the same system frequency, the inertia of the asynchronous motor with the same frequency support capability to the system can be equivalent to the inertia of the synchronous motor with the same characteristic;
and under the same inertia response time, the time domain integration is carried out,
equivalent inertia:
in the formula: t is t g Inertia response time;
when two motors with the same equivalent inertia are subjected to load disturbance of the same size of the system, the energy fed back by the two motors to the system is the same and the variation of the system frequency is the same before the intervention of primary frequency modulation under the inertia time scale.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116191478A (en) * | 2023-04-23 | 2023-05-30 | 国网山西省电力公司电力科学研究院 | Equivalent inertia evaluation and frequency response modeling method for multiple asynchronous motors |
| CN117175656A (en) * | 2023-08-30 | 2023-12-05 | 国网吉林省电力有限公司经济技术研究院 | Supporting capability assessment method for novel grid-structured energy storage lifting power system |
| CN117175656B (en) * | 2023-08-30 | 2024-05-10 | 国网吉林省电力有限公司经济技术研究院 | Supporting capability assessment method for novel grid-structured energy storage lifting power system |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116191478A (en) * | 2023-04-23 | 2023-05-30 | 国网山西省电力公司电力科学研究院 | Equivalent inertia evaluation and frequency response modeling method for multiple asynchronous motors |
| CN117175656A (en) * | 2023-08-30 | 2023-12-05 | 国网吉林省电力有限公司经济技术研究院 | Supporting capability assessment method for novel grid-structured energy storage lifting power system |
| CN117175656B (en) * | 2023-08-30 | 2024-05-10 | 国网吉林省电力有限公司经济技术研究院 | Supporting capability assessment method for novel grid-structured energy storage lifting power system |
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