CN117639123A - Virtual synchronous machine active power control method and device for network-structured converter - Google Patents
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Abstract
The invention discloses a virtual synchronous machine active power control method and device for a grid-connected converter, which are used for triggering an integrator when the output power and the angular frequency of the virtual synchronous machine meet certain conditions, so that the damping power is adjusted to zero in a steady state, and the contradiction problem between dynamic power oscillation and steady state power deviation existing in the conventional grid-connected converter virtual synchronous machine active power control is solved. According to the invention, the integrator is dynamically triggered according to the error between the angular frequency output by the virtual synchronous machine and the set angular frequency and the error relation between the active power output by the virtual synchronous machine and the set active power and the first power deviation, so that the damping power is dynamically adjusted to be slowly reduced to zero in a steady state, the damping power can be adjusted to zero in the steady state on the premise that the damping coefficient is not zero, the steady-state active power deviation is eliminated, and the active power control precision of the virtual synchronous machine of the grid-structured converter is improved.
Description
Technical Field
The invention relates to the technical field of new energy grid-connected power generation, in particular to a virtual synchronous machine active power control method and device for a grid-built converter.
Background
In order to enhance the adaptability and the supporting capability of the new energy grid-connected inverter to the power grid, in recent years, the grid-connected inverter and the control technology thereof are widely focused and studied. The virtual synchronous machine technology is a typical novel control strategy capable of realizing the operation of the new energy grid-connected inverter in a grid-formation mode, and can realize off-grid operation and grid-connected operation. Meanwhile, by introducing virtual inertia and damping, the virtual synchronous machine control technology can enable the new energy grid-connected inverter to simulate the characteristics of the synchronous generator, and the running stability of the new energy grid-connected inverter is enhanced. However, due to introduction of inertia and damping, the existing virtual synchronous machine often has power oscillation and overshoot when the active power reference value is suddenly changed, and the dynamic performance is poor. In addition, when the power grid frequency is offset, the virtual synchronous machine actively adjusts the output active power to support the power grid frequency offset. However, the introduction of the damping coefficient increases the steady-state deviation of the active power at the time of the grid frequency offset, reducing the control accuracy.
The invention patent' Yan Xiangwu, wang Desheng, wang Yuwei and the like.A self-adaptive control [ P ] of inertia parameters of a virtual synchronous machine under the condition of large disturbance, beijing: CN108494002A, 2018-09-04, provides a self-adaptive control method of the inertia parameters of the virtual synchronous machine under the condition of large disturbance, and active power oscillation during transient state is remarkably reduced through inertia self-adaption.
The invention patent Zhang Xing, chen Saiyu, witch space navigation and the like provides a virtual inertia sectional self-adaption design method based on a sectional self-adaption virtual inertia virtual synchronous machine frequency adjustment method [ P ]. Anhui province, CN114914912A, 2022-08-16, and improves frequency dynamic characteristics when a power grid frequency is shifted.
The invention patent Wang Junhai, yang, yin Jianbing and the like provides a self-adaptive inertia optical storage virtual synchronous generator control method and device [ P ]. Thunberg river province: CN116780640A, 2023-09-19.
Although the above document can reduce the oscillation and overshoot of power and frequency, the problem of steady-state deviation of active power when the grid frequency is shifted is not considered.
The patent documents Dan Rongliang, wang, huang Ji and the like disclose a grid-connected damping characteristic analysis and improvement strategy [ J ] of an energy storage virtual synchronous machine, solar report 2023,44 (07): 30-38 ], and a transient damping improvement strategy based on active power differential feedback. The method can simultaneously realize dynamic active power oscillation suppression and steady-state active power deviation elimination. However, this approach requires the use of differential algorithms, which can amplify the effects of noise and, in severe cases, reduce the stability of the system.
The invention discloses an active power control method and device (application number: 2024100328170) of a grid-structured converter virtual synchronous generator, which introduces a proportional-integral controller to adjust damping power. The method mainly has the following two disadvantages:
1. the introduced proportional-integral controller contains two parameters to be designed, namely a proportional coefficient and an integral coefficient. Therefore, if a better control effect is obtained, the proportional coefficient and the integral coefficient need to be designed and selected reasonably at the same time. This increases the design and debugging complexity of the system.
2. The introduced proportional-integral controller can adjust damping power in real time, and the introduced proportional-integral controller and the grid-structured converter virtually synchronize the damping of the generator control per se in the dynamic processes of steady state and active power mutation and grid frequency mutationCoefficients ofDMutual coupling and mutual influence have certain influence on the stable operation of the system.
According to the analysis, the problems of dynamic oscillation, overshoot and static difference of active power of the virtual synchronous machine of the traditional grid-structured converter can be solved in the prior art, but most algorithms mainly focus on dynamic power oscillation and frequency oscillation suppression, and the problem of steady-state deviation of the active power when the frequency of a power grid is offset is not fully considered. Although some documents consider the problems of dynamic active power oscillation suppression and steady-state active power deviation elimination at the same time, the method has the problems of needing to introduce differential operation, easily causing unstable system, needing to design a plurality of controller parameters and the like.
Disclosure of Invention
The invention discloses a virtual synchronous machine active power control method and device for a grid-built converter, aiming at solving the contradiction problem that the active power control dynamic state of the conventional grid-built converter has oscillation and the steady state has power deviation.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a virtual synchronous machine active power control method for a network-structured converter comprises the following steps:
step 1, setting rated angular frequency omega of a power grid 0 The angular frequency omega outputted by the virtual synchronous machine control strategy of the grid-structured converter is differenced and multiplied by a droop coefficient k ω Obtaining a first power deviationThe method comprises the following steps:
wherein,rated for the angular frequency omega of the power grid 0 The difference value of the rated angular frequency omega of the power grid and the angular frequency omega output by the virtual synchronous machine 0 100 pi rad/s;
step 2,Virtual synchronous machine active power reference value P to be set ref Deviation from the first power obtained in step 1Adding and subtracting the active power P output by the virtual synchronous machine e Obtaining a second power deviation->The method comprises the following steps:
step 3, the second power deviation obtained in the step 2Subtracting the damping power P D And performing an integration operation according to the following formula to obtain a first frequency deviation +.>The method comprises the following steps:
wherein s represents a Laplase operator, and J represents virtual inertia of the virtual synchronous machine; damping power P D According to the first frequency deviationAnd a second frequency deviation->Acquisition, second frequency deviation->According to damping power P D And an integration coefficient of the integrator is obtained;
step 4, obtaining the first frequency deviation in the step 3Rated with a set power gridAngular frequency omega 0 Adding to obtain the angular frequency omega output by the virtual synchronous machine, wherein the angular frequency omega satisfies the following conditions:
step 5, subtracting the actual angular frequency omega of the power grid from the angular frequency omega of the virtual synchronous machine output obtained in the step 4 g Then, integral operation is carried out to obtain a power angle delta output by the virtual synchronous machine, and the power angle delta satisfies the following conditions:
。
further, the virtual synchronous machine in step 2 outputs active power P e The calculation formula of (2) satisfies the following:
wherein,u is the amplitude of the voltage of the power grid, E is the amplitude of the output voltage of the virtual synchronous machine, and X is the equivalent line impedance of the power grid.
Further, the damping power P in step 3 D The following formula is adopted for calculation:
wherein D is a virtual damping coefficient of the virtual synchronous machine,is the second frequency deviation.
Further, the second frequency deviationThe calculation method of (2) is as follows:
when (when)When the integrator output switch S is closed, the second frequency deviation +.>The calculation method of (1) satisfies the following conditions:
wherein k is i Is an integral coefficient;
when (when)At this time, the integrator output switch S is turned off, and at this time, the second frequency deviation +.>Zero.
A virtual synchronous machine active power control device for a grid-tied converter, comprising:
a first power deviation calculation module for setting rated angular frequency omega of the power grid 0 The angular frequency omega outputted by the virtual synchronous machine control strategy of the grid-structured converter is differenced and multiplied by a droop coefficient k ω Obtaining a first power deviationThe method comprises the following steps:
wherein,rated for the angular frequency omega of the power grid 0 The difference value of the rated angular frequency omega of the power grid and the angular frequency omega output by the virtual synchronous machine 0 100 pi rad/s;
a second power deviation calculation module for setting the virtual synchronous machine active power reference value P ref Deviation from the first power obtained in step 1Adding and subtracting the active power P output by the virtual synchronous machine e Obtaining a second power deviationThe method comprises the following steps:
a first frequency deviation calculation module for calculating a second power deviationSubtracting the damping power P D And performing an integration operation according to the following formula to obtain a first frequency deviation +.>The method comprises the following steps:
wherein s represents a Laplase operator, and J represents virtual inertia of the virtual synchronous machine; damping power P D According to the first frequency deviationAnd a second frequency deviation->Acquisition, second frequency deviation->According to damping power P D And an integration coefficient of the integrator is obtained;
an angular frequency calculation module for calculating a first frequency deviationWith a set rated angular frequency omega of the power grid 0 Adding to obtain the angular frequency omega output by the virtual synchronous machine, wherein the angular frequency omega satisfies the following conditions:
the power angle calculation module is used for subtracting the actual angular frequency omega of the power grid from the angular frequency omega output by the virtual synchronous machine g Then, integral operation is carried out to obtain a power angle delta output by the virtual synchronous machine, and the power angle delta satisfies the following conditions:
。
further, the active power P output by the virtual synchronous machine e The calculation formula of (2) satisfies the following:
wherein,u is the amplitude of the voltage of the power grid, E is the amplitude of the output voltage of the virtual synchronous machine, and X is the equivalent line impedance of the power grid.
Further, damping power P D The following formula is adopted for calculation:
wherein D is a virtual damping coefficient of the virtual synchronous machine,is the second frequency deviation.
Further, the second frequency deviationThe calculation method of (2) is as follows:
when (when)When the integrator output switch S is closed, the second frequency deviation +.>The calculation method of (1) satisfies the following conditions:
wherein k is i Is an integral coefficient;
when (when)At this time, the integrator output switch S is turned off, and at this time, the second frequency deviation +.>Zero.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention has only one parameter to be designed, namely the integral coefficient of the trigger integratork i So long as it reasonably selectsk i The improved control strategy of the virtual synchronous machine of the grid-structured converter can simultaneously realize dynamic active power oscillation suppression and steady-state active power deviation elimination, and the design and debugging complexity of the system are simplified.
2. The invention triggers the integrator action only when certain conditions are met in the dynamic process. In steady state, the second frequency deviation of the introduced integrator output is 0, i.e. the introduced integrator is not functional in steady state. At this time, the working mode of the virtual synchronous generator is the same as that of the conventional method, and the system is ensured to have higher stability.
3. The invention does not need differential operation, does not amplify system noise and has better stability.
Drawings
FIG. 1 is a block diagram of active power control of a conventional networked converter virtual synchronous machine;
FIG. 2 is a control block diagram of a virtual synchronous machine active power control method for a grid-tied converter according to an embodiment of the present invention;
fig. 3 is a comparison simulation result of active power control of a conventional virtual synchronous machine and a network-structured transformer virtual synchronous machine according to the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 2, an embodiment of the present invention provides a virtual synchronous machine active power control method for a grid-connected converter, including the following steps:
step 1, setting rated angular frequency omega of a power grid 0 The angular frequency omega outputted by the virtual synchronous machine control strategy of the grid-structured converter is differenced and multiplied by a droop coefficient k ω Obtaining a first power deviationThe method comprises the following steps:
wherein,rated for the angular frequency omega of the power grid 0 The difference value of the rated angular frequency omega of the power grid and the angular frequency omega output by the virtual synchronous machine 0 100 pi rad/s;
step 2, setting an active power reference value P of the virtual synchronous machine ref Deviation from the first power obtained in step 1Adding and subtracting the active power P output by the virtual synchronous machine e Obtaining a second power deviation->The method comprises the following steps:
wherein, the active power P output by the virtual synchronous machine e The calculation formula of (2) satisfies the following:
wherein,u is the amplitude of the voltage of the power grid, E is the amplitude of the output voltage of the virtual synchronous machine, and X is the equivalent line impedance of the power grid.
Step 3, the second power deviation obtained in the step 2Subtracting the damping power P D And performing an integration operation according to the following formula to obtain a first frequency deviation +.>The method comprises the following steps:
wherein s represents a Laplase operator, and J represents virtual inertia of the virtual synchronous machine;
wherein the damping power P D The following formula is adopted for calculation:
wherein D is a virtual damping coefficient of the virtual synchronous machine,is the second frequency deviation.
Wherein the second frequency deviationThe calculation method of (2) is as follows:
when (when)When the integrator output switch S is closed, the second frequency deviation +.>The calculation method of (1) satisfies the following conditions:
wherein k is i Is an integral coefficient;
when (when)At this time, the integrator output switch S is turned off, and at this time, the second frequency deviation +.>Zero.
Step 4, obtaining the first frequency deviation in the step 3With a set rated angular frequency omega of the power grid 0 Adding to obtain the angular frequency omega output by the virtual synchronous machine, wherein the angular frequency omega satisfies the following conditions:
step 5, subtracting the actual angular frequency omega of the power grid from the angular frequency omega of the virtual synchronous machine output obtained in the step 4 g Then, integral operation is carried out to obtain a power angle delta output by the virtual synchronous machine, and the power angle delta satisfies the following conditions:
。
the embodiment of the invention also provides a virtual synchronous machine active power control device for the grid-connected converter, which comprises:
first power biasThe difference calculation module is used for setting rated angular frequency omega of the power grid 0 The angular frequency omega outputted by the virtual synchronous machine control strategy of the grid-structured converter is differenced and multiplied by a droop coefficient k ω Obtaining a first power deviationThe method comprises the following steps:
wherein,rated for the angular frequency omega of the power grid 0 The difference value of the rated angular frequency omega of the power grid and the angular frequency omega output by the virtual synchronous machine 0 100 pi rad/s;
a second power deviation calculation module for setting the virtual synchronous machine active power reference value P ref Deviation from the first powerAdding and subtracting the active power P output by the virtual synchronous machine e Obtaining a second power deviation->The method comprises the following steps:
wherein the active power P output by the virtual synchronous machine e The calculation formula of (2) satisfies the following:
wherein,u is the amplitude of the voltage of the power grid, E is the amplitude of the output voltage of the virtual synchronous machine, and X is the equivalent line impedance of the power grid.
A first frequency deviation calculation module for calculating a second power deviationSubtracting the damping power P D And performing an integration operation according to the following formula to obtain a first frequency deviation +.>The method comprises the following steps:
wherein s represents a Laplase operator, and J represents virtual inertia of the virtual synchronous machine; damping power P D According to the first frequency deviationAnd a second frequency deviation->Acquisition, second frequency deviation->According to damping power P D And an integration coefficient of the integrator is obtained;
damping power P D The following formula is adopted for calculation:
wherein D is a virtual damping coefficient of the virtual synchronous machine,is the second frequency deviation.
Second frequency deviationThe calculation method of (2) is as follows:
when (when)At the time, the integrator output endSwitch S is closed, at this time, second frequency deviation +.>The calculation method of (1) satisfies the following conditions:
wherein k is i Is an integral coefficient;
when (when)At this time, the integrator output switch S is turned off, and at this time, the second frequency deviation +.>Zero.
An angular frequency calculation module for calculating a first frequency deviationWith a set rated angular frequency omega of the power grid 0 Adding to obtain the angular frequency omega output by the virtual synchronous machine, wherein the angular frequency omega satisfies the following conditions:
the power angle calculation module is used for subtracting the actual angular frequency omega of the power grid from the angular frequency omega output by the virtual synchronous machine g Then, integral operation is carried out to obtain a power angle delta output by the virtual synchronous machine, and the power angle delta satisfies the following conditions:
。
in order to verify the effectiveness of the method provided by the invention, a comparison simulation study is carried out with a conventional active power control strategy (shown in figure 1) of a virtual synchronous machine of a network-structured converter. During simulation, active power reference value P ref 5kW before 2s, P at 2s ref Sudden increase from 5kW to 10kW, P at 4s ref From 10kW to 5kW, the actual angular frequency omega of the power grid at 6s g The burst was reduced from 100 pi rad/s (50 Hz) to 99.8 pi rad/s (49.9 Hz). Virtual inertia J of 0.5kg/m 2 Rated angular frequency omega of power grid 0 100 pi rad/s, sag factor k ω 2000, the peak value of the grid phase voltage is 311V, and the virtual synchronous machine outputs a voltage peak value 311. The line resistance of the power grid is 0.2 omega, and the line inductance is 20mH.
Fig. 3 shows the active power control comparison simulation results of the conventional grid-structured converter virtual synchronous machine and the grid-structured converter virtual synchronous machine provided by the invention. During simulation, the virtual damping coefficient D of the conventional virtual synchronous machine active power control method is respectively 0Ws/rad and 10Ws/rad. The virtual damping coefficient of the method is set to 10Ws/rad, and the integral coefficient k i 0.01.
As can be seen from fig. 3, when the virtual damping coefficient D is zero, the active power output by the conventional virtual synchronous machine control strategy has obvious oscillation and overshoot. When the virtual damping coefficient D is increased to 10, the oscillation is obviously inhibited. However, as can be seen from fig. 3, the increase of the virtual damping coefficient also causes a significant increase in the steady-state deviation of the active power when the grid frequency deviates (after 6 s). Therefore, the conventional active power control strategy of the virtual synchronous machine cannot realize active power dynamic oscillation suppression and steady-state static difference elimination simultaneously by adjusting the virtual damping coefficient. However, as can be seen from fig. 3, the virtual damping coefficient D increases to 10, and when the method provided by the invention is adopted, not only the active power oscillation is suppressed, but also the steady-state deviation of the active power approaches zero under the action of the designed trigger integral algorithm when the power grid frequency deviates (after 6 s). Therefore, the method provided by the invention can simultaneously realize active power dynamic oscillation suppression and steady-state static difference elimination by adjusting the virtual damping coefficient D and the integral coefficient of the introduced integrator. This demonstrates the effectiveness of the proposed method.
According to the error between the angular frequency output by the virtual synchronous machine and the set angular frequency and the error relation between the active power output by the virtual synchronous machine and the set active power and the first power deviation, the integrator is dynamically triggered, so that the damping power is dynamically adjusted to be slowly reduced to zero in a steady state, the damping power can be adjusted to zero in the steady state on the premise that the damping coefficient is not zero, the steady-state active power deviation is eliminated, and the active power control precision of the virtual synchronous machine is improved.
Different from the conventional method, the invention introduces a trigger integral algorithm, and when certain conditions are met, the action of an integrator is triggered, so that the damping power is adjusted to zero in a steady state, and the steady state power static difference is eliminated. Therefore, the improved active power control strategy of the virtual synchronous machine of the grid-structured converter has inertia and damping characteristics and no power steady-state error.
The foregoing is merely illustrative embodiments of the present invention, and the present invention is not limited thereto, and any changes or substitutions that may be easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (8)
1. The virtual synchronous machine active power control method for the grid-connected converter is characterized by comprising the following steps of:
step 1, setting rated angular frequency omega of a power grid 0 The angular frequency omega outputted by the virtual synchronous machine control strategy of the grid-structured converter is differenced and multiplied by a droop coefficient k ω Obtaining a first power deviationThe method comprises the following steps:
wherein,rated for the angular frequency omega of the power grid 0 The difference value of the rated angular frequency omega of the power grid and the angular frequency omega output by the virtual synchronous machine 0 100 pi rad/s;
step 2,Virtual synchronous machine active power reference value P to be set ref Deviation from the first power obtained in step 1Adding and subtracting the active power P output by the virtual synchronous machine e Obtaining a second power deviation->The method comprises the following steps:
step 3, the second power deviation obtained in the step 2Subtracting the damping power P D And performing an integration operation according to the following formula to obtain a first frequency deviation +.>The method comprises the following steps:
wherein s represents a Laplase operator, and J represents virtual inertia of the virtual synchronous machine; damping power P D According to the first frequency deviationAnd a second frequency deviation->Acquisition, second frequency deviation->According to damping power P D And an integration coefficient of the integrator is obtained;
step 4, obtaining the third step 3A frequency deviationWith a set rated angular frequency omega of the power grid 0 Adding to obtain the angular frequency omega output by the virtual synchronous machine, wherein the angular frequency omega satisfies the following conditions:
step 5, subtracting the actual angular frequency omega of the power grid from the angular frequency omega of the virtual synchronous machine output obtained in the step 4 g Then, integral operation is carried out to obtain a power angle delta output by the virtual synchronous machine, and the power angle delta satisfies the following conditions:
。
2. the method for controlling active power of virtual synchronous machine for network-structured converter as claimed in claim 1, wherein the active power P outputted by the virtual synchronous machine in step 2 e The calculation formula of (2) satisfies the following:
wherein,u is the amplitude of the voltage of the power grid, E is the amplitude of the output voltage of the virtual synchronous machine, and X is the equivalent line impedance of the power grid.
3. The method for active power control of a virtual synchronous machine for a grid-tied converter of claim 1, wherein the damping power P in step 3 D The following formula is adopted for calculation:
wherein D is a virtual damping coefficient of the virtual synchronous machine,is the second frequency deviation.
4. A virtual synchronous machine active power control method for a grid-tied converter as defined in claim 3, wherein the second frequency deviationThe calculation method of (2) is as follows:
when (when)When the integrator output switch S is closed, the second frequency deviation +.>The calculation method of (1) satisfies the following conditions:
wherein k is i Is an integral coefficient;
when (when)At this time, the integrator output switch S is turned off, and at this time, the second frequency deviation +.>Zero.
5. A virtual synchronous machine active power control device for a grid-tied converter, comprising:
a first power deviation calculation module for setting rated angular frequency omega of the power grid 0 Virtual synchronization with a grid-tied converterThe angular frequency omega outputted by the machine control strategy is differenced and multiplied by a droop coefficient k ω Obtaining a first power deviationThe method comprises the following steps:
wherein,rated for the angular frequency omega of the power grid 0 The difference value of the rated angular frequency omega of the power grid and the angular frequency omega output by the virtual synchronous machine 0 100 pi rad/s;
a second power deviation calculation module for setting the virtual synchronous machine active power reference value P ref Deviation from the first power obtained in step 1Adding and subtracting the active power P output by the virtual synchronous machine e Obtaining a second power deviation->The method comprises the following steps:
a first frequency deviation calculation module for calculating a second power deviationSubtracting the damping power P D And performing an integration operation according to the following formula to obtain a first frequency deviation +.>The method comprises the following steps:
wherein s represents a Laplase operator, and J represents virtual inertia of the virtual synchronous machine; damping power P D According to the first frequency deviationAnd a second frequency deviation->Acquisition, second frequency deviation->According to damping power P D And an integration coefficient of the integrator is obtained;
an angular frequency calculation module for calculating a first frequency deviationWith a set rated angular frequency omega of the power grid 0 Adding to obtain the angular frequency omega output by the virtual synchronous machine, wherein the angular frequency omega satisfies the following conditions:
the power angle calculation module is used for subtracting the actual angular frequency omega of the power grid from the angular frequency omega output by the virtual synchronous machine g Then, integral operation is carried out to obtain a power angle delta output by the virtual synchronous machine, and the power angle delta satisfies the following conditions:
。
6. the virtual synchronous machine active power control device for a grid-connected converter as set forth in claim 5, wherein the virtual synchronous machine outputs active power P e The calculation formula of (2) satisfies the following:
wherein,u is the amplitude of the voltage of the power grid, E is the amplitude of the output voltage of the virtual synchronous machine, and X is the equivalent line impedance of the power grid.
7. A virtual synchronous machine active power control device for a grid-tied converter as defined in claim 5, wherein the damping power P D The following formula is adopted for calculation:
wherein D is a virtual damping coefficient of the virtual synchronous machine,is the second frequency deviation.
8. The virtual synchronous machine active power control device for a grid-tied converter of claim 5, wherein the second frequency deviationThe calculation method of (2) is as follows:
when (when)When the integrator output switch S is closed, the second frequency deviation +.>The calculation method of (1) satisfies the following conditions:
wherein k is i Is an integral coefficient;
when (when)At this time, the integrator output switch S is turned off, and at this time, the second frequency deviation +.>Zero.
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