Adaptive control strategy of inertia and damping coefficients based on virtual synchronous generator

Virtual synchronous generator (VSG) has been generally concerned in the field of new energy power generation because of their ability to imitate the operational mechanism of synchronous generator. In order to solve the problem of power and frequency fluctuation or even off-limit caused by load changes, this paper summarizes the control strategy for the stable operation of the electricity grid supported by VSG. It combines the changes of various physical quantities in the transient process. It fully uses VSG virtual inertia and damping coefficient flexible and regulable advantages and puts forward an adaptive control strategy for inertia and damping coefficient. The control strategy can efficiently suppress the fluctuation of VSG output power and frequency in dynamic processes. It can cut down the transient adjustment time significantly and promote the stability of the system. The correctness and effectiveness of the proposed control strategy are verified by simulation experiment results.


Introduction
As fossil fuels run out, clean and pollution-free renewable energy becomes a good substitute.Therefore, distributed power supply based on microgrids has attracted people's attention.A large number of distributed power sources are connected to the electricity grid through power electronic devices.This results in loss of grid inertia and damping.Therefore, both domestic and international academics suggested using VSG to reduce the system's instability by inhibiting its own power and frequency variations through the implementation of control methods that replicate synchronous generator characteristics.Although VSG can simulate a synchronous generator, with traditional VSG control methods, large fluctuations in power and frequency can still occur when external disturbances are large.If the shock or oscillation during the transient process exceeds the device threshold, the device may run abnormally or even become unstable.To address the aforementioned issues, Alipoor et al. [1] proposes a VSG virtual inertia adaptive control algorithm based on Bang-Bang control.The inertia is given a lesser value when the rate of change of angular frequency is below a particular threshold and a higher value otherwise.However, this method is a stepwise adjustment, which cannot realize the effective tracking of the inertia to the frequency change.In [2], the auxiliary power obtained from the combination of power change quantity and change rate is added to the power side to realize the control of strengthening inertia.The results show that while the frequency change rate remains unchanged and the amplitude of the power deviation increases, the frequency deviation of the system has unquestionably improved.A virtual inertia adaptive control strategy is put forth in [3] and is based on the rate of angular frequency change of the VSG rotor.This strategy partially resolves adaptive tracking but ignores the effects of angular frequency deviation on the inertia and the adaptive role of damping.
In view of the shortcomings of the above studies, this work suggests an adaptive virtual inertia and damping collaborative control technique.It establishes the link between the system's frequency deviation and frequency change rate and the virtual inertia and damping coefficient.The virtual inertia and damping coefficient values vary adaptively in response to power disturbances in the system, depending on the frequency deviation and the rate of change.As a result, it is possible to successfully minimize the system's overshoot, shorten its transient phase, and increase its stability.

The basic principles of VSG
The hardware topology of VSG is the same as that of a typical grid-connected converter, as shown in Figure 1.VSG is essentially a distributed power supply that simulates the characteristics of traditional synchronous generators through specific control strategies to improve system stability [4].( ) where  is the inertia coefficient of the synchronous generator;  is the damping coefficient corresponding to the damping torque.The governor of the synchronous generator reacts to the frequency variation of the power grid, and the active output power is adjusted by modifying the mechanical torque.In a similar manner, the virtual frequency modulator may be used to change the VSG's frequency response.This device modifies the virtual torque in accordance with the discrepancy between the actual angular frequency  and the virtual rated angular frequency  , as displayed in Equation (2).

Δ ( )
Combined with the above two equations, the difference between the actual angular frequency  and the virtual rated angular frequency  is sent into the damping link, where the frequency sag coefficient  is actually equivalent to the damping coefficient .Then the governing equation of the active power of VSG is displayed in Equation (3) [5].

Influence of inertia and damping coefficients on VSG properties
VSG not only possesses frequency and voltage regulation capabilities., but also can overcome the defects brought by power electronic equipment so that the distributed generation system has inertia and damping.The characteristics of VSG are greatly affected by the two key parameters of inertia coefficient  and damping coefficient .To achieve better operational efficiency, the above two key parameters must be analyzed in detail.According to Figure 1, the current output by VSG is displayed in Equation ( 4) (Using the reference vector of the grid voltage, then  ).
The apparent power of VSG is displayed in Equation ( 5).
Then active and reactive power output from VSG are displayed in Equation ( 6).
As  ≫  ,  can be ignored, so   2 ⁄ .In reality, there is hardly any phase difference between the electromotive force of excitation and the voltage at the machine's end, so  0 .Therefore, the active output power of VSG is also displayed in Equation (7).
By combining Equation (3) and Equation ( 7), we can get the active power transfer model of VSG, as shown in Figure 2. From Figure 2, we can find the transfer function between the active power of the VSG's input and output, as displayed in Equation (8) [7].
From Equation (8), VSG root tracks of different  and  can be drawn, as shown in Figure 3 (the root locus of  increasing from 0 to infinity when  is taken as 0.2, 0.5, and 1 respectively). and  are a pair of the system's conjugate complex roots, traveling in the direction shown by the arrows in the following figure.As  increases,  and  move to the left in the complex plane at the same time, indicating the better dynamic performance of the system.If  continues to increase, both  and  will move in opposite directions on the real axis.At the moment, the system is in an overdamped condition, which will increase the system's adjustment time.Therefore, the damping coefficient  should not be too large.On the other hand, with the growth of , the convergence point of the root tracks gradually tends to 0; that is, it gradually moves to the imaginary axis, which causes the response of the system to become slower, so the inertia coefficient J should not be too large either [6].

Improvement of control strategy
The power angle and frequency response curves of the synchronous generator are shown in Figure 4.The selection of the inertia coefficient  is decided by both the amount and the rate of change in virtual rotor angular frequency from Figure 4.In contrast, the selection of damping coefficient  is only concerned with the amount of change in virtual angular frequency.In different stages of the system dynamic response, the principles for selecting the VSG inertia and damping coefficients are shown in Table 1.
Table 1.What happens to  and According to Figure 3 and Table 1, this paper designs the inertial and damping coefficient adaptive control strategy of VSG as displayed in Equation (9).

 
where  and  are the VSG's damping and inertia coefficients stabilized operation;  and  are adjustment coefficients of inertia and damping;  and  are angular frequency rate deviation and angular frequency deviation threshold.
According to Equation (9), the inertia and damping coefficients adaptive control concept diagrams are shown in Figure 5.
Adaptive control of damping coefficient Figure 5. Inertia and damping coefficient adaptive control schematic

Simulation experiments
To confirm the validity of the theoretical analysis and proposed control approach in this paper, a single VSG system simulation model is built on MATLAB/Simulink platform.The system's stability is analyzed when the active power is disturbed.The simulation duration is set to 2.5 s, with an initial active load of 2 kW, a sudden increase of 12 kW at 0.5 s, and a return to 2 kW at 1.5 s.The reactive load remains constant at 1 kVAR.7 show the active power and frequency variation curves of VSG under different control strategies, respectively.When the load is disturbed, the active power and frequency of VSG will go through a process of attenuation shock and tend to be stable.The active power's stable value is equivalent to the grid side power, and the frequency's steady value is about equivalent to the grid's rated frequency.When the load increases suddenly, the system with conventional fixed parameter VSG control has the largest overshoot and deviation of active power and frequency and the longest regulation time.The overshoot and deviation of active power and frequency of the system with inertia coefficient adaptive control are reduced, but the regulation time does not change significantly.The overshoot, deviation, and regulation time of active power with damping coefficient adaptive control are ulteriorly reduced.Still, the overshoot and deviation of frequency are not significantly changed compared with inertia coefficient adaptive control.However, the transient performance of active power and frequency with inertia and damping coefficient adaptive control is better than the previous three control strategies, with the minimum overshot, deviation, and adjustment time, in view of the rapidity, stability, and accuracy of the dynamic system response, better suppressing the system active power and frequency fluctuations, and also reflecting the flexibility of VSG.

Conclusions
In view of the grid power and frequency fluctuation caused by load disturbance when a variety of distributed power sources connect to the electricity grid, this paper adopts a small signal analysis method to analyze the established VSG dynamic model.By calculating the transfer function of active power, the root locus under the change of VSG active power control parameters is drawn.The influence of inertia coefficient  and damping coefficient  on the operating characteristics of the system is received.When the load power changes, the system frequency will change accordingly.Based on the relation between the change quantity and the change rate and virtual inertia and virtual damping, an adaptive control strategy of inertia and damping coefficient is designed to enhance the VSG control so that the control parameters can be adjusted within a certain range.The real-time dynamic automatic adjustment of  and  is realized to achieve a better stability effect.Simulation experiments were performed on Matlab/Simulink to compare the curves of VSG output active power and frequency under different control strategies and to demonstrate the efficacy and superiority of the proposed control strategy when the load power changes.

Figure 1 .
Figure 1.Equivalent relation between grid-connected inverter and synchronous generatorThe inertia and damping properties of the synchronous generator rotor appear in the mechanical equation.The analogous rotor motion equation is depicted in Equation (1) using the second-order model of the conventional synchronous generator.

Figure 2 .
Figure 2. The active power transfer model of VSG

Figure 3 .
Figure 3.The root locus for different  and

Figure 4 .
Figure 4.The power angle and frequency change curves of the synchronous generator

Figure 6 .Figure 7 .
Figure 6.Comparison of VSG output active power under different control strategies