Issue 
Wuhan Univ. J. Nat. Sci.
Volume 27, Number 3, June 2022



Page(s)  218  230  
DOI  https://doi.org/10.1051/wujns/2022273218  
Published online  24 August 2022 
Computer Science
CLC number: TP 305
Optimal Control Virtual Inertia of Optical Storage Microgrid Based on Improved Sailfish Algorithm
^{1}
School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai
201620, China
^{2}
College of Power Engineering, Shanghai University of Electric Power, Shanghai
200090, China
^{†} To whom correspondence should be addressed. Email: zenggh@sues.edu.cn
Received:
10
March
2022
The optical storage microgrid system composed of power electronic converters is a small inertia system. Load switching and power supply intermittent will affect the stability of the direct current (DC) bus voltage. Aiming at this problem, a virtual inertia optimal control strategy applied to optical storage microgrid is proposed. Firstly, a small signal model of the system is established to theoretically analyze the influence of virtual inertia and damping coefficient on DC bus voltage and to obtain the constraint range of virtual inertia and damping coefficient; Secondly, aiming at the defect that the Sailfish optimization algorithm is easy to premature maturity, a Sailfish optimization algorithm based on the leakproof net and the crossmutation propagation mechanism is proposed; Finally, the virtual inertia and damping coefficient of the system are optimized by the improved Sailfish algorithm to obtain the best control parameters. The simulation results in Matlab/Simulink show that the virtual inertia control optimized by the improved Sailfish algorithm improves the system inertia as well as the dynamic response and robustness of the DC bus voltage.
Key words: optical storage microgrid / virtual inertia / damping coefficient / improved Sailfish optimization algorithm / optimal control
Biography: LIAO Hongfei, male, Master candidate, research direction: DC microgrid intelligent control. Email: 15900935728@qq.com
Foundation item: Supported by the National Natural Science Foundation of China (52177184)
© Wuhan University 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
0 Introduction
Digital technology is leading the development and evolution of the Fourth Industrial Revolution and promoting industrial digital transformation. Promoting the deep integration of advanced digital technologies and power grids is an important way for the digital transformation of power grids^{[1,2]}. The shortage of fossil energy and environmental problems have accelerated the development of new power technologies for distributed generation based on renewable energy^{[3]}. The rapid development of microgrids has laid the physical foundation for the digital transformation of energy, interconnectivity, and mesh coverage^{[4,5]}. At present, on the power generation side, the output of mainstream photovoltaic units and energy storage units are all direct current (DC); on the power consumption side, the highfrequency devices in the market, such as electric vehicles, mobile phones, and LEDs, are all DC loads. In the optical storage microgrid, there is no need to consider issues such as phase and reactive power, and the highfrequency DCDC converter greatly reduces the space. The construction of the optical storage microgrid can effectively reduce the conversion loss of electric energy in the converter, and provide a great physical help for the development of the digital microgrid. The optical storage microgrid system composed of power electronic converters is a small inertial system. The load switching in the system and the intermittent power output will lead to violent fluctuations in the DC bus voltage, which in turn affects the safe and stable operation of the microgrid system^{[6]}. The energy storage unit in the microgrid plays an important role in stabilizing the bus voltage of the DC microgrid^{[7]}. Appropriate control improvements on the basis of the droop control can effectively enhance the inertial support of the DC microgrid system. Virtual synchronous generator control (VSG) provides inertial support for the system by simulating the rotor characteristics of traditional synchronous motors. At present, the application research of this control in the alternating current (AC) system has been relatively mature.
Wu et al ^{[8]} proposed a virtual inertia control strategy for bidirectional gridconnected converters of DC microgrid by analogy with the virtual inertia of AC microgrid. This strategy can effectively solve the stability problem caused by constant power load, but its control parameters are not adaptive. In the process of digitalization of the power grid, intelligent control is an important part. In order to realize the intelligent control of the control parameters, Ren et al ^{[9]} used the voltage fluctuation rate as a function variable, and carried out an adaptive function design for the virtual inertia and damping coefficient; Yang et al ^{[10]} added the voltage deviation to the adaptive function variable; Karimi et al ^{[11]} used fuzzy control to adaptively design the virtual inertia and damping coefficient. The above selfadaptive design is obtained from the analysis of the voltage fluctuation curve of the system disturbance. This method has fuzzy characteristics. It can only be adjusted by experience in the simulation project, and it is difficult to achieve digital accuracy.
Swarm intelligence optimization algorithm is a powerful tool to provide solutions to complex problems by simulating the behavior of some special groups in nature, and it has been widely used in many fields^{[1215]}. Injecting intelligent algorithms into VSG control can inject vitality into the development of digital power grids. Li et al ^{[16]} used the multiobjective particle swarm optimization algorithm to obtain the optimal inertia and damping coefficient of VSG control in AC system; Cheng et al ^{[17]} added the elimination mechanism to optimize the particle swarm optimization, which further improved the accuracy of particle swarm optimization; Yao et al ^{[18]} proposed a virtual inertial control based on neural network. Different from the engineering experience dependence of fuzzy control, the virtual inertial parameter design is realized by means of intelligent algorithm, which makes the virtual inertial control more accurate. However, the intelligent virtual inertial control of the above intelligent algorithm is applied to the AC system. This paper takes the bidirectional DC/DC converter with the energy storage unit connected to the optical storage microgrid as the research subject, obtains the virtual inertial control suitable for the bidirectional DC/DC converter through the analogy of the virtual inertial control of the AC system, then uses the improved AC sailfish optimization algorithm (ACSFO) to optimize virtual inertia and damping coefficients. Firstly, a smallsignal model is established, and the stability constraints of the virtual inertia and damping coefficient are analyzed by means of the transfer function Bode diagram; Secondly, the sailfish algorithm is improved by integrating the antileakage net strategy and the vertical and horizontal crossover variation propagation mechanism, and the validity of the algorithm is verified and analyzed by using the highdimensional test function. After verification, the improved sailfish optimization algorithm is used to obtain the optimal solution of virtual inertia and damping coefficient. Finally, the optimal control strategy of virtual inertia and damping coefficient based on the improved sailfish algorithm proposed in this paper is simulated by Matlab/Simulink,then the simulation results are used to verify its effectiveness and the correctness of theoretical analysis.
1 Optical Storage Microgrid Structure and VSG Control
1.1 Optical Storage Microgrid Structure and Control Strategy
Figure 1 shows the topology of the optical storage microgrid studied in this paper, which is mainly composed of photovoltaics, energy storage units, AC loads, DC loads and corresponding power electronic converters. The whole system uses the DC bus as the medium to exchange energy through the corresponding power electronic converters. The inverter connected to the photovoltaic unit uses maximum power point tracking to make full use of the new energy. The AC and DC loads are connected to the DC bus through a oneway voltage reducer. The energy storage unit is connected to the DC bus through a bidirectional DC/DC converter. The equivalent circuit diagram of the converter is shown in Fig. 2. The converter adopts VSG control and uses the improved sailfish algorithm to improve the virtual inertia and damping coefficient to achieve optimal control, which can improve system inertia as well as the dynamic response of DC bus voltage.
Fig. 1 Topology of DC microgrid 
Fig. 2 Bidirectional DCDC converter equivalent circuit diagram R: equivalent resistance; L: filter inductance; : DC bus voltage; i_{dc}: the converter output current; C: voltage regulator capacitor 
1.2 The Principle of VSG Control
The active powerfrequency control of the VSG in the inverter in the AC system is to improve the inertia of the system by simulating the rotor motion characteristics of the synchronous generator. The specific expression obtained from the simulation is
where , are the reference active power and output power, , are the angular frequency and rated angular frequency, and D, J are the damping coefficient and virtual inertia, respectively. According to the control analogy analysis of the AC system and the DC system in Ref. [13], the corresponding relationship of the parameters can be obtained, as shown in Table 1.
According to the parameter correspondence in Table 1, the virtual inertia control of the bidirectional DC/DC converter applied to the optical storage microgrid can be obtained, and its expression is
where is the reference output current, and are the virtual inertia and damping coefficient respectively, is the reference value of the DC bus voltage, and is the rated value of the DC bus voltage. The bidirectional DC/DC converter connected to the energy storage unit adopts the control method of formula (2), which can increase the inertia and damping characteristics on the basis of the droop control. When the DC bus voltage changes suddenly, the virtual inertia can quickly simulate the output current and enhance the inertial support of the system. When the DC bus voltage unit is changed, describes the active power change of the control output, and the damping coefficient can speed up the recovery of the DC bus voltage.
The bidirectional DC/DC virtual inertial control block diagram of the optical storage microgrid established according to the VSG control is shown in Fig. 3. Its control consists of three parts: droop control, virtual inertia control and voltage and current double closedloop control to stabilize the DC bus voltage.
Fig. 3 Virtual inertial control block diagram k _{d}: droop coefficient; i _{b}: output current of the energy storage unit 
Correspondence of VSG control parameters of DC system compared with AC system
2 Stability Constraint Analysis
2.1 Small Signal Modeling
In order to obtain the optimal configuration of virtual inertia and damping parameters through the ACSFO algorithm, a smallsignal model is established for the scenario where VSG control is applied to a bidirectional DC/DC converter. Constraints of relevant control parameters are obtained by small signal analysis.
According to Fig. 2, the small signal model of the bidirectional DC/DC converter is
where , , , , are the disturbance of the DC bus voltage , the output current of the energy storage unit , the duty cycle , the output current of the converter , and the output voltage of the energy storage unit , respectively; and , , are the steadystate values of , , , respectively.
From formula (3), after substituting the steadystate operating point, its system transfer function is
where is the load resistance value.
2.2 PI Parameter Setting
In order to eliminate the influence of the proportionalintegral (PI) parameters of the controller on the stability, it is necessary to design the PI parameters of the voltage and current double closedloop control. The proportional and integral parameters of the current inner loop are k _{ip}, k _{ii}, and the current inner loop compensation function is .The proportional and integral parameters of the voltage outer loop are k _{vp}, k _{vi}, and the voltage outer loop compensation function is . The switching frequency of the converter is 50 kHz, and the cutoff frequency of the current loop is set to 20% of the switching frequency. The obtained Bode diagram of the current inner loop correction is shown in Fig. 4.
Fig. 4 Bode diagram of current inner loop correction G _{i}: the current inner loop compensation function; G _{id}: Bode diagram before compensation; G _{l}: Bode diagram after compensation 
The designed current inner loop PI values are 0.068 02 and 2 467.4, respectively. It can be seen from Fig. 4 that the crossover frequency after system correction is 10 kHz, and the phase angle margin is 60°, which meets the requirements of the system stability.
The cutoff frequency of the voltage loop is set to 4% of the switching frequency, and the resulting Bode diagram of the voltage outer loop correction is shown in Fig. 5.
Fig. 5 Bode diagram of voltage outer loop correction G _{v}: the voltage outer loop compensation function; G _{3}: Bode diagram before compensation; G _{4}: Bode diagram after compensation 
The designed voltage outer loop PI values are 32.881 8 and 22 431.8, respectively. It can be seen from Fig. 5 that the crossover frequency after system correction is 2 kHz, and the phase angle margin is 60°, which meets the requirements of the system stability.
2.3 Virtual Inertia and Damping Coefficient Stability Constraints
From Eq. (4), we can know that the small signal model of the VSG equation is:
From Fig. 3, the transfer function of the output voltage deviation to the output current deviation after adding VSG control can be obtained as:
Substituting Table 4 and the designed double closedloop PI value into the transfer function can obtain the Bode diagram when the virtual inertia and damping coefficient change, as shown in Fig. 6 and Fig. 7.
Fig. 6 Bode diagram with D _{v} changed 
Fig. 7 Bode diagram with C _{v} changed 
From Fig. 6, when D _{v} increases within a certain interval, its phase margin decreases and the system cutoff frequency decreases, so the increase of the damping coefficient will reduce the system stability. When D _{v} =30, the phase margin is 39.6°. In engineering, the phase margin is generally 40° to 60°as the system stability criterion.
From Fig. 7, when C _{v} increases within a certain interval, its phase margin remains unchanged, and the system cutoff frequency remains unchanged, which does not affect the system stability. Therefore, the increase of virtual inertia within a certain range will not reduce the system stability. However, if the virtual inertia exceeds a certain value, the phase margin will decrease rapidly and the system will become unstable.
For the virtual inertia and damping coefficient, the limit range of the phase margin of 40° to 60° in engineering can be used as a constraint for the subsequent optimization of the algorithm to ensure its stability.
2.4 Droop Coefficient Stability Constraint
It can be seen from Fig. 3 that the transfer function of output voltage deviation to output current deviation under simultaneous droop control is
where is the droop coefficient. It can be seen from the above formula that as increases, both the virtual inertia and the damping coefficient are reduced. It can be seen from Fig. 5 that if the damping coefficient is too low, the phase margin will be reduced, and the system will become unstable. Considering the need to improve the inertial support and stable operation of the system, a smaller droop coefficient should be selected. Considering the current power limit of the converter and the fluctuation range of the DC bus voltage, the design formula of the droop coefficient is
where is output maximum current for the converter, and is the maximum value of DC bus voltage fluctuation. The output current of the converter is limited by its capacity, and a better droop coefficient can be designed by using formula (8).
3 Sailfish Optimization Algorithm and Its Improvement
3.1 Basic Sailfish Optimization Algorithm
The sailfish algorithm simulates the alternate hunting of sailfish in groups of sardines^{[19]}. First, the sardine and sailfish populations are randomly initialized; Second, the sailfish uses the attack alternately to break the collective defense of the sardines; Finally, the sailfish catches suitable sardines through hunting to complete the position optimization.
1) Sailfish location update
Sailfish adopts the method of attack substitution in the hunting process, and learns in coordination with each other during the attack process. The position update formula is as follows:
where is the current position of the sailfish, is updated position for sailfish, and is elite sailfish that the closest to the prey with the best fitness, is injured sardine with optimal fitness, is a random number from 0 to 1, and is the iteration coefficient of the ith iteration as in formula (10)
where PD is the prey density, and its variation formula is
where , are the numbers of sailfish and sardines, respectively. The number of sailfish is expressed as:
where is the total number of sailfish and sardine populations, and Percent is the proportion of sailfish in the total population.
2) Sardine location update
When the sardine is attacked, its position update formula is:
where , are the current and updated positions of the sardines, respectively, is a random number from 0 to 1, and is the best attack power for sailfish. The attack power of the sailfish will decrease with the number of iterations, which is expressed as:
where is the current number of iterations, and and control the conversion of attack power. The attack strength changes linearly from A to 0, and the reduction of the sailfish attack strength can speed up the convergence. When , we should update all the positions of the sardines with formula (5); when , we should update the sardine section location. Locations are represented as:
where is the number of sardines to update, is the number of dimensions to update, and is the number of variables.
3) Predation stage
During the final phase of the hunt, sardines injured by a sailfish attack during an iteration are quickly caught by the sailfish, in which the sailfish will update to the sardine's location as soon as it kills the sardine. Its position update formula is as follows:
where , are the current positions of sailfish and sardines, and , are the fitness of sailfish and sardines, respectively.
3.2 Improvement of Sailfish Optimization Algorithm
Compared with other swarm intelligence algorithms, the sailfish algorithm has good convergence speed and optimization accuracy, but it is easy to lag and fall into a local optimal state during the convergence process. In order to speed up the convergence, improve optimization accuracy, and enhance the optimal configuration effect for virtual inertia and damping coefficient, the following three improvement methods are proposed.
1) Cubic mapping initializing the population
Population initialization affects the convergence speed and accuracy of the algorithm. Using random numbers to generate the initialized population does not have good ergodicity, and the population will appear local aggregation, which will affect the performance of the algorithm. Cubic mapping is conducted with excellent maximum Lyapunov exponent and excellent ergodic performance. Its expression is as follows:
where is the control parameter. In mapping, takes a random number between 0 and 1. Experimental analysis shows that the best condition is = 2.95. The simulation is performed according to formula (18), and the simulation results are shown in Fig. 8. Compared with random distribution, the sequence distribution generated based on Cubic mapping is more uniform.
Fig. 8 Sequence release diagram generated by different methods 
2) Antileakage net strategy based on selftriggering mechanism
Sailfish keeps approaching the injured individual sardines during the iterative process and attacks them in a single way during the hunting process. During predation, some fastmoving sardines could not avoid escaping, which leads to the premature maturity of the algorithm; and as the number of iterations of the algorithm increases, sailfish populations will gather around the current optimal solution, causing the algorithm's falling into a local optimum.
In order to improve the predation efficiency of sailfish and avoid getting stuck in local optima, this paper proposes a selftriggering mechanism of the antileakage net strategy. After the sailfish is updated according to formula (9), the antileakage net strategy is used to perturb the position of the sailfish. The expression of the antileakage net strategy is as follows:
where , is a random number from 0 to 1, , are the upper and lower bounds of the search space, respectively, is a scaling factor that decreases linearly from 1 to 0 with the number of iterations, and is the expansion factor.
In formula (19), when , we reinitialize the current individual, expand the search range of the sailfish population in the global space, prevent sardines from escaping the encirclement, and prevent the algorithm from falling into local optimum. When , the individual sailfish will move to the vicinity of the current position in the proportion of p, get rid of the attraction of some sardines in a small range, and jump out of the local extreme value. The linearly decreasing p combines the characteristics that the sailfish algorithm needs a largescale search in the early stage of iteration and a smallscale finescale search in the later stage of the iteration, which enhances the algorithm's optimization ability.
In the antileakage net strategy, it will reinitialize the current individual when . The larger the value of β, the greater the probability of reinitialization, and it is difficult to avoid the decrease of the algorithm solving efficiency at this time. In order to solve the problem that the fixed β value leads to the decrease of algorithm solving efficiency, this paper adopts a dynamically changing β, and the formula is as follows:
where β will increase with the increase of the number of iterations, so the antileakage net strategy will move proportionally with a greater probability in the early stage of the iteration, and the antileakage net will increase the probability of reinitialization accordingly in the later stage of the iteration so as to avoid the decline of population diversity.
Considering that adopting the antileakage net strategy in each iteration will increase the running burden of the algorithm, a selftriggering mechanism is embedded to improve the burden of running the algorithm. Its expression is:
where , are the maximum value and the minimum value of the trigger factor , respectively (The preset maximum is 0.8 and the minimum is 0.2). When the random number is , the antileakage net strategy is triggered; otherwise, the antileakage net strategy is not used. is the adjustment factor.
The selftriggering curve is shown in Fig. 9. Compared with the linear increment , the nonlinear increment method has a slow growth of the γ value and a lower trigger probability in the initial stage of the algorithm iteration, which ensures the convergence speed in the early stage of the iteration. In the later stage of the iteration, becomes larger and grows rapidly, and the trigger probability increases. At this time, the sailfish will escape from the local extreme value space through the antileakage net strategy so as to avoid falling into the premature algorithm in the later stage of the iteration. The degree of concaveness of the nonlinear increasing function can be adjusted by . If the algorithm appears premature, can be appropriately reduced to improve the trigger probability in the early stage of iteration and avoid the algorithm from falling into local optimum.
Fig. 9 Relationship between trigger factor and iteration number 
3) Cross mutation propagation mechanism
To further adapt the algorithm to complex environments and to fully improve its global development ability and local exploration ability, this paper proposes a crossmutation propagation mechanism to improve the sailfish search method through the horizontal crossinformation propagation mechanism to allow sufficient information dissemination among individuals, and at the same time refers to elite individual information to avoid blind learning among individuals, which ensures the optimization efficiency while improving the optimization accuracy. The vertical crossvariation is to carry out crossvariation in different dimensions of the individual so as to prevent the individual from falling into the local optimum due to a stagnant dimension, and to improve the activity of the population and the ability to jump out of the local optimum.
The horizontal cross information dissemination mechanism can effectively allow two individuals(i and j) to learn from each other and produce highquality offspring. The specific improved crossover operation is as follows:
where , are the ddimension individuals generated by the sailfish individual , and the reference sailfish elite individual, , are random numbers from 0 to 1, and , are random numbers of [1,1]. The individuals generated by the horizontal crossover operation need to be preserved with the parent.
The vertical crossover operation mainly mutates one of the dimensions, allowing the dimensions to learn from each other so as to avoid the parental individual from falling into a local optimum due to the stagnation of a certain dimension. The specific mutation methods are as follows:
where is the offspring individual generated by and of the individual through longitudinal variation; is a random number between 0 and 1. The progeny and parent of the longitudinal variation are preferentially preserved. Through the preferential mechanism, the optimal dimension information in the individual sailfish can be retained and the stagnant dimension information can be removed to improve the population diversity.
The excellent individual information generated by the vertical mutation will be spread to other individuals through the horizontal crossover operation, and the activity of the whole population will be improved. The crossoptimization of the population through the crossmutation propagation mechanism improves the activity of the population, enhances the ability to jump out of the local optimum, and further improves the convergence speed and the performance of solving complex optimization problems.
3.3 ACSFO Algorithm Optimization Test
In order to test the effect of ACSFO algorithm on function optimization, this paper compares ACSFO algorithm with 4 classical intelligent algorithms (Particle Swarm Optimization (PSO) algorithm, MultiVerse Optimizer (MVO) algorithm, Grey Wolf Optimizer (GWO) algorithm, Mothflame optimization (MFO) algorithm) and the original sailfish optimization algorithm SFO in 4 typical test functions. The optimization is carried out in the test function. The four groups of test functions are shown in Table 2. The F _{1} and F _{3} test functions are shown in Fig. 10. The population size is 30, the dimension is set to 30, and the maximum number of iterations is set to 500 times. In order to avoid randomness, each algorithm is optimized 30 times. Taking the average fitness value of 30 calculations as the ordinate, and the number of iterations as the abscissa, the function convergence curve is shown in Fig. 11.
Fig. 10 Test function graph 
Fig. 11 Convergence curves of test functions under different algorithms 
It can be seen from Fig. 10 that F _{1} is a multidimensional singlepeak test function, which can test the global optimization ability of the algorithm, and F _{3} is a multidimensional multipeak test function, which can test the algorithm's ability to jump out of the local optimum.
From the convergence curves of F _{1}, F _{2}, F _{3} and F _{4}, it can be seen that, ACSFO has a great improvement in convergence speed and optimization accuracy compared with SFO. From F _{2}, F _{3}, and F _{4}, it can be clearly seen that the initialization of the population based on the Cubic map makes the generated initial value closer to the optimal solution and improves the diversity of the search space. F _{1}, F _{2}, F _{3}, and F _{4} found the optimal solution, indicating that after introducing the antileakage net strategy based on the selftriggering mechanism, the sailfish can expand the hunting range during the alternate hunting process, enhance the sailfish search ability, and avoid falling into the local optimum. It can be seen from F _{1}, F _{2} and F _{4} that in the later stage of the iteration, there is a tendency to fall into the local optimum. The addition of the horizontal crosspropagation mechanism makes the convergence speed faster, and the addition of the vertical crossmutation makes the stagnant dimension jump out of the local area. It can be clearly seen from F _{3} and F _{4} that the algorithm stagnates at 300 and 290 iterations respectively, and vertical crossmutation avoids the defect of dimensional iteration stagnation, and then quickly finds the optimal solution.
It can be seen that the ACSFO algorithm has a great improvement in the SFO algorithm, and its convergence speed and optimization accuracy are improved. Compared with other classical intelligent algorithms, it also has very superior optimization performance.
Test function
4 Improvement of VSG Control Based on ACSFO Algorithm
4.1 Fitness Function Design
The fitness function used to evaluate the position of the particle can guide the search direction of the algorithm, and plays a key role in the optimization algorithm to meet the convergence accuracy and convergence speed of the system.
In this paper, the integral of time multiplied by absolute value of error (ITAE) is adopted as the performance optimization objective of microgrid system. Its expression is:
where is the output error. Taking ITAE as the fitness function can make the transient response oscillation of the system smoother and the voltage followability strong.
In order to improve the inertial support of the microgrid system, obtain the optimal virtual inertia and damping coefficient, enhance the smoothness of the transient response of the system, and follow the voltage, the designed fitness function is:
where is the fitness function value of the population, and is the deviation of the DC bus voltage.
4.2 ACSFO Algorithm Flow Design
The main logic and flow of the ACSFO algorithm to improve virtual inertial control are shown as follows.
ACSFO algorithm flow 

1) Parameter initialization: sailfish population size, sardine population size, iteration times 
2) Chaos initialization population 
3) Calculate and sort the fitness values of sailfish and sardine respectively according to formula (26). Pick the best position in the two populations and record its position. 
4) while t<T 
5) for i = 1 to N _{SF} 
6) Calculate γ according to formula (21) 
7) if r _{1}>γ 
8) Update the sailfish position according to formula (9) 
9) end if 
10) Calculate β according to formula (20) 
11) if 
12) Update the sailfish position according to formula (19) 
13) end if 
14) end for 
15) if (AP<0.5) 
16) for i = 1 to α 
17) Update the sardine position according to formula (13) 
18) end for 
19) else 
20) for i = 1 to N _{S} 
21) Update the sardine position according to formula (13) 
22) end for 
23) end if 
24) Calculate the fitness values of sailfish and sardine populations separately 
25) for i = min(N _{SF}，N _{S}) 
26) if sardine fitness value < sailfish fitness value 
27) Sardine sailfish position swap 
28) end if 
29) end for 
30) Initialize the removed sardine position 
31) Calculate the fitness value of sardines, complete the sorting of sailfish and sardines according to the fitness value, and compare the two groups with each other to record the optimal individual 
32) for i=1: N _{SF}/2 
33) Get the ith pair of laterally propagated individuals 
34) for d = 1 to D 
35) According to formulas (22) and (23), calculate the offspring formed by horizontal crosspropagation, and compare with their parents to leave outstanding individuals 
36) end for 
37) end for 
38) for i=1: D/2 
39) for j=1: N _{SF} 
40) Calculate the offspring formed by longitudinal variation according to formula (24), and compare with their parents to leave outstanding individuals 
41) end for 
42) end for 
43) t = t+1 
44) end while 
5 Simulation Results
In order to verify the effectiveness of the improved sailfish algorithm proposed in this paper for the virtual inertia optimal control strategy and the correctness of the theory, the optical storage microgrid model shown in Fig. 1 is built in Matlab/Simulink, and the photovoltaic adopts the Maximum Power Point Tracking (MPPT) control. The bidirectional DC/DC converter connected to the battery grid adopts different control strategies according to the needs. The corresponding system parameters are shown in Table 3.
Figure 12 describes the effect of virtual inertia on the optical storage microgrid. The blue curve only adopts droop control, and the droop control means that we should set virtual inertia C _{v}=0. For the rest of the curves, the damping coefficient is set to 20, and the virtual inertia is a variable. Figure 12(a) describes the voltage dynamic response. When the reference voltage changes, the voltage rapidly changes to the voltage reference value in the droop control case; in the VSG control case, the voltage changes slowly to the voltage reference value, and the system inertial support is significantly improved. As the virtual inertia increases, the voltage changes more slowly, the inertial support is stronger, and the voltage quality improves. Figure 12(b) shows the influence of load power mutation on the DC bus voltage. Similarly, as the virtual inertia increases, the inertial support is stronger and the fluctuation is weakened. When t=1 s, the load power suddenly increases by 5 kW, at this time, the VSG control will reduce the power delivered to the microgrid; when t=1.5 s, the load power will suddenly drop by 5 kW, and the VSG control will increase the power delivered to the microgrid and enhance the inertial support of the microgrid.
Fig. 12 Influence of virtual inertia on optical storage DC microgrid 
Figure 13 describes the effect of the damping coefficient on the optical storage microgrid, setting the virtual inertia C _{v}=0 and the damping coefficient D _{v} as a variable. Figure 13(a) depicts the voltage dynamic response. In the case of VSG control, as the damping coefficient increases, the voltage response is faster and the deviation from the reference voltage is smaller, but it also reduces a certain inertia. In Fig. 13(b), when t=1 s, the load power suddenly increases by 5 kW, and when t=1.5 s, the load power suddenly drops by 5 kW. In the two cases of sudden change, with the increase of the damping coefficient, the deviation is smaller and the recovery of stable values is faster.
Fig. 13 Influence of damping coefficient on optical storage DC microgrid 
Through theoretical and simulation analysis, we can know that the larger the virtual inertia, the stronger the inertial support of the system, which avoids the violent fluctuation of the DC bus voltage, but at the same time the voltage recovery speed becomes slower. The larger the damping coefficient, the higher the voltage response speed, but the damping coefficient will have a certain weakening effect on the inertia. At the same time, it can be seen from the theoretical analysis in Fig. 6 that the damping coefficient is too large which will affect its stability. In order to realize the optimal solution
of virtual inertia and damping coefficient of VSG control, formula (26) is used as the fitness function, and the ACSFO algorithm is used to find the optimal solution of parameters. The value ranges of the virtual inertia and damping coefficient are set to [0, 2.5] and [0, 30], respectively, the number of algorithm population is 20, and the number of iterations is 50. The iteration curve is obtained as shown in Fig. 14.
Fig. 14 Iterative curve diagram of algorithm 
It can be seen from Fig. 14 that the ACSFO algorithm has a great improvement over the original SFO algorithm, showing great advantages in finding the opticient, and its convergence speed and convergence accuracy are greatly improved in the original SFO algorithm.
When the load power changes, the simulation comparison diagram of the optimal configuration of virtual inertial control using the ACSFO algorithm is shown in Fig. 15.
Fig. 15 DC bus voltage fluctuation curve under different control 
It can be seen from Fig. 15 that the ACSFO algorithm has better dynamic response ability, shorter recovery time and smaller fluctuation than the SFO algorithm.
System parameters
6 Conclusion
In order to promote the digitization process of the power grid, this paper uses an intelligent method to solve the voltage quality problem caused by the low inertia of the DC microgrid. Firstly, by analogy with the DC/AC inverter with VSG, the VSG control is applied to the DC bidirectional DC/DC converter of the optical storage microgrid. After that, the antileakage net strategy and the crossmutation propagation mechanism are integrated into the Sailfish optimization algorithm to improve the global optimization ability. Finally, an intelligent optimization control strategy of virtual inertia and damping coefficient is proposed.
Through theoretical analysis and experimental verification, the following conclusions are drawn:
1) The low inertia problem of the DC microgrid is effectively solved by constructing a VSG control strategy, and the voltage following performance is enhanced. Using ACSFO algorithm to realize the configuration of VSG control parameters can effectively improve its system adaptability and intelligence. Effectively using ITAE as a fitness function can take into account its error accuracy and convergence speed at the same time in parameter configuration, which can improve the following performance while enhancing the inertial support of the system, and provide ideas for the acquisition of electrical data in digital power grids.
2) The ACSFO algorithm integrates the antileakage network strategy and the vertical and horizontal crossover mutation propagation mechanism, which enhances the global development ability and local exploration ability of the SFO algorithm, greatly improves the algorithm optimization accuracy and convergence speed. By using the ACSFO algorithm, the optimal configuration of the VSG control parameters can be achieved.
3) This paper only aims to add VSG control based on ACSFO algorithm to the bidirectional DC/DC converter in a single optical storage microgrid, and does not consider the coordinated control of the intelligent microgrid system with mesh interconnection of the optical storage microgrid. The insufficiency of this paper is also the future research direction.
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All Tables
All Figures
Fig. 1 Topology of DC microgrid  
In the text 
Fig. 2 Bidirectional DCDC converter equivalent circuit diagram R: equivalent resistance; L: filter inductance; : DC bus voltage; i_{dc}: the converter output current; C: voltage regulator capacitor 

In the text 
Fig. 3 Virtual inertial control block diagram k _{d}: droop coefficient; i _{b}: output current of the energy storage unit 

In the text 
Fig. 4 Bode diagram of current inner loop correction G _{i}: the current inner loop compensation function; G _{id}: Bode diagram before compensation; G _{l}: Bode diagram after compensation 

In the text 
Fig. 5 Bode diagram of voltage outer loop correction G _{v}: the voltage outer loop compensation function; G _{3}: Bode diagram before compensation; G _{4}: Bode diagram after compensation 

In the text 
Fig. 6 Bode diagram with D _{v} changed  
In the text 
Fig. 7 Bode diagram with C _{v} changed  
In the text 
Fig. 8 Sequence release diagram generated by different methods  
In the text 
Fig. 9 Relationship between trigger factor and iteration number  
In the text 
Fig. 10 Test function graph  
In the text 
Fig. 11 Convergence curves of test functions under different algorithms  
In the text 
Fig. 12 Influence of virtual inertia on optical storage DC microgrid  
In the text 
Fig. 13 Influence of damping coefficient on optical storage DC microgrid  
In the text 
Fig. 14 Iterative curve diagram of algorithm  
In the text 
Fig. 15 DC bus voltage fluctuation curve under different control  
In the text 
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