
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12983-0
10.1016/j.heliyon.2024.e36952
e36952
Research Article
Optimization research on control strategies for photovoltaic energy storage systems considering multi-mode operation
Liu Fang
Li Zhongliang
Wang Xiaomeng XX50723@163.com
⁎
State Grid Henan Electric Power Company Jiaozuo Power Supply Company, Jiaozuo, 454000, China
⁎ Corresponding author. XX50723@163.com
27 8 2024
15 9 2024
27 8 2024
10 17 e369527 3 2024
24 8 2024
26 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
In this paper, a selective input/output strategy is proposed for improving the life of photovoltaic energy storage (PV-storage) virtual synchronous generator (VSG) caused by random load interference, which can sharply reduce costs of storage device. The strategy consists of two operating modes and a power coordination control method for the VSGs. Firstly, a selective VSG input strategy is proposed based on the magnitude of disturbances, a method of offline solving model equation is used for determine the VSG input time. An online method is used for matching the disturbance frequency variations, which enables a selective VSG startup method, allowing the grid to prioritize the utilization of the generator's physical inertia. Secondly, a dynamic VSG exit strategy is developed based on dynamic frequency characteristics to prevent secondary oscillations in the frequency recovery phase of the PV-storage VSG following grid disturbances. This strategy is crucial as grid variations may affect energy storage lifespan and reduce frequency recovery speed. Finally, the proposed approach is validated for correctness and effectiveness through computer simulations and semi-physical experiments using the NI-PXI + LabVIEW platform. Through the above optimization and research, the selective start of VSG is realized, the energy storage life is improved, the capacity of charge and discharge cycles is reduced by 37.82 % compared with the strategy without investment and withdrawal, and the life loss in the secondary charge and discharge process of PV-storage VSG is avoided, which is conducive to frequency recovery.

Graphical abstract

Image 1

Highlights

• An innovative control strategy to improve PV-storage VSG system life is proposed.

• VSG will not be activated until a large disturbance is detected in the system.

• Exit VSG during the frequency recovery phase after a large disturbance.

• The simulation model of PV-storage VSG grid-connected system is established.

• The total throughput of energy storage is reduced by 37.82 %.

Keywords

PV-Storage systems
Virtual synchronous generator (VSG)
Photovoltaic power
Storage life
Energy storage
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pmc1 Introduction

In the current context of prominent global energy security issues and severe environmental pollution problems, there is a dire need to vigorously develop wind power, solar power, hydropower, and other renewable energy sources to realize the transformation of energy production [[1], [2], [3], [4], [5]].

The conventional power system planning and design mainly considers the access of conventional thermal, hydro, or nuclear power, and the load shows a certain regularity [6,7]. Under the low penetration of renewable energy into the grid, the power system only needs to consider issues of random power generation of renewable energy systems by providing backup support [8]. However, on the one hand, with the expansion of the scale of the power system, the load capacity and its uncertainty increase substantially, and the grid's demand for the inertia of the AC system increases [9,10]. On the other hand, the increase of PV grid-connected capacity causes the reduction of inertia of the power system, which seriously affects the frequency stability of the power grid, and may cause problems such as PV off-grid and low-frequency load-shedding false starts [11,12].

At this stage, many scholars at home and abroad have studied the problems related to grid-connected renewable energy sources. VSG is the main control strategy to solve the problem of inertia deficiency in new energy power systems [13,14]. VSG is controlled by introducing virtual inertia and damping into the grid-connected variable current controller, which simulates the response of a conventional synchronous generator to the grid and provides external output characteristics such as damping, inertia, and sag to provide the necessary grid frequency support [15]. However, the load in the grid-connected PV-storage system is susceptible to random disturbances, and if the PV-storage VSG responds to all disturbances indiscriminately, it will cause unnecessary charging and discharging of the energy storage and thus reduce its life. Besides, the secondary charging and discharging of the VSG during the grid frequency recovery phase reduces the energy storage life and affects the grid frequency recovery speed.

At present, the frequency support control of VSG has been studied in literature [[16], [17], [18], [19], [20], [21], [22]]: Literature [16] proposed a grid-supported PV system that provides inertia and participates in grid frequency regulation through VSG and energy storage units, which can autonomously regulate the power imbalance between power generation and consumption. Literature [17] proposed a three-level hierarchical control scheme for VSG inverters, which can simulate the dynamic behavior of conventional synchronous generators by introducing virtual inertia and damping coefficients in the control loop. Literature [[18], [19], [20], [21]] proposed frequency control methods for wind power/photovoltaic/energy storage systems to improve the frequency stability of the grid. Literature [22] studies the influence of VSG control parameters on energy storage cost, and believes that the damping coefficient D, inertia constant J and FM coefficient K determine the VSG dynamic characteristics in the frequency modulation process, which affects the life of the energy storage. The literature mentioned above researched the principle of PV-storage VSG implementation and frequency support control strategy, however, different operation modes of PV-storage VSG and the influence on energy storage life are still not unknown, and the existing research on the cooperative operation of energy storage and photovoltaic power generation system is still not deep enough.

For solving the above problems, this paper proposes a method to improve the life of the PV-storage system by temporally exiting the VSG based on the configuration parameters and operating conditions of the PV-storage system. Firstly, an online matching selective start scheme is established for VSG to start selectively according to the disturbance size so that the grid preferentially uses physical generator inertia for disturbance suppression, reducing the number of storage charges and discharges, which enhances the life of energy storage. Secondly, the exit scheme of VSG is proposed based on the exit criterion of frequency profile, which avoids the loss of life of the PV-storage VSG in the secondary charging and discharging, and facilitates the frequency recovery. Finally, the effectiveness of the proposed method is verified by simulation and semi-physical experiments.

2 PV-storage system VSG working principle and operation mode

2.1 Working principle of VSG for PV-storage system

The main circuit topology of the PV-storage grid-connected system is shown in Fig. 1, in which the grid-connected inverter PV generation system and the battery storage system share an inverter, and virtual inertia and damping are achieved through the VSG control algorithm [23,24].Fig. 1 PV-storage grid-connected system main circuit topology diagram.

Fig. 1

The VSG active-frequency control is shown in Fig. 2. The PV-storage system measures the voltage amplitude (UG) and angular frequency (ωG) at the access point of the finite capacity grid, the voltage amplitude (E) and angular frequency (ω) at the outlet of the inverter and the VSG grid-connected current in real-time, and calculates the grid-connected power Pe. The power command is obtained according to the power given value Pref and the FM coefficient K and compared with the power measurement value Pe. The power difference is converted into a torque scale, and then the damping torque is subtracted. The resulting unbalanced torque adjusts the VSG virtual rotor to accelerate or decelerate and ω to increase or decrease, directing the electromagnetic power Pe to vary accordingly.Fig. 2 VSG active-frequency control block diagram.

Fig. 2

The inverter power control expression is equation (1), which is the same as the synchronous generator motion relation equation, so it is called virtual synchronous generator (VSG) control.(1) Jdωdt=Pref+K(ωn−ω)−Peωn−D(ω−ωG)

where J is the virtual rotational inertia of the PV-storage system, D is the virtual damping, and ωn is the rated angular frequency of the grid.

As can be seen from formula (1), due to the existence of virtual J and D, the inverter can simulate the inertia and damping of the synchronous machine. The VSG simulates the heavy inertia of the traditional power grid and enhances the power grid's ability to voltage and frequency regulation. Due to the introduction of virtual J and D, the input and output power show the consistent oscillation characteristics of the traditional power grid, so that the VSG can ensure the stable operation of the power grid. The photovoltaic equipment in the power grid cannot provide continuous energy storage, so in order to simulate the heavy inertia of the traditional power grid, the system must be equipped with energy storage units and ensure the continuous normal operation of the energy storage units.

2.2 PV-storage system VSG operation mode

The PV-storage system shown in Fig. 1 is used as a research object. The photovoltaic DC/DC unit works according to the maximum power tracking mode. The energy storage DC/DC unit adopts Buck/Boost circuit, which can perform bi-directional power exchange between energy storage charging and discharging; meanwhile, the energy storage DC/DC controls constant bus voltage and power balancing. After considering the storage configuration capacity and the possible working state of each link, this paper focuses on three operation modes of the optical storage system [25].1) Constant power VSG mode. In this mode, the storage capacity is large enough to balance the peak-to-valley variation of PV output and participate in grid peaking. The inverter can output at a given power, equivalent to a controllable power supply. At the same time, the grid-connected inverter can respond to grid frequency changes.

2) Tracking PV VSG mode. In this operation mode, the capacity of the energy storage configuration is small, and it is mainly used to smooth out the random fluctuation of PV output, so the output power of the grid-connected inverter in steady-state operation should track the PV output value after the energy storage is smooth out. Meanwhile, the grid-connected inverter can still provide inertia and damping for the grid. Still, the system cannot provide primary frequency regulation capability due to the small energy storage capacity.

3) Zero power VSG mode. It refers to the operation mode of the optical storage system which provides virtual inertia and damping when the reference power of the fixed power VSG mode is zero or tracking the PV VSG mode which provides virtual inertia and damping when the PV output is close to zero in bad weather.

3 Control strategies for different operation modes of PV-storage VSG

3.1 Power control of the inverter

The proposed power coordination control strategy based on different operation modes of PV-storage VSG is shown in Fig. 3.Fig. 3 Inverter power control logic block diagram.

Fig. 3

Where PPV is the PV power generation; PINV is the VSG grid-connected inverter output power command value; PSC is the storage unit charging power command; PSOC is the storage SOC control power; and LF is the low-pass filter to filter out the fluctuation of PV power. When the switch is in position 1, the PV-storage system tracks PV VSG operation mode. The PV power is low-pass filtered by the LF loop to obtain the smoothing component, which is used as the output power command of the grid-connected inverter. The PV power fluctuation component is then used as the charging power command PSC of the energy storage unit for PV power leveling. When the switch is placed in position 2, the PV-storage system is in constant power VSG mode. The output power command PINV of the grid-connected inverter in this mode consists of two components superimposed on the power reference value Pref and the primary FM power K(ωn - ω) of the PV-storage system. The grid regulation center determines the power reference value Pref according to the economic dispatch principle. The energy storage unit output power command PSC is the difference between the PV power output and the inverter power output.

3.2 Energy storage power and bus voltage control

This paper uses a typical PI control method with an external voltage loop and an internal current loop to maintain the PV-storage DC bus voltage of the energy storage unit, as shown in Fig. 4. Udc is the measured bus voltage, U0 is the commanded DC bus voltage, and Idc is the measured energy storage charging current. Although this method can indirectly achieve the real-time power balancing of energy storage, PV and inverter, the power balancing is achieved only by using the bus voltage as a parameter, which causes large fluctuations of bus voltage. Therefore, this paper constructs the power command PSC to directly control the static power part of the PV-storage system, the DC/DC of the energy storage. At the same time, the bus voltage control achieves the power balance for the dynamic power caused by damping and virtual inertia and the power control deviation of the energy storage and inverter.Fig. 4 Control strategy of bi-directional DC/DC converter.

Fig. 4

3.3 Energy storage unit SOC control

The key to the realization of VSG technology is that the generating side can provide enough energy buffer for frequency regulation and voltage stabilization. However, photovoltaic power generation has uncertainty, and its power fluctuation does not meet the energy requirements of virtual synchronization. As an energy buffer unit in microgrid, energy storage unit can not only calm photovoltaic fluctuations, but also provide enough energy buffer for the frequency regulation of VSG, and ensure the heavy inertia of distributed power generation system. Therefore, it is necessary to study the control of energy storage [26,27].

Before system operation, SOC should be in the pre-set instruction value Sref to ensure that the super capacitor has the same charge and discharge capacity in steady state, as shown in equation (2):(2) Sref=Smax+Smin2

Where, Smax and Smin are the working upper and lower limits of SOC respectively.

The physical constraints of energy storage are related to the J and D parameters of VSG. When the system power fluctuates, VSG will adjust the charge and discharge of energy storage. The charge and discharge power is adjusted as equation (3) [28]:(3) P=EUJωLω0s2+DJωLω0s+EUJωLω0ΔPes

where, ΔPe is the power fluctuation value. L is the synchronous inductance of the synchronous generator. P is energy storage charging and discharging power. When P > 0, the energy storage unit will discharge, and when P < 0, the energy storage unit will charge.

In the constant power VSG mode, the grid mainly regulates the energy storage SOC to ensure a reasonable range of energy storage. The SOC of the storage unit needs to be controlled locally based on the regulation errors that may cause the SOC to exceed the limit. The same is necessary for the storage SOC in the tracking PV VSG mode. This paper uses proportional-integral (PI) regulation to respond to the SOC to maintain the energy storage SOC in a reasonable range, keep the charging and discharge power smooth, and reduce the power disturbance to the grid. The proportional coefficient can be chosen as a smaller value to smooth the charging and discharging power. The energy storage SOC control relationship is as equation (4) and equation (5):(4) PSOC=KP×ΔESOC+Ki×∫ΔESOCdt

(5) ΔESOC={ESOC−ESOCmin,ESOC<ESOCmin0,ESOCmin≤ESOC≤ESOCmaxESOCmax−ESOC,ESOC>ESOCmax

Where, ESOC is the current charge of energy storage. ESOCmin, ESOCmax is the minimum and maximum allowable charge. Kp, Ki is the proportional, integral factor of the charging power.

The energy storage SOC control power command PSOC is shown in Fig. 3, where the grid-connected inverter power command is superimposed on the energy storage SOC power control component. It is also superimposed on the PSC energy storage power command, thus acting on the energy storage DC/DC control.

4 Selective start of VSG considering energy storage life

4.1 Power system frequency response characteristics

The mechanical inertia of synchronous generators is its inherent characteristic, and no response cost is required. The PV-storage VSG is provided by energy storage to provide the energy required for inertia action, the storage charging and discharging process has life loss, and the light-storage VSG has response cost. To save costs, some small disturbances that the generator can smooth out do not need to start VSG. A certain start-up threshold should be set for VSG response, and disturbances below the threshold VSG do not respond. The frequency characteristics of the power system equivalent generator have a 2nd order model, and the frequency characteristics of the VSG also have a 2nd order model. This paper focuses on the response of the VSG under load disturbance, which is a small disturbance category and can ignore the relative dynamics between generators. Thus, the power system frequency response has two characteristic roots regardless of whether or not the VSG is involved in frequency regulation. Let the frequency response of the grid under load disturbance and generator inertia and primary and secondary frequency regulation without VSG participation in frequency regulation have the form shown in equation (6), and the response curve is shown in the orange curve in Fig. 5. Let the VSG input at t0, the response changes to the green curve in Fig. 5 due to the increase of virtual inertia, and the response characteristics have the form shown in equation (7).(6) Δω=A1(e−α1t−e−α2t)

(7) Δω=A2(e−α3(t+τ)−e−α4(t+τ))

Where, A1, A2, α1, α2, α3, α4 are constants determined by the disturbance size, inertia parameters, primary and secondary regulation characteristics, load characteristics, etc., and can be considered as known numbers.Fig. 5 Response curve with and without VSG.

Fig. 5

4.2 VSG selective start scheme

Let the VSG start angle frequency threshold be Δωth; then, there are three cases according to the frequency response: 1) the load disturbance is small, and the dynamic frequency is not greater than the threshold without VSG participation. 2) the load disturbance is large and requires partial VSG participation to meet the dynamic frequency threshold. In this paper, we control the degree of VSG participation by controlling the VSG start time so that the dynamic frequency does not cross the threshold. 3) A large load disturbance requires full VSG participation.

An offline calculation and online matching are implemented to manage the VSG response scheme. The offline calculation process is as follows.(1) Let the moment of maximum dynamic frequency offset occurrence be tm, then the derivative of equation (5) at the moment of tm should be 0, so that equation (8) holds:

(8) dΔωdt|t=tm=0

(2) According to the above regulation scheme, the frequency deviation at the point tm with limited VSG participation should be the set threshold Δωth, which is obtained by substituting into equation (9).

(9) Δωth=A2[e−α3(tm+τ)−e−α4(tm+τ)]

(3) At the VSG input moment t0, equation (6) and equation (7) should be equal, then we have:

(10) A1(e−α1t0−e−α2t0)=A2[e−α3(t0+τ)−e−α4(t0+τ)]

Combining (8)-equation (10), we can find τ, t0 and tm. There are three possible cases: 1) no solution, at this time the VSG does not need to start, and the dynamic frequency will not exceed the threshold; 2) the solution is t0 > 0, which means that the VSG should be put in at the moment of t0, and 3) the solution is t0 ≤ 0, which means that the VSG should be put in immediately at the moment of disturbance.

The step load perturbation of the grid is made to occur at the zero moment, and the initial frequency change rate under different perturbations is found by substituting into equation (6). At the same time, the joint equation (8)-equation (10) solves whether the VSG is put in under the corresponding perturbation and the corresponding put-in time. The relationship between the initial frequency change rate and VSG input time under the corresponding perturbation is obtained by finding the perturbation values and the upper and lower boundaries that satisfy case 2).

In this paper, the frequency change rate caused by the disturbance is detected in real-time and matched with the relationship table. If the frequency change rate is less than the lower boundary of case 2), the VSG does not act. If the frequency change rate lies within the range of case 2), the VSG is put in according to the time delay given in the relationship table. If the frequency change rate is greater than the upper boundary of case 2), the VSG is instantaneously operated without delay.

5 VSG exit strategy considering energy storage lifetime

5.1 2 stages of the frequency response process

Taking Fig. 5 as an example, the frequency response process when a load disturbance occurs can be divided into a frequency deviation phase (before point N) and a frequency recovery phase (after point N). At the beginning of the frequency deviation phase, the response process is mainly responded by the inertia of the generator and VSG in the grid, and the grid primary and secondary FMs are almost useless. The rotor decelerates and provides inertial power to the grid, and the frequency gradually decreases. As the frequency deviation increases, the primary frequency regulation of the grid gradually takes effect, and the inertia and primary and secondary frequency regulation jointly suppress the frequency reduction. When the dynamic frequency of the grid reaches its lowest point, the inertia suppression of the frequency change is zero.

The frequency recovery phase is the process of recovering the speed and frequency under the effect of primary and secondary frequency regulation. It also restores the kinetic energy lost by the generator rotor and VSG virtual rotor to their original values. The virtual inertia of the VSG absorbs the FM power during this phase, which constitutes a secondary charge, resulting in slower frequency recovery and loss of energy storage life. Therefore, in order to reduce the amount of energy storage charging and discharging to improve the frequency recovery speed, the VSG inertia response should be withdrawn in time during this phase.

5.2 VSG selective exit criterion

The solution method for the maximum deviation moment tm of dynamic frequency is known according to Section 4.2. However, due to the complex grid disturbance condition, the theoretical value may deviate from the actual situation, so this paper derives the VSG exit moment by detecting the grid frequency trajectory. From the frequency response curve, it can be seen that the rate of change of frequency is the same as the sign of frequency difference in the frequency deviation phase, while the opposite is true in the frequency recovery phase.

The VSG frequency response exit strategy proposed in this paper is: the dynamic frequency ω(t)and the frequency change rate dω/dt are collected at certain sampling intervals during the VSG response, and the sign of dω/dt at each sampling point is dynamically refreshed. The real-time detection of whether dω/dt is equal to zero, if it is satisfied, let the moment be tm. Two points tm-1 and tm+1 are taken in the neighborhood of tm and the sign of dω/dt at that moment is recorded. Based on the sign of dω/dt at tm-1 and tm+1, determine whether equation (11) holds, and if it does, exit the VSG inertial response, if not, continue the detection.(11) {[ω(tm)−ωn]dωdt|t=tm−1<0[ω(tm)−ωn]dωdt|t=tm+1>0

After the VSG virtual inertia exits its role, it starts again if the next load perturbation satisfies the start-up conditions presented in Section 4. Since the load perturbation is random, the average charge for the VSG to perform a large number of perturbation responses should be equal to zero. Therefore, setting the VSG start-up and exit strategies can effectively avoid unnecessary storage charge and discharge times.

6 Algorithm simulation

6.1 Simulation of PV-storage control strategy

Since this paper studies the frequency problem under load perturbation, which is the overall balance of instantaneous power at the microscopic level, the impact of grid topology has not been considered in the research content of this paper. For that reason, the power system is represented by an equivalent synchronous generator with primary and secondary frequency regulation functions in the simulation. The optical-storage VSG is also represented by an equivalent virtual generator, as shown in Fig. 6. The rated power of the equivalent machine is 10 MW, and considering that the prime mover and exciter contain inertia, the inertia parameter of the equivalent grid machine is 1.2 × 105 kg m2. In the PV-storage system, the PV capacity is 250 kW, the energy storage capacity is 550 kWh, and the energy storage power is 250 kW, the VSG inverter capacity is 500 kW. The load on the VSG grid bus changes abruptly from 500 kW to 800 kW at 30s. Thus, the grid capacity is 20 times of the PV-storage VSG capacity, and the proportional relationship is reasonable. The load disturbance is 3 % of the grid capacity, which is consistent with the small disturbance characteristics. Since the relative swing of the rotor between the VSG and the grid equivalent during the frequency dynamics under the small grid disturbance is negligible, the damping is almost ineffective. The PV-storage system is simulated and analyzed under different operation modes according to the control strategy proposed in this paper.Fig. 6 Simulation of grid structure.

Fig. 6

6.1.1 Constant power mode

The PV-storage system is operated in constant power mode with the VSG inertia parameter of J = 2 × 104 kg m2 and the power reference value of Pref = 150 kW. The simulation results of each power curve during steady-state operation and load step disturbance are shown in Fig. 7. Changing the VSG inertia parameter so that J = 1 × 105 kg m2, the grid frequency variation curves for different VSG inertia parameters are shown in Fig. 8.Fig. 7 Power response curve under constant power mode.

Fig. 7

Fig. 8 Frequency curves under different inertia of VSG.

Fig. 8

As can be seen from Fig. 7, Fig. 8, before the disturbance, the PV-storage system and the grid provided 150 and 350 kW of power to the load, respectively. PV-storage VSG and the grid provide dynamic power in the disturbance time, the sum of the two is 800 kW. After stabilization, the PV-storage power is restored to the initial value of 150 kW, and the load increment is completely transferred to the grid. The frequency response curve shows that VSG can output inertial power as the frequency of the grid changes. When VSG inertia increases, under the same disturbance, the frequency decline speed decreases from 0.145 Hz/s to 0.0766 Hz/s, the dynamic frequency deviation decreases from 0.58 % to 0.46 %, and the recovery speed decreases from 0.0138Hz/s to 0.0105Hz/s, which is consistent with the theoretical analysis.

6.1.2 Tracking PV mode

According to the above parameters, the PV-storage system is operated in tracking PV mode, the initial PV output power is 150 kW, the PV power mutates to 200 kW at 20s, and the PV power mutates to 250 kW at 40s, and each power curve is shown in Fig. 9.Fig. 9 Power curve of PV step disturbance in tracking PV mode.

Fig. 9

As can be seen from Fig. 9, the PV-storage outputs power in the expected operating mode, which can correctly respond to grid frequency changes and output inertia power.

6.1.3 Zero power mode

Make the PV-storage system work in tracking photovoltaic mode and the photovoltaic power is zero, so that the system is in zero power mode. The power variation of load disturbance in this mode is shown in Fig. 10.Fig. 10 Power response curve in zero power mode.

Fig. 10

As can be seen from the analysis of Fig. 10, since VSG is in zero power mode, the energy storage power is zero under normal conditions, and the load power is provided by the power grid. At the moment of disturbance, the energy storage releases a certain inertia power to participate in disturbance suppression, and the PV-storage VSG and the power grid jointly provide dynamic power to the load, the sum of the two is 800 kW. After stabilization, the PV-storage power is restored to 0 kW, and the load increment is fully transferred to the power grid.

6.1.3.1 4Energy storage charge and discharge

When the energy storage charge is lower than the lower limit or higher than the upper limit, the PV-storage system will also add energy storage charging and discharging power. In the simulation, the lower limit and upper limit of the energy stored are set as 15 % and 75 % respectively, and the actual energy stored is set as 10 % and 80 % respectively. The energy storage power waveform in the charging and discharging process of load disturbance is shown in Fig. 11(a)–(b).Fig. 11 Energy storage power curve under load disturbance.

Fig. 11

As can be seen from Fig. 11, when the charged state of energy storage exceeds the limit, the control link can correctly control the charge and discharge of energy storage. In the process of charge and discharge, PV-storage VSG can still adjust the inertia power in response to load disturbance.

6.2 Simulation of PV-storage VSG selective input strategy for arithmetic cases

Based on the above simulation parameters, the grid frequency response parameters A1 = 2.58, α1 = 10.56, α2 = 5.63 when the VSG is not put into operation, and A2 = 1.57, α3 = 8.03, α4 = 3.55 when the VSG is put into operation. Let the allowable frequency shift threshold be 0.4 Hz, corresponding to the angular frequency shift threshold Δωth = 2.51 rad/s.

When the load is suddenly increased by 200 kW without VSG input, the frequency response is shown in curve 1 in Fig. 12. It can be seen that the angular frequency shift Δω = 1.95 rad/s, which does not exceed the allowable threshold and does not satisfy equation (8). It means that the dynamic frequency shift does not cross the limit without VSG involvement in the case of small disturbances.Fig. 12 Simulation curves of VSG plug in strategy in various disturbances.

Fig. 12

When the load is suddenly increased by 350 kW, the frequency response is shown in curve 2 in Fig. 12. It can be seen that the angular frequency shift Δω = 2.64 rad/s, which is beyond the allowable threshold, requires the VSG to participate in regulation. Solving equations (6), (7), (8) gives t0 = 32 s. The VSG starts at t0, and the frequency response is shown in curve 3 in Fig. 12. It can be seen that putting in the VSG at t0 = 32 s is just enough to keep the frequency excursion within the threshold.

When the load is suddenly increased by 500 kW, the frequency response is shown in curve 4 in Fig. 12, and the angular frequency shift Δω = 3.20 rad/s, which exceeds the allowable threshold. Solving equations (6), (7), (8) yields t0 = - 5 s, indicating that the VSG should be engaged immediately during a disturbance. The frequency response of the grid with VSG engaged is shown in curve 5 in Fig. 12, and the frequency shift is suppressed.

The above analysis shows that the VSG participation accords with the proposed strategy, and VSG control doesn't startup when the disturbances are not enough to significantly reduce the frequency of the system. The VSG is involved in dynamic FM regulation only in larger disturbances, reducing the charge and discharge of energy storage and extending the energy storage life.

6.3 Simulation of PV-storage VSG exit strategies for arithmetic cases

The effectiveness of the VSG exit strategy is verified based on the above simulation algorithm. The frequency response curve of the grid subjected to load disturbance with the VSG participating in grid frequency regulation is shown in curve 1 in Fig. 13. The sampling interval is 100 ms, and tm-1 and tm+1 are taken as tm-0.5 s and tm + 0.5 s, respectively. When tm = 32 s in the frequency response curve ω(tm) = 49.73 Hz, which is the maximum value of dynamic frequency shift. At this time:(12) {dωdt|t=tm−1=−0.54dωdt|t=tm+1=0.49

Fig. 13 Simulation curves of VSG plug-out strategy.

Fig. 13

Substituting equation (12) into equation (11), the exit criterion is satisfied, indicating that the exit criterion in this paper is valid. At this time, VSG can be respectively selected to hold or exit, than the curve 1 and curve 2 in Fig. 13 can be simulated respectively. It can be seen that the frequency recovery of curve 1 is faster than curve 2, indicating that timely exit VSG in the frequency recovery phase can avoid both the secondary charging of energy storage and facilitate frequency recovery.

6.4 Performance analysis of VSG input and exit policies

In order to verify the effectiveness of the selective input-exit scheme proposed in this paper, the daily throughput of energy storage under different disturbances is taken as an index and compared with the method proposed in the literature [29]. Assuming that the load disturbance is considered in step form and the average period is 20 s, a total of 4320 load disturbances occur every day. If the angular frequency offset threshold is Δωth = 2.51 rad/s, then according to the input strategy analysis in Section 4.2, VSG input is not required when the load disturbance is less than 290 kW. When the load is between 290 and 420 kW, VSG is partially input. When the load is greater than 420 kW, VSG needs to be fully invested. The frequency of disturbance within 290 kW is 60 %, and the average intensity is 220 kW. The frequency of disturbance between 290 and 420 kW accounted for 30 %, and the average intensity was 370 kW. The number of disturbances greater than 420 kW accounted for 10 %, and the average intensity was 620 kW. The comparison results are shown in Fig. 14.Fig. 14 Comparison of energy storage charging and discharging amount in VSG withdrawal strategy and no strategy.

Fig. 14

As can be seen from Fig. 14, when load disturbance of different degrees is given, the daily throughput of energy storage is 1.2 kWh, 12.9 kWh and 26.8 kWh respectively when VSG input strategy is adopted, while the daily throughput of energy storage is 3.2 kWh, 9.7 kWh and 15.1 kWh respectively when VSG exit strategy is adopted. However, the huff and puff power without the put-back strategy are 52.1 kWh, 33.8 kWh and 24.9 kWh, respectively. Since the random disturbance of positive and negative load is equal probability, half of the energy stored is the equivalent charge amount or discharge amount of energy stored. It can be seen that the use of energy storage using the selective investment and withdrawal strategy proposed in this paper is 37.82 % lower than that without the investment and withdrawal strategy. Therefore, the VSG selective reversion strategy proposed in this paper can signally improve the charging and discharging life of energy storage.

6.5 Semi-physical experiment

In order to further verify the effectiveness of the proposed control method, real-time hardware-in-the-loop simulation is carried out based on NI-PXI + LabVIEW platform, and the operation scenarios corresponding to the examples in this section are verified respectively. The real time simulator composed of PXI-1081 and FPGA board of NI Company is used, which runs in LabVIEW and builds the electrical model of the system and the underlying control system. The model outputs the voltage, current and power signals of each subsystem according to the instructions of the top-level control. The hardware platform is shown in Fig. 15. Power curves in different operating modes are shown in Fig. 16(a)–. (b) and (c).Fig. 15 Semi-physical simulation platform.

Fig. 15

Fig. 16 Experimental result.

Fig. 16

As can be seen from Fig. 16(a)–. (b) and (c), the semi-physical results are basically consistent with the Matlab/Simulink simulation results. The PV-storage system outputs power according to the expected working mode, correctly responds to the frequency change of the power grid and outputs inertia power. The effectiveness of the proposed method is verified.

7 Conclusions

Combined with the characteristics of PV-storage systems, this paper puts forward a VSG input and exit strategy to improve the life of PV-storage systems and draws the following conclusions.(1) According to the capacity and functional positioning of the energy storage configuration, PV-storage VSG can have different modes of operation. This paper puts forward the operation control strategy based on three operation modes of PV-storage VSG, which can effectively realize the control of different operation modes of PV-storage systems.

(2) A method to selectively start VSG based on disturbance conditions is proposed, so that the grid preferentially uses physical generator inertia for disturbance suppression, reducing the number of storage charges and discharges, which enhances the life of energy storage.

(3) Taking advantage of the flexible and adjustable parameters of PV-storage VSG, the exit strategy of PV-storage VSG in the frequency recovery stage is proposed, which can further reduce the energy storage throughput power, enhancing the life of energy storage and improving the frequency recovery speed of the power grid.

Due to the low power level of the example in this paper, the results of this study have great engineering significance for the operation and planning of microgrid and distribution network. However, when it come to the large power systems with high power levels, the results of this study have some limitations. Considering the above problems, the authors will conduct further research in the future.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Fang Liu: Conceptualization. Zhongliang Li: Software. Xiaomeng Wang: Validation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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References

1 Sabo A. Kolapo B.Y. Odoh T.E. Dyari M. Abdul Wahab N.I. Veerasamy V. Solar Wind and their hybridization integration for multi-machine power system oscillation controllers optimization: a review Energies 16 2023 24 10.3390/en16010024
2 Elsaraf H. Jamil M. Pandey B. Techno-economic design of a combined heat and power microgrid for a remote community in newfoundland Canada IEEE Access 9 2021 91548 91563 10.1109/ACCESS.2021.3091738
3 Masalha I. binti Masuri S.U. Badran O. bin Mohd Ariffin M.K.A. Abi Talib A.R. Alfaqs F. Theoretical and experimental study on the performance of photovoltaic using porous media cooling under indoor condition Int. J. Renew. Energy Dev. 12 2 2023 313 327 10.14710/ijred.2023.47686
4 Mustafa R. Mohd Radzi M.A.B. Hizam H.B. Che Soh A. An innovative air-cooling system for efficiency improvement of retrofitted rooftop photovoltaic module using cross-flow fan Int. J. Renew. Energy Dev. 13 2 2024 223 234 10.61435/ijred.2024.60068
5 Zha Y. Lin J. Li G. Wang Y. Yizhang Analysis of inertia characteristics of photovoltaic power generation system based on generalized droop control IEEE Access 9 2021 37834 37839 10.1109/ACCESS.2021.3059678
6 Xiong L.S. Zhuo F. Wang F. Static synchronous generator model： A new perspective to investigate dynamic characteristics and stability issues of grid-tied PWM inverter IEEE Trans. Power Electron. 31 9 2016 6264 6280
7 Gu H.J. F Y.A.N.R. Tapan K.S. Minimum synchronous inertia requirement renewable power systems IEEE Trans. Power Syst. 33 2 2018 1533 1543
8 Mao M. Qian C. Chang L. Du Y. Coordination control for paralleled inverters based on VSG for PV/battery microgrid 2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia) 2018 1472 1477 10.23919/IPEC.2018.8507844 3
9 Zhong Q.C. George W. Synchronverters：Inverters that mimic synchronous generators IEEE Trans. Ind. Electron. 58 4 2011 1259 1267
10 Zhang X. Gao Q. Hu Y. Zhang H. Guo Z. Active power reserve photovoltaic virtual synchronization control technology Chinese Journal of Electrical Engineering 6 2 June 2020 1 6 10.23919/CJEE.2020.000006
11 Liu Y. Wang Y. Wang M. Xu Z. Peng Y. Li M. Coordinated VSG control of photovoltaic/battery system for maximum power output and grid supporting IEEE Journal on Emerging and Selected Topics in Circuits and Systems 12 1 March 2022 301 309 10.1109/JETCAS.2022.3143716
12 Hasabelrasul H. Cai Z. Sun L. Suo X. Matraji I. Two-stage converter standalone PV-battery system based on VSG control IEEE Access 10 2022 39825 39832 10.1109/ACCESS.2022.3165664
13 Wu H. Ruan X.B. Yang D.S. Modeling of the power loop and parameter design of virtual synchronous generators Proceedings of the CSEE vol. 35 2015 6508 6518 24
14 Alipoor J. Miura Y. Toshifumi I. Stability assessment and optimization methods for microgrid with multiple VSG units IEEE Trans. Smart Grid 9 2 2018 1462 1471
15 Gao Jie Tong W.A.N.G. Zhao Wei Review on the development and prospect of active support technologies for wind power and photovoltaic stations to improve the security and stability level of power system New Type Power Systems 2 2 2024 201 222 10.20121/j.2097-2784.ntps.240013 (in Chinese)
16 Xu H. Su J. Liu N. Shi Y. A grid-supporting photovoltaic system implemented by a VSG with energy storage Energies 11 2018 3152 10.3390/en11113152
17 Yao G. Lu Z. Wang Y. Benbouzid M. Moreau L. A virtual synchronous generator based hierarchical control scheme of distributed generation systems Energies 10 2017 2049 10.3390/en10122049
18 Sultana U. Umer M. Shamoon M. Hasan M. Optimal planning of a photovoltaic-based grid-connected electric vehicle charging system using teaching–learning-based optimization (TLBO) Eng. Proc. 20 2022 28 10.3390/engproc2022020028
19 Wang Yang Yang Junfeng Yi Z.H.A.O. A joint frequency modulation strategy for wind/solar/storage based on SOC of energy storage and wind and solar power margin regulation Power System and Clean Energ 40 4 2024 150 158 (in Chinese)
20 Sonawane A.J. Umarikar A.C. Small-signal stability analysis of PV-based synchronverter including PV operating modes and DC-link voltage controller IEEE Trans. Ind. Electron. 69 8 Aug. 2022 8028 8039 10.1109/TIE.2021.3109506
21 ang Z.W. Research on the active power coordination control system for wind/photovoltaic/energy storage 2017 IEEE Conference on Energy Internet and Energy System Integration (EI2) 2017 1 5 10.1109/EI2.2017.8245403 Beijing, China
22 Zhang Xiaolei VSG Energy Storage Unit Configuration and Cost Analysis Taking into Account Primary Frequency and Inertia Support 2020 North China Electric Power University 10.27139/d.cnki.ghbdu.2020.000632
23 Chunming Tu Yang Yi Zheng Lan Secondary frequency regulation strategy in microgrid based on VSG Trans. China Electrotech. Soc. 33 10 2018 2186 2195 (in Chinese)
24 Jixiang Li Jinbin Zhao Keqing Qü Boundary analysis of operation parameters of microgrid VSG considering SOC characteristics Power Syst. Technol. 42 5 2018 1451 1457 (in Chinese)
25 Fang J. Tang Y. Li H. Li X. A battery/ultracapacitor hybrid energy storage system for implementing the power management of virtual synchronous generators IEEE Trans. Power Electron. 33 4 April 2018 2820 2824 10.1109/TPEL.2017.2759256
26 Zhang X. Gao Q. Hu Y. Zhang H. Guo Z. Active power reserve photovoltaic virtual synchronization control technology Chinese Journal of Electrical Engineering 6 2 June 2020 1 6 10.23919/CJEE.2020.000006
27 Liang W. Liu Y. Shen Y. Active power control integrated with reactive power compensation of battery energy stored quasi-Z source inverter PV power system operating in VSG mode IEEE Journal of Emerging and Selected Topics in Power Electronics 11 1 Feb. 2023 339 350 10.1109/JESTPE.2021.3137397
28 Song Qiong Zhang Hui Sun Kai Improved adaptive control of inertia for virtual synchronous generators in islanding micro-grid with multiple distributed generation units Proceedings of the CSEE 37 2 2017 412 424 (in Chinese)
29 Gao J.R. Li G J. Wang K.Y. Control of grid connected PV-battery virtual synchronous machine considering battery charging/discharging power limit Autom. Electr. Power Syst. 44 4 2020 134 150
