Operation Control Design of Grid-Connected Photovoltaic and Fuel Cell/Supercapacitor Hybrid Energy Storage System

Abstract

In order to smooth the fluctuation of photovoltaic (PV) power affected by irradiation conditions, weaken the frequent disturbance to the distribution network, and, thus, enhance its acceptance to PV, a fuel cell/supercapacitor hybrid energy storage device (FSHESS) is configured on the DC side of a grid-connected PV system, which is combined with the PV unit to form a hybrid PV power generation system, i.e., the PV-FSHESS. Based on the analysis of the electrical characteristics of the FC and the SC, an improved low-pass filtering method based on rules and considering the state of charge constraint of the SC is proposed for the power allocation of the FSHESS. With respect to the problem of DC-bus voltage stabilization, a modified variable speed integral nonlinear PI controller is presented for the purpose of overcoming the following disadvantages: (i) the ordinary PI controller cannot adaptively adjust the cumulative speed of the integral term in line with the deviation, which may cause large overshoot and oscillation; and (ii) the conventional variable speed integral controller has more parameters, which increases the difficulty of parameter tuning. The simulation verification is carried out under different operating conditions of PV output power and load demands, and the results prove the effectiveness of the proposed control scheme.

1. Introduction

Solar energy is a typical clean energy with unlimited reserves. Constructing photovoltaic (PV) power generation systems and fully utilizing the solar resources are conducive to environmental governance and protection [1,2]. However, due to changes in irradiance and temperature conditions, the PV output power is characterized by periodicity and intermittence. When the PV power generation system is connected to the distribution network (DN), the PV output power and the local load demands generally cannot completely match, and the resulting power difference will cause interference to the DN and affect its safe and stable operation [3,4,5]. In order to smooth the fluctuation of the PV output power, it has become an important and effective solution to configure energy storage (ES) systems because of their outstanding advantages, such as strong regulation ability and fast response speed [6,7,8,9]. Adding ES to the PV power generation system is equivalent to providing a buffer; that is, the power difference that originally needs to be compensated by the DN can be undertaken by the ES system, which reduces the frequent disturbances to the DN, owing to the mismatch between the PV output power and the load demands. In addition, the ES possesses the dual attributes of source and load, i.e., the ES cannot only absorb the surplus power generated by the PV system, like a load, but can also provide power as a source to meet the load demands when the PV output power is insufficient. All of these advantages are helpful in increasing the utilization of solar energy and improving the acceptance capacity of DN to PV power generation systems [10,11,12].

The performance indices of evaluating the ES mainly include energy density, power density, and service life. The ES devices can be divided into two categories according to their characteristics, namely, the energy type and the power type [13]. The energy-type ES devices, such as Li-ion batteries (LIBs) and fuel cells (FCs), are normally of large energy capacity and short lifetime. In contrast to the energy-type ES devices, the power-type ones, like supercapacitors (SCs), boast high power density and long cycle life. In real applications, it is difficult for a single type of ES device to meet the requirements of large storage capacity, high charging/discharging rate, and long service life. Therefore, the hybrid energy storage system (HESS), composed of two or more different types of ES devices, has been highly valued [14,15]. Many different combinations are presented in the published works, for instance, FC-LIB, LIB-SC, and FC-SC, to name just a few [16,17,18]. Compared with the LIB, the FC has a higher energy conversion rate, stronger overload capacity, and better environmental friendliness. Consequently, the combination of the FC-SC hybrid energy storage and the grid-connected distributed PV system (abbreviated as PV-FSHESS) is an eco-friendly solution and has promising application prospects for enhancing the autonomous regulating capability of the distributed PV systems and increasing its penetration rate in DNs [19,20,21].

For the purpose of ensuring the safety and stability of the grid-connected PV-FSHESS and making the FSHESS give full play to its ability to smooth the PV power fluctuation, it is essential to design a reasonable operation control scheme [22]. It is worth noting that such a control scheme includes two levels, i.e., the high-level strategy and the low-level control. The high-level strategy mainly aims to make reasonable decisions about how much power the FSHESS will release or absorb to mitigate the PV’s output power variation; the low-level control pays attention to the grid-connected inverter’s control, to be specific, by achieving simultaneous DC-bus voltage stabilization and unity power factor operation of the inverter, with satisfactory static and dynamic performance. It is of great significance to make the DC-bus voltage stable, since its instability will cause some negative effects, for instance, reducing the power conversion efficiency of the power electronic devices, endangering voltage-sensitive electrical equipment, and degrading the effectiveness of PV’s MPPT control. As a result, the DC-bus voltage must be regulated to its reference value with satisfactory closed-loop behavior.

On the subject of the high-level strategy for the FSHESS, since the properties of different kinds of ES units are quite different, it is compulsory to allocate the power borne by each ES unit in line with its own characteristics [23]. A detailed overview of the power distribution strategy of LIB-SC HESS based on different methods, such as rules, low-pass filters, and optimization, is presented in [24]. Unlike LIBs, which can be charged/discharged bidirectionally, FC has a unidirectional power flow; that is, it cannot directly absorb excess power. Therefore, in the FSHESS, when the PV output power is greater than the load demand, the SC needs to assume all of the power surplus. In this context, the SC’s state of charge (SOC) must be estimated and kept in a safe range for a configured SC unit with limited capacitance to ensure the safe operation of FSHESS. Apart from the operation strategy of the FSHESS, the PV and the inverter’s running mode also belong to the high level. In accordance with practice, the PV system usually runs in the maximum power point tracking (MPPT) mode to fully exploit the solar energy; the grid-connected inverter mainly operates in the unity power factor mode. With respect to the low-level control, it specifically refers to what kind of control algorithms are adopted to control the power electronic devices, like DC/DC and DC/AC. The widely used controller is PI; for instance, the double closed-loop PI control method is applied for the DC/AC inverter to realize the DC-bus voltage’s stabilization and grid-connected operation [25,26,27]. Since the integral coefficient of the ordinary PI controller is constant, the integral increment remains unchanged during the controller’s regulation process. When the regulation error is too large, it will result in integral accumulation, which will reduce the system’s dynamic performance, for example, large overshoot and oscillation [28]. In real applications, when the irradiance changes drastically, the PV output power will change accordingly in a large range, which will bring about excessive voltage deviation of the DC-bus voltage. As a result, the dynamic characteristics of the DC-bus voltage control with the ordinary PI controller will also deteriorate.

Based on the above analysis, we know that the design of a reasonable and reliable PV-FSHESS operation control scheme must comprehensively consider the characteristics of the FC and the SC, actual operating conditions, allowable SOC ranges, and the dynamic and steady-state performance of the controlled system. Aiming at the power allocation problem of FSHESS, this paper proposes a power allocation strategy based on rules and considering the SC’s SOC constraint; dealing with the problem that the ordinary PI controller with a constant integral constant cannot adjust the deviation adaptively, this study presents an improved variable speed integral PI control method. Simulation results under various operating conditions verify the effectiveness of the proposed PV-FSHESS operation control scheme.

The remainder of this paper is organized as follows: In Section 2, the structure of the grid-connected PV-FSHESS system is described. In Section 3, the power allocation strategy of the FSHESS is elaborated. In Section 4, the low-level controller design based on a modified variable speed integral PI approach is detailed. In Section 5, the case studies and the simulation results are illustrated. Finally, conclusions are drawn in Section 6.

2. Structure of the Grid-Connected PV-FSHESS System

The schematic diagram of the distributed PV power generation system configured with FSHESS is pictured in Figure 1. The PV units at each node are equipped with HESS and then connected to the DN via grid-connected inverters. Taking one node as an example, we perceive that from the arrow direction describing the power flow that the PV generates power, the local load consumes power, and FSHESS and DN can provide bidirectional power flow. Compared with the configuration without the FSHESS, the disturbance to DN caused by the power unbalance between the PV and the load can be significantly reduced if the FSHESS can compensate for the power difference as much as possible by designing a reasonable operational strategy.

Since the FC and the SC can be regarded as DC power sources, they can be connected to the DC-bus through DC/DCs, respectively. From the perspective of the power grid, the PV, the FSHESS, and the DC-bus together constitute a DC microgrid [29]. Then, the DC microgrid is coupled to the DN via a DC/AC inverter to work in the grid-connected mode. Such a configuration is depicted in Figure 2. With the fact of FC’s unidirectional power flow, the FC, the same as the PV, is connected to the DC-bus through a unidirectional DC/DC. The SC, which can absorb and release active power, takes a bidirectional DC/DC as the interface to the DC-bus.

3. Power Allocation Strategy of the FSHESS

From Figure 2, we can build the active power balance relationship of all the sources in the PV-FSHESS as follows:

$$\left\{\begin{array}{l}{P}_{pv}-P_{load}=P_{FSHESS}\hfill \\ P_{FSHESS}=P_{fc}+P_{sc}\hfill \end{array}\right.$$

(1)

where P_pv and P_load are the PV output power and the load demand, respectively; P_FSHESS represents the total power undertaken by the FSHESS, and P_fc and P_sc stand for the power provided by FC and SC, respectively.

It is obvious that when P_pv > P_load, P_FSHESS > 0, which is defined in this study as the absorbing power of the FSHESS; when P_pv < P_load, P_FSHESS < 0, the FSHESS releases power. Since the FC works in a discharging mode, when P_FSHESS > 0, only the SC absorbs power, and there is no power distribution problem between the FC and the SC units; when P_FSHESS < 0, both the FC and the SC release power together, and then the P_FSHESS needs to be allocated. In addition, due to the relatively low energy density of the SC, it is necessary to consider its SOC constraints when designing the power allocation strategy to ensure the safety of its operation.

3.1. Determination of Allowable SOC Range of the SC

During the SC’s charging/discharging process, the signals that can be directly measured include the current and the terminal voltage. Accordingly, the SC’s SOC needs to be obtained by estimation. A single cycle charging/discharging curve of a typical electric double-layer supercapacitor with a constant current is shown in Figure 3. It is clear that the relationship between the current and the terminal voltage is basically linear. Therefore, the first-order equivalent circuit model, as depicted in Figure 4, can accurately describe the external electrical characteristics of the SC.

When the equivalent series resistance R_es is ignored, the electrical characteristic model of the SC can be established as follows:

$$\left\{\begin{array}{l}{i}_{sc}=C_{sc}{\displaystyle \frac{d{u}_{sc}}{dt}}\hfill \\ P_{sc}=i_{sc}{u}_{sc}=C_{sc}{u}_{sc}{\displaystyle \frac{d{u}_{sc}}{dt}}\hfill \\ Q_{sc}={\displaystyle \int P_{sc}dt}={\displaystyle \frac{1}{2}}{C}_{sc}{u}_{sc}^2\hfill \end{array}\right.$$

(2)

where C_sc is the equivalent capacitance of the SC; i_sc and u_sc are the charging/discharging current and the terminal voltage; and P_sc and Q_sc are the power and the stored energy, respectively.

The commonly used definition of the SC’s SOC is given as follows [30]:

$$SOC={\displaystyle \frac{Q_{sc\_c}}{Q_{sc\_\max }}}\times 100\%={\left({\displaystyle \frac{u_{sc\_c}}{u_{sc\_\max }}}\right)}^2\times 100\%$$

(3)

where Q_{sc_c} is the real stored energy of the SC, and Q_{sc_max} is the maximum storage energy; u_{sc_c} and u_{sc_max} are the real terminal voltage and the maximum terminal voltage of the SC, respectively.

It is evident that the SC’s SOC can be estimated directly by measuring its terminal voltage. For example, when u_{sc_c} is half of the maximum terminal voltage, then the SOC equals 25%. Since the R_es and the parameters’ perturbation of the equivalent circuit model are ignored in the above analysis, the estimated SOC should be revised. Therefore, we add a loss coefficient to Equation (3) and obtain the expression adopted in this study as follows:

$$SOC=\zeta {\left({\displaystyle \frac{u_{sc\_c}}{u_{sc\_\max }}}\right)}^2\times 100\%$$

(4)

where ζ denotes the loss coefficient.

The value of the loss coefficient is related to the selection of the specific SC type. Additionally, when the terminal voltage of the SC is too low, in compliance with the power balance relationship, it is required for the SC to quickly increase the charging/discharging current to compensate for the fluctuation in the PV output power. Consequently, from the view of safety, the allowable working range of terminal voltage of the SC must be reasonably limited. With these facts in mind, we determine the allowable terminal voltage range of the SC as [0.5u_{sc_max}, u_{sc_max}], and the loss coefficient ζ = 0.9. Based on the settings, the allowable SOC range is calculated to be [22.5%, 90%].

3.2. Improved Power Allocation Strategy Based on Rules and SC Constraints

Since the FC and SC should meet different constraints during their running process, we define the operation state (OS) of them according to the power flow direction of the P_FSHESS as follows:

$$O{S}_{fc}=\left\{\begin{array}{l}1,P_{FSHESS}\le 0\hfill \\ 0,P_{FSHESS}>0\hfill \end{array}\right.$$

(5)

$$O{S}_{sc}=\left\{\begin{array}{l}1,P_{FSHESS}\le 0\hfill \\ -1,P_{FSHESS}>0\hfill \end{array}\right.$$

(6)

where 1, 0, and −1 represent the discharging, standing, and charging states, respectively.

Based on the OS of the FC and the SC, the power distribution strategy can be considered in two situations.

(1)

$P_{FSHESS}>0$, SC charging and FC standing.

In this situation, if the SC can realize full compensation for the power difference between the PV and the load demand, its charging current is calculated by the following:

$$i_{sc\_ch}={\displaystyle \frac{P_{FSHESS}}{u_{sc\_c}}}$$

(7)

where i_{sc_ch} is the charging current under the condition of full power compensation.

Considering the maximum allowable current and the SOC constraints of the SC, the actual charging current reference value i_{sc_ch_ref} can be obtained as follows:

$$i_{sc\_ch\_ref}=\left\{\begin{array}{ll}{i}_{sc\_ch},\hspace{1em}\hspace{1em}\hspace{1em}{i}_{sc\_ch}<i_{sc\_\max }\hspace{1em}\&\hfill & SOC<SO{C}_{\max }\hfill \\ i_{sc\_\max },\hspace{1em}\hspace{1em} i_{sc\_ch}\ge i_{sc\_\max }\hspace{1em}\&\hfill & SOC<SO{C}_{\max }\hfill \\ 0,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}SOC=SO{C}_{\max }\hfill & \hfill \end{array}\right.$$

(8)

where i_{sc_max} is the maximum allowable current for the SC, and SOC_max is the maximum allowable SOC.

(2)

$P_{FSHESS}\le 0$, SC discharging and FC discharging.

In this situation, in order to exploit the performance advantage of high energy density, the FC should support the main part of the total power demand. For this reason, a low-pass filter (LPF) can be applied to allocate the shared power for the FC and the SC. As a result, the power undertaken by FC and the SC is attained with the following:

$$P_{fc}=f_{LPF}\left(P_{FSHESS}\right)$$

(9)

$$P_{sc}=P_{FSHESS}-P_{fc}$$

(10)

where f_LPF is a first-order low-pass filter.

Furthermore, the discharging current of the FC and the SC can be acquired by the following:

$$i_{fc\_ref}={\displaystyle \frac{P_{fc}}{u_{fc}}}$$

(11)

$$i_{sc\_dis}={\displaystyle \frac{P_{sc}}{u_{sc\_c}}}$$

(12)

where i_{sc_dis} is the discharging current of the SC, i_{fc_ref} is the actual discharging current reference value, and u_fc is the terminal voltage of the FC.

Similarly, in order to ensure that the SC is not overdischarged, its actual discharging reference current value i_{sc_dis_ref} is calculated as follows:

$$i_{sc\_dis\_ref}=\left\{\begin{array}{ll}{i}_{sc\_dis},\hspace{1em}\hspace{1em}\left|i_{sc\_dis}\right|<i_{sc\_\max }\hspace{1em}\&\hfill & SOC>SO{C}_{\min }\hfill \\ -i_{sc\_\max },\hspace{1em}\left|i_{sc\_dis}\right|\ge i_{sc\_\max }\hspace{1em}\&\hfill & SOC>SO{C}_{\min }\hfill \\ 0,\hspace{1em}\hspace{1em}\hspace{1em} SOC=SO{C}_{\min }\hfill & \hfill \end{array}\right.$$

(13)

where SOC_min is the minimum allowable SOC of the SC.

Combining the above two situations, the improved LPF power allocation strategy based on rules and SC constraints is illustrated in Figure 5. After obtaining the current reference values of the two ES units with the proposed power allocation strategy, the low-level control can achieve current tracking by utilizing a PI controller for its respective DC/DC converter.

4. Grid-Connected Inverter Control Based on Modified Variable Speed Integral Nonlinear PI

Since the above-proposed high-level strategy does not consider the uncertainties that will cause power losses, like circuit parameter perturbation, non-ideal efficiency of power electronic devices, etc., the DC-bus voltage will still deviate from the reference value under the influence of these uncertainties. To guarantee that the DC-bus voltage is always stabilized at its reference value, the double closed-loop PI controller is commonly adopted to control the DC/AC inverter. However, the conventional PI controller has a constant integral coefficient, which tends to bring about integral accumulation when the deviation is too large and deteriorate the dynamic performance during the regulation process. Hence, to overcome such shortcomings, this study proposes a modified variable speed integral nonlinear PI controller to regulate the DC-bus voltage.

4.1. Mathematical Model of the Grid-Connected Inverter

The topology of a grid-connected three-phase DC/AC inverter is shown in Figure 6. Based on the dq synchronous rotating coordinate transformation, the active and reactive power control can be decoupled. As a result, we can adopt two independent PI controllers to realize the grid-connected control.

The mathematical model of the DC/AC in the dq coordinate system can be established as follows [31,32]:

$$\left\{\begin{array}{l}{e}_d=u_d-R{i}_d-L{\displaystyle \frac{d{i}_d}{dt}}+\omega L{i}_q\hfill \\ e_q=u_q-R{i}_q-L{\displaystyle \frac{d{i}_q}{dt}}-\omega L{i}_d\hfill \end{array}\right.$$

(14)

where L and R are the inductance and resistance values of the L-type filter, respectively; e_d and e_q are the d-axis and q-axis components of the DN’s voltage; u_d and u_q are the d-axis and q-axis components of the DC/AC’s output voltage; i_d and i_q are the d-axis and q-axis components of the grid-connected current; and ω is the angular frequency.

By applying Laplace transformation in Equation (14) and canceling the coupling terms with feedforward compensation, we obtain the following model in the complex frequency domain as follows:

$$\left\{\begin{array}{l}{E}_d\left(s\right)=U_d\left(s\right)-\left(sL+R\right)I_d\left(s\right)\hfill \\ E_q\left(s\right)=U_q\left(s\right)-\left(sL+R\right)I_q\left(s\right)\hfill \end{array}\right.$$

(15)

where s is the Laplace transformation operator; E_d (s) and E_q (s) are the Laplace transformations of e_d and e_q [31,32], respectively, U_d (s) and U_q (s) of u_d and u_q, and I_d (s) and I_q (s) of i_d and i_q.

When employing vector control based on grid voltage orientation, the instantaneous active power p and reactive power q of the system satisfy the following relationship:

$$\left\{\begin{array}{l}p={\displaystyle \frac{3}{2}}{e}_d{i}_d\hfill \\ q={\displaystyle \frac{3}{2}}{e}_d{i}_q\hfill \end{array}\right.$$

(16)

Consequently, the active and reactive power regulation of the grid-connected inverter can be achieved by controlling i_d and i_q independently. Additionally, if the DC/AC is operating in the unity power factor mode, the reference input for the q-axis current equals zero, i.e., i_{q_ref} = 0. With respect to the reference current for the d-axis, in order to stabilize the DC-bus voltage under uncertainties, the i_{d_ref} is determined by the DC-bus voltage control loop.

4.2. Modified Variable Speed Integral Nonlinear PI Algorithm

In contrast to the ordinary PI, variable speed integral PI can adjust the accumulating speed of integral terms adaptively and dynamically with reference to the real-time deviation, which is beneficial to improve the dynamic performance of the system. Given the expected value of the DC-bus voltage U_{dc_ref} and the actual measured value U_dc, the deviation at each sampling time can be calculated as follows:

$$U_{err}\left(k\right)=U_{dc\_ref}\left(k\right)-U_{dc}\left(k\right),k=1,2,3\cdots$$

(17)

where U_err denotes the DC-bus voltage deviation, and k denotes the sampling time.

With the aim of eliminating the oscillation induced by the frequent adjustment, a dead-zone nonlinear block is introduced to act on the real-time deviation U_err, which is shown in Equation (18). Apparently, when U_err is less than the preset threshold, the output of the dead-zone block is zero, and the following PI controller will not adjust.

$$e\left(k\right)=\left\{\begin{array}{l}0\hspace{1em}\hspace{1em}\hspace{1em} \left|U_{err}\left(k\right)\right|<\delta \hfill \\ U_{err}\left(k\right)\hspace{1em}\left|U_{err}\left(k\right)\right|\ge \delta \hfill \end{array}\right.,k=1,2,3,\cdots$$

(18)

where δ is the preset dead-zone threshold, and e is the output of the dead-zone nonlinear block.

The conventional variable speed integral PI controller has two parameters to be tuned [28]. To reduce the difficulty of tuning the controller’s parameters, we utilize the modified variable speed integral term, which only contains one parameter as follows:

$$f\left(e\left(k\right)\right)=\left\{\begin{array}{l}{\displaystyle \frac{\xi -\left|e\left(k\right)\right|}{\xi }}\hspace{1em}\left|e\left(k\right)\right|<\xi \hfill \\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \left|e\left(k\right)\right|\ge \xi \hfill \end{array}\right.,k=1,2,3,\cdots$$

(19)

where ξ is the setting parameter of the modified variable speed term, and f denotes the calculated weight coefficient of the variable speed integral term.

Furthermore, the reference current i_{d_ref} can be obtained as follows:

$$i_{d\_ref}\left(k\right)=k_{pu}e\left(k\right)+k_{iu}\left({\displaystyle \sum _{i=0}^{k-1}e\left(i\right)}+f\left(e\left(k\right)\right)e\left(k\right)\right)T$$

(20)

where k_pu and k_iu are the proportional and integral coefficients of the voltage loop, and T is the sampling period.

On the basis of the above demonstration, the block diagram of the modified variable speed integral PI control algorithm is pictured in Figure 7.

5. Results and Discussion

In this subsection, the configuration of the PV-FSHESS, as shown in Figure 2, is implemented in the Matlab/Simulink environment(Matlab R2024b) to test the performance and verify the effectiveness of the proposed operation control scheme under different working conditions. The PV-FSHESS’s circuit parameters in the simulation model are listed in

Table 1. Circuit parameters of PV-FSHESS.

Circuit Parameter	Value	Parameter Description
R1/Ω	0.0005	Input equivalent resistance of the boost DC/DC
L1/H	0.001	Input inductance of the boost DC/DC
R2/Ω	0.0005	Input equivalent resistance of the bidirectional DC/DC
L2/H	0.001	Input equivalent inductance of the bidirectional DC/DC
Cdc/F	0.0022	Capacitance of the DC-bus capacitor
Esc/V	300	Terminal voltage of the SC
Efc/V	350	Terminal voltage of the FC
Udc_ref/V	750	Reference value of the DC-bus voltage
Ppv_max/kW	30	Maximum output power of the PV
L3/H	0.0018	Inductance of the grid-connected filter
R3/Ω	0.0005	Equivalent resistance of the grid-connected filter
ugrid/V	380	RMS of the grid-connected voltage
f/Hz	50	Frequency of the DN

. The simulation step is set as 1e-6 s in all of the following cases.

5.1. Power Allocation Effect Analysis of the FSHESS

The simulated PV output power versus the load demand and the power difference between them is shown in Figure 8a. Under this working condition, the initial SOC of the SC is set to 30%, 60%, and 90%, respectively. The results of the power allocation for the FC and the SC based on the proposed strategy are depicted in Figure 8b. The SOC’s tendency is displayed in Figure 8c.

We can recognize that when P_FSHESS > 0, only the SC is charged, which is consistent with the FC and the SC’s power flow constraint. Additionally, if the SOC reaches the allowable upper limit (90%), whether in the initial or during the running process, the SC will not absorb power in case it is overcharged, since the power allocation strategy considers the safe working range of the SC; when P_FSHESS < 0, both the FC and the SC discharge together. However, the FC supports the main part of the total power demand, while the SC provides extra power compensation when the load demand suddenly changes based on the low-pass filter, which takes advantage of the FC and the SC’s performance characteristics.

5.2. Control Effect Analysis of the DC-Bus Voltage

Under the influence of the uncertainties, the DC-bus voltage will deviate from its reference value. Especially when the control action cuts in, or the PV output power and the load demand fluctuate severely, the DC-bus voltage will suffer a large deviation. In this subsection, to verify the DC-bus voltage control performance of the presented improved variable speed integral PI compared to the ordinary PI, simulations are carried out without considering the role of FSHESS. The specific control parameters are listed in

Table 2. Parameters of the modified PI controller.

Controller Parameters	Value	Parameter Description
δ	5	Dead-zone threshold
ξ	200	Variable speed integral threshold
kpu	0.1	Proportional coefficient of the voltage loop
kiu	100	Integral coefficient of the voltage loop
kpc	1.5	Proportional coefficient of the current loop
kic	0.0005	Integral coefficient of the current loop

. The running conditions are set as follows: the DC/AC starts to operate at 0 s; the PV output power changes from 0 kW to 26 kW at 0.5 s and then from 26 kW to 0 kW at 1.5 s; and the load demand of 37.5 kW switches in at 1 s. The responses of the DC-bus voltage are depicted in Figure 9.

It is evident that the DC-bus voltage deviation reaches the maximum when the DC/AC cuts in. Comparing the responses of the two control methods, we conclude that the ordinary PI with a constant cumulative speed of the integral term will produce serious overshoot and oscillation. On the contrary, the improved variable speed integral PI control can effectively improve the dynamic performance during the regulating process, namely, significantly reduce the system’s overshoot and oscillation under uncertainties.

5.3. Operation Effect Analysis of the Grid-Connected PV-FSHESS

In this subsection, we take the working condition of the SC with an initial SOC of 30% as the simulation case to demonstrate the operation effects of the proposed grid-connected PV-FSHESS control scheme. The results are displayed in Figure 10.

From the DC-bus voltage responses, as shown in Figure 10a, we can confirm that the DC-bus voltage’s stability control is effectively achieved based on the proposed power allocation strategy for the FSHESS and the modified variable speed integral nonlinear PI control. When the power fluctuates, the FSHESS can make rapid power compensation so that the DC-bus voltage is always kept stable. Figure 10b,c display the FC and the SC’s current responses, respectively. When the FC and the SC share the power demand together, the proposed power allocation algorithm can exploit the FC’s advantage of high energy density and the SC’s high power density. Figure 10d shows the active power response of the DN side. Since the presented power allocation strategy does not consider the power losses caused by uncertainties, like parameter perturbation and line losses, and the actual power compensation provided by the FSHESS is also limited by the SOC constraint, as a consequence, the DN must offset the uncertainties to ensure the regulation accuracy of the DC-bus voltage. Figure 10e pictures the grid-connected current waveform of one phase. Apparently, its amplitude changes are consistent with the trend of the active power response curve, which also verifies the operation control’s correctness of the grid-connected PV-FSHESS.

6. Conclusions

The PV output power fluctuates under the influence of irradiance. When the PV runs in the grid-connected mode, it will cause frequent disturbances to the DN, which impacts its safe and stable operation. In this study, the HESS, composed of the FC and the SC, is employed as a physical means to smooth the fluctuation of the PV output power. A complete control scheme, including a high-level power allocation strategy and a low-level DC-bus voltage controller design method, is proposed. The main conclusions are drawn as follows:

(1)

The presented improved power allocation approach based on the low-pass filter and rules fully takes into account the specific characteristics of each ES unit in the FSHESS and the constraints for the SC’s safe operation, i.e., keeping the SC’s SOC in a reasonable range. With this strategy, the FSHESS can successively not only compensate for the power difference between the PV output power and load demands but also maintain the SC’s SOC in its allowable range.

(2)

The modified variable speed integral nonlinear PI control algorithm for the DC-bus voltage control can adaptively adjust the strength of the integral action according to the actual deviation between the reference value and real-time measurement of the DC-bus voltage, which can significantly reduce the system’s overshoot and oscillation. In addition, the introduction of the dead-zone nonlinear block is beneficial to decrease the power loss of the DC/AC generated by frequent adjustment of the controller.