Hybrid Inverter and Control Strategy for Enabling the PV Generation Dispatch Using Extra-Low-Voltage Batteries

Abstract

This paper proposes a dispatchable photovoltaic (PV) hybrid inverter for output power tracking without any dependency on the converter’s efficiency and with no power closed loop. The system uses an extra-low-voltage battery energy storage system (BEES) based on a Li-ion battery pack to be applicable for use inside homes and other installations close to the end-user. A bidirectional isolated current-fed dual-active bridge (CF-DAB) converter associated with the batteries provides a wide conversion voltage ratio and ensures safety for the users. The proposed control system shares the DC bus voltage controller between the ac grid interfacing converter (AC-DC) and CF-DAB (DC-DC), eliminating the converter’s efficiency in the reference equations. When dispatchable power is not required, or according to the user’s request, the battery’s charge/discharge current can be specified. A disturbance rejection technique avoids low-frequency current ripple on the battery side. It contributes to the battery’s lifespan. Experimental results presenting the dc bus voltage control, current disturbance rejection, and power dispatching are included to validate the proposal.

1. Introduction

The growth of photovoltaic systems (PV) has increased in the last few years, and according to [1], it should supply up to 32% of electricity globally. The high penetration of PV systems brings some challenges to the power grid due to the stochastic characteristic of this energy generation source. BESS can mitigate the impact of the stochastic generation profile on the grid, as described in [2,3,4,5]. This approach involves dedicated high power and high voltage BESS and usually is under some grid operator’s responsibility.

Even with some aspects still being studied to improve performance for high-power applications and because attention is needed for the cooling systems [6,7], lithium-ion batteries are already receiving attention for BESS applications. This is due to their advantages, such as a deep-cycle capability, low maintenance requirements, high energy density, and a high number of charge–discharge cycles, especially when compared to the traditional lead-acid batteries [8]. Lithium-ion batteries are also preferred over other technologies for BESS applications when economic aspects are considered [9,10,11].

Multifunctional or hybrid systems based on power converters have appeared in new developments to add energy storage capabilities to conventional PV systems. These hybrid systems operate with batteries to provide dispatchable energy to the ac grid [12,13]. They can also offer other advantages to the end-user, including load-peak reduction [14], cost optimization [15,16,17], and supply of critical load during lack-of-energy periods or blackouts [18].

In PV generation, it is common to use PV strings of some hundred volts installed outside the buildings to implement these systems [19,20]. Therefore, the DC-DC PV converters usually do not require wide conversion voltage ratios. On the other hand, batteries can be located inside homes, offices, or other places close to the end-user. This can increase safety issues due to the obligation to ensure isolation and protection against electric shocks [21,22,23]. In these cases, an alternative to adding extra safety features is to use extra-low-voltage batteries for energy storage, such as 48 V Li-ion batteries [24]. On the other hand, this is a challenge from the point of view of power converter design because it is necessary to develop wide-conversion-voltage-ratio DC-DC converters [23]. Both isolated and non-isolated converters may provide wide voltage ratios [25,26]. However, non-isolated converters are not capable of providing galvanic isolation. Galvanic isolation is required for noise reduction, safety in cases of overloading or internal faults, and mainly to simplify grounding and protection schemes [26,27]. Therefore, when batteries are installed close to the end-user, galvanic isolation for the battery pack is an important feature of the converter.

Several advances have been made in integrating PV systems into BESS in a single device, as presented in [28,29,30,31,32]. All these works focused on developing DC-DC power converters to connect the PV panels and batteries to a DC bus. However, they did not consider the inverter necessary to connect the system to the AC grid. In [33], the output inverter was integrated into the system. In all these works, except for [32], the converter that connected the battery to the DC bus did not provide galvanic isolation. The proposals of [29,32] demand a battery always be connected for operation. This would be an issue when the battery requires maintenance, as the entire system would need to be disconnected. Therefore, the PV generation would not be available.

Several developments have been made in isolated DC-DC converters, including modulation and control strategies [21,23] and hardware developments [22]. The main solutions are based on the dual-active bridge (DAB) [23] and current-fed dual-active bridge (CF-DAB) converters [21]. The CF-DAB has advantages for extra-low-voltage energy storage because it results in a wide conversion voltage ratio and low current ripple [21]. Therefore, the CF-DAB is an interesting topology for a hybrid PV converter using extra-low-voltage batteries.

For the AC grid connection, it is well known that low-frequency ripples appear in the DC bus voltage because of the AC-DC converter’s operation. These voltage ripples can also appear on the batteries’ side, negatively affecting their lifespan [34]. A proposal for disturbance rejection was used in [34] to mitigate the low-frequency ripple effects over the PV or battery current. The method is based on a notch filter and a third-order general integrator. Other more straightforward and effective disturbance rejection approaches, such as [35,36,37], are available in the literature. However, they intend to improve the distortion of the injected grid current.

Another problem related to the hybrid PV inverter control is that many control strategies found in the current literature result in steady-state power error when the hybrid inverter (PV + BESS) operates with dispatchable output power [38]. This occurs because the BESS reference current used to compensate for the PV generation intermittency depends on the converter’s efficiency, as described in [13,38,39,40]. The converter’s efficiency may range from 85% to 98%, depending on the converter’s topology, the power levels processed, semiconductor technologies, magnetic materials, switching frequency, and operating points [41,42,43,44,45]. As a result, accurate reference power tracking is not guaranteed. This is shown in [13]. An efficiency estimate is one alternative to attenuating the BESS reference current error. However, in addition to being complex, this method is inaccurate because the efficiency depends on the power processed, and the estimation must be performed for each operation point [13,40]. In [28,29,30,31,32,46] simple control structures considering only a DC load are presented. The output inverter and its control loop are disregarded. Consequently, its interaction with the DC bus and the low-frequency ripple effects over the battery current controller are not analyzed. In [33], a control strategy that does not depend on efficiency is proposed. However, the DC bus controller switches during different operation modes, which can lead to some undesired transients. The low-frequency current disturbance rejection of the battery current is also not considered.

Based on the scenario mentioned above, this paper proposes the dispatchable hybrid PV inverter shown in Figure 1 that uses a 48 V, extra-low-voltage Li-ion battery. The hybrid inverter structure is based on the DC-DC bidirectional converter presented in [21], the CF-DAB, with a-PWM modulation. The converter provides galvanic isolation for the battery, a wide conversion voltage ratio, and little battery current ripple. Unlike the traditional DAB converter, the inductance $L_1$ allows controlling the current to the DC bus and avoids current surges. Additionally, the current-fed feature is indispensable for the control strategy proposed in this paper. The a-PWM strategy proposed in [21] simplifies the control system because the modeling of the converter is straightforward, as is its control. However, ref. [21] did not explore it. Therefore, the current proposal presents a series of improvements compared to [21].

This paper also proposes a control strategy to improve the output power tracking capability of hybrid PV inverters, without any dependency on the converters’ efficiency or closed-loop power, even under PV generation intermittency. Therefore, it is guaranteed that the hybrid converter will track any output power reference without any steady-state power error. The contribution is a shared DC bus controller between the DC-DC bidirectional converter associated with the battery and the output inverter. This guarantees smooth operation even with commutation between different operation modes. Additionally, a straightforward yet functional rejection disturbance structure was designed and integrated into the bidirectional DC-DC converter current-control loop to reduce the effects of the DC bus’s low-frequency battery current ripple. It is important to ensure the battery’s lifespan, which can be affected by unappropriated current ripples. In addition, it avoids oversized filters in the bidirectional DC-DC converter that would negatively impact the converter’s cost and size.

A 500 W prototype was built, and several results are presented to validate the hybrid converter proposals and its operation in different scenarios.

2. Proposed Hybrid Inverter and Control Structure

In the proposed hybrid inverter depicted in Figure 1, the single-phase, full-bridge DC-AC converter is connected to the grid through an LCL filter. The DC-DC boost converter controls the PV array voltage at the maximum power point (MPP) and adjusts the voltage levels between the PV array and the DC bus. The bidirectional DC-DC converter integrates the battery with the DC bus and is responsible for the power flow control during charging and discharging. Considering that the bidirectional DC-DC converter is disabled, the DC-AC and the DC-DC boost converters coupled by the DC bus originate the typical non-dispatchable PV system operating on the MPP [13,45].

The perturb and observe (P&O) maximum power point tracking (MPPT) algorithm is adopted for tracking the maximum power [47]. A proportional-integral (PI) controller $C_{PV}\left(s\right)$ is used to maintain the boost converter input voltage $V_{PV}$ in the MPP with an adequate dynamic response. The control diagram for MPPT is shown in Figure 2a, where $G_{PV}\left(s\right)$ is the transfer function that relates $V_{PV}$ and the control law $d_{pv}$.

Considering that the bidirectional DC-DC is disabled, Figure 2b shows a typical control structure for a grid-tied DC-AC converter applied to PV systems. Based on [37,48], the DC-AC converter operates on the stationary reference frame $\alpha \beta$. The synchronization uses a second-order, generalized integrator frequency-locked loop (SOGI-FLL) that also estimates the grid frequency ($\widehat{\omega })$. A PI controller $C_{DC}\left(s\right)$ controls the DC bus voltage $V_{DC}$ acting on the reference of the inverter output current $i_{inv}^{*}$. The output of $C_{DC}\left(s\right)$ is the control law $I_{DC}$. The reference current $i_{inv}^{*}$ is given by

$$i_{inv}^{*}=2\frac{v_{\alpha }(P^{*}-P_{DC})-v_{\beta }{Q}^{*}}{v_{\alpha }^2+v_{\beta }^2},$$

(1)

where $P_{DC}$ reflects the DC-bus-power oscillations; $Q^{*}$ is the reactive power reference; $v_{\alpha }$ and $v_{\beta }$ are the in-phase and in-quadrature components of the point of common coupling voltage $v_{PCC}$, respectively; and $P^{*}$ is the active power reference, which can not be tracked due to the $P_{DC}$ effect. The available power on the DC bus, i.e., the amount of power that can be injected into the grid, is $P^{*}-P_{DC}$. Therefore, $P^{*}$ can be interpreted as a bias value for the DC bus voltage controller. In Figure 2, $G_{DC}\left(s\right)$ is the transfer function that relates $V_{DC}$ and the output inverter current $i_{inv}$, and $G_{LCL}\left(s\right)$ is the transfer function that relates $i_{inv}$ and the control law $v_u$. A proportional-resonant (PR) controller $C_{inv}\left(s\right)$ [49] controls the inverter output current. A first-order low-pass filter $LPF\left(s\right)$ attenuates the low-frequency on $V_{DC}$ measurement.

The PV inverter can become dispatchable when the bidirectional DC-DC converter is enabled. The BESS supplies the lack and absorbs the excess of generated PV power. For that, an appropriate control strategy is needed. The proposed control strategy is shown in Figure 3 and will be detailed in what follows.

For the bidirectional DC-DC converter control, in Figure 3, $C_B\left(s\right)$ is the $I_{L1}$ current controller, and $G_B\left(s\right)$ describes the dynamics of $I_{L1}$ in relation to the control law $d_{L1}$. The disturbance rejection structure $D_B\left(s\right)$ aims to mitigate the effects of low-frequency oscillations of $V_{DC}$ in the current $I_{L1}$, and consequently, in the battery current $I_B$. The dynamics of this disturbance are represented by $G_{BD}\left(s\right)$.

When the switch $s{w}_1$ is in position 1, the bidirectional DC-DC converter controls $V_{DC}$ instead of the DC-AC converter. The proposed structure cascades the $V_{DC}$ controller with the $I_{L1}$ controller. Additionally, $P_{DC}=0$ in Equation (1) to evaluate the current reference $i_{inv}^{*}$. Therefore, the inverter accurately tracks $P^{*}$ with no error, even without a power closed loop. This is possible because the battery provides or absorbs the lack or excess of the PV generated power ($P_{PV}$) through the DC bus to keep the DC bus voltage at the reference $V_{DC}^{*}$.

When $s{w}_1$ is in position 2, there are two possibilities: (1) The bidirectional DC-DC converter is disabled due to the low state of charge, for example. In this case, $EN=0$. The system operates as a typical PV inverter, and the DC-AC converter control structure becomes the same as the one shown in Figure 2b. (2) The DC-AC converter control structure becomes the same as the one depicted in Figure 2b, and the reference $I_{L1}^{*}$ can be manually defined. It is impossible to track $P^{*}$ accurately in the second case. However, this operation mode can be helpful when a higher-level power management system aims to improve the battery’s lifetime, predefining its charging or discharging current. It is also possible to generate $I_{L1}^{*}$ using any power balance equation. For comparison purposes, the following BESS reference current, which depends on the converter’s efficiency $\eta$, is also reported [38].

$$I_{L1}^{*}=\frac{P^{*}-P_{PV}}{\eta V_{DC}}$$

(2)

The $s{w}_1$ switching block consists of a limiter to enable or disable the bidirectional DC-DC converter when $u_{DC}$ has small values. The hysteresis region shown in Figure 4 avoids constant changes in $s_{w1}$ due to low-value current references.

When $s{w}_1=1$, the bidirectional DC-DC converter controls $V_{DC}$. If the control law $u_{DC}$ becomes too small, the bidirectional DC-DC converter is disabled to avoid its operation in discontinuous conduction mode (DCM). Then, $s{w}_1$ is switched to position 2, and the DC-AC converter controls $V_{DC}$. When $u_{DC}$ reaches a suitable value, $s{w}_1$ returns to position 1, and the bidirectional DC-DC converter is enabled again. The proposed control strategy ensures a smooth transition when $s{w}_1$ switching occurs due to sharing the DC bus voltage controller.

As previously mentioned, the importance of the $L_1$ inductor for the proposed control strategy is that $G_{DC}\left(s\right)$ can represent $V_{DC}$ dynamics regarding both $I_{L1}$ and $i_{DC}$, as shown in what follows. Therefore, it is possible to share the controller $C_{DC}\left(s\right)$ between the bidirectional DC-DC and the DC-AC converters. Additionally, $I_{DC}$ and $I_{L1}^{*}$ are similar for the same operating point. This contributes to smooth transitions during the current-control loop changes when the BESS is enabled or disabled.

2.1. DC Bus Modeling and Control

According to [37,50], Figure 5 shows the diagrams used for the DC bus modeling for the DC bus controller design for both the DC-AC and the bidirectional DC-DC converters. Based on the model obtained, the DC bus voltage controller $C_{DC}\left(s\right)$ was designed so that the control loop achieves a bandwidth of approximately 20 Hz. The $C_{DC}\left(s\right)$ controller is presented in

Table A1. Controllers of the system.

Control System	Controller Abbreviation	Continuous-Time Transfer Function
Voltage controller	$C_{DC}\left(s\right)$	$0.0385+0.27515/s$
Low-pass filter	$LPF\left(s\right)$	$303.03/(s+303.03)$
Current controller	$C_{inv}\left(s\right)$	$3.2+4000s/(s^2+{\widehat{\omega }}^2)$
Current controller	$C_B\left(s\right)$	$175(s+398.5)/s(s+5361)$
Disturbance rejection	$D_B\left(s\right)$	$2s/[s^2+{\left(2\widehat{\omega }\right)}^2]$
Voltage controller	$C_{PV}\left(s\right)$	$-0.0028-0.5/s$

.

2.1.1. DC-AC Converter

By considering Figure 5a, noting that $v_{PCC}=v_{\alpha }$, supposing that the DC-AC converter only processes active power, and disregarding the converter and filter losses, the following relation can be written:

$$i_{inv,in}=\frac{v_{\alpha \left(rms\right)}{i}_{inv\left(rms\right)}}{V_{DC}}.$$

(3)

Figure 5a also gives

$$I_1-C_b\frac{d{V}_{DC}}{dt}=i_{inv,in}.$$

(4)

From (3) and (4),

$$I_1-C_b\frac{d{V}_{DC}}{dt}=\frac{v_{\alpha \left(rms\right)}{i}_{inv\left(rms\right)}}{V_{DC}}.$$

(5)

The small-signal linearization of Equation (5) leads to

$$G_{DC}\left(s\right)=\frac{{\tilde{V}}_{DC}\left(s\right)}{{\tilde{i}}_{inv\left(pk\right)}\left(s\right)}=\frac{-R_o{v}_{\alpha \left(pk\right)}}{2V_{DC}(C_b{R}_{o}s+1)},$$

(6)

where $\tilde{}$ represents a perturbation around the quiescent value of the indicated variable, $\left(pk\right)$ designates the associated variable’s peak value, $C_b$ is the capacitance of the DC bus, and $R_o$ describes a load in the DC bus that is equivalent to the output power of the converter in an operating point. To design the controller $C_{DC}\left(s\right)$, $R_o$ is obtained considering the system’s nominal output power.

By considering (6) and (1) and disregarding the effects of $P^{*}$ and $Q^{*}$—that is, the $i_{inv}^{*}$ depends only on the DC bus control—the transfer function seen by the DC bus voltage controller is obtained. Hence,

$$G_{DC}^{{}^{\prime }}\left(s\right)=\frac{{\tilde{V}}_{DC}\left(s\right)}{{\tilde{I}}_{DC}\left(s\right)}=\frac{R_o}{C_b{R}_{o}s+1}.$$

(7)

2.1.2. Bidirectional DC-DC Converter

The equivalent circuit seen by the bidirectional DC-DC converter consists of an RC network, as shown in Figure 5b. Therefore,

$$G_{DC}^{{}^{″}}\left(s\right)=\frac{{\tilde{V}}_{DC}\left(s\right)}{{\tilde{I}}_{L1}\left(s\right)}=\frac{R_o}{C_b{R}_{o}s+1}.$$

(8)

Since the transfer functions (7) and (8) have the same dynamics, the same DC bus controller $C_{DC}\left(s\right)$ can be used regardless of whether the manipulated variable is $I_{DC}$ or $I_{L1}$.

2.2. Bidirectional DC-DC Converter Modeling and Control

The bidirectional DC-DC converter’s output depends on the DC bus voltage $V_{DC}$ and the battery voltage E. Therefore, the linearized dynamic response of $I_{L1}$, in CCM, related to the duty cycle $d_{L1}$, can be represented by [21]

$$G_B\left(s\right)={\left.\frac{{\tilde{I}}_{L1}\left(s\right)}{{\tilde{d}}_{L1}\left(s\right)}\right|}_{V_{DC}=0}+{\left.\frac{{\tilde{I}}_{L1}\left(s\right)}{{\tilde{d}}_{L1}\left(s\right)}\right|}_{E=0}.$$

(9)

Taking the system’s parameters presented in

Table A2. Main parameters of the system.

Parameter	Abbreviation	Value
Grid phase voltage	$V_g$	127 V${}_{RMS}$
Grid nominal frequency	$f_g$	60 Hz
Grid equivalent resistance	$R_g$	0.4 $\Omega$
Grid equivalent inductance	$L_g$	1 mH
DC-bus nominal voltage	$V_{DC}$	400 V
DC-bus capacitor	$C_b$	$500\mathsf{\mu }$F
DC-bus nominal load	$R_o$	$320\Omega$
DC-AC conv. filter inductors	$L_{1f}-L_{2f}$	$370\mathsf{\mu }$H–155 $\mathsf{\mu }$H
DC-AC conv. equivalent resistances	$R_{1f}-R_{2f}$	$140\Omega$–77 $\Omega$
DC-AC conv. filter capacitor	$C_f$	4.7 $\mathsf{\mu }$F
DC-AC conv. damping resistor	$R_f$	2 $\Omega$
DC-DC conv. filter inductor	$L_{PV}$	1.3 mH
DC-DC conv. filter capacitor	$C_{PV}$	6.8 $\mathsf{\mu }$F
DC-DC conv. equivalent resistance	$R_L$	$80$m$\Omega$
DC-DC conv. equivalent resistance	$R_C$	$20$m$\Omega$
$u_{DC}$ higher threshold	$u_{DCH}$	0.15 A
$u_{DC}$ lower threshold	$u_{DCL}$	0.10 A
Nominal battery voltage	$V_B$	48 V
Battery series resistance	$R_B$	0.06 $\Omega$
Bid. DC-DC conv filter inductors	$L_1$–$L_2$	$1050\mathsf{\mu }$H–365 $\mathsf{\mu }$H
Bid. DC-DC conv. filter capacitors	$C_1$–$C_2$	$2.2\mathsf{\mu }$F–10 $\mathsf{\mu }$F
Bid. DC-DC conv. filter resistors	$R_d$–$R_{L1}$	1 $\Omega$–130 m$\Omega$
Bid. DC-DC conv. filter resistors	$R_{C2}$–$R_{L2}$	12 m$\Omega$–80 m$\Omega$
Bid. DC-DC conv. transformer ratio	$1:n$	1:5
Sampling frequency for all conv.	$f_s$	20 kHz
Switching frequency for all conv.	$f_{sw}$	20 kHz
System nominal power	P	500 W

or the modeling procedure of [21] leads to $G_B^d\left(s\right)$ or $G_B^c\left(s\right)$, representing the transfer functions for the discharging and charging operation modes, respectively. At the nominal duty cycle, when there is any power flow, $G_B\left(s\right)=G_B^d\left(s\right)=-G_B^c\left(s\right)$. The nominal duty cycle for discharging is 0.4, and for charging it is 0.6. Hence,

$$G_B\left(s\right)=\frac{-2033s^2-5.92\times {10}^{8}s+7.3\times {10}^{12}}{s^3+1521s^2+2.99\times {10}^{8}s+1.19\times {10}^{11}}.$$

(10)

Since the bidirectional DC-DC converter dynamics are similar for the charging and discharging operation modes, except for the ${180}^{\circ }deg$ phase difference, a similar controller $C_B\left(s\right)$ can be used. This is just needed to account for a signal change in the controller depending on the operation mode. For the design of $C_B\left(s\right)$, the nominal transfer function (10) is used. The controller is designed based on the bandwidth of the DC bus voltage controller. For the former case, a bandwidth of 20 Hz was defined. Therefore, to decouple the control loops, a bandwidth of approximately 200 Hz is desired for $C_B\left(s\right)G_B\left(s\right)$. Hence, the controller $C_B\left(s\right)$ presented in Table A1 is obtained.

To verify the design of the controller $C_B\left(s\right)$, Figure 6 depicts the open-loop frequency response of the compensated system for different duty cycles for the discharging and charging modes. Figure 6a considers the discharging mode, and Figure 6b considers the charging mode. In both scenarios, the bandpass has approximately the required value (≈200 Hz) to decouple the voltage and current loops. Again, for both scenarios, there are plenty of gain margin (GM) and phase margin (PM). The presented gain and phase margins guarantee stability and enough damping to avoid undesired oscillations in the output current $I_{L1}$, even for duty cycles ($D_{L1}$) other than the nominal values.

In Figure 3, $D_B\left(s\right)$ is responsible for rejecting the $V_{DC}$ ripple disturbance that impacts $I_{L1}$, and consequently, $I_B$. It is based on the idea of [35,36], who used it to improve the power quality of the injected grid current of DC-AC converters. The effect of the $V_{DC}\left(s\right)$ ripple on the tracking error $e_{L1}\left(s\right)$ is described by

$$e_{L1}\left(j{\omega }_D\right)=-\frac{G_{BD}\left(j{\omega }_D\right)V_{DC}\left(j{\omega }_D\right)}{1+G_B\left(j{\omega }_D\right)(C_B\left(j{\omega }_D\right)+D_B\left(j{\omega }_D\right))},$$

(11)

where ${\omega }_D=2\widehat{\omega }$ is the disturbance frequency and $\widehat{\omega }$ is the estimated grid frequency. Based on Equation (11), if $|D_B\left(j{\omega }_D\right)|>>1$, the effects of the disturbance are negligible. Therefore, $D_B\left(s\right)$ uses a resonant structure given by

$$D_B\left(s\right)=\frac{2k_{id}s}{s^2+{\left(2\widehat{\omega }\right)}^2}$$

(12)

described in Table A1.

3. Experimental Results

The experimental results were obtained with a 48 V/20 Ah lithium-ion battery and a PV emulator. A controllable power source, ITECH IT6018C-800-60, was used to emulate the PV generation. A string of four CanadianSolar KuMax CS3U-350P panels connected in series was considered for the PV emulation. The irradiance profile used was obtained from real data and was between 200 and 400 W/m${}^2$. All the converters were implemented, and the controllers were programmed in a TI TMS320F28335 DSP. Table A1 shows the parameters of the continuous-time controllers that were discretized using the Tustin method. Table A2 presents the main parameters of the system.

3.1. Disturbance Rejection

Initially, the effectiveness of $D_B\left(s\right)$ in rejecting the effects of the DC bus voltage ripple on $I_{L1}$, and consequently on $I_B$, was verified. Figure 7 shows the system’s main waveforms considering $s{w}_1$ in position 2 and $EN$ in position 1. Thus, the DC-AC converter controls $V_{DC}$, and the bidirectional DC-DC converter controls $I_{L1}$. The reference $I_{L1}^{*}$ was manually set in different step values between −1.25 and 1.25 A, resulting in a maximum power level of $\pm 500$ W in the 400 V DC bus. The DC-DC boost converter was disabled. It was a hypothetical operation scenario only to verify the disturbance rejection structure $D_B\left(s\right)$. Figure 7a presents the results with no disturbance rejection structure. The largest ripple $\Delta I_B$ was approximately 2.4 A. In Figure 7b, the disturbance rejection is active. The maximum $\Delta I_B$ was about 700 mA, a significantly smaller value. The maximum percentage of the 120 Hz ripple reduction was 70.8%.

For the results depicted in Figure 8, $s{w}_1$ was in position 1. Thus, the bidirectional DC-DC converter controls $V_{DC}$ through $I_{L1}$. The DC-DC boost converter remained disabled. Larger DC bus voltage ripple, and consequently, larger disturbances in $I_{L1}$ and $I_B$, occurred when large amounts of power were processed. Therefore, $P^{*}$ is defined to result in approximately $\pm 500$ W on the DC bus, depending on the operation mode.

Figure 8a,b depict the results when the disturbance rejection is disabled and enabled, respectively, in the charging mode. The power reference $P^{*}$ was negative. Thus, the DC-AC converter operated as an active rectifier, and the bidirectional DC-DC converter charged the battery. With no disturbance rejection, Figure 8a shows that the 120 Hz ripple in DC bus voltage was reflected in $I_{L1}$ and $I_B$. In this case, $\Delta I_B$ was approximately 2.04 A. With disturbance rejection, $\Delta I_B\approx 720$ mA, according to Figure 8b. The percentage of the 120 Hz ripple reduction was 64.7%.

For the discharging operation mode, Figure 8c,d present the results considering the disturbance rejection as disabled and enabled, respectively. Now, $P^{*}$ is positive. Thus, the DC-AC converter injects current into the electrical grid, and the bidirectional DC-DC converter discharges the battery. Without the disturbance rejection, $\Delta I_B\approx 1.68$ A and 1.20 A when the disturbance rejection was enabled. The percentage of the 120 Hz ripple reduction was 28.57%.

3.2. Power Tracking

The dispatchable characteristic of the proposed converter is illustrated considering a variable irradiance profile. Therefore, the PV generation power $P_{PV}$ characteristic is also variable in the following results.

Figure 9 shows the waveforms of the PV generation power ($P_{PV}$), the inverter output active power ($P_{inv}$), the BESS power ($P_{BESS}$), and the output power reference ($P^{*}$) for the proposed control strategy. The switch $s{w}_1$ changes its position according to the control law $u_{DC}$. When $P_{PV}\approx P^{*}$, $u_{DC}\approx 0$ and the bidirectional DC-DC converter is disabled ($EN=0$ and $s{w}_1=2$). The $u_{DCL}$ and $u_{DCH}$ values for implementing the $s{w}_1$ switching block of Figure 4 are presented in Table A2. The thresholds were defined experimentally according to the converter’s response. Outside the $u_{DCH}$ limit, with respect to the hysteresis, $s{w}_1=1$ and $EN=1$. In Figure 9, two regions of interest ($R_{g1}$ and $R_{g2}$) are highlighted. The experimental results throughout this section correspond to these regions.

For Figure 9, during $t_1$, the BESS was disabled ($EN=0$) and $s{w}_1=2$. Therefore, the system operated as a typical PV inverter tracking the varying MPP. The DC-AC converter controlled $V_{DC}$ and $i_{inv}$, and the DC-DC boost converter controlled the PV array voltage, always trying to reach the MPP. The variable $P_{PV}$ profile is reflected in the $P_{inv}$. Since the $P_{PV}$ was variable, the reference $P^{*}$ could not be tracked.

During $t_2$, shown in Figure 9, the BESS was enabled ($EN=1$) and $s{w}_1=1$. Thus, the control system became the proposed structure for accurately tracking $P^{*}$. In this case, the DC-AC converter controlled $i_{inv}$, the DC-DC boost converter controlled $V_{PV}$ at the MPP, and the bidirectional DC-DC converter operated in the charging mode, controlling $V_{DC}$ through $I_{L1}$. During $t_2$, $P_{BESS}$ compensated for the intermittent $P_{PV}$ profile and guaranteed the accurate tracking of $P^{*}$.

As shown in Figure 9, during $t_3$, $s{w}_1=2$ and $EN=0$. The BESS was disabled, and the DC-AC converter operated as a typical PV inverter. Again, it was not possible to track $P^{*}$. During $t_4$, $EN=1$ and $s{w}_1=1$. In this case, the bidirectional DC-DC converter operated in the discharging mode. As expected, the BESS compensated for the intermittency of $P_{PV}$ to track $P^{*}$ accurately.

Figure 10 shows the main voltage and current waveforms corresponding to $R_{g1}$ of Figure 9. At the beginning of $R_{g1}$, $s{w}_1$ was switched from position 2 to position 1, and the power compensation started. The bidirectional DC-DC converter assumed control of $V_{DC}$ instead of the DC-AC converter. The transient on $V_{DC}$ was negligible when $s{w}_1$ was switched. Figure 10 also depicts the waveforms during $t_2$. In this time interval, due to the BESS compensation ($I_{L1}$), the amplitude of $i_{inv}$ was kept constant regardless of the $P_{PV}$ variation, and $P_{inv}$ tracked $P^{*}$ accurately. At the end of $t_2$, the power compensation was interrupted. Thus, $s{w}_1$ was switched to position 2, and the AC-DC converter assumed control of $V_{DC}$ again. The transition of the associated converter that controls the DC bus voltage was smooth, having no impact on the DC bus voltage.

Figure 11 presents details of the waveforms when the bidirectional DC-DC converter is in charging mode. Figure 11a shows when the power compensation started, which corresponds to the beginning of $R_{g1}$ in Figure 9. Figure 11b exhibits the moment when the power compensation was interrupted. The system presented adequate performance without inadequate transients.

Figure 12 shows the main voltage and current waveforms corresponding to $R_{g2}$ of Figure 9. Similarly, as in $R_{g1}$, at the beginning of $R_{g2}$, $s{w}_1$ was switched from position 2 to position 1, and the power compensation started. In this case, the bidirectional DC-DC converter operated in the discharging mode, since the $P_{PV}$ was insufficient to supply the desired output power $P^{*}$. The compensation provided by the BESS ($I_{L1}$) kept the amplitude of $i_{inv}$ constant regardless of the $P_{PV}$ variation, and $P_{inv}$ tracked $P^{*}$ accurately. In addition, the transition of the converter responsible for the DC bus voltage control was smooth; there was no significant transient in the waveforms.

Figure 13 presents a detailed view of the waveforms when the bidirectional DC-DC converter is in discharging mode. Figure 13a shows when the power compensation started corresponding to the beginning of $R_{g2}$ in Figure 9. In addition, Figure 13b depicts the moment when the power compensation was interrupted. It can be seen that all the waveforms present good behavior.

Figure 14 shows the power waveforms for a control strategy that depends on the converters’ efficiency in tracking $P^{*}$ that is typically used in the literature [12,13,38,39]. During $t_1$, the system operated as a typical PV inverter, as previously discussed ($s{w}_1=2$ and $EN=0$). During $t_2$, $s{w}_1$ remained in the same position. Therefore, the DC-AC converter controlled $V_{DC}$ and $i_{inv}$. Additionally, $EN$ changed to 1. Thus, it is possible to define $I_{L1}^{*}$ according to (2).

In Figure 14, during $t_2$, the BESS absorbs energy in excess due to $P_{PV}$. However, it is possible to note significant error between $P^{*}$ and $P_{inv}$ due to the system’s efficiency. The same occurred when the BESS operated in the discharge mode during $t_4$. A system efficiency estimate can compensate for power errors, but it requires complex theoretical or experimental procedures. In addition, efficiency depends on several parameters, such as the operating point and temperature. Thus, it is not constant for all the operating ranges. When $s{w}_1=1$, $I_{L1}^{*}$ was automatically generated through the proposed control loop, and the power error got close to zero.

3.3. Output Power Step Response

This subsection examines the system’s behavior for step changes in the reference of the output power $P^{*}$. Figure 15 presents the main waveforms of the system. For this test, the generated power, $P_{PV}$, was 500 W. The output power reference $P^{*}$ changed from 410 to 210 W and then to 410 W. The surplus between $P_{PV}$ and $P^{*}$ was sent to the battery to guarantee constant power flow to the grid. Thus, the power step in $P^{*}$ implies a power step in the battery. The output current $i_{inv}$ was proportional to the power reference, and the currents associated with the bidirectional DC-DC converter ($I_{L1}$ and $I_B$) were inversely proportional to $P^{*}$, as expected. The DC bus voltage presented small transients after the power reference step changed, but the voltage converged quickly to the reference. The parameters associated with the PV panels also behaved accordingly.

Figure 16 details the waveforms presented in Figure 15 during the step changes in $P^{*}$. Figure 16a exhibits details for $P^{*}$ changing from 410 to 210 W. Figure 16b shows the details for when $P^{*}$ changed from 210 to 410 W. It can be seen that all the waveforms did not present significant transients or overshooting.

To verify the transients when the power flow direction on the bidirectional DC-DC converter is changed, the photovoltaic generation was defined as $P_{PV}\approx 250$ W, and $P^{*}$ was set to approximately 100 W. The bidirectional DC-DC converter absorbs the surplus power between $P^{*}$ and the available power. Thus, the battery was charging, and $s{w}_1=1$. Figure 17 shows the main system’s waveforms. Then, $P^{*}$ changed to 300 W, and the BESS power flow reversed. During the power-flow reversal, $s{w}_1$ changed to position 2 due to the non-operating region of the bidirectional DC-DC converter for small currents. The DC-AC converter assumed control of $V_{DC}$ during the power-flow reversal. When the BESS current was outside the region of non-operation, $s{w}_1=1$ and the bidirectional DC-DC converter assumed control of $V_{DC}$ again. Next, $P^{*}$ changed to 500 W and then to 300 W. As expected, the output current $i_{inv}$ increased and decreased according to the power reference. The same occurred with the BESS currents $I_{L1}$ and $I_B$.

Details of the power-flow reversal are shown in Figure 18a, where it can be seen that the system behaved adequately. Details of the $P^{*}$ steps to 500 and 300 W are depicted in Figure 18b,c, respectively. These detailed waveforms corroborate the excellent performance of the system.

3.4. $V_{DC}$ Control Loop’s Influence on $i_{inv}$

When $s{w}_1$ is in position 2, $i_{inv}^{*}$ is given by Equation (1). Considering $Q^{*}=0$, (1) can be represented as

$$i_{inv}^{*}{|}_{{}_{s{w}_1=2}}=\frac{2v_{\alpha }(P^{*}-P_{DC})}{(v_{\alpha }^2+v_{\beta }^2)}.$$

(13)

Since $P_{DC}$ depends on the control law $I_{DC}$, and on the voltage $V_{DC}$, which oscillates at 120 Hz, $P_{DC}$ also has a 120 Hz component. Considering $v_{\alpha }$ as an ideal 60 Hz sinusoid, the reference $i_{inv}^{*}$ (13) contains the 60 Hz fundamental component and 180 Hz resulting from the multiplication between $P_{DC}$ and $v_{\alpha }$. Therefore, even considering an ideal electrical grid, the reference current has the third harmonic in addition to the fundamental component. However, when $s{w}_1$ is in position 1, $i_{inv}^{*}$ does not depend on $P_{DC}$; that is,

$$i_{inv}^{*}{|}_{{}_{s{w}_1=1}}=\frac{2v_{\alpha }{P}^{*}}{(v_{\alpha }^2+v_{\beta }^2)}.$$

(14)

Thus, the third harmonic originating from $V_{DC}$ is not present in $i_{inv}^{*}$.

Figure 19 shows the waveforms used to obtain the total harmonic distortion (THD) and the individual harmonic components. When $s{w}_1=2$, the THD was 2.72%, whereas with $s{w}_1=1$, the THD was reduced to 1.98%. The improvement in the THD when the bidirectional DC-DC converter controlled the DC bus voltage was 27.2%.

Figure 20 shows the individual harmonic components of $i_{inv}$ as percentages of the fundamental component of $i_{inv}$. It was possible to note a reduction of approximately 21% in the third harmonic when the bidirectional DC-DC converter controlled the DC bus voltage ($s{w}_1=1$).

4. Conclusions

This paper proposed a dispatchable hybrid inverter (PV + BESS) using extra-low voltage batteries and a control solution for accurately tracking an output power reference. The use of low-voltage batteries is possible due to an isolated bidirectional converter with a wide conversion voltage ratio, the CF-DAB converter. The isolated converter has easy modeling and control, ensuring safety for the end-user. To validate the proposal, a 500 W prototype using a $48$ V Li-ion battery was built.

The proposal does not need an output power loop, nor does it depend on the converters’ efficiency in tracking the output power reference. The DC bus voltage controller is shared between the DC-AC converter and CF-DAB (DC-DC) to achieve that. When a controlled power dispatch is desired, the BESS is enabled, and the bidirectional DC-DC converter controls the DC bus voltage. When the BESS is disabled, the DC-AC converter controls the DC bus. The shared control loop guarantees smooth transitions during the changing of operation mode between charging and discharging of the batteries.

A disturbance rejection structure reduces the effects of the DC bus voltage ripple perturbation on the battery current. During the charging process, the reduction is 64.7%. In discharge, the reduction is 28.57%. If the converter operates as a traditional PV converter where the inverter controls the DC bus voltage and an external battery current is defined, the rejection disturbance reaches 70.8%. This helps reduce the associated filters’ size and enhances the battery’s lifespan.

The proposed control structure helps reduce the third-order harmonic of the inverter output current when the bidirectional DC-DC converter controls the DC bus voltage. The reduction of the third harmonic, in this case, is approximately 21%. This impacts the overall THD of the inverter output current because the output current reference does not depend on the DC-bus-power oscillations. When the bidirectional DC-DC converter controls the DC bus voltage, $THD=1.98\%$. Considering a traditional PV converter where the inverter controls the DC bus voltage, $THD=2.72\%$. The proposal improved $THD$ to $27.2\%$.

Extensive experimental tests were presented to show the system’s good behavior in different operation scenarios, including dc bus voltage control, step changes in the output power reference, transition between charging and discharging the battery bank, and current disturbance rejection. The control strategy also allows an external power management system to control the battery’s charging/discharging current if the application requires it.

The prototype of the hybrid inverter we built and tested validated the proposal. It presents multi-function operating modes and allows the integration of batteries with a PV system, providing safety for the end-user.