1. Introduction
Ensuring energy resilience and reaching net zero emissions by 2050 while electricity demands are increasing calls for the faster adoption of renewable sources (e.g., solar PV, wind). The incremental energy demand of the building sector is projected to be 70% by 2050 due to the electrification of heating systems [
1]. At the same time, building-integrated PV (BIPV) systems are being increasingly used and interfaced with the grid. The BIPV market has increased substantially, reaching 500 MWp in 2022, and is expected to reach 726 MWp by the end of 2023 [
2]. Battery system and PE interfaces are two significant entities to exploit in such combined PV systems. In stationary battery energy storage systems, Li-ion batteries (LIBs) are being increasingly used in comparison with other battery technologies. The relevant studies reveal that 80% of the installed stationary energy storage systems were LIB-based in 2020, and a compound annual growth rate of 17.4% is expected during 2022–2030 [
3,
4]. This is mainly due to the higher cycle life, lower self-discharge rate, higher charging and discharging efficiencies, and lower cost trending due to the homogeneous nature of LIBs in stationary and electromobility applications resulting in huge market share [
5,
6].
However, the performance of PE interfaces, such as AC/DC and DC/DC converters, used in the PV combined with battery energy storage system (BESS) plays a vital role in ensuring an optimal conversion from supply to demand. For grid-interfacing AC/DC converters, the injected grid current distortion level is one of the key parameters linked to power quality. In that regard, IEEE Standard 1547-2003 and IEC Standard 61727 have urged ensuring less than 5% of the total harmonic distortion (THD) for the grid current [
7,
8]. Additionally, the converter for such energy storage systems can suffer from different stability issues due to the shared DC-link voltage and strict power quality requirements. The DC/DC converter is critical to charging and discharging the battery system with improved battery roundtrip energy efficiency and battery lifetime [
9]. In addition, passive components and control techniques that are applied in the power converter system can support reaching the standard power delivery for the PV combined with BESS application.
Furthermore, it has been reported that the performance of the PE interface, as determined by the controller, can have a significant impact on the selected components and may result in failure due to the operational stress induced by load requests, applied voltage, current, and generated heat [
10]. Consequently, the lifetime of the PE interface may be reduced, thereby necessitating additional maintenance requirements and causing downtime for system servicing.
Several works have been carried out exploring PE interface design and assessment for PV–BESS applications. In [
11], the authors designed a grid-interfacing AC/DC converter for a PV–BESS application in which they showed that with the designed passive components and control (current and voltage), it could achieve the highest efficiencies of 95.98% and 95.55% in the charging and discharging modes, respectively, at full-load operation. Moreover, in [
12], the authors studied the quality of the feed-in grid current from single-phase inverters by designing a tailor-made current controller composed of a proportional-resonant controller (PR) and an RC controller. The study showed that a THD of 2.28% for the grid current could be achieved. However, other control strategies of the current have been advocated to reduce THD, such as PI, PR, current hysteresis, dead beat, model-predictive, and cascaded harmonic control [
13,
14]. However, PR is the most popular strategy in terms of implementation because it avoids Park transformations and requires less computational power for current regulation in single-phase PV applications [
15,
16].
Moreover, in [
17], the authors studied the full-bridge bidirectional DC/DC converter for battery charging and discharging, where the maximal efficiency of the DC/DC converter was measured to be 96.0% during battery charging and 96.9% during discharging. In addition, in [
18], a robust controller was designed for the DC/DC converter with the isolation structure of a voltage-fed dual active bridge to prevent battery voltage overshoot while achieving an efficiency of 95% for both modes of operation.
The aforementioned references have thoroughly studied the grid and battery side conversions in terms of proposed controllers and passive components with a fixed switching frequency. The system performance under the influence of switching frequency has not been investigated for such an application. Moreover, the reliability has not been considered in the design and assessment of the converters, while it can have a critical impact on the system’s service lifetime [
19].
The primary contribution of this research lies in the development of a control system capable of effectively managing partial loading within a stable region. Furthermore, the research focuses on analyzing the electro-thermal performance of the system while varying the switching frequency for the controllers. The investigation of lifetime modeling and the impact of varying the system and control parameters is also a significant aspect of this work. In summary, the novelty of this research centers around an assessment of performance and control parameter variation for a two-stage bidirectional converter under different load transients, while also examining control stability. Additionally, the study estimates the lifetime of the converter by considering various stress factors.
The organization of this paper is as follows: in
Section 2, the modeling of the PE interface and battery is discussed.
Section 3 covers the corresponding control of the PE interface. In
Section 4, the lifetime estimation of the PE converter is detailed. Finally, the results and discussion are presented in the concluding section, which includes the performance of control, electrical parameters, losses, and useful lifetime prediction.
2. Battery Energy Storage System Modeling
The design of the two-stage bidirectional converter for interfacing the grid of a stationary energy storage system is illustrated in
Figure 1. The battery pack was charged and discharged from the single-phase AC power grid. Full-bridge AC/DC (230 Vrms to 400 Vdc) and half-bridge DC/DC (400 Vdc–200 Vdc) power stages were used by coupling a common DC-link for bidirectional power flow. The DC-link in the topology of the highlighted section was used to inject the PV power by using a boost DC/DC converter to the DC-link voltage. Please note that, in this paper, positive power flow is defined as the charging state and negative power flow is defined as the discharging state of the battery pack. For grid synchronization, generally a phase locked loop (PLL) is used for grid-interfaced converter. The single-phase PLL can be implemented using the Hilbert transformation. In this work, the single-phase feedforward PLL was implemented. Additionally, as shown in
Figure 1, the complementary switching signals for the MOSFET(
Q) switches—
Q1 and
Q2—are denoted by
S1 and
S2, respectively, in the AC/DC converter. Notably, during charging operation,
Q1 and
Q4 were turned on, whereas during discharging operation, the
Q2 and
Q3 switches were turned on. It is important to mention that the switching signals were converted into the dq frame during AC/DC converter modeling. In addition,
Q5 was turned on during battery charging, and vice versa during battery discharging. The duty cycle, represented by
D, served as the control signal for the DC/DC converter.
2.1. Modeling of AC/DC Converter
The active front-end converter was utilized for grid interfacing with a high-order passive filter (LCL filter), as per the topology utilized. The LCL filter comprises two inductances,
Ls and
Lc, for the grid and converter sides, respectively, along with the resistances of the series inductance,
rs and
rc. The filter capacitance is represented by
Cf, with damping resistance
Rd. Among these parameters,
Lc holds the most significance in the voltage source converter [
20]. The DC side of the converter is characterized by the DC-side capacitor,
Cdc, DC-side voltage,
vdc, and DC-link current,
idc. The switching operation in the synchronously rotating dq frame is represented by the functions
Sd and
Sq. The mathematical model of a single-phase voltage-source converter is formulated in the synchronous dq frame using single-phase feedforward modeling, as presented in Equations (1) to (3) [
21,
22], where
and
serve as the dq components of the AC input voltage;
and
are the corresponding currents; and
is the angular frequency.
2.2. Modeling of DC/DC Converter
A bidirectional DC/DC power converter is required to regulate battery voltage (low side), which changes with state of the charge (SoC) and reaches the DC-link voltage (high side) while transferring power in the charging (buck) and discharging (boost) modes. The power stage dynamics of the DC/DC converter are modeled using Equations (4) and (5), utilizing an inductor and capacitor denoted by
L0 and
C0, respectively, with damping resistor
R0 as a filter while charging the battery. In addition, the duty ratio is denoted by
, and
serves as the derived coefficient during discharging mode. When formulating the transfer function (
Gid) for the buck and boost modes, the load (battery) is considered with resistance
RL. The current through the load and voltage across the load are denoted by
iL and
vL, respectively. The control transfer functions of the charging and discharging modes for the converter are given below in Equations (6) and (7), where
s and
Gid are the representations of the Laplace operator and open loop transfer function for both modes, respectively. Further details regarding the modeling of the bidirectional DC/DC converter can be found in references [
23,
24].
2.3. Li-Ion Battery
The modeling of a lithium-ion battery involves the use of an electrical equivalent circuit in order to effectively map the various dynamics of this chemistry [
25]. A simple internal resistance-based model is widely used for battery voltage, current, and SoC performance [
26,
27]. The simple lithium-ion/LFP model [
28] adopted here is illustrated in
Figure 2. In the figure, the
Vcharge and
Vdischarge states are modeled by Equations (8)–(10):
where
V0 represents the constant voltage (V);
K denotes the polarization resistance (Ω);
denotes the filtered current (A);
and
refer to the maximum and extracted capacities (Ah), respectively;
A represents the exponential voltage (V); and
B represents the exponential capacity (Ah
−1).
3. Control Design for the Two-Stage Bidirectional Converter
The stability of a PE converter’s operation is heavily dependent on the effectiveness of its control system. Generally, a two-stage power converter can maintain stability within a specific range of switching frequencies, each of which has a unique cut-off frequency closely related to the PE device’s switching frequency. This switching frequency, which determines the rate at which devices switch on and off to control the power flow, must be sufficiently below the cut-off frequency to avoid system instability and aliasing. Thus, the cut-off frequency is a critical parameter in the design of PE control systems as it affects the stability, response, and bandwidth of the system. Furthermore, variations in switching frequency can impact system efficiency, as electro-thermal performance differs depending on the frequency of operation. Therefore, careful consideration of the cut-off frequency is essential to ensure the system’s performance and reliability.
In line with the two-stage bidirectional converter concept in
Section 2, the AC/DC interface used a PI controller for controlling the voltage and a PR controller for controlling the current to improve the system’s stability. For the battery side, a PI control was used to control the battery voltage and current. A brief description of the applied control strategy for the assessment is presented in the subsequent sections.
3.1. Control of AC/DC Converter
In this study, a feedforward control strategy was implemented, which consisted of the voltage controller as the external loop and current controller as the inner loop for the
d-axis and
q-axis current control [
21]. The
and
references can be determined by following Equations (11) and (12), respectively. Consequently, the injected current can be modeled according to Equations (13) and (14). Finally,
vd and
vq can be represented as a function of
and
and
and
, as shown in Equations (15) and (16), where
Kp and
Ki are the gains of the PR controller.
The voltage and current controllers are designed based on the controller time constants,
τv and
τi, respectively. The current controller performs four to five times quicker than the voltage controller. However, the PR controller was adopted because of its advantageous resonant term to grid frequency and simplicity for development. For this reason, the PR controller was used in the current controller to improve controller performance. The gains of the PI and PR controllers are determined following Equations (17)–(22):
where
and
represent the PI controller gain for the voltage control loop, while
and
are the gains for the current control loop.
,
, and
respectively symbolize the controller’s proportionality gain, natural oscillation frequency, and cut-off frequency.
Gpv(
s) refers to the open-loop transfer function, while
φm represents the phase margin in degrees, which is obtained from the Bode plot of the open-loop transfer function.
3.2. Control of DC/DC Converter
A cascaded control structure was used for the bidirectional DC/DC converter. The closed-loop current and voltage controller equations are presented in Equations (23) and (27). This also comprises the voltage controller as an outside level and the current controller as an inside level, where the inside level performs tenfold quicker than the outside level. The inside level regulates the average inductor current,
iL0, using a PI controller. The continuous duty ratios from the controllers were then sent to the PWM modules to generate the switching signals for the two discrete power MOSFETs. The output voltage was likewise controlled by a PI controller. The basis of the PI controller gains for battery voltage and current control is presented in Equations (24)–(26) and Equations (28)–(30), respectively:
where
and
respectively denote the closed-loop transfer functions for the current and voltage control loops.
and
respectively represent the transfer functions from voltage to duty for the voltage control loop and from current to duty for the current control loop.
and
refer to the transfer functions of the PI controllers for the current and voltage loops, respectively. The gain and phase margins were utilized to determine the PI gains using the current and voltage plant transfer functions.
4. Power Electronics Interface Degradation
This section describes the PE interface degradation towards mean time to failure caused by stress factors generated in the converters. The PE interface lifetime degradation estimation of the two-stage power converter is illustrated in
Figure 3. As seen in
Figure 3, the approach is composed of three parts: the electrical domain, which comprises the power stage and control part; the electro-thermal domain, which considers losses and resulting temperatures; and the failure domain, which incorporates possible failure rates and part stress factors to enable the inspection of the useful lifetime of the two-stage PE interface. Of these three domains, the electro-thermal domain is of utmost importance for assessing the degradation of the most failure-prone components in the PE interface, namely switches and capacitors [
29]. The previously discussed electrical domain modeling was followed by loss modeling, thermal modeling, and finally, failure modeling in the subsequent sections to evaluate the impact of variations on the system response.
4.1. Loss Modeling
Accurately estimating the loss incurred by the PE interface during operation is complex but important because of its influence on performance and reliability. The semiconductor switching loss behavioral model is adopted to more accurately assess performance [
30].
Owing to the fact that driver losses account for a small share of the total power loss, the total loss incurred is modeled with conduction and switching losses. The MOSFET conduction and switching losses are formulated by Equations (31)–(34). Similarly, Equations (35)–(38) are applied for the diode. To capture the behavior within operational variations of voltage, current, on-state resistance, frequency, and junction temperature, the lookup table approach was utilized for the selected SiC MOSFET switch [
31,
32].
where
represents the total losses of the MOSFET;
is the conduction losses;
is the sum of turn-on and turn-off losses;
Vds is the on-state voltage;
Ids is the current drain-source current through the MOSFET; and
Tj represents the junction temperature.
where
Prr represents the turn-off power losses;
Vf is the forward voltage drops;
If is the forward diode current; and
Err is the reverse recovery energy.
Additionally, the inductor and capacitor losses can be formulated by Equations (39) and (40):
where
Irmsy is the average current through the inductor, capacitor;
RL is the Litz wire resistance of the inductor; and ESR is the equivalent series resistance of the capacitor.
4.2. Thermal Modeling
To obtain a good estimation of the junction and case temperatures, thermal modeling is considered with three key aspects. Firstly, the device case temperature is a direct result of the total loss generated by the device. Secondly, the temperature of the device is subject to variations arising from losses. Lastly, the influence of changes in the ambient temperature is imperative to consider.
The thermal modeling approach for the PE interface is detailed in [
33]. With the former aspects, the switch thermal model is formulated by Equations (41)–(44), the capacitor by Equation (45), and the inductor by Equations (46) and (47):
where
is the junction to case thermal resistance (°C/W),
is the response time,
is the case to ambient temperature change,
is the case temperature,
is the junction temperature, and
is the thermal resistance.
where
and
are the hotspot temperatures of the inductor and capacitor, respectively, and
A is the radiating surface area of the inductor.
4.3. Failure Modeling
The possible failure of the PE interface under the conditions of being in good and degraded states can be described with Equation (48), as per the Markov chain model [
34]:
where
denotes the possibility of normal operation with the components being in good state;
denotes the possibility of being in a degraded state with a failure of any of the components; and
is the failure rate while transitioning from good to degraded states.
Assuming the initial operating state as good, the operational reliability can be expressed by Equation (49):
The failure rates of the two-stage converter are calculated using the parts stress method, as formulated by Equation (50) [
35]:
where
λD,
λSw,
λCap,
λind, and
n denote the failure rates of the diode, switch, capacitor, inductor, and the number of these components used, respectively. According to MIL-HDBK-217F [
36], the failure rate of a device is affected by the quality of the components, the environment, contact construction, capacitance, and temperature.
6. Conclusions
In this work, a comprehensive performance assessment of a two-stage power electronic (PE) converter for interfacing the grid of a lithium-ion battery energy storage system in BIPV applications has been presented. The control strategy for the AC/DC and DC/DC converters was assessed for a given 5–30 kHz switching frequency range, and the voltage and current loops’ robustness was analyzed using Bode plots and pole-zero mapping. It was observed that the poles for the voltage and current loops for both converters were in the left half of the plane for the complex domain up to 30 kHz switching frequency.
It was also further observed that increasing the switching frequency by the same amount offered diminishing returns in terms of reduction in settling time. For example, increasing the switching frequency from 10 to 15 kHz reduced the settling time by 34.6%, whereas increasing the switching frequency from 20 to 25 kHz only reduced the settling time by 23.1%. To obtain a balanced trade-off between a responsive PE converter and to reduce loss, a switching frequency of 10 kHz was selected.
The system’s electrical performance was also presented, indicating that the DC-link voltage ripple was lower than 2% in the stable region for the charging and discharging operations within the given switching frequency range. Moreover, the grid current THD was around 2.9% during the discharging operation, indicating that the controller allowed for good-quality power injection by the battery energy storage system through the power converter.
Moreover, the overall electro-thermal performance was summarized by assessing the efficiency map for the charging and discharging operations. It was observed that the discharging efficiency was 0.5% lower than the charging efficiency. This phenomenon showed that the power stage faced significant losses during the discharging operation. Additionally, the lifetime was analyzed by considering the component-level stress factors. The system lifetime was estimated to be 10 years, with a system-level reliability of 90%. The MOSFET lifetime was mostly affected by the diode during the discharging operation.
Finally, this work provides valuable insight into the performance assessment of a two-stage bidirectional PE for PV–BESS system application. However, the study’s innovation lies in its assessment of the impact of regulating different switching frequencies at partial- to full-load operation. The results presented in this study can aid in the design and development of efficient and robust power converters for BIPV applications.