Figure 1.
Overview of power flow in V2G [8] and the DC-DC converter.
Electric vehicles (EVs) are an emerging technology that contribute to reducing air pollution. This paper presents the development of a 200 kW DC charger for the vehicle-to-grid (V2G) application. The bidirectional dual active bridge (DAB) converter was the preferred fit for a high-power DC-DC conversion due its attractive features such as high power density and bidirectional power flow. A particle swarm optimization (PSO) algorithm was used to online auto-tune the optimal proportional gain (KP) and integral gain (KI) value with minimized error voltage. Then, knowing that the controller with fixed gains have limitation in its response during dynamic change, the PSO was improved to allow re-tuning and update the new KP and KI upon step changes or disturbances through a time-variant approach. The proposed controller, online auto-tuned PI using PSO with re-tuning (OPSO-PI-RT) and one-time (OPSO-PI-OT) execution were compared under desired output voltage step changes and load step changes in terms of steady-state error and dynamic performance. The OPSO-PI-RT method was a superior controller with 98.16% accuracy and faster controller with 85.28 s-1 average speed compared to OPSO-PI-OT using controller hardware-in-the-loop (CHIL) approach.
Citation: Suliana Ab-Ghani, Hamdan Daniyal, Abu Zaharin Ahmad, Norazila Jaalam, Norhafidzah Mohd Saad, Nur Huda Ramlan, Norhazilina Bahari. Adaptive online auto-tuning using Particle Swarm optimized PI controller with time-variant approach for high accuracy and speed in Dual Active Bridge converter[J]. AIMS Electronics and Electrical Engineering, 2023, 7(2): 156-170. doi: 10.3934/electreng.2023009
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Electric vehicles (EVs) are an emerging technology that contribute to reducing air pollution. This paper presents the development of a 200 kW DC charger for the vehicle-to-grid (V2G) application. The bidirectional dual active bridge (DAB) converter was the preferred fit for a high-power DC-DC conversion due its attractive features such as high power density and bidirectional power flow. A particle swarm optimization (PSO) algorithm was used to online auto-tune the optimal proportional gain (KP) and integral gain (KI) value with minimized error voltage. Then, knowing that the controller with fixed gains have limitation in its response during dynamic change, the PSO was improved to allow re-tuning and update the new KP and KI upon step changes or disturbances through a time-variant approach. The proposed controller, online auto-tuned PI using PSO with re-tuning (OPSO-PI-RT) and one-time (OPSO-PI-OT) execution were compared under desired output voltage step changes and load step changes in terms of steady-state error and dynamic performance. The OPSO-PI-RT method was a superior controller with 98.16% accuracy and faster controller with 85.28 s-1 average speed compared to OPSO-PI-OT using controller hardware-in-the-loop (CHIL) approach.
Global warming is a radically aggravating phenomenon due to many causes. One such cause is the burning of fossil fuels in line with the growing of energy consumption. Among the many approaches that have been implemented to mitigate the environmental problems, power electronics (PE), which is efficient in deploying energy, has been identified as the key player in producing green energy [1]. Progression of renewable energy (RE) and smart microgrid have instigated the growth of PE applications such as electric vehicles (EVs) and energy storage units [2].
The development of EVs was predicted to grow rapidly as have the features of clean technology [3]. Moreover, the implementation of RE sources in EVs has significantly reduced the dependency on fossil fuels [4]. Plug-in Hybrid Electric Vehicles (PHEV) is an example of a vehicle-to-grid (V2G), which is built-in with battery pack and grid connection [4,5]. Having said that, there are two types of EV chargers, namely the on-board charger and off-board charger, the AC and DC types, respectively [6]. This study, however, designed a system to be compatible with the off-board DC charger of CHAdeMO 1.2 type standard with 200 kW rated power and 400 A maximum current [7]. This study only considers the bidirectional DC-DC converter as depicted in Figure 1.
The bidirectional power flow in DC-DC converter acts as an interface between DC high voltage bus and EVs battery. The bidirectional power flow can be classified into a non-isolated and isolated structure. Based on the variable voltage conversion ratio and safety benefits, isolated configuration is usually chosen instead of the non-isolated structure [9,10]. Having said that, the dual active bridge (DAB) isolated DC-DC converter is most preferred in the energy storage system (ESS) applications [11,12].
DAB converter was introduced in the 1990s [13]. In DAB there are bidirectional power flow features that are it capable of storing energy during charging and the energy is sent back to the grid during the discharging mode [4,14]. Apart from that, the promising soft switching, high efficiency, high power density, simple control strategy and galvanic isolation of the DAB DC-DC converter made it popular recently [15,16].
The DAB system employs many optimization techniques. Among the available techniques, the particle swarm optimization (PSO) algorithm is the most widely accepted due to fewer parameters, high speed of convergence time and simple mathematical equation [17,18] compared to Lagrange Multiplier [19] and analytical method based on Karush–Kuhn–Tucker [20]. Several studies have proposed an offline method to determine optimal phase-shift angle, ϕ using PSO to minimize reactive power [21] and current stress [22]. Despite the advantages of the offline method such as reducing the computing cost [23], its implementation in real time has a downside whereby the parameter or setting needs to be adjusted in the prepared lookup table if there are any changes. Meanwhile, online optimization method in DAB using an analytical method based on global optima technique was developed to minimize backflow power [24] and root mean square (RMS) current [25].
On the other hand, the proportional-integral (PI) controller is a linear controller that is widely used in various applications, including power electronic applications due to its simple design and effectiveness [18]. PI controller is also used to regulate the output voltage in the DAB system. However, the PI controller tuning process has demerits in term of time consuming and stability guaranteed because of the trial-and-error method used and it only delivers satisfactory performance for narrow operating range [26]. Hence, PSO is the most preferred method for tuning and obtaining the optimal PI parameters [27,28,29] that results in less overshoot, low total harmonic distortion and improves the fast response.
Even though the offline and online tuning of PI using PSO have already been researched, the online auto-tuned PI controller using PSO algorithm have not been evaluated yet in DAB DC-DC converter in analyzing steady-state error, eSS and transient response in order to evaluate the system accuracy and speed's controller, respectively. Hence, this paper presents the development of DAB DC-DC converter using online auto-tuned by re-tuning features through the PSO-PI method. This method is crucial in the DAB system, especially in EV or transportation applications due to the system’s robustness and high dynamic response [30,31]. The re-tuning method was introduced to address the issue of the fixed gains restriction, which provided the same responses to the applied changes in dynamic system [32]. Moreover, recent research has incorporated artificial intelligence substantially in the use of EVs, such as voltage control strategy based on deep reinforcement learning [33] and multiagent reinforcement learning method [34]. Yet, the PSO algorithm is still relevant due to less computational methods and is efficient to be embedded in the system environments [18].
The online auto-tuned PSO-PI with re-tuning approach (OPSO-PI-RT) based on the single-phase-shift (SPS) modulation is proposed in this study and is compared with online auto-tuned PSO-PI with a one-time execution (OPSO-PI-OT) technique. The SPS modulation was chosen due to its competition efficient feature for the system design.
Section Ⅱ of this paper discusses the DAB system and SPS control. Section Ⅲ outlines the overview of the PSO and how PI is tuned using the stochastic optimization. The setup of Hardware-in-the-Loop (HIL) is detailed in Section Ⅳ. Meanwhile, the experimental results of the eSS and dynamic performance of the four methods are analyzed in Section Ⅴ. Lastly, Section Ⅵ concludes this study.
The DAB, as depicted in Figure 2, is a DC-DC converter of two active bridges. Both bridges are interfaced through a high frequency transformer. The leakage inductance, Lk, is the main element of energy transferring in the DAB. The equivalent topology of DAB converter is illustrated in Figure 3, where V1 is the voltage at primary side, V2 is the voltage at secondary side, ILk is the current of leakage inductance and VLk is the voltage of leakage inductance. The pulse width modulation (PWM) switching at each bridge is set to 50% of the duty cycle to enable both bridges to produce a symmetrical square-wave pulse with a ϕ value between the bridges. A constant switching frequency is used in the design.
SPS is one of the modulation strategies that have been applied in DAB. It is the simplest strategy that produces high efficiency when operated under narrow voltage variations, where voltage conversion ratio, k is close to one [35]. Despite the improvement of phase-shift modulation, such as extended phase-shift (EPS), dual phase-shift (DPS) and triple phase-shift (TPS), the SPS is still preferred as it is easy to implement and reliable [30,36,37].
SPS only needs to control one ϕ to control the magnitude and direction of power flow in DAB. The primary side leads to the second part in a forward direction and conversely in reverse power flow. The power transmission of DAB can be obtained using (1), where Ts denotes switching the interval. Following mathematical manipulations, the power flow can be expressed as (3), in which Vi represents input voltage, Vo output voltage, n transformer turns ratio and fs switching frequency.
| P=1Ts∫t4t0V1(t)iLk(t)dt | (1) |
| P=12π∫2π0V1(t)iLk(t)dt | (2) |
| P=nViVoϕ122πfsLk(1−ϕ12π);ϕ12=ϕ1−ϕ2 | (3) |
The maximum power can be calculated as (4), which occurs when ϕ is 90° (π2). The transformer turns ratio, n and voltage conversion ratio, k can be calculated using (5) and (6) respectively, where NP and NS represent the primary turn and secondary turn of the transformer correspondingly.
| Pmax=nViVo8fsLk | (4) |
| n=NPNS | (5) |
| k=nVoVi | (6) |
Figure 4 indicates the square waveform at each bridge and leakage inductance voltage, VLK when V1 = 750 V and V2 = 500 V with maximum ϕ at 90°. Only one ϕ need to be controlled in this system since the SPS modulation is used.
PSO is a stochastic algorithm based on the social behavior of bird flocking or fish schooling that was introduced in 1995 [39]. This swarm intelligence conducts a search process using a group of particles. Each particle represents a candidate solution to the given problem. Particles set with initial parameters will explore and exploit iteratively following the objective function until the desired outcome is achieved. In each iteration, the particles will update the particle best, Pbest, then global best, Gbest will be selected from the best of Pbest solution. The velocity and position of the particles involved are adjusted using (7) and (8) respectively.
| vi(k+1)=wvi(k)+c1r1[Pbesti−xi(k)]+c2r2[Gbest−xi(k)] | (7) |
| xi(k+1)=xi(k)+vi(k+1) | (8) |
where w is the inertia weight, c1 and c2 are the acceleration coefficient, r1 and r2 are the random number between 0 to 1, Pbest is the personal best position of particle i, Gbest is best position of the particles and k represents the iteration number.
In the proposed method, PI controller is used to regulate the ϕ as to control the desired Vo. Hence, optimal proportional gain (KP) and integral gain (KI) values using PSO will produce the suitable ϕ as to yield the desired Vo. The block diagram of the proposed method is illustrated in Figure 5.
The objective function is defined by the minimum root mean square error (RMSE) as shown in (9).
| RMSEmin=√1N∑Ni=1(Vref−Vo)2 | (9) |
The PSO parameter of w, c1, c2, r1 and r2 in the proposed method are fixed values. The three particles which represent the three pairs of KP and KI are used during the search process through time variant [40,41] as illustrated in Figure 6. Each particle is limited to 0.5 ms for each iteration. In the first iteration, the initial KP and KI values evaluate the objective function using (9). The fitness values of each particle are represented by the minimum RMSE of the DAB system. The KP and KI values with the best fitness values will represent Pbest for each particle. Then, the Gbest values were selected from the best fitness values of Pbest, with least minimum RMSE. This is followed by the new velocity and position of particles that are updated using (7) and (8) correspondingly. The new KP and KI produced the right ϕ as to generate the gate signal to all eight switches (S1 to S8) in trying to regulate the Vo. In the second iteration, the new Pbesti is compared with the old Pbesti, whereby a new Gbest is updated accordingly. Then, the velocity and position are also updated based on updated values. This process is repeated continuously until all the particles are converged at certain values. Finally, the appropriate ϕ is obtained from the optimal values of KP and KI, where the DAB system generates the desired output with minimum eSS voltage.
On the other hand, the system of the proposed method is updated with reset features, whereby the KP and KI values change according to the new load or desired Vo. When the step changes occurred, PSO algorithm was triggered to allow the re-tuning process. Then, the particles are initialized again at the initial position when all reset requirements, such as all particles must be in convergence state; error voltage, Ve must be greater and equal than certain values and all fitness values for each particle must converge with each other satisfactorily. Those requirements are vital to avoid the PSO from performing sudden re-tuning at the initial iteration while Ve is still large.
All particles continued with the optimization process as reflected in the new condition, with these procedures being iterated several times until reaching the termination criterion by assuming that no step-changes occurred again. However, if the step-change occurred for the second time before the termination and fulfilled the re-tuning principles, the re-tuning process will be repeated to regulate the output as desired. Then, the new KP and KI will be optimized following the previous steps to conceive a DAB system with minimum eSS. Therefore, with re-tuning ability, PSO can make new searches to adapt with new conditions to regulate new Vo. Figure 7 and Figure 8 depict the flowchart and overview of the working re-tuning in the proposed method, respectively.
Meanwhile, the one-time execution method (OPSO-PI-OT) follows a similar concept to OPSO-PI-RT. However, the difference lies during the step change or disturbances, where the KP and KI values in OPSO-PI-OT maintain and try to regulate the desired output with the old optimal PI values.
In real-time implementation, the algorithms of the DAB controller for all methods were implemented using Texas Instrument F28335 DSP card control. The hardware emulator, Typhoon-HIL 402 was used to develop the power circuit of the DAB converter. Moreover, a built-in field-programmable gate array (FPGA) in the Typhoon enables the modelling system to perform under a real-time form. Figure 9 presents the controller hardware-in-the-loop (CHIL) setup for a 200 kW DAB system designed using the parameters tabulated in Table 1. The Vo from DAB system in Typhoon-HIL is fed to the DSP card controller.
| Components | Values |
| Transformer turns ratio, n | 2 :1 |
| Rated power, Pmax | 200 kW |
| Input voltage, Vi | 750 V |
| Output voltage, Vo | 500 V |
| Leakage inductance, Lk | 24 µH |
| Switching frequency, fs | 20 kHz |
DownLoad:
CSV
The controller of the PSO algorithm and PI controller was implemented in MATLAB/Simulink (MATLAB Support Package for TI C2000 library) and loaded into the DSP board. Then, the ϕ that was produced was sent to the gate signal of the switches in DAB circuit through enhanced pulse width modulator (ePWM) module. The deadtime was set to 0.6 µs and the DAB converter operated at a fixed switching frequency of 20 kHz.
Table 2 presents the steady-state and transient response performances of the DAB converter during load step-change at 270 V, 375 V and 420 V. The eSS is measured during the steady-state response after applying the disturbance or step change to the system. The steady-state performance was initially evaluated by applying the load-step change during half load (100 kW) to full load (200 kW) condition. When the load was stepped-up from 100 kW to 200 kW at 270 V as depicted in Figure 10, the eSS of the OPSO-PI-OT has a higher percentage of eSS with 1.47% compared to OPSO-PI-RT. The proposed OPSO-PI-RT method yielded the least eSS with 1.39%, where it was 5.44% more accurate than OPSO-PI-OT. Besides, the best accuracy is exhibited by OPSO-PI-RT when the load was stepped at 375 V, where the accuracy was 5.56% superior to OPSO-PI-OT as illustrated in Figure 11. There is just a slight difference in values of eSS between OPSO-PI-OT and OPSO-PI-RT when the load was changed at 420 V, which OPSO-PI-RT only has 0.6% best performance than OPSO-PI-OT.
| Load Step-change | Vref (V) | Average eSS (%) | Average settling time (ms) | ||
| OPSO-PI-OT | OPSO-PI-RT | OPSO-PI-OT | OPSO-PI-RT | ||
| 100kW to 200kW | 270 | 1.47 | 1.39 | 15.80 | 15.60 |
| 375 | 1.44 | 1.36 | 13.70 | 13.20 | |
| 420 | 1.66 | 1.65 | 9.50 | 10.10 | |
| 150kW to 70kW | 270 | 4.13 | 3.20 | 10.50 | 10.05 |
| 375 | 1.54 | 1.57 | 9.90 | 10.80 | |
| 420 | 3.84 | 1.70 | 11.10 | 10.60 | |
DownLoad:
CSV
When the load was stepped-down from 150 kW to 70 kW at 270 V (k = 0.72), as presented in Figure 12, the proposed OPSO-PI-RT exhibited 22.52% better performance by producing the smaller ripple voltage with 3.20% of eSS relative to OPSO-PI-OT that produce 4.13% of eSS. As shown in Figure 13, the OPSO-PI-RT has a tremendous performance at 420 V by producing 55.73% better accuracy than OPSO-PI-OT. With that percentage, it shows that the tuned optimal KP and KI values at 150 kW in the OPSO-PI-OT method are not the ideal values for the 70 kW system. Thus, it shows the significant advantages of the proposed OPSO-PI-RT that allows KP and KI values to update continuously according to the changes and it can eliminate more ripple voltage compared to OPSO-PI-OT.
In summary, the comparative percentage of eSS between OPSO-PI-RT and OPSO-PI-OT indicate that the OPSO-PI-RT has good accuracy with 14.65% superior performance than OPSO-PI-OT. Thus, by updating the KP and KI optimal values for current system conditions has diminished the ripple in the DAB system and guarantees the proposed OPSO-PI-RT is more precise than OPSO-PI-OT in both load step conditions. It proves that the KP and KI obtained in this method change according to the new load and ensure better performance of the DAB system with minimal eSS.
The DAB converter was further analyzed by measuring the dynamic response in terms of settling time during the disturbances or step changes in the system. The settling time for OPSO-PI-OT was longer, taking 15.80 ms for the Vo to reach desired value compared to OPSO-PI-RT with 15.60 ms during the load change from 100 kW to 200 kW at 270 V as shown in Figure 10. From Figure 11, the OPSO-PI-OT recorded the settling time of 13.20 ms to regulate back to the desired value after the load change at 375 V, which was 0.5 ms faster than OPSO-PI-OT.
Furthermore, when the load was changed from 150 kW to 70 kW at 270 V, as demonstrated in Figure 12, it is visibly shown that OPSO-PI-RT gives 0.45 ms faster recovery during transient than OPSO-PI-OT by producing 10.05 ms of settling time. Besides, the settling time of OPSO-PI-RT was shorter compared to OPSO-PI-OT as shown in Figure 13, where the settling time was 11.10 ms and 10.60 ms for OPSO-PI-OT and OPSO-PI-RT, respectively.
This evaluation will determine the speed of the controllers where it refers to the inversion of the settling time as shown in (10).
| speed(s−1)=1000settlingtime(ms) | (10) |
As predicted, the proposed OPSO-PI-RT achieved the best speed even after going through the reset process during the step change or disturbance by producing 85.28 s-1 compared to OPSO-PI-OT with 85.10 s-1. The re-tuning in OPSO-PI-RT proved that it does not get distracted nor does it delay the system, and yet can still yield faster control than OPSO-PI-OT.
This paper proposed a bidirectional DAB DC-DC converter using SPS modulation. A 200 kW system with online auto-tuned PI using PSO algorithm was developed to improve system accuracy and improve the controller's speed. The main analyses, including CHIL results, were discussed for step change load disturbance at different voltage conversion ratios. The performance of the proposed OPSO-PI-RT method was compared with OPSO-PI-OT. The effectiveness of the proposed OPSO-PI-RT method was verified through CHIL experiments. It recorded least eSS of less than 4% in all conditions tested. The proposed OPSO-PI-RT exhibited the faster dynamic response with minimal settling time in regulating back to the desired value after experiencing step change or disturbances in the DAB system. With the noteworthy outcomes of high accuracy and high speed that the proposed controller realized, both features are being expected to give the better performance of high power EV charger application. With these improvements, the EVs will receive significant consideration from users as the charger technology would feature rapid charging and fast system response by maintaining its system accuracy.
The authors would like to thank the University Malaysia Pahang for providing financial support under an internal research grant (Grant Number: RDU220309).
All authors declare no conflicts of interest in this paper.
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Figures(13) / Tables(2)
Suliana Ab-Ghani, Hamdan Daniyal, Abu Zaharin Ahmad, Norazila Jaalam, Norhafidzah Mohd Saad, Nur Huda Ramlan, Norhazilina Bahari. Adaptive online auto-tuning using Particle Swarm optimized PI controller with time-variant approach for high accuracy and speed in Dual Active Bridge converter[J]. AIMS Electronics and Electrical Engineering, 2023, 7(2): 156-170. doi: 10.3934/electreng.2023009
| Components | Values |
| Transformer turns ratio, n | 2 :1 |
| Rated power, Pmax | 200 kW |
| Input voltage, Vi | 750 V |
| Output voltage, Vo | 500 V |
| Leakage inductance, Lk | 24 µH |
| Switching frequency, fs | 20 kHz |
DownLoad:
CSV
| Load Step-change | Vref (V) | Average eSS (%) | Average settling time (ms) | ||
| OPSO-PI-OT | OPSO-PI-RT | OPSO-PI-OT | OPSO-PI-RT | ||
| 100kW to 200kW | 270 | 1.47 | 1.39 | 15.80 | 15.60 |
| 375 | 1.44 | 1.36 | 13.70 | 13.20 | |
| 420 | 1.66 | 1.65 | 9.50 | 10.10 | |
| 150kW to 70kW | 270 | 4.13 | 3.20 | 10.50 | 10.05 |
| 375 | 1.54 | 1.57 | 9.90 | 10.80 | |
| 420 | 3.84 | 1.70 | 11.10 | 10.60 | |
DownLoad:
CSV
| Components | Values |
| Transformer turns ratio, n | 2 :1 |
| Rated power, Pmax | 200 kW |
| Input voltage, Vi | 750 V |
| Output voltage, Vo | 500 V |
| Leakage inductance, Lk | 24 µH |
| Switching frequency, fs | 20 kHz |
| Load Step-change | Vref (V) | Average eSS (%) | Average settling time (ms) | ||
| OPSO-PI-OT | OPSO-PI-RT | OPSO-PI-OT | OPSO-PI-RT | ||
| 100kW to 200kW | 270 | 1.47 | 1.39 | 15.80 | 15.60 |
| 375 | 1.44 | 1.36 | 13.70 | 13.20 | |
| 420 | 1.66 | 1.65 | 9.50 | 10.10 | |
| 150kW to 70kW | 270 | 4.13 | 3.20 | 10.50 | 10.05 |
| 375 | 1.54 | 1.57 | 9.90 | 10.80 | |
| 420 | 3.84 | 1.70 | 11.10 | 10.60 | |
