In today's world, traditional thermal power plants are unable to meet consumer demand through grid utility. Renewable energy resources (RES) such as solar and wind energy have received a lot of attention owing to their reliance on natural phenomena. The global cumulative wind power is expected to reach 2000GW by the year 2030, which is an increment at a rate of 1719%. Therefore, it would play an important role in supplying
The availability of permanent magnet material and newer advancements in power converter technology have attracted wind turbine manufacturers’ attention toward directdrive permanent magnet synchronous generators (DPMSGs)^{ }
Solid state transformers are capable of efficiently converting and regulating AC power, making them a suitable option for connecting the AC output of a wind energy conversion system (WES) to a distribution or transmission system. However, in the event of a fault in an islanded modeoperated WES, the SST functions as an isolator between the WES and the connected load. The SST offers superior characteristics and is a feasible substitute for a conventional 50Hz transformer^{ }
Numerous power converter topologies have been proposed for solidstate transformers (SSTs) ^{6, 7}. The threestage SST, which comprises a rectifier, a DAB converter, and an inverter (as depicted in
.
In the SPS control technique, the phase difference between the primary and secondary side of the highfrequency transformer (HFT) is denoted by D1 as shown in
(a). 0 ≤ D_{1} ≤ D_{2} ≤ 1, (b). 0 ≤ D_{2} ≤ D_{1} ≤ 1
(a). D_{1} inner phase shift at h_{1}bridge, (b). D_{3} inner phase shift at h_{2}bridge
To enhance the efficiency of boost operation, the EPS control technique was introduced in
The triplephaseshift control technique was proposed in ^{13}, wherein different inner phaseshift ratios D_{1} and D_{3 }are provided in the primary bridge and secondary bridge of HFT, respectively. Phaseshiftratio D_{2} is given in between both hbridges h_{1} and h_{2}. The TPS control technique can achieve minimum current stress, low switching, and conduction losses, low power loss, and maximum ZVS range with the use of three phaseshift ratios, namely D_{1}, D_{2}, and D_{3}^{ }
The TPS control technique has six different modes, with the output AC voltage waveform of h_{1} and h_{2} bridges shown in
The inductor current


modea 
0 ≤ 
modeb 
0 ≤ 
modec 
0 ≤ 
moded 
0 ≤ 
modee 
0 ≤ 
modef 
0 ≤ 
Due to its odd symmetry, the inductor current satisfies the condition of
The power transfer P and inductor current stress S calculation equations for the DAB converter were as follows:
Substituting the values of
In order to simplify the analysis, the power transfer and current stress in per unit system are expressed as:
where p and s are per unit transfer power and current stress, respectively, with
Moded to modef have high inductor current, as a result of reduced converter efficiency. Therefore, these modes cannot be deduced by this analytical method. Only modea to modec is deduced by this method in which modea is discussed above. Similarly, modeb and modec might be determined in the same way. As a result, for the three highefficiency modes, the power transfer and current stress expressions are as follows:
The transmission power ranges for modea, modeb, and modec are p1 = [0, 1], p2 = [0, 2/3], and p3 = [1/2, 1/2] respectively, as shown in Eq. (9). As can be observed, modea has the largest power transfer range, covering the entire operational region, while modec can achieve bidirectional power transfer. The current stress for both modea and modeb is the same as derived in Eq. (10). In modec, the magnitude of the current stress is governed by both D_{1} to D_{3} and the transformation ratio (k).
The control strategy comprises two parts: (1) the steadystate part, which aims to minimize current stress, and (2) the dynamic state part, which employs virtual power control to address the DAB converter's dynamic behaviour. To determine the minimal current stress, the Lagrangemultiplier technique (LMM) is commonly utilized ^{16}. However, the LMM mathematical model has the issue of the power transfer range overlapping in various operating modes ^{17}. As a result, finding optimal solutions for current stress is challenging due to power transfer and phase shift ratio limitations^{ }
Where n denotes the control variable,
The above expression is known as cost function optimization (CFO), and through this modea is calculated as follows:
After solving the above equation, we get:
where the range of
Similarly, in modeb, the CFO equation is obtained as follows:
Where the range of
For modec, the optimized phaseshift relation is difficult to find due to the disturbance in current stress. As the domain boundary is the same for modeb and modec, the optimal result is also equal.
The virtual power component (VPC) is defined below to increase the dynamic performance of the DAB converter:
Where
Similarly, the optimal phaseshift ratios for modeb and modec were equal and as follows:
The optimal unified TPC control strategy is presented as a result of the foregoing analysis, as shown in
With the help of the MATLAB Simulink environment, the designed DCDC DAB converter is simulated. The simulation results are illustrated in the figures below based on appendix. The switching pulses for the DAB converter are shown in
The SPS control technique for the DAB converter is commonly employed owing to its simplicity and ease of implementation on hardware but its efficiency decreases when the value of voltage transformation ratio (k) deviates far from unity. Moreover, SPS control does not provide a full power range optimal supply and requires an additional ZVS component that in turn increases the cost. Combining the TPS control technique with the virtual power component minimizes the current stress and therefore improves the efficiency of the DAB converter. This further increases the range of ZVS and minimizes the number of passive components. In this paper, detailed mathematical analysis is carried out and MATLAB Simulinkbased simulation results are compared for three control phase shift control techniques viz. SPS, EPS, and TPS, in which 140 V input voltage is converted to 50 V DC output voltage. According to the simulation results, the use of the proposed virtual power control technique results in a 23% and 9% reduction in peak inductor current compared to the conventional SPS and EPS phase shift modulation technique. The proposed optimal TPS control technique shows a stable output voltage and reduced current stress for IGBTs.
Input voltage: 140V, output voltage: 50V, input, and output capacitance: 500µF, turn ratio: 52:30, total leakage inductance: 30µH, frequency: 50KHz, load: 510 ohm.