# Hybrid, Multi-Megawatt HVDC Transformer Topology Comparison for Future Offshore Wind Farms

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## Abstract

**:**

## 1. Introduction

## 2. Computer Simulation

#### 2.1. Simulation Models

_{in}) between the fully rated generator rectifier and hybrid transformer (Figure 1). Steady state operation at the rated power was assumed throughout the simulations with the generator rectifier allowing a variable speed turbine operation. The transformer output connects to a ±300 kV HVDC via a shunt connection.

_{out}) and reactive power (Q

_{T}) are governed by the algorithms shown in Figure 4, where voltage (v

_{p}) and current (i

_{p}) inputs are taken at the locations shown in Figure 2. The primary and secondary DC bus resistances are embodied by R

_{p}and R

_{s}respectively, and the magnetic transformer has a turns ratio of 1:100. It is known that the power transferred through the transformer (P

_{T}) is given by (1) for a primary and referred secondary voltage (v

_{p}and v

_{s}′ respectively), transformer reactance (X

_{T}), and load angle (δ).

_{p}and v

_{s}′ are fixed by the turbine specifications, the δ range is determined by the transformer inductance (L

_{T}) and should be selected to maintain stable control and allow 6.5 MW to be transferred. Moreover, L

_{T}was designed to prevent high frequency voltage harmonics generated by switching events from showing in the arm current and magnetic flux waveforms, and hence prevent core saturation. With these considerations, L

_{T}lumped on the primary side was chosen to be 0.1 mH.

_{p}) and secondary (CS

_{s}) converter blocks in Figure 2. Connection points a and d are positive and negative DC bus points respectively, while b and c are the AC live and neutral points. In both converters, each valve is composed of n Insulated-Gate Bipolar Transistors (IGBTs) in series and parallel to withstand the voltage and current stresses. The y Sub Modules (SMs) in the MMC are composed of two valves (V

_{y}and Vx

_{y}) and a module capacitor C

_{mod}.

#### 2.2. Active and Reactive Power Control Algorithms

_{p}and i

_{p}, particularly in the HB configurations, makes this complicated, as their magnitudes are not accurately calculated by the Fast Fourier Transform (FFT) and the time domain does not directly provide their phase (θ). A combined approach was therefore taken, where θ was calculated using an FFT and time domain calculations were used to determine the apparent power (S

_{T}).

_{p}and i

_{p}measurements, their means were calculated and subtracted from the recorded values. The reactive power was then calculated from:

_{out}with respect to the power generated, or lowered by decreasing it. However, as the bus is represented by a DC source in the model, its voltage magnitude is raised or lowered to achieve the same effect.

#### 2.3. MMC Control Algorithm

_{c}). Depending on the direction of the arm current (i

_{arm}), the module capacitors will either charge or discharge when they are switched in or placed in the current path. Modules are switched in when Sx

_{y}is conducting and bypassed when S

_{y}is conducting to create the desired voltage steps. Sx

_{y}and S

_{y}must never both conduct though, or the module capacitor will be short-circuited. Multiple module combinations are possible for each voltage level, apart from the maximum and minimum voltage level (Figure 5).

_{arm}is positive. If the current is negative, the module with the lowest voltage is switched out. This module is then removed from the selection process until the reference voltage gradient becomes negative. At this point, all of the modules are placed once again into the decision matrix, and if the arm current is positive the module with the lowest voltage is switched in; otherwise, the highest voltage module is used. The algorithm selects the modules in Arm 2 similarly, except the inverse reference voltage gradients are used. In this way, the duty ratio of each module varies between cycles to effectively balance the capacitor voltages. However, each module only switches in and out once per cycle, minimizing switching losses.

## 3. Transformer Loss Calculation

#### 3.1. Converter Losses

_{ce rate}= 1.2 kV and I

_{c rate}= 400 A, respectively. This fast switching IGBT was selected as it was found to be the most efficient in the MF range, and was used for both the CS

_{p}and CS

_{s}to simplify their construction and maintenance. In the loss calculation, the junction temperature was assumed to be at the rated value (125 °C), a reasonable assumption since the wind turbine was operating at rated power.

_{on}) and losses during switching vary with collector current i

_{c}. This relationship was not adequately accounted for by Simulink, so ideal switches were used in the simulations and in the conduction and switching losses calculated later in MATLAB. The switch datasheets provided by the manufacturer were used to derive equations relating i

_{c}to v

_{ce}and the diode forward voltage (v

_{F}) through the use of a curve fitting tool. Combining with the piecewise linear current waveforms from the Simulink models, the conduction loss (P

_{con}) can be calculated as follows:

_{step}is the length of each time step i, ES

_{con}and ED

_{con}are the conduction energy losses for the IGBT and diode for the y

^{th}valve composed of n IGBTs and antiparallel diodes, and T

_{cycle}is the period over which the energy calculation took place.

_{IGBT}) and reverse recovery (E

_{Diode}) losses for the IGBT and antiparallel diode to I

_{c}or I

_{F}, respectively, to calculate the switching losses. Here, a switching operation is determined to have occurred when I

_{c}or I

_{F}increases or decreases from 0, respectively. The total switching loss (P

_{switch}) can therefore be calculated from:

_{total}, the diode reverse recovery loss is given by EDs

_{total}, and E

_{IGBT}and E

_{Diode}are the switching and reverse recovery losses for each IGBT, respectively.

#### 3.2. Core Losses

_{core}is the per volume power loss for the magnetic core, $\widehat{B}$ is the maximum flux density, and k, α, and β are constants collectively named the Steinmetz Parameters. The SE is only valid for sinusoidal flux density waveforms though [22], and so cannot be used in this analysis. The power electric converters on either side of the magnetic transformer create stepped, square voltage waveforms. From (12), it can be seen that flux density is the integral of voltage and so is also non-sinusoidal.

_{e}the effective core area, and v(t) the time varying voltage.

_{c}individual cycles, and then further into its rising and falling sections; i.e., the cycle’s global minimum to maximum and global maximum to minimum, respectively. If there are multiple global maxima or minima, either can be chosen. An example flux density waveform is shown in Figure 7. It has been split into its rising and falling sections, with the minor loops in each identified in red; the black line forms the major loop of the rising and falling sections.

_{1}, until a negative gradient is detected, i.e., point J in Figure 7. A new set is then created (s

_{1+1}), and each point is added to this until either the next negative gradient is reached (J’), after which an additional set is created or the end of the section is reached. Each set is then examined, starting at the final set s

_{q}. Any points greater than the set’s initial flux density, i.e., point J’ for the last set in this example or point J for the second set, are moved to the lower set, i.e., s

_{q−1}, until the first set s

_{1}is reached. Now s

_{1}contains a monotonically increasing major loop with sets s

_{1+1}to s

_{q}holding each minor loop. The power loss can then be calculated separately for each loop and cycle using (13) and (14).

_{o}is the core loss for each major or sub loop of the l

^{th}cycle, δB

_{i}and δt

_{i}are the change in flux and time between time step i and i−1, and T

_{cycle}and T

_{o}are the periods of the cycle of the o

^{th}loop.

_{max}) is 90% of the core’s saturation flux density (B

_{sat}) and the core volume and hence area should be minimized, A

_{e}can be found from (20).

## 4. Results

_{p}with six modules, as this is the optimum number of Voltage Levels (OVL) at 500 Hz, and was paired with an 11L CS

_{s}. The OVL is defined here as the fewest voltage levels and hence modules required to withstand peak voltage (including safety margin) with only one series connected to the IGBT in each module valve. In the second combination (11-11L MMC), an 11L CS

_{p}was paired with an 11L CS

_{s}to demonstrate the impact of increasing the number of CS

_{p}levels above the minimum requirement to withstand the applied voltage stress. In the third combination (11-25L MMC), an 11L CS

_{p}was paired with a 25L CS

_{s}to investigate increasing the number of CS

_{s}levels. In practice, the CS

_{s}would consist of hundreds of modules to resist the exhibited voltage stress, resulting in the generation of many levels. A very high number of switching elements would be required to generate such a waveform, greatly increasing the computational time for such a model. By limiting the CS

_{s}to 25L and only modelling the IGBT valves in each module (i.e., Figure 8), the model’s run time was greatly reduced while allowing the impact of increasing the number of voltage levels on transformer performance to be investigated. It should be noted that the number of switches within the valves were varied to resist the different voltage and current stresses of each configuration. This did not impact on simulation time, as only the valves were simulated as the number of switches was only taken into account for the loss calculations.

#### 4.1. Power Control

_{out}with increasing frequency and δ is shown in Figure 8a for the three topologies operating at 0.5 and 2 kHz. Since the HB-HB and HB-MMC configurations have a higher gradient than the MMC-MMC configuration, it can be said that their control is more sensitive. Therefore, a small deviation in δ can translate to large response in P

_{out}, potentially destabilizing the control, especially in the lower frequency range. While this does improve at higher frequencies, the lower gradient offered by the MMC-MMC configuration provides improved stability across the whole frequency range.

_{p}increases, particularly at higher frequencies.

#### 4.2. System Losses

## 5. Discussion

_{p}and P

_{out}in the HB-HB configuration. The MMC-MMC configurations have a much lower THD though, resulting in a smaller change in the voltage drop across L

_{T}. The rise in P

_{out}is therefore also smaller, thereby improving the converter’s stability. Secondly, the peak primary voltage created by the HB converter is twice that of the MMC converter. As P

_{out}is calculated from (1) and v

_{p}≈ v

_{cp}, doubling v

_{cp}means sin δ must reduce by a factor of four to keep P

_{out}constant. Power is therefore more sensitive to small changes in δ. While increasing the number of primary turns—and hence L

_{T}—could mitigate this, e.g., with a turns ratio of 1:100, it would greatly affect the hybrid transformer volume. Given this, the MMC-MMC configuration may prove better at lower frequencies for the given hybrid transformer parameters.

_{T}through reducing the number of primary windings, although A

_{e}would have to increase to compensate for the increased flux.

^{3}at 500 Hz is assumed, then the core losses would be 0.33% compared to 1% converter loss for the HB-HB configuration. Clearly, converter losses dominate core losses, demonstrating the importance of the converter’s design. While the literature [28] suggests that the MMC configuration has lower losses, this is based on the HB using Pulse Width Modulation (PWM). Without PWM, the HB-HB configuration has fewer losses (1.21% vs. 1.31% at 500 Hz) over the whole frequency range, and hence lower total hybrid transformer losses. The higher efficiency of the HB-HB configuration is considered to outweigh the improved controllability offered by the MMC one, and so is recommended here.

## 6. Conclusions

_{out}was very sensitive, particularly at low operating frequencies. The MMC-MMC configuration increased P

_{out}stability, but to improve Q

_{T}control above 700 Hz, the number of transformer windings should be reduced. The higher efficiency of the HB-HB topology is preferred overall, particularly at higher frequencies. However, the MMC-MMC configuration at the OVL may prove beneficial at lower frequencies if the hybrid transformer volume is reduced significantly.

## Acknowledgments

## Author contributions

## Conflicts of Interest

## References

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**Figure 1.**A High Voltage Direct Current (HVDC) offshore wind farm using the proposed hybrid HVDC transformer to step-up the turbine’s Medium Voltage Direct Current (MVDC) bus to the HVDC grid.

**Figure 3.**Converter topologies used to evaluate different transformer configurations (

**a**) H-Bridge (HB) and (

**b**) Modular Multilevel Converter (MMC). Abbreviation: SM = Sub Module.

**Figure 8.**(

**a**) Power output for MMC and HB configurations vs. increasing load angles at 0.5 kHz and 2 kHz; (

**b**) Voltage increase due to Q

_{T}compensation vs. increasing frequencies.

**Figure 9.**Normalized losses for the: (

**a**) Converter and (

**b**) Transformer core over the medium frequency (MF) range.

**Figure 10.**v

_{cp}, v

_{p}, and resulting i

_{p}waveforms for the (

**a**) HB and (

**b**) 11-11L MMC configurations.

Frequency Range (Hz) | k | α | β |
---|---|---|---|

500–2000 Hz | 230.76 | 1.09 | 2.81 |

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**MDPI and ACS Style**

Smailes, M.; Ng, C.; Mckeever, P.; Shek, J.; Theotokatos, G.; Abusara, M. Hybrid, Multi-Megawatt HVDC Transformer Topology Comparison for Future Offshore Wind Farms. *Energies* **2017**, *10*, 851.
https://doi.org/10.3390/en10070851

**AMA Style**

Smailes M, Ng C, Mckeever P, Shek J, Theotokatos G, Abusara M. Hybrid, Multi-Megawatt HVDC Transformer Topology Comparison for Future Offshore Wind Farms. *Energies*. 2017; 10(7):851.
https://doi.org/10.3390/en10070851

**Chicago/Turabian Style**

Smailes, Michael, Chong Ng, Paul Mckeever, Jonathan Shek, Gerasimos Theotokatos, and Mohammad Abusara. 2017. "Hybrid, Multi-Megawatt HVDC Transformer Topology Comparison for Future Offshore Wind Farms" *Energies* 10, no. 7: 851.
https://doi.org/10.3390/en10070851