Electronic power transformers (EPTs) have been identified as emerging intelligent electronic devices in the future smart grid, e.g., the Energy Internet, especially in the application of renewable energy conversion and management. Considering that the EPT is directly connected to the medium-voltage grid, e.g., a10 kV distribution system, and its cascaded H-bridges structure, the common mode voltage (CMV) issue will be more complex and severe. The CMV will threaten the insulation of the entire EPT device and even produce common mode current. This paper investigates the generated mechanism and characteristics of the CMV in a cascaded H-bridge EPT (CHB-EPT) under both balanced and fault grid conditions. First, the CHB-EPT system is introduced. Then, a three-phase simplified circuit model of the high-voltage side of the EPT system is presented. Combined with a unipolar modulation strategy and carrier phase shifting technology by rigorous mathematical analysis and derivation, the EPT internal CMV and its characteristics are obtained. Moreover, the influence of the sinusoidal pulse width modulation dead time is considered and discussed based on analytical calculation. Finally, the simulation results are provided to verify the validity of the aforementioned model and the analysis results. The proposed theoretical analysis method is also suitable for other similar cascaded converters and can provide a useful theoretical guide for structural design and power density optimization.

Recently, renewable energy sources (RESs), e.g., photovoltaic and wind power, with a rising penetration in the modern power grid, have attracted more attention and been exploited widely due to their renewable and environmentally friendly nature relative to traditional fossil fuel energy. Distributed generations and micro-grids are regarded as promising directions and technologies for the reasonable development and utilization of RESs [

However, as the fundamental elements in the legacy grid, traditional line-frequency transformers are not well suited for the exploitation and utilization of RESs. Therefore, a multifunctional grid interface or energy router is required for the Energy Internet.

Electronic power transformers (EPTs) [

When an EPT is connected to a high or medium voltage power grid, e.g., a 10 kV distribution system, due to the limit of blocking the voltage rating of insulated gate bipolar transistors (IGBTs) or other switching devices, a series-input/cascaded structure has been the most reasonable and popular choice for EPTs [

It is well known that pulse width modulation (PWM) converters always generate common mode voltage (CMV) [

Due to the long power cables connecting to the grid or motors, the traveling high-rise-rate CMV wave reflected by the terminals of cables will further result in overvoltage for terminal devices and cause bearing currents that reduce the life of the motors.

High

Since an EPT is composed of cascaded H-bridges on the high-voltage side, the aforementioned CMV phenomenon and problems will exist as well and would be more serious and complex, which directly affects the insulation performance and safety operation of the EPT.

For the CMV in traditional two-level PWM converters or grid-connected photovoltaic inverters, since the generation mechanism and analysis are relatively simple, much literature deals with it by improving PWM strategy and employing common mode filters or improved topologies [

In this paper, the analysis of the generation mechanism and the characteristics of the CMV in the CHB-EPT, for both the under balanced and fault grid conditions, are presented, based on the simplified circuit model of CHB-EPT and the corresponding PWM strategy, which can provide theoretical guidance for the insulation design and power density optimization of cascaded converters. The analysis method is also applicable for other cascaded converters, e.g., CHB-STATCOM and CHB-inverters.

In this section, the configuration of the considered CHB-EPT system and its internal CMV are introduced.

This paper mainly focusses on the CMV problem at the high-voltage side of EPT. Although the CMV appears at the low-voltage side as well, it is not significant relative to the high-voltage side in terms of insulation design. In addition, due to the isolation stage embedded MFTs, which block the mutual transmission and influence of the CMVs on both sides, the CMV at the low-voltage side will not be considered in this paper.

At the high-voltage side, the CHB rectifier connects to the MV grid directly. Especially when a long connecting power cable is employed, the CMV problem will be more complicated and worse due to voltage reflection phenomena and cable to ground capacitance, which will result in overvoltage, even resonance [

Referring to the left VSC H-bridge in

Referring to the modeling methods and equivalent circuits in [

In

The CMV between point

Normal grid: For the three-phase balanced power grid, the voltage between the virtual grid neutral g (see the location in

Single-phase to ground fault: The voltage between the neutral point g of the grid and ground will shift up to phase voltage when a single-phase to ground fault occurs. For a balanced EPT, the CMV at neutral point N with respect to ground will be shifted synchronously. Then we have:

In addition, other types of grid faults will not be considered because they are not within the normal operating range of the EPT.

Taking phase A for example, from

As seen from

In this section, an analytical method for calculating the CMV at neutral points and the voltage potential of HVPCs in an EPT system is proposed. The proposed analytical procedure is described as follows:

Calculate the CMV at neutral point

Calculate the voltage between

Finally, obtain the voltage potential with respect to ground

For the input stage of the EPT, there are following relationships:

Under the balanced utility grid conditions,

Taking phase A, for example, the reference sinusoidal wave

Then, the voltage between the two input terminals of the front-end H-bridge can be given by:

Finally, the phase A stack output voltage can be given by:

Similarly, for phases B and C, the corresponding expression can be obtained by replacing

When single-phase to ground fault occurs, e.g., phase C to ground fault, according to Equation (3), Equation (18) should be rewritten as:

Still taking phase A for example, for H-bridge

Therefore, the voltage

The other voltages between the midpoints and

According to Equations (5) and (18), the CMV with respect to ground at point

Similarly, for phase B and C, by replacing

In the case of the occurrence of a single-phase earth fault, Equation (23) just needs to have the corresponding fault phase-voltage subtracted.

The analysis of the above mathematical expressions will be presented in this section.

From Equation (18), the significant feature is that the fundamental frequency component does not appear in

Assuming that

The relationship between the amplitude of the CMV harmonics component and the modulation ratio

Equation (18) shows that the lowest harmonic group corresponds to

As shown in

The relationship between the amplitude of CMV harmonics and its order

From (23), it can be found that the expression of the voltage with respect to ground at the midpoint

It should be noted that the fundamental component appearing in Equation (23) is an effective component in the output voltage generated by the cascaded H-bridges; in other words, it cannot be eliminated by means of improving the PWM strategies.

When the values of the dc-link voltage and the modulation ratio

The effects of SPWM dead time on the CMV are not considered in the above analysis and results for the sake of simplifying the calculation and highlighting the distribution characteristics of the CMV. It should be pointed out that, in practice, the dead time

The practical output voltage of phase A stack

From Equations (18) and (26), it can be seen that the dead time does not bring a fundamental component to the CMV at the neutral point

To display the waveforms and characteristics of the CMV directly and illustrate the correctness of the analysis presented in

A model of three-phase 10 kV/400 V 1 MVA EPT with the same structure as shown in

In addition, SPWM natural sampling is employed in the simulation, and the SPWM dead time is set as 4

This paper has investigated the generated mechanism of the CMV in a CHB-EPT, presented the characteristics of the CMV by using an analytical calculation method, and validated them with simulation results. The main analysis results can be concluded as follows:

The CMV at the neutral point

The voltage potential at each equivalent midpoint of the HVPC with respect to ground, not only includes the high-order harmonics components, but also contains the line-frequency fundamental component. Furthermore, the magnitude of the latter will increase with an increase of the sequence number of the HVPC. Obviously, the highest electrical stress will appear in the top HVPC, which provides a theoretical guide for the structural design and further power density optimization of the EPT.

SPWM dead time has little effect on the magnitude of the CMV. In addition, it will not bring a fundamental component to the CMV at the neutral point.

In conclusion, through the analysis of the CMV in the EPT, a theoretical guide can be put forward for insulation design and power density optimization. In addition, the proposed analysis method can also be applied to other cascaded converters, e.g., CHB-STATCOM and CHB-inverters.

This work was supported by the National Key R & D Program of China (2017YFB0903604) and the China Postdoctoral Science Foundation (No. 2017M612457).

The paper was a collaborative effort of the authors. Yun Yang contributed to the analytical calculation and simulations and wrote this paper. Chengxiong Mao and Dan Wang conceived the idea and supervised the research. Jie Tian and Ming Yang performed the analysis of the results and revised the manuscript.

The authors declare no conflicts of interest.

Schematic diagram of (

(

Unipolar sinusoidal pulse width modulation (SPWM) modulation strategy for an H-bridge.

Equivalent circuit for common mode voltage analysis in three-phase CHB-EPT.

The relationship between Bessel

Relationship between the amplitude of CMV harmonics and its order.

Phase A stack output voltage.

The waveforms and corresponding the fast Fourier transformation (FFT) analysis of the CMV between

A comparison of magnitude values of CMV harmonics in the theoretical calculation and the simulation results.

Simulation results: Related voltages under normal and fault conditions. (

Main parameters of the 10 kV/400 V 1MVA EPT.

Parameter | Value |
---|---|

Number of cascaded H-bridges | 6 per phase |

Number of paralleled H-bridges | 6 per phase |

Rated high voltage dc-link | 1500 V |

Rated low voltage dc-link | 360 V |

Capacitance in one high-voltage dc-link | 2200 |

Capacitance in one low-voltage dc-link | 56 mF |

Inductance of rectifier | 30 mH |

Filter inductance of the inverter | 0.2 mH |

Filter capacitance of the inverter | 250 |

Rated ratio of the MFIT | 4.17:1 |

Switching frequency at high-voltage side | 1 kHz |

Switching frequency at low-voltage side | 4 kHz |