# Optimized Design of Modular Multilevel DC De-Icer for High Voltage Transmission Lines

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Circuit Configuration and Operation Principle

- Ice-melting Mode. When there is an ice-covered line to melt in the winter, the disconnectors are close to connect the MMC-DDI and the transmission line together, and the other terminal of the transmission line is artificially three-phase short-circuited to form a DC current loop. Then, the MMC-DDI provides a controlled DC voltage to generate the required current through the ice-covered line. At that time, the operation mode of MMC-DDI is similar to the MMC rectifier station in the VSC-HVDC transmission system, except that the DC-side output voltage almost remains unchanged in the VSC-HVDC system while it may vary with the line parameters in the MMC-DDI system. In addition, the typical control methods for the common MMC system are also applicable to MMC-DDI system, such as the capacitor voltage control, the active and reactive current control, the capacitor voltage balancing control, the circulating current control, etc.
- SVG Mode. When there is no icing line, the de-icing disconnectors can be open circuit. Then, the upper three arms and the lower three arms can operate as two parallel conventional SVGs, and provide reactive power compensation or alleviate other power quality problems.

## 3. Converter Characteristic of MMC-DDI

#### 3.1. Arm Voltage and Current

_{sA}, i

_{sA}are the AC-side input phase voltage and current of converter. u

_{ap}, u

_{an}are respectively the output voltage of the upper arm and lower arm. i

_{ap}, i

_{an}are respectively the arm current of the upper and lower arms. U

_{p}is the electric potential of the neutral point of 1#SVG, relative to the grid neutral point. U

_{n}is the electric potential of the neutral point of 2#SVG. R and L represent the equivalent resistance and inductance of the connection reactance in each arm:

_{dc}and I

_{dc}are the DC-side output de-icing voltage and current of MMC-DDI.

_{m}, I

_{m}are the root mean square (RMS) values of the AC-side input phase voltage and current of MMC converter. $\omega $ is the angular frequency of gird voltage while ϕ presents the AC-side power factor angle.

_{arm_peak}, U

_{arm_peak}present the peak values of arm current and arm voltage.

_{arm_RMS}, U

_{arm_RMS}present the RMS values of the arm current and arm voltage.

- (1)
- The arm voltage/current of MMC-DDI contains both DC and AC components, while in the conventional SVG, there is only AC component.
- (2)
- The arm voltage/current no longer equals the AC-side input voltage/current in MMC-DDI.
- (3)
- The peak value of the arm voltage/current is no longer than $\sqrt{2}$ times of its RMS value.
- (4)
- Due to these differences, although the MMC-DDI is structurally similar to a pair of common star-connected SVGs, their inner converter characteristics are quite different.

#### 3.2. Influence of AC Side Input Voltage

_{dc}is the output ice-melting power, cosϕ is AC-side power factor and generally cosϕ = 1.0.

_{dc}. This is quite different from common SVG. In an SVG, in the case of a certain output reactive power, with the increasing of the AC-side voltage, the arm voltage peak increases proportionally while the arm current peak decreases and tends to 0.

#### 3.3. Converter Rating of MMC-DDI

_{c}presents the converter rating. n presents the total number of arms. U

_{pi}, I

_{pi}are the output voltage and current peak of the i-th arm.

_{sp}, I

_{sp}are respectively the RMS values of AC-side phase voltage and phase current, S

_{out}presents the output apparent power of SVG.

_{m}= 0.5 U

_{dc}, the converter rating gets its minimum value, and the minimum rating is 2.91 times the output ice-melting power. This conclusion can be expressed as

## 4. The Proposed Optimization Design Method

#### 4.1. General Design Process of IMD

_{icing}is the required de-icing current and R

_{line}is the phase resistance of transmission line. k

_{icing}corresponds to the ice-melting mode, k

_{icing}= 2 when the de-icing current is passed down one phase conductor and back along another, and k

_{icing}= 1.5 when down one and back along the other two [16].

#### 4.2. The Proposed Circuit Configuration and Its Economic Analysis

- (A)
- When should the transformer be desired and when is it undesired?
- (B)
- If a transformer is inserted, what are the specifications and parameters of the transformer?

_{m}= 0.5 U

_{dc}, corresponding to a line voltage $\sqrt{3}\times 0.5{U}_{dc}$. In summary, the specification of the transformer can be determined as

_{Tran}is the transformer rating, and T

_{r}is the transformer rating voltage radio.

_{no}presents the cost of MMC-DDI with no transformer, and ${P}_{con}\uff08{u}_{s}={u}_{g}\uff09$ presents the cost of the MMC converter when its AC-side voltage is equal to the grid voltage. P

_{with}presents the cost of the MMC-DDI with a transformer; P

_{trans}presents the transformer cost. ${P}_{con}\uff08{u}_{s}=\sqrt{3}\times 0.5{U}_{dc}\uff09$ presents the cost of the MMC converter with an AC-side input voltage of ${u}_{s}=\sqrt{3}\times 0.5{U}_{dc}$.

#### 4.3. Applicable Scope of the Proposed Configuration

- A
- The converter cost is approximately considered to be proportional to the converter rating.
- B
- The transformer cost is a quarter of the same rating MMC converter cost.

- When the ratio of the grid line voltage to DC-side output voltage exceeds 2.0 or falls below 0.25, the overall cost of MMC-DDI with a transformer is less than that without transformer, i.e., a transformer can be inserted on the AC side of a converter to improve the system economy.
- When the ratio is between 0.25–2.0, the cost of the transformer exceeds its revenue. In that case, no transformer is required.

## 5. Design Example and Simulation Results

#### 5.1. A Typical Design Example

^{2}, wherein the converter chain occupies 163 m

^{2}(17.6 m × 9.25 m).

^{2}to place the transformer, but the converter area is reduced from 296 m

^{2}to 133 m

^{2}, namely a reduction of 163 m

^{2}. As a result, the overall footprint of MMC-DDI system is reduced by 91 m

^{2}, corresponding to a ratio of 22%. It shows that the optimized scheme also has an advantage in the land occupation. On the other hand, the optimized scheme requires a transformer with weight of 38 Ton, but its converter weight is reduced by 35 Ton, thus the total weight was slightly increased by 5 Ton. It shows that the optimized scheme have no advantage in weight. However, the DC de-icer built for high voltage transmission lines up to 500 kV is generally installed in the substations, so this weight disadvantage is still acceptable.

#### 5.2. Simulation Results

## 6. Discussion

- (1)
- In an SVG, both the arm voltage and current contain only an AC component. As a result, in the case of a certain output power, the arm voltage is inversely proportional to arm current, thus the converter rating remains basically constant under any AC-side voltage. In that case, if a transformer was configured on the AC side of MMC converter, it has little influence on the converter rating while increasing a transformer. Therefore, in the common SVG, it tries to avoid a transformer.
- (2)
- In the MMC-DDI, the arm voltage and arm current of converter contain both DC and AC components. As a result of the crossover between the DC and AC components, the converter rating of MMC-DDI varies greatly with its AC-side voltage. Due to such converter characteristics, a transformer can affect the converter rating. In this case, although the introduction of transformer will increase transformer cost, it can cause a cost increment or reduction of the converter. As long as the reduction of the converter cost is sufficient to offset the transformer cost, the introduction of the transformer is cost-effective. In addition, because the unit cost of MMC converter is generally much higher than that of the transformer, the above condition is easy to satisfy under the typical DC ice melting system parameters. Therefore, the optimized configuration scheme proposed in this paper is cost-effective in many cases.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Table A1.**The minimum de-icing current and maximum endure current for typical power lines [5].

Conductor Type | Min. De-Icing Current (A) (−5 °C, 5 m/s, 10 mm, 1 h) | Max. Endure Current(A) (5 °C, 0.5 m/s, No Icing) |
---|---|---|

LGJ-4 × 400/50 | 3475 | 4764 |

LGJ-2 × 500/45 | 1989 | 2698 |

LGJ-2 × 240/40 | 1218 | 1716 |

LGJ-1 × 240/40 | 609 | 858 |

LGJ-1 × 185/45 | 515 | 733 |

LGJ-1 × 150/35 | 441 | 633 |

LGJ-1 × 95/55 | 345 | 500 |

No. | Project Location | Rated Voltage (kV) | Rating (MVA) | Deal Price ^{1} ($1000) | Unit Cost (1000 $/MVA) |
---|---|---|---|---|---|

1 | Kunming, Yunnan | 35 | 10 | 154 | 15.4 |

2 | Zhangjiakou, Hebei | 35 | 12 | 175 | 14.6 |

3 | Huimin, Shandong | 35 | 15 | 215 | 14.4 |

4 | Huangpi, Hubei | 35 | 16 | 251 | 15.7 |

5 | Tongyu, Gansu | 35 | 20 | 269 | 13.5 |

6 | Hua County, Henan | 35 | 20 | 257 | 12.8 |

7 | Chenzhou, Hunan | 10 | 20 | 330 | 16.5 |

8 | Qiaojia, Yunnan | 35 | 30 | 385 | 12.8 |

9 | Linwu, Ningxia | 35 | 40 | 458 | 11.5 |

10 | Dabancheng, Xinjiang | 35 | 50 | 615 | 12.3 |

11 | Yinan, Shandong | 35 | 60 | 1023 | 17.1 |

12 | Haixi, Xinjiang | 35 | 60 | 1154 | 19.2 |

13 | Hami, Xinjiang | 35 | 80 | 1508 | 18.8 |

14 | Huaping, Yunnan | 35 | 100 | 2109 | 21.1 |

15 | Xiangtan, Hunan | 35 | 120 | 2615 | 21.8 |

^{1}The deal price covers a complete set of SVG equipment (including the converter chain, connection reactance, startup circuit, cooling system, control system and other ancillary facilities) and its technical service.

No. | Project Location | Rated Voltage (kV) | Rating (MVA) | Deal Price ($1000) | Unit Cost (1000 $/MVA) |
---|---|---|---|---|---|

1 | Baoding, Hebei | 10/5 | 10 | 86 | 8.6 |

2 | Changsha, Hunan | 10/7 | 14 | 110 | 7.8 |

3 | Changsha, Hunan | 35/6 | 24 | 166 | 6.9 |

4 | Xinyu, JiangXi | 35/12 | 56 | 246 | 4.4 |

5 | Chongqing | 35/15 | 86 | 284 | 3.3 |

6 | Zhuzhou, Gansu | 35/17 | 100 | 323 | 3.2 |

7 | Hengyang, Hunan | 35/19 | 120 | 361 | 3.0 |

Parameter | Symbol | Dual-SVG | Conventional MMC-DDI | Optimized MMC-DDI |
---|---|---|---|---|

AC-side rated voltage | U_{S} | 35 kV | 35 kV | 5 kV |

AC-side rated current | I_{M} | (0.38 kA) ^{2} | (0.38 kA) | (2.68 kA) |

AC-side rated power | +23.2 Mvar | (23.2 MW) | (23.2 MW) | |

Arm inductance | L | 35 mH | 35 mH | 1 mH |

Arm equivalent resistance | R | 0.1 Ω | 0.1 Ω | 0.02 Ω |

DC-side output de-icing voltage | U_{dc} | 0 | (5.8 kV) | (5.8 kV) |

DC-side output de-icing current | I_{dc} | 0 | 4.0 kA | 4.0 kA |

Resistance of de-icing line | R_{dc} | - | 1.45 Ω | 1.45 Ω |

Inductance of de-icing line | L_{line} | - | 32 mH | 32 mH |

Submodule number of each arm | N | 4 | 4 | 4 |

Submodule capacitance | C_{cap} | 4 mF | 4 mF | 10 mF |

Submodule capacitor voltage | U_{cap} | 9.0 kV | 8.0 kV | 1.8 kV |

Switching frequency | 500 Hz | 500 Hz | 500 Hz |

^{2}The parameters in parentheses indicate the calculated value, while the parameters in parentheses indicate the values directly set in the simulation.

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**Figure 2.**Influence of the AC side input voltage on the peaks of arm voltage and current (

**a**) on the current (

**b**) on arm voltage.

**Figure 5.**Simulation results of dual-SVGs system. (

**a**) arm voltage (fileted high frequency ripple), (

**b**) arm current, (

**c**) arm voltage (unfiltered), (

**d**) DC-side voltage (fileted high frequency ripple), (

**e**) capacitor voltage of the first submodule in upper three arms, (

**f**) original DC-side voltage (unfiltered).

**Figure 6.**Simulation results of the conventional MMC-DDI. (

**a**) arm voltage (fileted high-frequency ripple), (

**b**) arm current, (

**c**) arm voltage (unfiltered), (

**d**) DC-side voltage (fileted high frequency ripple), (

**e**) submodule capacitor voltage, (

**f**) DC-side voltage (unfiltered), (

**g**) DC-side output voltage and current during melting-ice startup process, (

**h**) arm current during melting-ice startup process.

**Figure 7.**Simulation results of the optimized MMC-DDI. (

**a**) arm voltage (fileted high-frequency ripple), (

**b**) arm current, (

**c**) arm voltage (unfiltered), (

**d**) DC-side voltage (fileted high frequency ripple), (

**e**) submodule capacitor voltage, (

**f**) DC-side voltage (unfiltered), (

**g**) DC-side output voltage and current during melting-ice startup process, (

**h**) arm current during melting-ice startup process.

**Table 1.**Electrical parameter comparison of the MMC-DDI under conventional configuration and optimized configuration.

Parameter | Symbol | Conventional Configuration (with No Transformer) | Optimized Configuration (with Transformer) |
---|---|---|---|

Rated DC voltage | U_{dc} | 5.8 kV | 5.8 kV |

Rated DC current | I_{dc} | 4.0 kA | 4.0 kA |

Rated output DC power | P_{dc} | 23.2 MW | 23.2 MW |

AC-side phase voltage | U_{m} | 20.2 kV | 2.9 kV |

AC-side phase current | I_{m} | 0.38 A | 4.6 kA |

Arm voltage peak | U_{arm_peak} | 31.5 kV | 7.0 kV |

Arm current peak | I_{arm_peak} | 1.6 kA | 3.2 kA |

Converter rating | S_{c} | 151 MVA | 68 MVA |

Transformer | None | 23 MVA–35 kV/5 kV | |

Submodule number in each arm | N | 39 | 9 |

Submodule capacitor voltage | U_{c0} | 900 V | 900 V |

Submodule capacitance | C_{c} | 10 mF | 20 mF |

**Table 2.**Cost comparison of the MMC-DDI under conventional configuration and optimized configuration.

Component | Original Cost (Million Dollar) | Optimized Cost (Million Dollar) |
---|---|---|

Converter | 2.26 | 1.01 |

Transformer | - | 0.17 |

Total | 2.26 | 1.18 |

Items | 100 Mvar SVG | Conventional MMC-DDI | Optimized MMC-DDI |
---|---|---|---|

Main components | Converter (2 × 50 Mvar) | Converter (151 MVA) | Converter + Transformer (68 MVA) (24 MVA) |

Number of power units | 2 × 63 | 2 × 117 | 2 × 54 |

Number of power cabinets | 2 × 11 | 2 × 20 | 2 × 10 |

Submodule capacitor voltage | 900 V | 900 V | 900 V |

Size of each submodule | 0.7 m × 0.7 m × 0.8 m | 0.7 m × 0.7 m × 0.8 m | 0.7 m × 0.7 m × 0.8 m |

Weight of each submodule | 250 kg | 250 kg | 250 kg |

Total weight of submodules | 31.5 t | 59 t | 26 t |

Transformer weight | - | - | 38 t |

Converter area | 163 m^{2} | 296 m^{2} | 133 m^{2} |

Transformer area | None | None | 72 m^{2} |

Other floor area | 117 m^{2} | 117 m^{2} | 117 m^{2} |

Total floor area | 280 m^{2} | 413 m^{2} | 322 m^{2} |

Total weight | 31.5 t | 59t | 64 t |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lu, J.; Huang, Q.; Mao, X.; Tan, Y.; Zhu, S.; Zhu, Y.
Optimized Design of Modular Multilevel DC De-Icer for High Voltage Transmission Lines. *Electronics* **2018**, *7*, 204.
https://doi.org/10.3390/electronics7090204

**AMA Style**

Lu J, Huang Q, Mao X, Tan Y, Zhu S, Zhu Y.
Optimized Design of Modular Multilevel DC De-Icer for High Voltage Transmission Lines. *Electronics*. 2018; 7(9):204.
https://doi.org/10.3390/electronics7090204

**Chicago/Turabian Style**

Lu, Jiazheng, Qingjun Huang, Xinguo Mao, Yanjun Tan, Siguo Zhu, and Yuan Zhu.
2018. "Optimized Design of Modular Multilevel DC De-Icer for High Voltage Transmission Lines" *Electronics* 7, no. 9: 204.
https://doi.org/10.3390/electronics7090204