Improve the Three-Phase Unbalance Rate of Railway System Under 2% By Three Kinds of Special Transformer Wiring

: Because imbalanced power will cause the loss of the propulsion motor of the railway vehicle, and the increase in temperature will shorten the service life of the electric vehicle. Not only this, but also increase the cost of electricity and maintenance. In the past, the industry only focused on methods to improve power quality such as load capacity, relay setting, and harmonic resolution. Now, the consider of three-phase unbalance rate (TPUR) must be applied. I propose special transformers wiring (STW) to improve the three unbalance rates and provide different transformer wiring methods. According to the IEEE Committee, in the future, power companies will need to install balanced relay stations to improve three-phase unbalance rate. the internal regulations of Taipower must be less than 4.5% (voltage unbalance rate (NPSUR)of 2.5% and motor temperature rise of 12.5%). the derivation of the transformer "three-phase unbalance rate" model is the focus of the railway system. This research is based on the model derivation of different wiring methods to improve the hot problem caused by the three-phase imbalance and improve the service life of the train. And pointed out that Scott, Le-Blanc, Modified-Woodbridge three wiring methods can be applied to future railway system routes to improve the three-phase unbalance rate, in line with the IEEE standard of less than 2%.


II. How to Define the Voltage Unbalance Rate
The definition of voltage unbalance rate varies from country to country, and the calculation formulas are also different. In this chapter, three types are proposed for comparison. According to IEEE regulations, the three-phase unbalance rate needs to be within 2%, and other calculation formulas can be applied.

II. Derivation of Voltage Unbalance Rate of Special Transformer
Special transformer wiring is divided into V-V wiring, Scott wiring, Le-Blanc wiring, Modified-Woodbridge wiring, and Star-Zigzag wiring. Because the electric vehicle is a three-phase unbalanced load, most of the voltage unbalance is caused by the incomplete transposition of the three-phase unbalanced load on the transmission line, so the system unbalance rate is mostly caused by the three-phase unbalanced load. In order to solve this problem, the railway traction power substation can consider using a special transformer wiring method to improve the three-phase unbalance problem [6]. Simplified from Fig. 1 to Equivalent Circuit Fig. 1.
Station substation Traction power substation

A. Scott Wiring Transformer
Scott Transformers used in non-grounded systems in England and Japan. The Scott transformer connection method is shown in Fig. 2.

B. Le-Blanc Wiring Transformer
Le-Blanc transformer is used in German railway system, and its Le-Blanc transformer connection method is shown in Fig. 3.

C. Modified-Woodbridge Wiring Transformer
Modified-Woodbridge transformer is used in Japanese grounding system, and its transformer connection method is shown in Fig. 4 Iab I1 Ia : Voltage source to ground impedance, Substituting (10) (11) (12) into (13) gives(15): among them = 1 Knowing the three-phase imbalance rate by symmetric component analysis.
When the three-phase load is not considered, the three-phase unbalance rate is ( ) Important discussion: This situation is likely to be greater than 2% of the IEEE international standard, which is less suitable for railway TSS power.

B. Le-Blanc Wiring Transformer Relational Derivation
The relationship between Le-Blanc wiring transformers calculated according to Fig. 4 is as follows: The three-phase symmetrical component matrix is: Will Le-Blanc the connection equations (7) Among them, positive phase sequence voltage of voltage source; self-inductance; mutual inductance; impedance of voltage source to ground; , It is known from the symmetrical component analysis method that the three-phase imbalance rate is: When the three-phase load is not considered, the three-phase unbalance rate is Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 15 November 2021 ( ) discuss focused on: Usually GS ＞＞ G1, G2, If the denominators G1 and G2 are ignored, then (21) is: In this way, GS ＞＞ G1, G2, and the molecules are very small, so the three-phase unbalance rate is less than 2%, and the probability is very high. It is one of the ways to consider for traction power substation of MRT.

C. Modified-Woodbridge Relational Derivation of Wiring Transformer
The relationship between Modified-Woodbridge wiring transformer calculated according to Among them, positive phase sequence voltage of voltage source; self-inductance; mutual inductance; impedance of voltage source to ground; It is known from the symmetrical component analysis method that the three-phase unbalance rate is: When the three-phase load is not considered, the three-phase unbalance rate is ( )  (26) and (16), it can be seen that Scott / Le-Blanc wiring transformer and Modified-Woodbridge wiring transformer ignore the three-phase load (that is, no-load) and G1, G2. the same.
2) In this way, GS ＞＞ G1, G2, and the molecules are very small, so the three-phase unbalance rate is less than 2%, and the probability is very high. It is one of the ways to consider for traction power substation of railway system.

IV. Derivation of Voltage Unbalance Rate for Traditional Transformer and V-V Wiring Star-Zigzag Wiring
Traditional transformer wiring is divided into single-phase wiring and three-phase Wye-Delta wiring. Because Taipower adopts a central feeding system, on single-phase wiring transformers, the power source with a feeding point is strong, and the substation also has the favorable factor of small traction load, which is easier in emergency or maintenance. At present, the Taiwan Railway Bureau uses this system. The railway system does not use single-phase wiring transformers because of large harmonic problems and excessive reactive power [7].

A.Single-phase Wiring Transformer
Single-phase wiring transformer is used in Italian railway system, New Zealand railway system, Taiwan railway system, and its transformer connection method is shown in Fig. 5.
Among them, the symmetric component analysis method shows that the three-phase unbalance rate is: When the three-phase load is not considered, the three-phase unbalance rate is discuss focused on: Usually GS ＞＞ G. If the denominator G is negligible, then is: It is impossible to judge whether the three-phase unbalance rate will exceed the international standard of 2% under no load [8].

B. Three-phase Wye-Delta Wiring Transformer
Three-phase Wye-Delta wiring transformers are used in mainland China MRT and railway systems, Taipei MRT Tamsui Xindian line, and the transformer connection method is shown in Fig. 6. According to Fig. 6, the three-phase Wye-Delta calculation shows that the relationship of the wiring transformer is as follows: among them When the three-phase load is not considered, the three-phase unbalance rate is 1) The wiring mode of three-phase Wye-Delta wiring is that the power at the feed point is weak, the substation has a large load, and emergency or maintenance is not easy, but because the MRT station is very short, and there are traction power substations about every two stations. In emergency situations or maintenance, there are 24 hours of personnel on standby, and the replacement of spare parts is fast, which can make up for the shortcomings of the three-phase Wye-Delta wiring in this regard.
2) There is a three-phase imbalance problem in this wiring method. According to the calculation in (43), the molecule has an operator. and it is easy to produce an unbalance rate greater than 2%, so there is room for improvement.

C. V-V Wiring Transformer
V-V transformer is used in the national railway system of Finland, and its V-V transformer connection method is shown in Fig. 7.
among them Knowing the three-phase unbalance rate by symmetric component analysis ( ) When the three-phase load is not considered, the three-phase unbalance rate is ( ) Important discussion: This situation is likely to be greater than 2% of the IEEE international standard, which is less suitable for power of railway system

D. Star-Zigzag Wiring Transformer
Star-Zigzag The transformer is applied to the British subsea tunnel system, and its transformer connection method is shown in Fig. 8.
Among them, positive phase sequence voltage of voltage source; self-inductance; mutual inductance; impedance of voltage source to ground; It is known from the symmetrical component analysis method that the three-phase unbalance rate is: When the three-phase load is not considered, the three-phase unbalance rate is ( ) Important discussion: This involves the angle of the operator. The molecules G1, G2, and G3 cannot be omitted, and the three-phase unbalance rate is easy to exceed 2%, so it is not suitable for power of railway system.