Electrical characteristics of new three-phase traction power supply system for rail transit

A novel three-phase traction power supply system is proposed to eliminate the adverse effects caused by electric phase separation in catenary and accomplish a unifying manner of traction power supply for rail transit. With the application of two-stage three-phase continuous power supply structure, the electrical characteristics exhibit new features differing from the existing traction system. In this work, the principle for voltage levels determining two-stage network is dissected in accordance with the requirements of traction network and electric locomotive. The equivalent model of three-phase traction system is built for deducing the formula of current distribution and voltage losses. Based on the chain network model of the traction network, a simulation model is established to analyze the electrical characteristics such as traction current distribution, voltage losses, system equivalent impedance, voltage distribution, voltage unbalance and regenerative energy utilization. In a few words, quite a lot traction current of about 99% is undertaken by long-section cable network. The proportion of system voltage losses is small attributed to the two-stage three-phase power supply structure, and the voltage unbalance caused by impedance asymmetry of traction network is less than 1‰. In addition, the utilization rate of regenerative energy for locomotive achieves a significant promotion of over 97%.


Introduction
Single-phase AC 27.5 kV system and DC 1500 V system are commonly implemented in existing electrified railway and urban rail transit with their respective characteristics in China [1]. In order to reduce the adverse influence of negative sequence, the AC 27.5 kV system connects the traction substation with the public network by transposing the phase sequence. As is well known, the electrical phase separation, as the weakest link of traction network, seriously affects the reliability of power supply system and the increase in train speed [2]. In contrast, the DC 1500 V power supply system highlights its advantage of eliminating electrical phase separation, but stray current leads to serious corrosions of urban underground metal [3]. Additionally, another challenging problem for the DC 1500 V system is that the regenerative energy cannot be directly fed back to the power grid; as a result, special equipment is required for feedback processing. However, it does not seem to be technically perfect and economically superior nowadays.
Abstract A novel three-phase traction power supply system is proposed to eliminate the adverse effects caused by electric phase separation in catenary and accomplish a unifying manner of traction power supply for rail transit. With the application of two-stage three-phase continuous power supply structure, the electrical characteristics exhibit new features differing from the existing traction system. In this work, the principle for voltage levels determining two-stage network is dissected in accordance with the requirements of traction network and electric locomotive. The equivalent model of three-phase traction system is built for deducing the formula of current distribution and voltage losses. Based on the chain network model of the traction network, a simulation model is established to analyze the electrical characteristics such as traction current distribution, voltage losses, system equivalent impedance, voltage distribution, voltage unbalance and regenerative energy utilization. In In order to overcome the shortcomings of the existing traction power supply system, a new single-phase continuous power supply scheme is proposed by combining the power cable with co-phase power supply technology [4,5]. Taking the advantage of long power supply distance and high transmission power of the power cable into account, the interconnection of trunk railways and urban railways can be successfully achieved via effectively extending the traction power network. Discussions regarding new cable traction power supply system (CTPSS) have dominated research in recent years. Reference [6] presents the unified calculation model of CTPSS for the analysis on voltage change of traction network and power distribution, which is certified to possess the high accuracy for calculating the electrical characteristics. Reference [7] compares power supply capacity of overhead catenary and power cables, extrapolating that the contact strip applied in CTPSS is superior to other contact forms. Meantime, it discusses the calculation method of voltage losses and current distribution, which proposes suggestions for voltage level of two-stage power supply network. In Refs. [8,9], to investigate the extreme power supply distance, nominal voltage levels are compared in various aspects by building a CTPSS model. It is noteworthy that the voltage level of 6 kV is evidenced for the superior performance in power supply capability. In Ref. [10], the equivalent circuit of train-network coupling system was built via dual-port network analysis method to investigate current transmission law in cable traction network, indicating that the fundamental current is mainly transmitted in the power supply section where the train is located. Zhang et al. [11] explored resonance and harmonic transmission problems in CTPSS, and proved the new system shows better resonance performance compared with AT (auto transformer) traction system through theoretical analysis and simulation. Furthermore, a cable power supply scheme for heavy-haul railway powered by AT outstands advantages in power supply distance and economic benefit [12]. To overcome the limitation of theoretical analysis, some literatures [12,13] focused on the certain line as an example to compare the scheme design. As expected, CTPSS is validated to effectively extend the power supply distance and increase the flexibility of external power supply location. Another feature which needs to be considered in CPTSS is the capacitance effect of cable network and the capacitor charging current in system due to the application of power cable [14].
The above-mentioned research about cable power supply system belongs to the connection structure of single-phase "one-wire and one-ground"; that is, overhead catenary and steel rail are used as the energy transfer pathway. Li's team [15] initiated a technical solution of a three-phase traction power supply system with two-stage voltage levels and "two-wire and one-ground" structure, which combines the advantages of traction supply system of AC 27.5 kV and DC 1500 V. The novel three-phase traction power supply system (TTPSS) accomplishes a unifying manner of traction power supply for rail transit through the cable power supply system, contact power supply system and vehicle transmission system. However, there are few research literatures on TTPSS at present. In this work, the system structure and power supply principle are elaborated, and the voltage levels of the two-stage network are determined. The equivalent circuit of TTPSS is established to derive the formula of current distribution and voltage losses. Then the parametric circuits of cable and contact strip are analyzed for modeling the novel system. Electrical characteristics such as traction current distribution, voltage losses, system equivalent impedance, voltage distribution, voltage unbalance and regenerative energy utilization are simulated and validated.
2 Composition of three-phase traction power supply system

System structure
As shown in Fig. 1, TTPSS includes the main substation (MSS), three-phase cable traction network (CTN), traction transformer ( TT i ), three-phase traction network (TTN), vehicle traction system (VTS), etc. Three-phase cables are fed out of the three-phase buses on the secondary side of MSS, and CTN is in parallel with TTN, laid along the railway line. The primary side of TT i is connected to CTN, and the secondary side is connected to TTN; that is, TT i is connected in parallel between CTN and TTN ( i=1, 2, …, N). TTN consists of power supply rails A and B (T A and T B ) and rail (T C ). The VTS of the train is powered through the contact system by the TTN [15]. Herein, the CTN and TTN between TT i are also called, respectively, as long section and short section. In order to improve the reliability of system and the simplicity of maintenance, electrical subsections can be set in each short section, and the corresponding state identification and protection schemes can be applied to limit the adverse effects after a fault to a small range [16]. The three-phase traction network is no longer suspended overhead, but installed on track bed under the train. It is Fig. 1 Three-phase traction power supply system 77 Electrical characteristics of new three-phase traction power supply system for rail transit 1 3 Rail. Eng. Science (2023) 31(1):75-88 composed of contact strip and rail, forming a "two-wire and one-ground" contact structure, as shown in Fig. 2. The contact strip is paved in the middle of the two rails, consisting mainly of power supply rails A and B, insulating base and insulating cover. To facilitate passage through switches, the installation height of the power supply rails A and B is higher than the top of the rails.
The three-phase two-winding Yd11 transformer bank is adopted in TT. The terminals a, b, and c of TT secondary side are, respectively, connected to power supply rail A, power supply rail B, and the rails of TTN.
The VTS is composed of current collector named as electric plough, the vehicle-mounted cable and three-phase AC-DC-AC converter, as shown in Fig. 3. The electric plough includes collector rods A and B, and spring. The vehicle-mounted cable includes single-core cables A and B, and ground wire. The single-core cables A and B contact, respectively, with the power supply rails A and B, and the ground wire contacts with the rail by brush. The terminals on the secondary side of AC-DC-AC converter are connected to the three terminals of the three-phase motor.

System voltage levels
The external power supply of MSS is generally obtained from the 110 kV or 220 kV high-voltage power grid. In view of the large traction load of TTPSS, the voltage level of 220 kV with larger short-circuit capacity can be allowed.
The voltage level of 35 kV is preferred for CTN, or a new voltage level can be designed in view of 27.5 and 55 kV cables. Given the superiority of power supply capacity and extensive implementation in rail transit and distribution networks [7], the voltage level of 35 kV can be used as the voltage level of medium-voltage cable traction network.
The voltage level of TTN is lower than CTN, owning to the following factors: 1. As contact strip is laid between rails with the limited insulation space among rails and bottom of the train, the voltage of TTN should not be too high, for example, not higher than 11 kV. 2. The voltage level of traction drive system generally ranges from 1 to 2.75 kV due to various constraints at present. Given the development of power electronics technology and the demand for the capacity of traction drive system, it is appropriate to increase the voltage level moderately. 3. The power supply capacity should be able to meet the power demand of long marshaling trains, such as not less than 20 MVA. 4. The ampacity of the contact strip should not be lower than that of the rigid suspension, such as 4000 A. 5. It should follow the related standards.
In addition to satisfying the above conditions, a higher voltage level contributes to improving power supply capacity of system and the economy. It is shown that the higher the traction network voltage, the higher the voltage level that of traction drive system should match. As the traction converter is the most important part of the traction drive system, the key factors restricting the voltage of traction network are the withstand voltage of traction converter power device and the converter topology.
Classified by the nominal voltage of traction converter power device, the IGBTs (insulated gate bipolar transistors) with 1.7, 3.3, 4.5 and 6.5 kV voltage series are widely applied. Among them, 3.3 kV IGBT is the widely used in electric multiple units (EMU), 6.5 kV IGBT in CRH3 and CRH5, and 1.7 kV and 4.5 kV IGBTs in the fields of new energy and industrial frequency conversion.
Two-level and three-level topologies are currently mature, among which three-level topology can withstand higher voltage under the devices of same nominal voltage.  Referring to the standard voltage specification in China [17], the three-level topology of 6.5 kV IGBT cannot reach national standard voltage level of 6 kV. Appropriately, the three-level topology with 4.5 kV IGBT is available for national standard voltage level of 3 kV. Therefore, 3 kV is selected as the rated voltage level of TTN. Meantime, 4.5 kV IGBTs with three-level topology should be adopted for traction converters in traction drive system.

Analysis on electrical characteristics of three-phase traction power supply system
With the appliance of the "two-wire and one-ground" structure in TTPSS, the derivation process for the traction current distribution law, voltage drops in the traction network are different from those in the existing single-phase AC traction system. As a result, the three-phase traction network presents distinctive electrical characteristics. Based on the equivalent assumptions of the traction system [9], the electrical characteristics of TTPSS are theoretically analyzed in this section.

System equivalent model and short-section current distribution
According to the equivalent method of the single-phase traction power supply system and the structural characteristics of TTPSS, there are following assumptions: 1. Ignoring the leakage reactance of TT. 2. Ignoring the impedance difference between contact strip and rail. 3. The traction current is drawn from two adjacent traction substations in the short section. 4. Ignoring the electromagnetic coupling between CTN and TTN due to the shielding effect of the cable sheath.
Taking a vehicle in a short section as an example, the section between the adjacent traction stations of the vehicle is defined as a short section, and the section between the vehicle operating area and MSS is a long section. Based on the above assumptions, the equivalent model of TTPSS is established and shown in Fig. 4.
In Fig. 4, x is the distance between the vehicle and the left traction station in short-section; D is the distance between the traction stations on both sides of the vehicle; l is the distance between the vehicle and MSS. In the long-section, ̇I LA , ̇I LB , ̇I LC are the currents of CTN, and ̇I TA , ̇I TB , ̇I TC are the currents of TTN. In the short-section, ̇I CA , ̇I CB , ̇I CC are the currents of CTN, and ̇I A1 , ̇I B1 , ̇I C1 and ̇I A2 , ̇I B2 , ̇I C2 are the currents drawn by the vehicle on the left and right sides of TTN, respectively. Ė A , Ė B , Ė C represent the voltages of MSS, and U ′ 1 , U ′ 2 and U 1 , U 2 represent the A-phase voltages of CTN and TTN at the position of the traction station, respectively. C A , C B , and C C represent A-phase, B-phase, C-phase cables, respectively. The self-impedance of three-phase cables and the mutual impedance between any two phases are equal due to the equilateral-triangle arrangement. Herein, z Cz and z Ch represent the unit self-impedance and mutual impedance of the cable. z Tz and z Th represent the unit self-impedance and mutual impedance ofhe traction network. k is the transformation ratio of TT. According to the topology of the circuit in phase A, there is The voltage losses of the traction network and the traction cable in the short-section can be expressed as Substitute Eq. (1) into Eqs. (2) and (3) to simplify Suppose z 1 = z Tz − z Th , z 2 = z Cz − z Ch ; then Eqs. (4) and (5) can be further simplified as Since ̇I A =̇I A1 +̇I A2 , the current collecting from two sides in the short-section can be expressed as The above formula can be fully expanded as Similarly, the same distribution law can be derived when the above-mentioned analysis is applied to other two phases B and C.

Voltage drops and loss for a single vehicle
Voltage drops ΔU is defined as the difference of voltage phasor between the two ends of the line, whose modulus ΔU is called as the voltage losses [9]. Based on this concept, the voltage drops and loss of TTPSS for a single vehicle are deduced in this section.
Due to the symmetry of three phases, the theoretical analysis is performed with A-phase circuit for simplicity. Assume that the voltage of vehicle at the supply rail A is U A ; then the voltage drops between the position of vehicle and MSS can be expressed as where U lon and U sho are defined as the voltage drops of vehicle in the long and short section, respectively.
In the long section of CTN, the voltage drops can be expressed as Then the current in cable can be expressed as In the long section of TTN, the voltage drops can be expressed as Then the traction current can be expressed as According to Kirchhoff's current law, Substituting Eqs. (14) and (16) into (17), the voltage drops of the long section are expressed by Correspondingly, in the short section of TTN, the voltage drops are Combining Eqs. (11), (12), (18) and (19), the voltage drops of the vehicle can be written as In Eq. (20), z lon and z sho are the unit impedance of the long section and short section, respectively, which is The equivalent impedance of the whole system to the vehicle can be represented by Since voltage losses is applied as the index of power supply capacity of traction system in practical applications, the voltage losses is deduced as where z lon = r 1 + jx 1 , z sho = r 2 + jx 2 , z � lon = r 1 cos + x 1 sin ,z � sho = r 2 cos + x 2 sin , and is the power factor angle of the vehicle.
The analysis for phases B and C is omitted due to the analogous process. .

Voltage drops and loss for multiple vehicles
As there is generally no more than one vehicle in the same short section in practice, it is assumed that only one vehicle runs in each short-section. After converting the medium-voltage cable circuit to the low-voltage traction network circuit, the voltage drops of the vehicle in the terminal section of system can be expressed through the superposition principal: where ̇I i is the current drawn by the ith vehicle on the supply rail A and ̇I n is the current drawn by the nth vehicle; l i is the distance between the ith vehicle and MSS; x n is the distance between the nth vehicle and the left traction substation.
The voltage losses of the terminal vehicle can be deduced via replacing the vehicle current ̇I with its amplitude I , and sho = r 2 cos n + x 2 sin n , and i is the power factor angle of the ith vehicle.
However, the derivation of the voltage losses above is based on the approximation that the phase difference θ between the initial and terminal voltage is tiny. With the increase in vehicle power factor in recent years, it is demonstrated from the geometric relationship that θ will gradually increase, resulting in further gap of voltage losses after ignoring θ [7]. Therefore, the exact value of voltage losses without ignoring θ is derived in this section.
The phasor diagram of voltage losses is manifested through the geometric relationship in Fig 4 Modeling three-phase traction power supply system

Chain network model of traction network
Since the wires in CTN and TTN are parallel to each other, the system can be equivalent to a composite chain network model according to the multi-conductor transmission line theory [18], as shown in Fig. 6. Through the specific cutting of CTN, TTN, traction substation, and electric locomotive in TTPSS, the chain network model of traction network is established while maintaining its distribution parameter characteristics. The chain network model consists of longitudinal series impedance element and transverse parallel admittance element [19,20]. In Fig. 6, Z 1 , Z 2 , … , Z N−1 represent the multi-conductor transmission line model of traction network between two sections; Y 1 , Y 2 , … , Y N represent the transverse parallel  From the chain network model, the multi-conductor transmission line of the traction network can be equivalent to the π-type equivalent circuit [20], as shown in Fig. 7. Z L and Y L are the series impedance matrix and parallel admittance matrix of multi-stage transmission wire in traction network.

Parameter calculation of CTN
XLPE single-core cable with coaxial structure is advocated due to the superior adaptability in CTN, which is normally composed of wire core, main insulation, metal sheath, sheath insulation, armor layer and rubber sheath [21]. The cables are laid in equilateral-triangle arrangement. Noteworthily, the coupling effect between CTN and TTN can be ignored since the intervals of cables are much smaller than those of between CTN and TTN [7].

Calculation of cable impedance matrix
The core and metal sheath of the single-core cable are equivalent to two coaxial loops for analysis; thus the impedance matrix of the three-phase single-core cable can be indicated as a 6 × 6 symmetric matrix: where Z iC,iC and Z iS,iS represent the self-impedance of the core and the sheath in each phase; Z iC,iS is the mutual impedance between the core and the sheath in each phase; Z iC,jC is the mutual impedance of the core between each two-phase; Z iS,jS is the mutual impedance of the sheath between each two-phase; Z iC,jS is the mutual impedance between the core and the sheath in different phases, where i , j=A, B, C and i ≠ j.
The elements in the matrix can be calculated by Cason formula or Schelkunoff impedance formula [22]. Here Cason formula is applied as • Self-impedance of "core-earth" loop: • Self-impedance of "sheath-earth" loop: • Mutual impedance between any two loops: where r C and r S are unit AC resistance of core and sheath; R C and R S are equivalent radius of core and sheath; d ij is the distance between corresponding wires; D g is the equivalent depth of the earth circuit.

Calculation of cable admittance matrix
Owing to the shielding effect of the metal sheath, capacitance exists only between the core and sheath in the cable, but not between the cables [21]. The capacitance distribution of the single-core cable is shown in Fig. 8. C CS is the capacitance between the core and the sheath. C SE is the capacitance between the sheath and the ground; U C , U S and I C , I S represent the voltage and current of each loop, respectively.
Capacitance between the core and the sheath is Capacitance between the sheath and the ground is (29) Fig. 7 The π type equivalent circuit of traction network Fig. 8 Schematic diagram of capacitance of single-core cable where 0 is vacuum permittivity,; CS and SE are relative permittivity of main insulation and sheath insulation, respectively; d ia and d oa are the inner and outer radii of main insulation, respectively; d ib and d ob are the inner and outer radii of sheath insulation, respectively.
The admittance parameter can be obtained by

Parameter calculation of TTN
Similarly, TTN composed of contact strip and rail can be equivalent to three-wire transmission model via multi-conductor transmission line theory. Consequently, the abovementioned impedance calculation for π-type equivalent circuit is also available to TTN. The specific calculation formula is referred to in Sect. 4.2.1 or Ref. [7]. Reference [7] has illustrated the rationality of equating the model of contact strip to cable; therefore, the admittance calculation of contact strip refers to Eqs. (31) and (32) in Sect. 4.2.2. Apart from that, the admittance calculation formula for rail is illustrated in Refs. [10] and [12].

Simulation analysis of three-phase traction power supply system
In this section, the simulation of TTPSS is established in Matlab/Simulink combined with the modeling method in Sect. 3, and the electrical characteristics of the system are analyzed through the simulation model.

System simulation model
In the simulation model shown in Fig. 9, 35 kV and 3 kV are determined as the nominal voltage levels of CTN and (33) TTN, respectively. Referring to the existing traction power supply system, the secondary side of TT takes 1.05 times the nominal voltage; that is, the actual voltage of CTN is 3.15 kV. The total power supply distance is set to 50 km with traction substation interval of 10 km in simulation model. The transformer of MSS rated 100 MVA obtains power from 220 kV three-phase power grid with short-circuit capacity of 2000 MVA. The Yd11 transformer bank is adopted in TT and the nominal capacity is 10 MVA. The load is specified as urban rail type-A vehicle with nominal power of 4000 kW and power factor of 0.993 [9].
At the maximum ampacity, 35 kV single-core cable with cross-sectional area of 630 mm 2 is adopted in CTN. The model of rail is P60 with parameters referenced to [7]. Since the contact strip is paved between the rails, it can be installed with a large cross-sectional area, referring to the single-core cable with 1000 mm 2 . The main parameters are shown in Table 1, where Z s and Z m are the self-impedance and mutual impedance, and C is the capacitance to ground.

Current distribution of short-section
To verify the current distribution law of the short-section, it is assumed that the vehicle is operating in the third short-section. The comparison of short-section current between the theoretical value and the simulation value is demonstrated in Table 2, where I L and I R represent the current collecting from the left and right sides of the vehicle, respectively.
The theoretical and simulation values of current shunt ratio in short-section are acquired by current distribution data as shown in Fig. 10.
From Table 2 and Fig. 10, it is demonstrated that the theoretical calculation value of the short-section current distribution is exceedingly close to the simulation value, which validates the derived short-section current distribution formula from the simulation.

Current distribution of two-stage power supply network
Due to the properties of two-stage power supply structure in TTPSS, CTN and TTN undertake part of traction current in long-section, respectively. The current distribution law is investigated in CTN and TTN via simulation. When the vehicle runs to Sects. 2, 3, 4, and 5, respectively, the relationship between the vehicle current I and the current I C collecting through long-section CTN is listed in Table 3.
In various sections, the load current carried by CTN and TTN in the long-section is shown in Fig. 11. Table 3 and Fig. 11 illustrate that the main traction current is undertaken by CTN in the long-section, while few by TTN. According to the theory of impedance conversion, when the transformation ratio of TT is k , the impedance of TTN converted to the side of CTN is k 2 times of its nominal value. In the condition of the simulation, CTN undertakes about 99% of traction current, and therefore, the stray current and step voltage can be well suppressed via TTPSS.

Voltage losses of traction network
To verify the voltage losses of traction network, assuming that the vehicle is collecting current in the third short-section, the comparison of voltage losses of traction network calculated by the theoretical formula and the simulation is shown in Fig. 12. The position in the figure represents the distance between the vehicle and the traction station on the left side of the short-section.
From Fig. 12, the voltage losses calculated by the derived formula has the same trend as that obtained by the simulation. Specifically, the deviation of peak value is barely 0.7%, which proves the high accuracy of the derived formula for voltage losses. From the simulation, as the vehicle operates in short-section, the voltage losses first increase and then decrease, with the local maximum value appearing in the middle of short-section. Combined with the analysis in the previous section, the voltage losses of traction network    Fig. 11 Relationship of long-section current distribution can be reduced for the improving of power supply capacity when narrowing the distance between two traction stations or applying larger cross-sectional cables.

Equivalent impedance of traction network and vehicle
Toward the vehicle, the equivalent impedance of the entire system will manifest a certain variation law according to the position of vehicle. In the case of the parameters applied in Sect. 4.1, the curve of the equivalent impedance for traction network with the change in the vehicle position is demonstrated in Fig. 13. The equivalent impedance of the traction network is composed of long-section impedance and short-section impedance as shown in Fig. 13. Along with the increasing distance, the impedance of the long-section augments proportionally with a slight slope, which is mainly determined by the impedance of cables. Meanwhile, the impedance curve of short-section is saddle shaped, reaching a local maximum in the middle of short-section. Overall, the equivalent impedance of traction network combines the characteristics of both long-section and short-section, generally showing an upward trend with distance, and a local peak value appears in the middle of each short-section.
Toward TTPSS, as the vehicle moving the equivalent impedance of the vehicle accordingly alters in terms of a particular law. Referring to the parameters applied in Sect. 5.1, the variation curve of the equivalent impedance for the vehicle running from the beginning to the terminal of the route is shown in Fig. 14.
In the short-section, due to the current drawn by the traction transformer, the impedance of vehicle gets to a local maximum value at the position of the traction substation. The declining voltage of the traction network results in the local minimum impedance in the middle of short-section. In general, the equivalent impedance of vehicle manifests a downward trend, gradually decreasing with the falling voltage of traction network.

Voltage distribution at no load
According to the capacitive effect of the cable, the system voltage will rise along the line at no load. Figure 15 illustrates the voltage distribution in three different cross-sectional cables of 400, 630, and 800 mm 2 , indicating that the larger the cable cross-sectional area, the higher the system voltage.
From Fig. 15, it is demonstrated that under three crosssectional cables of 50 km, the no-load voltage shows a slight rise for the capacitive effect, with the maximum value of 35.55, 35.61 and 35.64 kV in CTN, while 3200, 3204 and 3208 V in TTN, respectively. The maximum no-load voltage appears at the end of the route in CTN, while in TTN it does in the middle of the terminal short-section. Under the conditions, the no-load voltages of CTN and TTN are all steady within the standard range, and no compensation is required. If necessary, the reactive power compensation device can be employed to optimize the voltage distribution of the system.

Voltage distribution at tight operation
When the train running closely, it is set with the vehicle speed of 80 km/h referring to urban rail type-A vehicle and the tracking interval of 3.75 min. Figure 16 reveals the voltage distribution with different cross-sectional cables at closely running in TTPSS.
In Fig. 16, in the case of cables with three cross-sectional areas, the lowest voltages are 0.915, 0.939, and 0.952 pu in CTN, and 0.862, 0.892, and 0.904 pu in TTN, respectively. According to the characteristics of working voltage and power of locomotives, the locomotives can contribute the rated power as the voltage of TTN is between 80 and 110% of the rated voltage [23]. In view of the fact that the minimum voltage reaches more than 86% of the rated voltage, it meets the power supply requirements for tight operation. Due to the symmetry of the line, when the MSS is arranged in the middle of the route, the power transmission surpasses 100 km, enhancing with the increasing cross-sectional cables.
In order to compare with the power supply capability of TTPSS, the simulation model of DC 1500 V system is established. The locomotive parameters and tracking interval in DC 1500 V system are set consistently with those in TTPSS. The cross-sectional area of 400, 600, and 800 mm 2 are adopted in 35 kV medium-voltage cables. CTA150 and JTM120 are selected as the models for contact wire and messenger wire, respectively. For the practical power supply capacity of DC 1500 V system, the total power supply distance is set to 30 km with traction substation interval of 3 km in simulation model. Figure 17 reveals the voltage distribution at closely running in DC 1500 V system. Due to the lower voltage level of traction network in DC 1500 V system, the traction current and voltage drops of locomotive in short section of traction network are greater than that in TTPSS. In Fig. 17, in the case of cables with three cross-sectional areas, the lowest voltages are 0.978, 0.984, and 0.987 pu in medium-voltage network; and 0.832, 0.869, and 0.891 pu in traction network, respectively. Limited by the power supply capacity, there are more traction substations and shorter power supply distance in DC 1500 V system. Apparently, TPPSS outstands in power supply capability compared with DC 1500 V power supply scheme, supplying the demand of urban rail transit and regional railway.
Similarly, the simulation model of AC 27.5 kV system is established for the comparison with the voltage level of TTPSS. The locomotive parameters and tracking interval in AC 27.5 kV system are set consistently with those in TTPSS. TCG100 and TJ95 are adopted for contact wire and messenger wire, respectively. The total power supply distance is set to 50 km, which is powered by two traction substations (TSS1, TSS2). In one-side feeding power supply scheme, the length of power supply arm of each traction substation is set to 25 km, with the section post placed at 25 km. Figure 18  With the higher voltage grade adopted in AC 27.5 kV system, the voltage drops of traction network are naturally lower. In Fig. 17, the lowest voltage of the whole line reaches 0.916 pu, better than 0.862 pu in TTPSS, appearing at the end of the power supply arm. Noteworthily, the existence of phase separation inevitably affects the AC 27.5 kV system, especially in case of heavy traffic density, short station interval and low vehicle speed in rail transit. At the same time of possessing relatively great power supply capacity, the phase separation is canceled through continuous structure in TTPSS, which eliminates the adverse issues, such as electrical transient, tractive force loss, short circuit resulted from phase separation device failure. With the improvement of traction drive technology, the voltage level of TTN can be further improved, and then TTPSS will exert greater superiority in long-distance electrified railways.
In the scenario of trunk railways, TTPSS is still feasible. Although the power of locomotives in trunk railways is higher than that of the urban rail transits, the departing interval is much longer, resulting in the approximate load of overall system. Via adjusting the interval between the traction stations and the operation diagram, TTPSS can also be well applied in trunk railways. For simplicity, the analysis of trunk railways scene is omitted.

Three-phase voltage unbalance factor
Theoretically, the new electric locomotive collects current symmetrically from three phases system and will not produce negative-sequence components in the system. However, the impedance of TTN is not completely symmetrical by virtue of the difference in impedance between contact strip and rail. In order to assess the voltage unbalance, the simulation is performed in different cross-sectional contact strips as shown in Table 4, in which the system is at closely running with shortcircuit capacity of 2000 MVA. Since the voltage unbalance is quite similar under contact strips with different cross-sectional areas, Fig. 19 shows the voltage and current waveforms of MSS with cross-sectional area of 630 mm 2 as an example.
According to the power quality regulations published in GB/T 15543-2008, during normal operation, the voltage unbalance of PCC cannot exceed 2% in the long term and 4% in the short term [24]. The simulation result in Table 4 indicates that the voltage unbalance caused by asymmetry of traction network impedance is thoroughly within the allowable range of the national standard in China. In addition, with the increasing cross-sectional area of contact strip, the impedance asymmetry of TTN will further weaken, resulting in a slighter voltage unbalance.

Utilization rate of regenerative energy
With the continuous structure of TTPSS, in the same traction power supply arm, traction and regeneration conditions may simultaneously exist in vehicles. Meanwhile, the utilization rate of regenerative energy is improved in the long-distance continuous structure, since the regenerative power is preferentially provided to the vehicles under traction condition. To investigate the utilization of regenerative energy of TTPSS, it is simulated that the traction vehicle runs in S5 and the   Fig. 19 Voltage and current waveforms of MSS: a three-phase voltage; b three-phase current regenerative vehicle is located in S1-S5, respectively, as shown in Fig. 20.
When the regenerative vehicle operates in different sections, the utilization rate of regenerative energy is displayed in Table 5, wherein P reg and P L represent the regenerative and tractive power of the vehicle, and P MSS the output power of MSS.
In the existing traction power supply system, there are fewer vehicles in the same section due to the subsection of power supply arm, resulting in low utilization rate of regenerative energy and frequent phenomenon of energy feedback. According to Table 5, it is the continuous structure of TTPSS that the regenerative energy can be transmitted to the vehicle under traction condition for a long distance. The utilization rate of regenerative energy declines with increasing distance between the vehicles under the two working conditions, yet reaches more than 97%. Compared with the existing traction system, the effective utilization rate of regenerative energy avoids the feedback of electric energy, reduces the waste of resources, and furthermore, diminishes the capacity configuration of MSS.

Technical comparison of different power supply schemes
To compare the differences and advantages between the proposed TTPSS and the traditional traction power supply systems, Table 6 shows the technical comparison of TTPSS, single-phase 27.5 kV system and DC 1.5 kV system in several aspects, which indicates the significant technical advantages of TTPSS.

Conclusion
The novel TTPSS outstands its superiority for unifying traction power supply in rail transit. In this work, we focus on the electrical characteristics of TTPSS through theoretical derivation and simulation analysis. The conclusions are as follows: 1. The traction current of electric locomotive is supplied from traction substations of entire electrified railway line. The shunt ratio of short-section current is approximately in inverse proportion to distance, relating to the position of vehicle, and the impedance of CTN and TTN. Under the voltage levels of this work, about 99% of traction current is undertaken by long-section CTN, accordingly, the stray current and step voltage can be well suppressed in three-phase traction system. TT1   TT2  TT3  TT4  T T5  TT6   S1  S3  S2 S4 S5 Fig. 20 Schematic diagram of locomotive layout 2. The equivalent impedance of traction network regularly changes in accordance with saddle shape, generally showing an upward trend with distance, and a peak value is obtained in the middle of each short-section. Correspondingly, the equivalent impedance of vehicle generally manifests a downward trend due to the decline of traction network voltage, and a local minimum value appears in the middle of each short-section. 3. The proportion of system voltage losses is thin due to the new two-stage power supply structure. The power supply distance surpasses 100 km referring to the parameters of this work, making evident advantages of TTPSS versus DC 1500 V in power supply capability. 4. Negative-sequence component caused by asymmetry of CTN impedance is within the allowable range of national standard with below 1‰ in the parameters of this work. Compared with single-phase AC 27.5 kV system, the adverse effects resulting from the phase separation can be effectively disposed of. The utilization rate of regenerative energy for locomotive vehicle is significantly promoted via continuous power supply structure, reaching over 97%.

MSS
Finally, the electrical characteristics of TTPSS are mainly based on theoretical and simulated analysis in the work, and more consideration should be shifted toward the influence of double-line full parallel mode, which will be studied.