1. Introduction
Modern electrified railway networks systems are complex distributed power systems facing different challenges today and in the near future. These challenges appear in several domains, like the need to incorporate and deal with distributed renewable energy sources [
1] and to increase the flexibility and resilience of the energy supply [
2] during higher power consumption. At the same time, the growing number of passengers pushes towards increasing the trains’ speed and traffic density but keeping the reliability, availability and safety of the energy supply at the highest levels, namely when crossing neutral zones [
3].
In electrified railway networks, the active power supplied by one substation (SST) mainly depends on the number of trains present in the line and the power consumption of each one. Thus, there are situations in which an SST is supplying high power and eventually is in an overload condition. On the contrary, in another situation, the SST can be supplying very low power. An additional issue can be considered: situations when a train is in braking/regenerative mode and some amount of active power is injected into the catenary [
4,
5]. As known, overload conditions are not particularly appreciated and should be avoided as much as possible; they give origin to high losses, temperature rises and larger voltage drops, and the power peaks are penalized by the energy supplier [
6,
7].
Large asymmetries in the power supplied by two neighbouring SSTs contribute to a higher unbalance factor seen by the electric grid at either high-voltage (HV) or extra-high-voltage (EHV) levels [
8]. Then, the Transmission System Operator or Distribution System Operator (TSO/DSO) could penalize the infrastructure manager according to the level of the voltage unbalance factor [
9]. Additionally, there are conditions when regenerative power is not allowed to be injected into the catenary system or, if allowed, is penalized. Then, the possibility of redirecting this energy should be considered [
10,
11,
12]. Therefore, a power-electronics-based converter system connecting the two sections could manage both active and reactive power at the neutral zone [
13,
14,
15].
This converter has been designated by several names: sectioning-post rail power conditioner (sp-RPC) [
11], power transfer device (PTD) [
15,
16], and railway interline power flow controller (RIPFC) [
17], which is the designation adopted in this work. The RIPFC system can play an important role in those scenarios, and some of them will be addressed in the following. The main objective of the RIPFC system is twofold: to be able to allow double-side feeding between two conventional (transformer-based) traction substations in a first step, thus supplying active power to the trains from two adjacent substations [
15,
18]; the second objective is to manage the reactive power in both nodes to which it is connected, thus stabilizing the voltage in those nodes [
19].
The first objective can be fulfilled by the following actions that the system controller should allow: enable active power transfer between two collateral substations while respecting the following constraint: the overall losses should not be increased compared to those occurring in conventional feeding under the same traffic. Regarding the second objective (reactive power compensation in the two sectors to which it is connected) the main requirements are: the power factor at the substations should not be degraded compared to what it would have been in the conventional case under the same traffic. Additionally, the RIPFC system should: (i) be sized large enough to enable both of the above actions and (ii) improve the voltage level on both sectors (when loaded) compared to what would happen in conventional feeding. The fulfilment of these objectives is done with regard to other important requirements: the voltage magnitude, harmonic content and other disturbance levels should be met at all times [
20,
21]. The control strategy should be adapted to allow double-side feeding whenever it is useful and whenever it can bring benefits compared to the conventional situation.
The paper is organized as follows: in
Section 2, the RIPFC system is described in both the power structure and the control modes and approaches; in
Section 3, the voltage profile at the section end and the power factor at the substation are deduced using simplified diagrams.
Section 4 presents a time-domain analysis using different compensation modes and traffic scenarios, and finally, in
Section 5, the conclusions are drawn and discussed.
2. The RIPFC System
Architectures for supplying electrified railways vary to some extent. Indeed, the neutral zone can be a complex subsystem where the redirection of active power needs careful analysis due to the use of power electronic converters connecting different lines and sections [
15]. In this section, we use a simplified architecture for demonstration purposes using steady-state phasor analysis. A basic insight regarding the possible advantages of using an RIPFC system can be made by analysing the circuit represented in
Figure 1.
The substation voltage, noted as
, provides current
to the load/train through the line/catenary with lumped impedance
. Impedance
is fixed, and
represents the lumped impedance of the catenary at some distance from the substation where the train is located. Due to the line impedance, an absolute voltage drop occurs. The phasor diagram of the simplified circuit is shown in
Figure 2, wherein
has been neglected.
The relative voltage drop
is created and defined in (1). The calculation of the voltage drop is obtained using the phasor diagram as:
In the load, the relation between current and power is:
where * is the conjugate operator. Then, (1) can be rewritten as in (3):
Equation (3) shows that the voltage drop has two components: a longitudinal one in-phase with
and a quadrature one. The last one is not of high relevance to system operation; it means that the instantaneous voltage has a phase lag in relation with the substation voltage. However, the in-phase voltage drop can substantially reduce the magnitude of the voltage at the pantograph. Assuming that the angle between
and
is small and that the magnitudes are similar, then (3) can be simplified as (4):
The expansion of (3) would contain additional terms (coming from the product
) that are not present in the approximated (4). However, these terms have a small contribution to the voltage drop. The assumption is used just to highlight the most relevant dependences between voltage drop and reactive power consumption through the term
. Focusing only on the in-phase voltage drop, it is given by (5) as:
The voltage drop depends on the train’s active and reactive power ( and , respectively), the catenary impedance and the substation voltage . With a moving train, the considered line impedance changes according to the different train positions, thus affecting the drop. The farther the train is from the substation, the higher the voltage drop is. Therefore, the voltage drop is basically influenced by the train’s active and reactive power and the train’s position, assuming the substation voltage is almost constant.
In abstract, the RIPFC system can manage active and reactive power (
and
, respectively). Then, if the converter could be connected in parallel with the load, the in-phase voltage drop would be given by (6):
The term
is an active power one; the RIPFC can, in fact, in some circumstances, control active power. However, the influence of this term is small since its contribution depends on
R, which should be small. As an example, for a train with
= 0.9i and a typical catenary with
R = 0.15
/km and
= 5.6, the ratio between the two terms is
= 0.37. This compensation type is discussed later and is used mainly for balancing the active power in the substations. The term
is a compensating reactive power that can impose a null in-phase voltage drop. This means that the reduction in
can be done by reactive power compensation, which can be achieved by the RIPFC system. Then, controlling the reactive power in (6) means controlling the voltage drop, although the total active power flow also has a role. The circuit diagram in
Figure 3 includes a compensation current,
, in quadrature with voltage
(this is similar to the operation of the RIPFC converter but with regard to reactive power control only).
If the goal is to impose a unitary power factor in the substation, then the resulting phasor diagram is represented in
Figure 4.
It can be seen that the in-phase voltage drop is much smaller than before; the voltage at the connection point is higher. The RIPFC operates as an SVC but has the objective of imposing a unitary power factor at the substation; the voltage drop reduction is a positive side effect.
2.1. Structure and Capabilities
The basic power diagram of the RIPFC system is illustrated in
Figure 5. Mainly, the RIPFC is constituted by two single-phase AC/DC/AC back-to-back converters with a common DC bus and two transformers to connect each converter to the catenary system. The specific converter structure can be based on different approaches, but the most common is a multilevel one built with cascaded H-bridges, multi-point clamped or modular multilevel converters. The transformers are designed according to the power level to be transferred between sections, the reactive power injected in the neutral zone and the voltage and current levels in the converters. Also, a parameter of high relevance in the RIPFC design both in the transformer and in the converters is the efficiency level in order to keep losses at a minimum and thus not compromise the overall losses when using the RIPFC system, particularly in the active power transfer mode.
The RIPFC has two fundamental properties: it can inject variable reactive power into the end points of both sections where it is connected and independently for each section ( and ), thus controlling the AC voltage level. It is very similar to the operation of a static var compensator (SVC) but using a PWM-controlled voltage-source converter. Additionally, if the DC buses of both DC/AC converters are electrically connected, then there is the possibility of transferring active power () between both AC sides and then reducing the power supplied by the heavily loaded SST and increasing the power of the lightly loaded one.
2.2. Voltage and Power Factor Characteristics
We first study the voltage and power factor characteristics of the system without any compensation. Then, a compensation strategy, as already pointed out before, is implemented and analysed. The base diagram is illustrated in
Figure 6. In this work, we use the following assumptions: (i) the converter/compensator is located at the end of the section (the neutral zone (
)), (ii) the use of lumped parameters is valid (analysis at 50 Hz only), and (iii) only one load (train) is considered. The simplified analysis for operation without compensation is made using the diagram in
Figure 6. For operation with reactive power compensation, the simplified diagram is shown in
Figure 7. In the model,
is the open-circuit voltage of the substation,
is the equivalent impedance of the circuit constituted by the TSO/DSO grid,
is the equivalent impedance of the substation transformer, and
is the concentrated parameters of the catenary line, which depend on the distance between the load (train) and the substation. All these impedances are modelled by the impedance
. The load/train is modelled as an apparent load:
. Also, in this model, the distributed line capacitance is ignored. For the voltages, the following equation applies:
Load power is given by (8):
Multiplying by
in the voltage equation gives:
It should be mentioned that (9) can be solved for . In the subsequent analysis and results, we use the following assumptions: (i) is constant, which is a simplification; and (ii) the apparent load power is an independent variable.
2.2.1. Without Compensation
The first set of results addresses operation without compensation. The main parameters used for the substation are: = 27.5 kV and = 16 MVA. The catenary parameters are: = 0.15 /km and = 3. For these results, the train is located 20 km away from the substation and has a nominal power of 8 MVA; its additional parameters are: fixed power factor = 0.95i.
Using (7) and (8), the evolution of the voltage magnitude at the connection point is expected to show an important drop almost linearly dependent on the train’s active power: in fact, it drops from 27.5 kV to 25.8 kV (
Figure 8 (left), trace “uncompensated”). Additionally, we expect a reduction in the power factor at the substation level (it varies from 0.95i to 0.92i when
varies between 0 and 8 MW); this is also of concern since it implies higher currents and more losses in the system.
The second analysis, still without compensation, is related to the influence of the train’s position with the same parameters for the train voltage and substation power factor. For this illustration, the train consumes its nominal power (
S = 8 MVA with
= 0.95i) and travels along the whole catenary length. With constant apparent power, we expect both a reduction in the voltage at the pantograph connection and a reduction in the power factor at the substation. Specifically, when analysing the same parameters, the train voltage has a strong reduction when it travels near the neutral zone: it drops from 27.5 kV to 24.5 kV when the train moves from
d = 0 to
d = 30 km; after 20 km, the voltage reduction is quite fast (
Figure 8 (right), trace “uncompensated”). Regarding the substation power factor, the conclusion is similar; there is a more-pronounced reduction for larger distances: from 0.95i to 0.90i.
2.2.2. With Compensation
As known, and this is the main objective of an SVC, the RIPFC can be controlled in order to stabilize the voltage at the PCC (the neutral zone). Differently, the compensation strategy defined for demonstrating the RIPFC’s capabilities is to impose a unity power factor in the substation. The same two analyses are performed: variable train power with constant power factor (
= 0.95i) maintaining the train in a fixed position and constant train power with variable position. In both cases, the other fundamental parameters were maintained.
Figure 7 shows the associated diagram for the analysis.
The lumped impedance
is the equivalent catenary impedance between the train position and the neutral zone. When using reactive power compensation, the active and reactive power balance equation is given by:
In the right loop, the power balance is given by:
The goal is to impose a unitary power factor at the substation using only reactive power, i.e.,
Then, the three equations can be solved for , and .
The results in
Figure 8 (left) are to be compared (“uncompensated” versus “compensated” traces). As highlighted earlier, there is a much more constant voltage at the connection point, though this is somewhat dependent on the train’s power; the power factor in the substation is unitary as this was set as the objective of the compensation. For the other test, the train power is constant (
S = 8 MVA,
= 0.95i) and the position is variable. The results for the same variables are shown in
Figure 8 (right).
The voltage profile provides the same conclusion: the voltage drop is quite small (less than 4%) in the whole section.
2.2.3. Discussion
Without compensation, the voltage drop at the load/train can be relevant and can impose limited power consumption in some conditions. Also, a reduction in the substation power factor is noticed, thus increasing the system losses. Both parameters depend on the train’s load factor, the catenary impedance and the train’s distance to the substation. The RIPFC converter, when compensating the power factor in the SST, not only can reduce the system losses through reduction in the current’s rms value but also highly limits the voltage drop at the pantograph connection.
The RIPFC’s operation is based on knowledge of the power factor in the substation. This variable must be supplied to the converter, which is tens of kilometres away from the substation; this implies that a fast and reliable communication link between the two is necessary [
22]. This issue is out of the scope of this paper but will appear again when the RIPFC system is implemented to control the active power flow between the two sections.
4. Discussion
Regarding reactive power compensation, we proposed to compensate the power factor at the substation instead of the voltage magnitude at the neutral zone, and this is the main contribution of this paper. The opposite could be selected: nearly constant voltage at the weakest connecting point (the neutral zone) would be achieved but with the negative impact of a lower power factor at the substation level. This is the same feature of an SVC connected to the neutral zone; the presented approach adds flexibility to the system: giving the infrastructure manager a degree of freedom.
When redirecting active power between the two sections while maintaining the compensation of reactive power in the substation, a double-side feeding condition is achieved, i.e., both neighbouring substations supply the same active power but, as pointed out before, a different sharing factor is possible if a specific requirement is received from a supervisory layer.
There are two topics not addressed in this work that should be considered for further analysis: (i) the need for substation measurements and communication links between the substation SCADA system and the RIPFC control system and (ii) the trade-off between system power losses (in the catenary, transformer and converter) and double-side feeding; in some cases, the system losses become higher with the RIPFC system.
The final assessment of the use of the RIPFC system must be made by considering its important advantages for the electric traction system (unitary power factor at the substation or voltage stabilization at the neutral zone, and double-side feeding effect) and possible weaknesses (communication link and system losses).