Before designing the control strategy, the following assumptions were made.
Because the line loss accounts for a small proportion of all RBE, the line loss was neglected and the power transmission loss by converters alone was considered. The capacity design of the ESS will be an optimization topic, and is not the focus of this paper. Therefore, in this paper, the capacity limits of the ESSs were not considered and the capacities of the ESSs for storing regenerative energy were sufficient.
3.1. Centralized Control Strategy
To utilize the RBE and improve the power quality of the railway using the modified system, a centralized control algorithm was designed in this paper. In order to realize the highly efficient utilization of RBE, the control rules in [
36] can be used as a reference. The steps of the designed centralized control algorithm are then described as follows:
Step 1: Adjacent transmission by single EPTD or PTD. Screening out the power supply sections where the RBE is located, and calculating the regenerative power and traction power of each power supply section. According to the power relationship, the regenerative power is delivered to the adjacent power supply section where the traction power is located by a single EPTD or PTD. Then, the transmission power PPTD_1,j of each PTD and EPTD in step 1 can be obtained.
Step 2: Transmission between two power supply sections by EPTD and PTD. After step 1, the power supply section adjacent to the section with regenerative power has no traction power. Then, recalculating the regenerative power and traction power of each power supply section. According to the residual regenerative and traction power relationship, delivering the RBE between two sections via an EPTD and a PTD. The transmission power PPTD_2,j of each PTD and EPTD in step 2 can then be obtained.
Step 3: Storage of the surplus RBE in ESS. Because the transmission efficiency to deliver regenerative power between three sections via PTDs and EPTDs is lower than it utilizing regenerative power via ESS, it is more economical to store the surplus RBE in ESSs [
37]. After step 1 and step 2, if the RBE is still surplus, the surplus RBE will be stored in ESS. Then, the charge power
PES_3,j in step 3 can be calculated.
Step 4: Release of the energy in ESS. To efficiently utilize RBE, it is necessary to release the previously stored RBE. After steps 1–3, no power supply section with RBE remains. If there is traction power in some sections, the previously stored RBE will be released to supply the traction power. Then, the discharge power PES_4,j in step 4 can be calculated.
Step 5: Improving the power quality of the railway. After steps 1–4, all RBE generated by locomotives and RBE stored in ESSs have been effectively utilized, and there is only the surplus of traction power in the overall railway system. Screening out the power supply sections of surplus traction power and storing the number of the power supply sections in variables
j and
j + 1, as shown in
Figure 7. The surplus traction power in step 5 is defined as
PL_5,j and
PL_5,j+1. Since EPTD is located between two power supply sections of the same TS, EPTD can then eliminate three-phase current imbalance by regulating active powers
PE,j,1,
PE,j,2 and compensating reactive powers
QE,j,1,
QE,j,2. Currently, RPC is widely used to improve the power quality in AC-fed railways, so the control strategy of RPC improving power quality can be used for reference in control of EPTD
j. Since the stored energy of ESS
j has been released in step 4, the ESS
j will not be able to supply for traction power. Therefore, ESS
j will not operate in step 5.
Case 1: PL_5,j > 0, PL_5,j+1 > 0
There is traction power on both power supply sections connected to EPTDj. According to the control rules of RPC, in order to eliminate the current imbalance, first of all, the feeder power of the two power supply sections needs to be regulated to be the same as the EPTDj for delivering surplus traction power, which can relieve current imbalance to some extent. Then the corresponding reactive power is compensated according to the type of traction transformer, thus eliminating the current imbalance completely. This paper takes the V/v transformer as an example to calculate the regulating power of EPTDj.
(i) if PL_5,j < PL_5,j+1
According to the control rules of RPC improving power quality, the regulating power of EPTD
j can be calculated as follows [
44]:
The positive directions of active and reactive power in (2) are shown by green and red arrows in
Figure 7.
(ii) if PL_5,j ≥ PL_5,j+1
The regulating power of EPTD
j can then be calculated as follows:
Case 2: PL_5,j > 0, PL_5,j+1 = 0
Among the two power supply sections connected with EPTD
j, only the
j power supply section has traction power. To improve power quality, EPTD
j needs to deliver half of the traction power from the
j power supply section to the
j + 1 power supply section, and then compensate the reactive power. The regulating power of EPTD
j can then be calculated as follows:
Case 3: PL_5,j = 0, PL_5,j+1 > 0
Among two power supply sections connected with EPTD
j, only the
j + 1 power supply section has traction power. Therefore, EPTD
j needs to deliver half of the traction power from the
j + 1 power supply section to the
j power supply section, and then compensate the reactive power. In this case, the regulating power of EPTD
j can be calculated as follows:
In other cases, both power supply sections connected with EPTDj have no traction power, and the public grid does not need to supply the railway system (e.g., the case of PL_5,j = 0 and PL_5,j+1 = 0), so the railway will not cause three-phase current imbalance to the public grid. In addition, since the RBE has been utilized completely after steps 1-4, there will be no power supply sections with RBE. Therefore, in the analysis in step 5, this paper does not consider the cases of existing RBE, i.e., the case of PL_5,j < 0 or PL_5,j+1 < 0 will not occur.
Then, the regulated power references of EPTDs and PTDs and the charge and discharge power references of ESSs can be calculated using
PPTD_1,j,
PPTD_2,j,
PES_3,j,
PES_4,j and
PE,j,1,
PE,j,2,
QE,j,1,
QE,j,2. These references are calculated by EMS and are delivered to the PTDs and EPTDs via bidirectional communication equipment. Finally, the utilization of RBE and power quality improvement in the railway can be realized by the proposed centralized control strategy. The control diagram of the centralized control strategy is shown in
Figure 3.
3.2. Decentralized Control Strategy
In the centralized control, the operation of PTD and EPTD largely depends on the state of the EMS and communication. If the EMS or communication equipment fails, the utilization effect of RBE is seriously affected. To tackle this issue, a decentralized control strategy is proposed in this paper. In case of the centralized control strategy failure, the LCs can still perform the decentralized control strategy to control the PTDs and EPTDs by themselves, thus enabling the RBE to continue to be utilized within the railway system.
To design the decentralized control strategy, the running state of the PTDs and EPTDs must be first analyzed. The running state of the PTDs and EPTDs can be shown in
Figure 8. The locomotive load powers in S
j and S
j+1 are respectively defined as
PL,j and
PL,j+1. The directions of arrows are the positive direction of power. Then, the feeder power of
j section and
j + 1 section can be obtained as follows:
Then, according to (6), the total power of TS can be calculated as follows:
It can be seen from (7) that the transmission power of EPTDj has no influence on the total power of TS, and the total power of TS will be affected by the transmission power of PTDj-1, PTDj+1 and charge and discharge power of ESSj.
According to the principle of control strategy to improve the power quality in [
34], the regulated power of EPTD
j eliminating three-phase current imbalance can be expressed as follows:
Then, after EPTD
j eliminating three-phase current imbalance, the feeder power of the two power supply sections will be expressed as follows:
Compared with (7) and (9), it can be found that the effect of EPTDj on the overall feeder power is similar to that when running according to the centralized control strategy and according to the control strategy of eliminating three-phase current imbalance. Furthermore, it also can be seen from (8) that the active powers of j and j + 1 power supply sections can be automatically balanced when EPTDj implements the control strategy of eliminating three-phase current imbalance. That means, when eliminating three-phase current imbalance, EPTDj can automatically deliver RBE from the section with RBE to the section with traction power, realizing the automatic utilization of RBE. This paper will make full use of this characteristic of EPTD to design the decentralized control strategy.
Besides, it can also be seen from (7) that the overall feeder power of TS will be affected by the regenerative power delivered by PTDj-1, PTDj+1 and the charging and discharging power of ESSj. Therefore, in order to realize the utilization of RBE, it is necessary to control the regulated power of the PTDs and the charge and discharge power of the ESSs in the decentralized control strategy. Then, a decentralized control principle was designed in this paper, and its principles are as follows:
- (1)
EPTD automatically performs the function of improving the power quality to realize the automatic utilization of RBE between two power supply sections in the same TS, and according to the locomotive load power of two power supply sections, calculates the charge and discharge power of EES.
- (2)
PTD automatically performs the function of regulating the RBE to realize the utilization of RBE between two power supply sections in the adjacent TSs, and according to the locomotive load power of two power supply sections, calculates the regulated power of PTD.
Using the above mentioned principles, the LCs can automatically control each PTD and EPTD without establishing communication with each other, so as to ensure that the RBE can still be utilized when the centralized control fails.
According to the decentralized control principles, the decentralized control of the PTDs and EPTDs is designed as follows:
(a) the control strategy of LCs in PTDs
The operation states of power supply sections on both sides of PTD
j are shown in
Figure 9. It needs to judge the locomotive load power of two power supply sections to calculate the regulated power of PTD
j.
Case 1: PL,j > 0, PL,j+1 > 0
No transmission.
Case 2: PL,j ≤ 0, PL,j+1 ≤ 0
No transmission.
Case 3: PL,j > 0, PL,j+1 < 0
The regenerative power in the
j + 1 power supply section is delivered to the
j power supply section. The RBE should be maximized transmission. Therefore, the regulated power
PPTD,j can be calculated as follows:
Case 4: PL,j < 0, PL,j+1 > 0
The regenerative power in the
j power supply section is delivered to the
j + 1 power supply section. Therefore, the regulated power
PPTD,j can be calculated as follows:
(b) the control strategy of LCs in EPTDs
The operation states of power supply sections on both sides of EPTD
j are shown in
Figure 10. It needs to judge the locomotive load power of two power supply sections to calculate the regulated power of EPTD
j and the charge and discharge power of ESS
j.
Since EPTD
j can automatically deliver RBE from the section with RBE to the section with traction power when eliminating three-phase current imbalance, in the control process of EPTD
j, the regulating power of EPTD
j can always be calculated as follows:
It can be seen from (12) that EPTDj does not need to judge and quantify the locomotive load power, but only needs to detect the locomotive load power on both power supply sections and substitute it to (12) to realize the utilization of RBE and improve power quality. However, whether ESSj in EPTDj needs to be charged or discharged, as well as the value of its charge and discharge power, needs to be determined according to the locomotive load power on both power supply sections and the capacity of ESSj. Subsequently, the control strategy of ESSj is designed as follows:
Case 1: PL,j > 0, PL,j+1 > 0
There is traction power on both power supply sections connected to EPTD
j. If there is surplus RBE stored in ESS
j in EPTD
j, it will be released to power the traction power on both power supply sections. If there is sufficient RBE, ESS
j will release the energy just equal to power the traction power. If the energy stored in ESS
j in EPTD
j is less than the traction power, the energy stored in the ESS
j can be released completely. Then, the discharge power of EPTD
j can be calculated as follows:
where
EES,j is the energy stored in ESS
j.
Case 2: PL,j < 0, PL,j+1 < 0
There is regenerative power in both power supply sections connected to the EPTD
j. If the available capacity of ESS
j in EPTD
j is sufficient, all the RBE in both power supply sections will be stored in ESS
j in EPTD
j. If the available capacity of ESS
j in EPTD
j is less than the regenerative power, only the RBE equal to the available capacity of ESS
j will be stored in ESS
j. Then, the charge power of EPTD
j can be calculated as follows:
where
CES,j is the overall capacity of the ESS
j.
Case 3: PL,j > 0, PL,j+1 < 0
(i) if |PL,j|≥ |PL,j+1|
In this situation, the traction power on the
j power supply section is more than the regenerative power on the
j + 1 power supply section. First of all, the regenerative power is delivered from the
j + 1 power supply section to the
j power supply section to supply the traction power, and then the remaining traction power on the
j power supply section will be supplied by ESS
j. If there is sufficient RBE, ESS
j will release the energy just equal to power the traction power. If the energy stored in ESS
j in EPTD
j is less than the traction power, the energy stored in ESS
j can be released completely. Then, the discharge power of EPTD
j can be calculated as follows:
(ii) if |PL,j|< |PL,j+1|
In this situation, the traction power on the
j power supply section is less than the regenerative power on the
j + 1 power supply section. First of all, the regenerative power is delivered from the
j + 1 power supply section to the
j power supply section to supply the traction power, and then the surplus regenerative power on the
j + 1 power supply section will be stored in the ESS
j. If the available capacity of ESS
j in EPTD
j is sufficient, the surplus RBE in the
j + 1 power supply section will be stored in the ESS
j in EPTD
j. If the available capacity of ESS
j in EPTD
j is less than the regenerative power, only the RBE equal to the available capacity of ESS
j will be stored in ESS
j. Then, the charge power of EPTD
j can be calculated as follows:
Case 4: PL,j < 0, PL,j+1 > 0
(i) if |PL,j|≥ |PL,j+1|
In this situation, the regenerative power on the
j power supply section is more than the traction power on the
j + 1 power supply section, similar to case 3(ii). After delivering the regenerative power via EPTD
j, the surplus regenerative power will be stored in the ESS
j. The charge power of EPTD
j can be calculated as follows:
(ii) if |PL,j|< |PL,j+1|
In this situation, the regenerative power on the
j + 1 power supply section is less than the traction power on the
j + 1 power supply section, similar to case 3(i). After delivering the regenerative power via EPTD
j, the remaining traction power will be supplied by the ESS
j. The discharge power of EPTD
j can be calculated as follows:
The LCs use the above decentralized control steps to control each PTD and EPTD separately, which can realize the utilization of RBE. In the decentralized control, the LCs can autonomously operate without communication with the EMS. Each LC independently uses the local available information to control the operation of each PTD and EPTD. Nevertheless, the decentralized control can achieve only the local instead of global optimal utilization of RBE. In fact, the decentralized control strategy is similar to the first step in the centralized control strategy, so the decentralized control cannot achieve the global optimal utilization of RBE. Due to the independent operation between the LCs, there may be surplus RBE in a certain local area. At this time, the surplus RBE can only be fed back to the public grid, so that part of the RBE cannot be utilized within the railway. Accordingly, the disadvantage of decentralized control is that it cannot achieve global optimal control, but even so, it can still ensure a part of the RBE can be utilized within the railway. Therefore, the addition of decentralized control can make the modified system still operate when the centralized control strategy fails, thus enhancing the reliability of the modified system.