Investigate on a Simpliﬁed Multi-Port Interline DC Power Flow Controller and Its Control Strategy

: A DC power ﬂow controller (DCPFC) can help to facilitate power ﬂow routing in the multi-terminal high-voltage direct current (HVDC) transmission system. Realizing its multi-port output can e ﬀ ectively improve the device regulate range and capability. Based on analysis of the traditional multi-port interline DC power ﬂow controller (MI-DCPFC), this paper presents a switches reduced topology of MI-DCPFC. In addition, for solving the problem of coupling of the port-output voltage of the traditional MI-DCPFC, a novel control strategy based on carrier phase shifting pulse width modulation (CPS-PWM) is proposed. It implements the decoupling of the port-output voltage of MI-DCPFC, which can ensure completely independent tracking of the power ﬂow regulating commands for di ﬀ erent controlled lines. Moreover, key relationships between the system state variables are also analyzed and detailed in this study. Finally, the performance of the proposed controller and control strategy are conﬁrmed with the simulation and experiment studies under di ﬀ erent conditions.


Introduction
Realizing the development and utilization of green and clean energy has become a major trend to solve problems such as traditional energy shortages and environmental degradation. To ensure the consumption and efficient use of the large scale new energy, effective transmission technology is needed as a support [1]. As the multi-terminal high-voltage direct current (HVDC) transmission system has the advantages of long transmission distance capability, large capacity and a flexible operation mode, etc., it has therefore become one of the main means to facilitate grid connections of large-scale renewable energy [2].
Unreasonable distribution of the transmission line currents can introduce unnecessary transmission line losses, or even an overload of the converter station. In order to facilitate the power flow management inside the DC transmission network, inspired by the idea of power flow control devices developed in the AC transmission system, such as a unified power-flow controller (UPFC) and thyristor controlled series compensator (TCSC), a DC power flow controller (DCPFC) can be introduced in the multi-terminal HVDC transmission system [3]. However, since the DC system does not have reactive power, reactance and phase angle, its power flow control can only be realized by adjusting the resistance or DC voltage Energies 2019, 12,2480 2 of 28 of the transmission line. Therefore, there are two general design approaches for the DCPFC, which are a resistance control type and a DC voltage control type.
(1) For the resistance control type DCPFC, different implementation schemes have been designed in reference [4] and reference [5]. This kind of control scheme is simple to implement, but it can only adjust the equivalent resistance of the line in one direction, which limits its power flow control ability.
(2) For the DC voltage control type DCPFC, according to the voltage regulation means, it can be further divided into three main types, which are 1 a DC transformer type [6][7][8][9][10], 2 an auxiliary voltage source type [11][12][13][14][15] and 3 a capacitor-based interline energy-exchanged type [3,[16][17][18][19][20][21][22][23][24]. In comparison, the DCPFC of capacitor-based interline energy-exchanged type has more advantages and better application prospects. For instance, it has fewer power devices; does not require an external power supply device; and can avoid withstanding the system-level high voltage and power, which help reduce the stress requirements of the power devices and system losses. Therefore, it has become a kind of DCPFC which is currently more researched and heavily focused on [3,20].
The capacitor-based interline energy-exchanged type DCPFC is usually called the interline DCPFC (IDCPFC). As shown in Figure 1, its main control idea is to exchange the power between different transmission lines by charging/discharging the capacitor of IDCPFC, thereby achieving the power flow control of the transmission lines. Based on the concept depicted in Figure 1a, two current flow controller (CFC) topologies were first proposed in reference [16], however, only the basic conceptualization is introduced, its working principles and control method are not investigated enough. Focus on one topology of the CFC, its control strategy and operation principles were discussed in reference [17]. Focus on the control method of another method was designed in references [18,19]. In addition, its operation states were analyzed, and an average mode which can be used for perform steady-state analysis was derived in reference [19]. Furthermore, in order to simplify the CFC circuit structure, an improved CFC topology was proposed in reference [20], and its characteristics were detailed compared to the traditional CFC topology proposed in reference [16]. Based on the concept depicted in Figure 1b, by increasing the DC capacitor number and introducing coupled inductors, a novel type of IDCPFCs with independent connections of the capacitor in two lines were respectively investigated in references [3,[21][22][23]. In reference [24], the application modular multilevel converter (MMC) device was also considered, and an MMC-based IDCPFC was proposed. These schemes in reference [3,[21][22][23][24] avoided the capacitor switching in the line. However, it should be noted that all the above existing topologies are characterized by two-port characteristics, which can only assist in regulating the current on one line. If the power flow control of multiple lines is required at the same time, the corresponding multi-port topology should be developed, and this problem is also an area that this paper deals with. in reference [4] and reference [5]. This kind of control scheme is simple to implement, but it can only adjust the equivalent resistance of the line in one direction, which limits its power flow 48 control ability.  [16][17][18][19][20]; (b) The dual-capacitor control type in references [3,[21][22][23][24].
Currently, the research on multi-port IDCPFC (MI-DCPFC) is still in its infancy. Based on the MMC-based IDCPFC proposed in reference [24], a MI-DCPFC topology based on MMC was developed in reference [25]. However, it requires multi-winding transformers and needs to connect MMC in each Energies 2019, 12, 2480 3 of 28 control line, which leads to higher system costs. In addition, with the controlled line number being increased, its circuit topology and control system become relatively complicated. In reference [26], a MI-DCPFC topology based on identical insulated gate bipolar transistor (IGBT) half-bridge was proposed. Its system structure is simple, and the cost of the port expansion is low. However, as only a basic control method is introduced, it can not achieve independent tracking of the current regulation commands for each transmission line, where the power flow regulating has limited freedom.
Combining the precious work in reference [26], this paper presents a switches reduced topology of MI-DCPFC. In addition, for solving the problem of coupling of the port-output voltage of the traditional MI-DCPFC, a novel control strategy based on carrier phase shifting pulse width modulation (CPS-PWM) is proposed. This strategy achieved the decoupling of the port-output voltage, which can ensure independent tracking of the power flow regulating commands for different controlled lines. Moreover, key relationships between the system state variables were also detailed in this study. Finally, two five-terminal HVDC transmission systems were developed, and the performance of the proposed controller and control strategy were confirmed with the simulation and experiment studies under different conditions. The remainder of this paper is organized as follows: the traditional MI-DCPFC including its topology and control strategy is analyzed in Section 2. The topology and operation principles of the simplified MI-DCPFC are analyzed in Section 3. The novel control strategy is designed and the relationships between the system state variables are discussed in Section 4. The simulation and experiment verifications are respectively carried out in Section 5 and 6. Finally, a conclusion is given in Section 7.

Multi-Terminal HVDC Transismion System
The following work actually can be applied to any high voltage direct current (HVDC) transmission system. For this study, in order to facilitate the verification of the three-and four-port multi-port interline DC power flow controller (MI-DCPFC) in the subsequent simulations and experiments, a monopole five-terminal HVDC transmission system, as shown in Figure 2, was adopted as an example to carry out the related analysis. The voltage source converter (VSC) 4 is set as the DC voltage regulator node, which operates in the constant DC voltage control mode; The VSC1-3 and VSC5 are set as power regulator nodes, which operate in the constant power control mode.

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half-bridge was proposed. Its system structure is simple, and the cost of the port expansion is low.

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However, as only a basic control method is introduced, it can not achieve independent tracking of 90 the current regulation commands for each transmission line, where the power flow regulating has 91 limited freedom.

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Combining the precious work in reference [26], this paper presents a switches reduced  Figure 4 shows the conduction diagrams of the traditional MI-DCPFC under working-mode 1.

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The shunt branches connected to the terminals P1, P2 and P3 are respectively named line 1, line 2 139 and line 3. According to the conduction states of the switches Sai, the working process can be 140 Figure 3. Topology of the traditional three-port MI-DCPFC [26].

Traditional Control Method
According to different line current directions and different control targets, there are total 12 working modes of the traditional three-port MI-DCPFC, which are shown in Table 1. Under the traditional control method, the switches S ai (i = 1, 2, 3) and S bi are pulsed by the obtained PWM signals under the forward and reverse direction, respectively. On this basis, all other swtiches remain in the on or off state, where the specific conduction states of the switches S ci and S di are shown in the Table A1 in the Appendix A. Take the working-modes 1 and 6 as examples to provide further analysis, respectively.

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The shunt branches connected to the terminals P1, P2 and P3 are respectively named line 1, line 2 139 and line 3. According to the conduction states of the switches Sai, the working process can be 140 8 reverse I p2 I p1 and I p3 9 reverse I p3 I p1 and I p2 10 reverse I p1 and I p2 I p3 11 reverse I p1 and I p3 I p2 12 reverse I p2 and I p3 I p1 Figure 4 shows the conduction diagrams of the traditional MI-DCPFC under working-mode 1. The shunt branches connected to the terminals P 1 , P 2 and P 3 are respectively named line 1, line 2 and line 3. According to the conduction states of the switches S ai , the working process can be divided into the following two stages: Energies 2019, 12, 2480 5 of 28 (i) Stage 1: switches S ai are truned-off. During this period, as shown in Figure 4a, the current I p1 is charging the capacitor through the feedback diodes of S b1 and S c1 , while the currents I p2 and I p3 are flowing out directly through the S d2 , feedback diode of S b2 and S d3 , feedback diode of S b3 , respectively. (ii) Stage 2: switches S ai are truned-on. During this period, as shown in Figure 4b, the current I p1 is flowing out directly through the S a1 and feedback diode of S c1 , while the currents I p2 and I p3 are discharging the capacitor through S a2 , S d2 and S a3 , S d3 respectively. The charging and discharging states are kept interchanging to transfer the power from line 1 to lines 2 and 3. As a result, the the current I p1 is reduced, I p2 and I p3 are increased.

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(ii) Stage 2: switches Sai are truned-on. During this period, as shown in Figure 4b, the current Ip1 is  153 Figure 5 shows the conduction diagrams of the traditional MI-DCPFC under working-mode 6.
According to the conduction states of the switches Sai, the working process can also be divided into

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Concluding the analysis in the previous section, we found that:  Figure 5 shows the conduction diagrams of the traditional MI-DCPFC under working-mode 6. According to the conduction states of the switches S ai , the working process can also be divided into two stages. (i) Stage 1: switches S ai are truned-off. During this period, as shown in Figure 5a, the current I p2 and I p3 is charging the capacitor, while the current I p1 is flowing out directly. (ii) Stage 2: switches S ai are turned-on. During this period, as shown in Figure 5b, the current I p2 and I p3 was flowing out directly, while the currents I p1 was discharging the capacitor to transfer the power from lines 2 and 3 to line 1. As a result, the current I p1 was increased, while I p2 and I p3 were reduced.

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(ii) Stage 2: switches Sai are truned-on. During this period, as shown in Figure 4b, the current Ip1 is   According to the conduction states of the switches Sai, the working process can also be divided into

Summarizing of the Traditional Topology and Control Strategy
Concluding the analysis in the previous section, we found that: (1) When completing the conduction states selection for the switches S ci and S di in combination with Table A1, MI-DCPFC can achieve the power flow control by only pulsing the switches S ai or S bi under different working-modes. In addition, we can further observe that the switches S ai and S bi are always pulsed synchronously in the forward and reverse direction, respectively. Therefore, the switches S ai and S bi actually can be simplified as the upper switch and lower switch in one half-bridge, respectively. (2) In the working-mode 1, the reduction control of I p1 can be realized by pulsing the switches S ai with the obtained PWM signal. However, the lines 2 and 3 are always synchronized to discharge the capacitor, so the equivalent reverse polarity voltages introduced to the lines 2 and 3 are equal, which indicates that the specific increased amounts of the currents I p2 and I p3 cannot be controlled separately under the tradition control. (3) In the working-mode 6, the reduction control of I p2 and I p3 can be simultaneously realized by also pulsing the switches S ai . However, the lines 2 and 3 are always synchronized to charge the capacitor, so the equivalent forward polarity voltages introduced to the lines 2 and 3 are equal, which indicates that the specific reduced amounts of the currents I p2 and I p3 cannot be controlled separately under the tradition control. (4) Generalizing the conclusions (ii) and (iii), it shows that among all the lines connected to MI-DCPFC, if there are multiple line currents that will be increased, an improved control strategy needs to be proposed to ensure that their respective increased values can be controlled independently.
Similarly, if there are multiple line currents that will be reduced, the improved control strategy also needs to guarantee their respective reduced values can be independently controlled.

Topology
According to the analysis in conclusions (1) in Section 2.4, a simplified MI-DCPFC topology is presented in this study. Its specific circuit diagram is shown in Figure 6. For an n-port MI-DCPFC, it consists of n + 1 identical IGBT half-bridges and a DC capacitor C. S a and S b are the upper and lower switches of HB 0 , respectively. T ia and T ib (i = 1, 2... n) are the upper and lower switches of HB i , respectively. Terminal T is taken from HB 0 , and terminals P i are taken out from HB 1 to HB n , respectively, the terminal T and P i respectively compose n different output ports TP i of the MI-DCPFC. I Pi are the DC currents flowing into MI-DCPFC through the different transmission lines; I T is the DC current flowing out of MI-DCPFC.       When the simplified MI-DCPFC is connected to a multi-terminal HVDC transmission system, the diagram can also be depicted as Figure 2. It should be noted that the adopted five-terminal HVDC transmission system is unipolar, so it is only necessary to consider adding the DCPFC to the positive pole or negative pole of the system. However, for the bipolar system, in order to ensure the symmetry of the system, DCPFC needs to be simultaneously added to the positive and negative pole of the system.
In addition, compared with the traditional MI-DCPFC, in order to achieve independent control of the current of all controlled lines, the new working principle of the simplified MI-DCPFC needs to be considered, which is detailed in the next section.

Operation Principles
For easy analysis, a three-port simplified MI-DCPFC was adopted as an example, and the shunt branches connected to the terminals P 1 , P 2 and P 3 were also respectively named line 1, line 2 and line 3. Similar to the traditional MI-DCPFC, the three-port simplified MI-DCPFC has the same 12 working-modes, as shown in Table 1. In order to facilitate comparison with the traditional MI-DCPFC, we also chose working modes 1 (where control I p1 reduced; I p2 and I p3 increased) and 6 (where control I p1 increased; I p2 and I p3 reduced) to carry out detailed analysis.

Working-Mode 1
In this working-mode, according to the different conduction states of the switches in each half bridge, the working process of the MI-DCPFC can be divided into the following four stages. The conduction diagrams of the MI-DCPFC under this working-mode are depicted in Figure 7.    (i) Stage 1: turn on T 2b and T 3b . During this period, as shown in Figure 7a, the current I p1 is charging the capacitor through the feedback diodes of T 1a and S b , while the currents I p2 and I p3 are flowing out of the terminal T directly. (ii) Stage 2: keep T 2b and T 3b turned-on and turn on S a . During this period, as shown in Figure 7b, the current I p1 is flowing out of the terminal T directly, while the currents I p2 and I p3 are discharging the capacitor through T 2b , S a and T 3b , S a respectively. (iii) Stage 3: only keep T 3b and S a turned-on. During this period, as shown in Figure 7c, the currents I p1 and I p2 are directly flowing out of the terminal T, while the current I p3 continues to discharge the capacitor through T 3b and S a . (iv) Stage 4: only keep T 3b turned-on. During this period, as shown in Figure 7d, the currents I p1 and I p2 are charging the capacitor through the feedback diode of T 1a , S b and feedback diode of T 2a , S b respectively, while the current I p3 is flowing out of the terminal T directly.
With charging and discharging by the line currents, we assumed that the capacitor voltage of MI-DCPFC is balanced at U c . Concluding the analysis of the above, we can obtain the DC voltage introduced to the transmission line through the MI-DCPFC at various stages, as shown in Table 2.
It can be observed that compared to the traditional MI-DCPFC, the stages 3 and 4 are added by auxiliary pulsing the lower switch of HB 2 . Based on this, the equivalent reverse polarity voltage introduced to the line 2 can be independently regulated, which indicates that the specific increased amounts of the currents I p2 and I p3 can be controlled individually at this time.

Working-Mode 6
In this working-mode, according to the different conduction states of the switches in each half bridge, the working process of the MI-DCPFC can also be divided into the following four stages. (i) Stage 1: only turn on T 1b ; (ii) Stage 2: keep T 1b turned-on and turn on T 3b ; (iii) Stage 3: keep T 1b and T 3b turned-on and turn on S a ; (iv) Stage 4: only keep T 1b and S a turned-on. The conduction diagrams during stages 1 to 4 are shown in Figure 8a-d, respectively.
Referring the previous analysis method, we can obtain the DC voltage introduced into the transmission line at various stages under this working-mode, which are shown in Table 3. It can be found that with auxiliary controlling the lower switch of HB 3 in the simplified MI-DCPFC, the stages 2 and 3 are added to the operating process compared to the traditional MI-DCPFC. Based on this, the equivalent forward polarity voltages introduced to the lines 2 and 3 can be independently regulated, which indicates that the specific reduced amounts of the currents I p2 and I p3 can be controlled separately. In addition, according to the symmetry, when auxiliary pulsing the HB 2 lower transistor, we can also achieve the control of the I p1 that was increased and the I p2 and I p3 that were reduced.

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Referring the previous analysis method, we can obtain the DC voltage introduced into the 254 transmission line at various stages under this working-mode, which are shown in Table 3. It can be transistor, we can also achieve the control of the Ip1 that was increased and the Ip2 and Ip3 that were 261 reduced.

Other Working-Modes
As shown in Table 1, there are four other working-modes including 2, 3, 4 and 5 besides the above two analyzed working-modes. Similarly, when the current direction is reversed, six other working-modes are also derived. However, their working principles are similar to the analyzed working-modes 1 and 6. The corresponding switching state of each transistor under different working-modes can be analyzed in a similar way. However, it is worth noting that since this type of MI-DCPFC cannot realize the reverse control of line current, when it is actually applied to a multi-terminal HVDC transmission system, it is relatively more suitable for the "multi-to-one" (such as multiple green and new energy are aggregated) or "one-to-many" (such as powering multiple zones) type of interconnected transmission structure.
Furthermore, when the MI-DCPFC is extended to the other ports number, its main working principle is similar to that of the three-port MI-DCPFC, which is reasonable to use to charge/discharge the capacitor on the different transmission lines. We will summarize the general control method of an arbitrary port MI-DCPFC in Section 4.3.

CPS-PWM Control Strategy
As analyzed in the Section 2.4, in order to achieve simultaneous tracking of the different current regulation commands for multiple transmission lines, the normal operation of MI-DCPFC needs to meet two regulation requirements: (i) When multiple line currents are increased, achieve independent amplification control of each line current (control-mode 1); (ii) When multiple line currents are reduced, achieve independent reduction control of each line current (control-mode 2).
To solve this problem, a control strategy that is easier to implement based on the CPS-PWM control was designed. Firstly, we describe the specific implementation of the two control-modes detailed in combination with the three-port MI-DCPFC.

Control-Mode 1
Combined with the previous analysis in Section 3.2.1, it can be seen that when MI-DCPFC is operating in working-mode 1, it is necessary to coordinate the amplification control of I p2 and I p3 by using the control-mode 1. Taking tracking the power flow regulating command of I p2 as an example, the control block diagram is shown in Figure 9. I p1 * is the regulation command of the current of line 1. It subtracts the sampling current I p1 , where the error is sent to a PI regulator. Its output is compared with the triangular carrier, thereby obtaining the driving pulse of transistor S a . Meanwhile, the next step involves tracking the error between the regulation command I p2 * and sample current I p2 of line 2 with a PI regulator, and then scaling it by the coefficient k 1 (k 1 = −T s /2, where T s is the carrier period) to obtain the phase-shifted value of the original carrier. Finally, when comparing the phase-shifted carrier with the duty D of pulse signal of S a , the driving pulse of transistor T 2b can be obtained by NXORing the result with the pulse signal of S a .

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To solve this problem, a control strategy that is easier to implement based on the CPS-PWM 285 control was designed. Firstly, we describe the specific implementation of the two control-modes 286 detailed in combination with the three-port MI-DCPFC.

Control-Mode 2
When the MI-DCPFC is operating in working-mode 6, it needs to achieve the reduction control of I P3 synchronized with the I P2 reduction control by the control-mode 2. The control block diagram is shown in Figure 10

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To solve this problem, a control strategy that is easier to implement based on the CPS-PWM 285 control was designed. Firstly, we describe the specific implementation of the two control-modes 286 detailed in combination with the three-port MI-DCPFC.     Similarly, we used the PI regulator tracking the correction current on line 2 and then comparing with the triangular carrier to obtain the drive pulse of the switch S a . Also, we used the PI regulator tracking the correction current on line 3 and scaling it by the coefficient k 2 (k 2 = T s /2) to obtain the phase-shifted value. Finally, the phase-shifted pulse signal XORs with the pulse signal of S a can obtain the T 3b drive pulse.

Relationship of the System State Variable
According to Figure 9, the timing chart diagram of the driving pulses under control-mode 1 can be obtained as Figure 11a.
obtain the phase-shifted value. Finally, the phase-shifted pulse signal XORs with the pulse signal of Sa can obtain the T3b drive pulse.

Relationship of the System State Variable
According to Figure 9, the timing chart diagram of the driving pulses under control-mode 1 can be obtained as Figure 11a.
corresponds to the stage 3 of working-mode 1. Further, the following equations can be established 320 by combining Figure 7c: Where V is DC side voltage of the converter node to which the terminal T is connected. V1, V2,

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By defining x T = [iP1, iP2, iP3, uc] as the state variable of the system, the equations (1) to (4) can be 327 rewritten to a matrix form, as shown in equation (5). Assuming that the phase-shifted time is t 1 , T 3b and S a will be in the on-state during 0-t 1 , which corresponds to the stage 3 of working-mode 1. Further, the following equations can be established by combining Figure 7c: where V is DC side voltage of the converter node to which the terminal T is connected. V 1 , V 2 , and V 3 are the DC side voltages of the converter nodes to which the terminal P 1 , P 2 and P 3 are connected, respectively. R 1 , R 2 , R 3 and L 1 , L 2 , L 3 are the equivalent resistance and inductance values of the transmission lines 1 to 3, respectively. i P1 , i P2 , i P3 are the instantaneous current of the transmission lines 1 to 3, respectively. u c is the capacitor voltage of the MI-DCPFC.
By defining x T = [i P1 , i P2 , i P3 , u c ] as the state variable of the system, the Equations (1)-(4) can be rewritten to a matrix form, as shown in Equation (5). where: Besides, it is easy to observe that the time periods t 1 -t 2 , t 2 -t 3 and t 3 -T s in Figure 11a correspond to stage 2, stage 4 and stage 1 in the working-mode 1, respectively. Therefore, the system matrix equations in each time period can be written as Equations (7)-(9) in the same way, respectively.
In order to facilitate the subsequent analysis, the coefficient λ is introduced to establish the quantitative relationship between the phase-shifted time t 1 and the duty ratio D of S a drive pulse: Combining Equation (10) and Figure 11a, we further obtained: Concluding Equations (5)-(13), the system state equation of MI-DCPFC in one control period T s can be integrated as: When the system is operating stable, the change of the state variable can be ignored, and the Equation (14) can be further written as: Solving the matrix equation shown in Equation (15), we can obtain the average capacitor voltage expression of the MI-DCPFC as: In the same way, we can obtain the timing chart diagram of the driving pulses under control-mode 2 firstly, as shown in Figure 11b. Then, the coefficient µ characterizing the phase-shifted time in this control-mode is introduced, where µ = (t 2 − t 1 )/DT s . Finally, the average capacitor voltage expression of MI-DCPFC under this case can be obtained as: Concluding Equations (16) and (17), it can be observed that when MI-DCPFC participates in the system power flow regulation, its capacitor voltage is related to the voltage drop and the rated parameters of the DC transmission line. This conclusion is also similar to the analysis results of the traditional CFC in reference [26]. In addition, it should be noted that as this type of MI-DCPFC cannot realize the reverse control of line current, the most extreme power regulation condition it faces is when all line currents are increased at the line with the largest line resistance. In other words, we can think that for the controlled lines, the capacitor voltage provided by DCPFC is the largest voltage under this condition. In this way, we can estimate the capacity design requirements of the MI-DCPFC, so as to ensure that it will not be damaged by the capacitor overvoltage when it is inserted into the system under normal operation. Furthermore, since this capacitor voltage is also the voltage level that the MI-DCPFC switches need to withstand, it can help to select the suitable switching devices.

Control Method Extension of an Arbitrary Port MI-DCPFC
In previous analysis, we take a three-port MI-DCPFC as the example, its basic working principle and implementation of control method are analyzed in detail. To make the results more general, we extend for an arbitrary port MI-DCPFC in this section.
Assuming that n shunt lines are connected to the MI-DCPFC, and m line currents need to control reduced, the other n − m lines currents that need to be controlled increased. This result can follow the following main control principles during the implementation process: (1) Selection of controlled lines: all lines that currents need to be reduced and nm + 1 lines that currents need to be increased are under an active-controlled state. In this way, by tracking the current regulation commands of n − 1 branches, the overall control of n line currents can be realized; (2) Generation of HB 0 drive pulse: to appropriately balance the carrier phase-shifted margin between both of the control-modes, the branch that he current reduced was centered among the m branches can be selected as a reference, and then generated the drive pulse of HB 0 ; (3) Generation of HB i drive pulse: on this basis of step (2), the remaining n − 2 active-controlled branches are tracking the current reduced and increased regulation commands through the control-mode 1 and -mode 2, respectively. Then generate the corresponding driving pulses of HB i , respectively. In addition, the upper and lower switches of the only one branch that remained are kept turned-off and turned-on, respectively.
According to the above ideas, it should be assumed that the branches 1 to m are current reduced lines, and the branches m + 1 to n are current increased lines. Taking the forward current direction as the example, Figure 12 shows the overall control block diagram of the MI-DCPFC when the branch 1 is adopted as the reference branch.

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According to the above ideas, it should be assumed that the branches 1 to m are current 379 reduced lines, and the branches m + 1 to n are current increased lines. Taking the forward current 380 direction as the example, Figure 12 shows the overall control block diagram of the MI-DCPFC when 381 the branch 1 is adopted as the reference branch.

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To confirm the proposed MI-DCPFC topology and control strategy, the related verification was Figure 1 (repainting it as Figure 13a) and a more complicated five-terminal HVDC transmission 386 system with four-port MI-DCPFC as shown in Figure 13b were developed, respectively.

Simulation Results
To confirm the proposed MI-DCPFC topology and control strategy, the related verification was carried out in MATLAB/SIMULINK. The five-terminal HVDC transmission system as shown in Figure 1 (repainting it as Figure 13a) and a more complicated five-terminal HVDC transmission system with four-port MI-DCPFC as shown in Figure 13b were developed, respectively.   Table 4.  The converter node VSC4 controls the systems DC bus voltage at 200 kV. The converter nodes VSC1 to VSC3 and the converter node VSC5 respectively inject P1 = 80 MW, P2 = 100 MW, P3 = 60 MW and P5 = 80 MW active power into the system. The main parameters of each transmission line are shown in Table 4. The working-mode 1 (I 14 is reduced; I 24 and I 34 are increased) was verified in this case. In addition, to make it easy to compare and analyze each one, the simplified MI-DCPFC with the traditional and novel control methods were both tested, respectively.
The performance of the MI-DCPFC with the traditional control method in this case is shown in Figure 14a-c. The MI-DCPFC is accessed into the system at 0.2 s, and with the command controlling line.14 current reduces to I 14 = 0.1 kA. It can be seen that before adjusting the line currents, the system is operating at a stable rate, and the values of each line current are about I 14 = 0.35 kA; I 24 = 0.62 kA; I 34 = 0.23 kA; I 45 = 0.40 kA; I 12 = 0.06 kA; I 23 = −0.07 kA, respectively. When the MI-DCPFC is inserted to the system at 0.2 s, the controlled line current I 14 quickly respond to the command value and maintain stable operation, as shown in Figure 14a. In addition, as shown in Figure 14b,c, the voltage V TP1 introduced in the line 14 is stably switched between 0 and U c ; while the voltages introduced in line 24 and line 34 are synchronized to switch between 0 and −U c , so I 24 and I 34 automatically respond to I 24 = 0.82 kA and I 34 = 0.28 kA, respectively. We found that the specific increased amounts of the currents I 24 and I 34 cannot be controlled separately at this time, which is consistent with the theoretical analysis in the previous section.
The performance of the MI-DCPFC with the novel control method is shown in Figure 14d-g. The MI-DCPFC is inserted to the system at 0.2 s, and with the command in control, I 14 reduces to I 14 = 0.1 kA and I 24 remains unchanged. When operating to 1.2 s, the regulation command is re-changed, where with controlling I 14 reduced to 0.1 kA, but control I 24 increases to 0.7 kA. It can be observed that when the MI-DCPFC is accessed in the system, the controlled line current I 14 can also quickly respond to I 14 = 0.1 kA and maintain stable operation, as shown in Figure 14d. What is more, it can be found that unlike with the traditional control method, as the voltage V TP2 introduced in the line24 can be controlled and stably switched between U c , 0 and −U c , so the increased amounts of the current I 24 can be controlled freely at the same time.
The above simulation results show that the simplified MI-DCPFC with the novel control strategy can achieve the power flow control quickly and stably under the working-mode 1. Furthermore, when compared to the traditional control strategy, on the basis of the reducing control of the line current, the increased value of other line currents can be also controlled freely at the same time. In addition, the capacitor voltage fluctuation is small, and the voltage state introduced in the connection line by the output port is consistent with the theoretical analysis.

Case 2
The working-mode 6 (I 24 and I 34 are reduced; I 14 is increased) was verified in this case. Similarly, to make it easy to compare and analyze the simplified MI-DCPFC with the traditional and novel control methods were tested, respectively.
The performance of the MI-DCPFC with the traditional control method in this case is shown in Figure 15a-c. The MI-DCPFC is accessed into the system at 0.2 s, and with the command controlling line 34, the current reduces to I 34 = 0.15 kA. It can be observed that the controlled line current I 34 quickly responds to the command value and maintains stable operation when the MI-DCPFC is accessed in the system at 0.2 s, as shown in Figure 15a. However, as shown in Figure 15b,c, since the voltage V TP2 introduced in the line 24 and voltage V TP3 introduced in line 34 are synchronized to switch between 0 and U c , although the I 34 is also reduced, its specific reduced amounts cannot be controlled separately at this time.

467
In order to further test the performance of the MI-DCPFC, the verification of a four-port 468 MI-DCPFC was carried out. When the system starts up normally, it is tested with the following 469 three different conditions, and the performance of the MI-DCPFC is shown in Figure 16; the 470 measurement values of each line current under different test conditions are shown in Table 5. The performance of the MI-DCPFC with the novel control method is shown in Figure 15d-g. The MI-DCPFC is accessed in the system at 0.2 s, and with the command in control, I 24 and I 34 are reduced to I 24 = 0.5 kA and I 34 = 0.15 kA, respectively. When operating to t 4 , the power flow control command is re-changed, where with controlling occurring, I 34 was reduced to 0.15 kA, but control I 24 further reduces to 0.4 kA. It can be observed that when the MI-DCPFC is accessed in the system, the controlled line current I 34 quickly responded to I 34 = 0.15 kA and maintained stable operation, as shown in Figure 15d. What is more, the reduced amounts of the current I 24 can simultaneously be controlled freely with the reducing control of I 34 . Correspondingly, the voltage V TP2 introduced in the line 24 is controlled and stably switched between U c , 0 and −U c , as shown in Figure 15e-g.
The simulation results in this case show that the simplified MI-DCPFC with the novel control strategy can achieve the power flow regulation quickly and stably under the working-mode 6. Furthermore, compared to the traditional control strategy, independent reduction control of each line current can be achieved when multiple line currents are reduced. Meanwhile, the capacitor voltage fluctuation is small, and the voltage state introduced in the connection line by the output port is consistent with the theoretical analysis.

Four-Port MI-DCPFC Verified Results
In order to further test the performance of the MI-DCPFC, the verification of a four-port MI-DCPFC was carried out. When the system starts up normally, it is tested with the following three different conditions, and the performance of the MI-DCPFC is shown in Figure 16; the measurement values of each line current under different test conditions are shown in Table 5.   It can be observed that under the different control conditions, the controlled lines can all quickly track the corresponding power flow control commands, and then maintain stable operation. In addition, we can note that in the test conditions 1 and 3, MI-DCPFC only operates in control-mode 1 and control-mode 2, respectively; in test condition 2, control-mode 1 and -mode 2 participate in the regulation work simultaneously.
Concluding all previous simulation studies in this section, it can be seen that with the CPS-PWM control strategy proposed in this paper, the simplified MI-DCPFC can achieve effective power flow control under different power flow regulation requirements and its response speed is faster.

Experiments
To verify the proposed MI-DCPFC topology and control strategy, the five-terminal HVDC transmission system consistent with the simulation was built in the laboratory. Figure 17 shows the photograph of the platform. Each module in the Units 1 to 3 has half-bridge and full-bridge as two different topology modes that could be selected. Different MI-DCPFC topologies can be formed by an appropriate selection and combination, as shown in Table 6. VSC1-VSC5 adopts a ITECH programmable digital power IT series, where VSC4 controls the systems DC bus voltage at 80 V; VSC1 to 3 and VSC5 respectively inject I 1 = 8 A, I 2 = 10 A, I 3 = 6 A and I 5 = 8 A into the system. The transmission line parameters are shown in Table 7. In addition, in order to facilitate the comparison and verification of the simulation results, the verified cases in the experiment are the same as for the simulation.     Table 6. Implementation of the MI-DCPFC topology in the experiment.

519
performance of the MI-DCPFC with the traditional control method in this case is shown in Figure   520 19a-c. The MI-DCPFC is accessed into the system at t1, and with the command controlling I14 521 reduces to I14 = 2 A. It can be seen that before adjusting the line currents, the system is operating in a 522 stable manner. When the MI-DCPFC is inserted to the system at t1, the controlled line current I14 523 quickly responded to the command value and maintained stable operation, as shown in Figure 19a.

524
In addition, as shown in Figure 19b The working-mode 1 (I 14 is reduced; I 24 and I 34 are increased) was confirmed in this case. The performance of the MI-DCPFC with the traditional control method in this case is shown in Figure 19a-c. The MI-DCPFC is accessed into the system at t 1 , and with the command controlling I 14 reduces to I 14 = 2 A. It can be seen that before adjusting the line currents, the system is operating in a stable manner. When the MI-DCPFC is inserted to the system at t 1 , the controlled line current I 14 quickly responded to the command value and maintained stable operation, as shown in Figure 19a. In addition, as shown in Figure 19b,c, the voltage V TP1 introduced in line 14 stably switched between 0 and U c ; the voltages introduced in line 24 and line 34 were synchronized to switch between 0 and −U c , so I 24 and I 34 automatically responded to I 24 = 16.8 A and I 34 = 6 A respectively, where the specific increased amounts of the currents I 24 and I 34 cannot be controlled separately at this time.   Figure   533 19(e); (g) enlarged view 2 of Figure 19(e).

534
The performance of the MI-DCPFC with the novel control method is shown in Figure 19d-g.

535
The MI-DCPFC is inserted to the system at t2, and with the command in control, I14 reduces to I14 = 2

536
A and I24 remains unchanged. When operating to t3, the regulation command is re-changed, where 537 with controlling I14 reduced to 2 A, but control increased I24 to 15 A. It can be observed that when 538 the MI-DCPFC is accessed into the system, the controlled line current I14 also quickly responded to 2

539
A and maintained stable operation, as shown in Figure 19d. What is more, unlike with the The performance of the MI-DCPFC with the novel control method is shown in Figure 19d-g. The MI-DCPFC is inserted to the system at t 2 , and with the command in control, I 14 reduces to I 14 = 2 A and I 24 remains unchanged. When operating to t 3 , the regulation command is re-changed, where with controlling I 14 reduced to 2 A, but control increased I 24 to 15 A. It can be observed that when the MI-DCPFC is accessed into the system, the controlled line current I 14 also quickly responded to 2 A and maintained stable operation, as shown in Figure 19d. What is more, unlike with the traditional control method, since the voltage V TP2 introduced in line 24 can be controlled stably switched between U c , 0 and −U c , the increased amounts of the current I 24 can also be controlled freely at the same time. The working-mode 6 (I 24 and I 34 are reduced; I 14 is increased) was confirmed in this case. The performance of the MI-DCPFC with the traditional control method in this case is shown in Figure 20a-c. The MI-DCPFC is accessed into the system at t 4 , and with the command controlling I 34 reduces to I 34 = 3 A.
Energies 2016, 9, x FOR PEER REVIEW 23 of 28 switched between Uc, 0 and −Uc, the increased amounts of the current I24 can also be controlled 542 freely at the same time. The working-mode 6 (I24 and I34 are reduced; I14 is increased) was confirmed in this case. The

545
performance of the MI-DCPFC with the traditional control method in this case is shown in Figure   546 20a-c. The MI-DCPFC is accessed into the system at t4, and with the command controlling I34  It can be observed that the controlled line current I 34 quickly responded to the command value when the MI-DCPFC was inserted to the system at t 4 , as shown in Figure 20a. However, as shown in Figure 20b,c, as the voltage V TP2 introduced in line 24 and voltage V TP3 introduced in line 34 were synchronized to switch between 0 and U c , although the I 34 is also reduced, its specific reduced amounts could not be controlled separately at this time.
The performance of the MI-DCPFC with the novel control method is shown in Figure 20d-g. The MI-DCPFC is accessed into the system at t 5 , and with the command controlling I 24 and I 34 are reduced to I 24 = 3 A and I 34 = 10 A, respectively. When operating to t 6 , the power flow control command is changed again, where with controlling, I 34 reduced to 3 A, but control further reduces I 24 to 8A. It can be observed that when the MI-DCPFC is accessed into the system, the controlled line current I 34 also quickly responded to 3 A, as shown in Figure 20d. What is more, the reduced amounts of the current I 24 can simultaneously be controlled freely with the reducing control of I 34 . Correspondingly, the voltage V TP2 introduced in line 24 is controlled and stably switched between U c , 0 and −U c , as shown in Figure 20e-g.

System Test
With the topology of the transmission system shown in Figure 13b, Figure  It can be observed that the controlled line current I34 quickly responded to the command value 555 when the MI-DCPFC was inserted to the system at t4, as shown in Figure 20a. However, as shown 556 in Figure 20b,c, as the voltage VTP2 introduced in line 24 and voltage VTP3 introduced in line 34 were 557 synchronized to switch between 0 and Uc, although the I34 is also reduced, its specific reduced 558 amounts could not be controlled separately at this time.

559
The performance of the MI-DCPFC with the novel control method is shown in Figure 20d-g.

560
The MI-DCPFC is accessed into the system at t5, and with the command controlling I24 and I34 are 561 reduced to I24 = 3 A and I34 = 10 A, respectively. When operating to t6, the power flow control 562 command is changed again, where with controlling, I34 reduced to 3A, but control further reduces current I34 also quickly responded to 3A, as shown in Figure 20d. What is more, the reduced 565 amounts of the current I24 can simultaneously be controlled freely with the reducing control of I34.   The four-port MI-DCPFC is confirmed in this section. Same as the simulation, the following 579 three different cases are respectively confirmed when the system starts up normally. 580 1) At t1, control I14 reduces to 1 A, and control I24 and I45 increase to 14 A and 10 A, respectively; 581 2) At t2, control I14 and I45 reduce to 4 A and 6 A, respectively; and control I24 increases to 14 A;

583
The main experiment results are shown in Figure 22; the measurement values of each line 584 current under different test conditions are shown in Table 8. It can be observed that under the

Case Studies
The four-port MI-DCPFC is confirmed in this section. Same as the simulation, the following three different cases are respectively confirmed when the system starts up normally.
(1) At t 1 , control I 14 reduces to 1 A, and control I 24 and I 45 increase to 14 A and 10 A, respectively; (2) At t 2 , control I 14 and I 45 reduce to 4 A and 6 A, respectively; and control I 24 increases to 14 A; (3) At t 3 , control I 14 , I 45 and I 24 reduce to 4 A, 6 A and 8 A, respectively.
The main experiment results are shown in Figure 22; the measurement values of each line current under different test conditions are shown in Table 8. It can be observed that under the different control conditions, the controlled lines can all quickly track the corresponding power flow control commands, and then maintain stable operation. In addition, the capacitor voltage fluctuation is small, and the voltage state introduced in the connection line by the output port is stable.