Multiport DC–DC Autotransformer for Interconnecting Multiple High ...

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 12, DECEMBER 2015

Multiport DC–DC Autotransformer for Interconnecting Multiple High-Voltage DC Systems at Low Cost Weixing Lin, Member, IEEE, Jinyu Wen, Member, IEEE, and Shijie Cheng, Fellow, IEEE

Abstract—This paper proposes a multiport dc–dc autotransformer (multiport dc auto) that is used to interconnect multiple HVDC systems with different voltage levels. The multiport dc auto is able to reduce 50–80% the converter cost compared with conventional dc–ac–dc technology. Different from the conventional dc–ac–dc technology using magnetic coupling at the ac sides of the converters, there is direct electrical connection between the interconnected dc systems in the multiport dc auto. Such direct electrical interconnection significantly reduces the used power converters in the multiport dc auto. Taking interconnecting a ±250, ±320, and ±400 kV dc system with the rated exporting/importing dc power at each of the dc system being 500, 1000, and 1500 MW as an example, the conventional multiport dc–ac–dc technology requires a total of 3000 MW power converters while only 775 MW power converter is required in the multiport dc–dc autotransformer. The required power converter in the multiport dc–dc autotransformer is only 26% of the converter used in the conventional multiport dc–ac–dc technology. Cost and operating power loss is therefore significantly reduced. Index Terms—DC power systems, dc power transmission, dc–dc power conversion, HVDC converters, HVDC transmission.

I. INTRODUCTION ITH the increasing size of offshore power parks and the need for new interconnectors, there has be growing interest in developing dc grids in the Europe [1]–[5]. The Future European Super Grid will be developed using dc transmission as the ac transmission is already highly congested and incapable of integrating the intermittent nature of renewable energy sources [1]–[5]. In other countries such as China, large numbers of HVDC lines are now operating as point-to-point links. There would be significant operational and cost benefit if these lines could be interconnected or tapped on dc side [6]. A dc grid requires significant investment and will likely be completed in steps over many years [1]–[4]. A possible scenario is to first build point-to-point HVDC and regional multiterminal

W

Manuscript received September 18, 2014; revised December 12, 2014; accepted January 12, 2015. Date of publication January 29, 2015; date of current version August 21, 2015. This work was supported in part by the National Natural Science Foundation of China under Grant 51377067. Recommended for publication by Associate Editor J. H. R. Enslin. The authors are with the School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2015.2397172

HVDC systems which later may be connected and integrated to form a large dc grid [1]–[4]. As technology progresses, the planned HVDC links will be operating at different dc voltages from the existing ones [7]– [9]. DC–DC transformers are required to interconnect different dc voltage levels. There are also many conventional line commutated converters HVDC lines in operation. By using dc–dc transformers, it may be possible to interconnect these existing dc schemes with new voltage-source converter (VSC) HVDC converters to form hybrid multiterminal HVDC systems [9]. A number of dc–dc converters dedicated for HVDC application have been studied in the literature [10]–[20]. The study in [10] compares the cost and performance of the multilevel modular dc converter [11] and the modular dc–dc converter constructed by serial connection of multiple dual-active bridge units (DAB) [12]. Results show that the modular dc–dc converter based on DAB employs lower amount of semiconductors than the multilevel modular dc converter of [11]. The DAB is a conventional dc–ac–dc technology that all the transferred power requires a two stage ac/dc converting. High-power high-voltage dc/dc converters based on inductor– capacitor–inductor (LCL) resonant circuit were proposed in [13]–[15]. The LCL dc/dc converter is able to achieve highvoltage stepping ratio without the need of ac transformers. Because of the removal of ac transformers, the LCL dc/dc converter can be built by constructing two modular multilevel converters (MMC) and link the ac terminals of these two MMC using the LCL circuit. The LCL dc/dc converter is able to achieve high operating frequency around kilohertz without the capacity limit of ac transformer. While for the modular dc–dc converter based of DAB, a modularized structure is required as there is an upper power rating limit of each single high frequency ac transformer. Despite the above advantages, the LCL dc/dc converter is still a conventional dc/ac/dc technology that all of the transferred dc power will subject to a two stage ac/dc converting. The dc/dc converter presented in [16] using medium frequency ac transformer is also a conventional dc–ac–dc technology. In the conventional dc–ac–dc technology, the total required power converter is twice the amount of the interchanged power. As all the transferred power needs a two stage ac/dc converting, power loss of the conventional technology is high. Total power rating of the ac link is also high. A recent progress of the dc–dc transformer without full dc– ac–dc converting has been developed in [17]–[20]. They are mainly developed from the idea of using the lower voltage dc system to share part of the converter arms of a higher voltage

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LIN et al.: MULTIPORT DC–DC AUTOTRANSFORMER FOR INTERCONNECTING MULTIPLE HIGH-VOLTAGE DC SYSTEMS AT LOW COST

Fig. 1.

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Circuit diagram of the conventional multiport dc–dc converter.

MMC. The technologies presented in [17]–[20] are economically competitive to interconnect two dc systems of different voltage ratings. To interconnect multiple dc systems of different voltage ratings, one way is to interconnect each of the two dc systems by use of dc–dc converters. Such method requires large number of dc–dc converters and the interchanging power between different dc systems are not flexible. Another way is to use multiport dc–dc transformer. A number of multiport dc–dc transformer have been proposed in the literature [21]–[27], but they are not dedicated for use at the HVDC level but mainly dedicated to be use at distribution level for integration of distributed renewable sources, electric vehicles, energy storage or photovoltaic panels. The multiport dc–dc transformer based on multiport ac transformer of [27] can be extended to be used at HVDC level if high-power high-voltage ratings multiport ac transformers are used. Though, it is still conventional multiport dc–ac–dc technology. The multiport LCL dc hub proposed in [28] is able to be used at the HVDC level. It employs an LCL circuit to interconnect ac terminals of multiple VSCs of the same or different voltage levels. Power transfer between the interconnected dc systems requires a full dc–ac–dc converting (two-stage ac/dc). In order to provide link between multiple dc systems of different voltage levels at relatively low cost, a multiport dc–dc autotransformer technology that can significantly reduce the used power converter is proposed in this paper. II. BASIC TOPOLOGIES A. Topology of the Conventional Multiport DC–AC–DC Converter Fig. 1 shows the topology of a conventional multiport dc–dc converter employing the dc–ac–dc converting technology. It is used to interconnect four dc systems with voltages E1 –E4 . The four dc systems are simply represented by dc voltage sources. Four converters (preferably VSCs) are used to, respectively, link the dc side of the four dc systems. AC sides of the VSCs are connected through ac link. Depends on the employed technology, the ac link could employ a multiport LCL circuit [28], multiple port ac transformer [27] or multiple two-port ac transformers connected at the ac sides [16]. Taking E1 and E2 transferring power to E3 and E4 as an example, the transferred power will be first converted from dc to ac by VSC1 and VSC2, transferred to ac side of VSC3 and

Fig. 2.

Circuit diagram of a three-port dc–dc autotransformer.

VSC4 through “ac link” and then rectified from ac to dc by VSC3 and VSC4. All the transferred power needs a two-stage ac/dc converting. The total required power converters and the power loss of such technology are high. The linking through ac transformer is known as magnetic coupling; there is no direct electrical connection between the dc systems. B. Topology of the Multiport DC–DC Autotransformer Fig. 2 shows the circuit diagram of the proposed multiport dc–dc autotransformer (multiport dc auto). A three-port dc autotransformer is illustrated. It is used to interconnect three dc systems with voltage levels E1 , E2 , and E3 , E1 < E2 < E3 . The three-port dc auto is mainly composed by serial connection of five VSCs VSC1– VSC5. DC terminals of VSC3 are connected to the dc terminals of E1 . The positive terminal of VSC2 and negative terminal of VSC4 are, respectively, connected to the positive and negative terminals of E2 . The positive terminal of VSC1 and negative terminal of VSC5 are, respectively, connected to the positive and negative terminals of E3 . Depending on the application field, the VSCs can employ the conventional two-level/three-level VSC topology or MMC topology. AC terminals of VSC1–VSC5 are connected to a common ac bus Bus through certain ac components such as transformer or phase reactor. Since VSC1, VSC2, VSC4, and VSC5 employ asymmetrical monopole topology, a Y/Δ connected transformer is used to interface ac terminals of these converters to eliminate the dc bias at the dc side. Comparing Figs. 2 with 1, we can see that there is direct electrical connection between E1 , E2 , and E3 through the dc sides of the VSCs, while there is only magnetic coupling in the conventional dc–ac–dc technology. In practical application, MMC is preferred to be used at each of the VSCs. Detailed circuit diagram of a three-port dc

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 12, DECEMBER 2015

Fig. 4.

Circuit diagram of a four-port dc–dc autotransformer.

Fig. 5.

Circuit diagram of two-port dc autotransformer.

Fig. 3. Circuit diagram of a three-port dc–dc autotransformer employing a three-phase MMC.

autotransformer employing MMC is shown in Fig. 3. In Fig. 3, each arm of the MMC is represented by a half-bridge submodule. Positive terminal and negative terminal of the five VSCs are successively connected in series. AC output of the MMC converters is connected to a three-phase common ac bus through ac transformer or phasor inductors. Fig. 4 further illustrates the circuit diagram of a four-port dc– dc autotransformer. In total, seven VSCs are used. The circuit diagram appears more complex than the conventional four-port dc–ac–dc technology shown in Fig. 1. It will be demonstrated later in this paper that the total used power converters in the multiport dc auto are only around 30% the used power converters in the conventional multiport dc–ac–dc technology. C. DC Voltage Rating of Each of the VSCs in the Multiport DC Auto From the topology of the three-port dc–dc autotransformer shown in Fig. 2, dc voltage ratings of the five VSCs can be,

respectively, dimensioned as E3 − E 2 2 E2 − E 1 = 2

EVSC1 = EVSC5 = EVSC2 = EVSC4

(1)

EVSC3 = E1 . D. Power Flow Conclusion of Two-Port DC–DC Autotransformer Power flow conclusion of two-port dc–dc autotransformer will first be summarized to derive the power flow in a multiport dc auto. Fig. 5 shows the topology of a two-port dc–dc autotransformer. For better elaboration, the three converters are labeled as CON1, CON2, and CON3 in the two-port dc–dc autotransformer. Suppose E1 transfers PN power to E2 , output

LIN et al.: MULTIPORT DC–DC AUTOTRANSFORMER FOR INTERCONNECTING MULTIPLE HIGH-VOLTAGE DC SYSTEMS AT LOW COST

dc current of E1 is therefore idc1 = PN /E1 . The dc current injecting into E2 is idc2 = PN /E2 . From Kirchhoff’s current law, the dc current flowing into CON2 is idc1 –idc2 . The power inverted by CON2 is therefore   E1 Pcon2 = E1 (idc1 − idc2 ) = PN 1 − . (2) E2 As the power flows into the ac Bus equals the power flows out of Bus, the power rectified by CON1 and CON3 is half the value of the power inverted by CON2. Therefore,   PN E1 . (3) Pcon1,3 = 1− 2 E2 III. DECOMPOSED POWER FLOW ANALYSIS OF MULTIPORT DC AUTO A. Decomposition of the DC Power Transferred From E1 to E3 From the power flow conclusion of two port dc–dc autotransformer, a decomposed power flow analysis for the multiport dc auto will be first proposed in this section. Denote the power transferred from E1 to E3 as Pdc1 . For this component of dc power, the three-port dc auto shown in Fig. 2 can be viewed as a two-port dc auto. The serial connection of VSC1 and VSC2 functions as CON1 in the two-port dc auto. The serial connection of VSC4 and VSC5 in Fig. 2 functions as CON3. VSC3 functions as a CON2. According to (2), for Pdc1 , the power inverted by VSC3 is   E1 1 to 3 P3 = Pdc1 1 − . (4) E3 where the superscript “1 to 3 ” indicates E1 transferring dc power to E3 , the subscript “3 ” denotes VSC3. The power inverted by VSC1, VSC2 and VSC4, VSC5 because of Pdc1 are the same and expressed as   1 E1 1 to 3 1 to 3 P12 = P45 = − Pdc1 1 − . (5) 2 E3 In (5), the negative sign means that direction of the ac power is actually rectifying not inverting. The share of VSC1, VSC2, VSC4, and VSC5 for the power of (5) is proportional to the dc voltage ratings of each VSC illustrated in (1), therefore,   E3 − E2 1 E1 Pdc1 1 − P11 to 3 = P51 to 3 = − (6) E3 − E 1 2 E3   E2 − E1 1 E1 Pdc1 1 − . (7) P21 to 3 = P41 to 3 = − E3 − E 1 2 E3 B. Decomposition of the DC Power Transferred From E2 to E3 Denote the dc power transferred from E2 to E3 as Pdc2 . For Pdc2 , the serial connection of VSC2–VSC4 of Fig. 2 functions as CON2 of Fig. 5 while VSC1 and VSC5, respectively, functions as CON1 and CON3 of Fig. 5. The total inverted power of the

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serial connection of VSC2–VSC4 for the Pdc2 component is   E2 2 to 3 P234 = Pdc2 1 − . (8) E3 The share of VSC2, VSC3, and VSC4 for (8) is   E2 − E1 E2 2 to 3 = Pdc2 1 − P2 2E2 E3   E1 E2 Pdc2 1 − P32 to 3 = 2E2 E3   E2 − E1 E2 Pdc2 1 − . P42 to 3 = 2E2 E3 The inverted power of VSC1 and VSC5 for Pdc2 is   −Pdc2 E2 P12 to 3 = P52 to 3 = . 1− 2 E3

(9) (10) (11)

(12)

Adding up (4), (6), (7), (9)–(11), and (12) for each individual VSC, the net inverted power of each VSC is   Pdc1 + Pdc2 E2 Pac1 = Pac5 = − (13) 1− 2 E3 Pac2 = Pac4 = −

Pdc1 E2 − E1 2 E3

Pdc2 (E2 − E1 )(E3 − E2 ) (14) 2 E2 E3     E1 E1 Pdc2 E2 = Pdc1 1 − + . (15) 1− E3 E2 2 E3 +

Pac3

C. Demonstration of Decomposed Power Flow Analysis For the test three-port dc auto with its rated dc voltage and dc power of each port listed in Table II, there are four rated operating scenarios. 1) E1 exports 500 MW power; E2 exports 1000 MW power. 2) E1 exports 500 MW power; E2 imports 1000 MW power. 3) E1 imports 500 MW power; E2 exports 1000 MW power. 4) E1 imports 500 MW power; E2 imports 1000 MW power. Cases 1 and 4 are duality cases while cases 2 and 3 are also duality cases. Fig. 6 shows the decomposed power flow analyzing result of the three-port dc auto. Each VSC is denoted as a numbered box. The solid lines denote the power flow due to E1 exporting/importing 500 MW dc power while the dashed lines denote the power flow due to E2 exporting/importing 1000 MW dc power. In Fig. 6(a), for the 500 MW dc power transferred from E1 to E3 , 312.5 MW will be transferred by the direct electrical connection. The remaining 187.5 MW will first be inverted by VSC3 and then rectified by VSC1, VSC2 and VSC4, VSC5. In Fig. 6(a), for the 1000 MW dc power transferred from E2 to E3 , 800 MW will be transferred from E2 to E3 by the direct electrical connection while the remaining 200 MW will first be inverted by VSC2–VSC4 and then rectified by VSC1 and VSC5. We can see from the previous analysis that the majority of the power transfer in a multiport dc–dc autotransformer is achieved by the direct electrical connection.

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 12, DECEMBER 2015

TABLE I COMPARISON OF THE POWER LOSS RATIO AND COST Case P d c 1 (MW) P d c 2 (MW) P d c 3 (MW) P V

SC

1 (MW) PV S C 2 (MW) PV S C 3 (MW) PV S C 4 (MW) PV S C 5 (MW)

Power loss ratio

Converter cost

DC–AC–DC DC Auto DC–AC–DC DC auto (a) (b)

500 500

1000 −1000

−1500 500

−150 50

−21.875 −65.625

343.75 31.25

Fig. 7.

−21.875 −65.625

−150 50

1.85% 1.26%

0.42% 0.17%

330 M€

85.3 M€

General diagram for power flow analysis of four-port dc auto.

as 65.625 MW. Results of dimensioning the power and voltage rating of each of the VSC in the test three-port dc auto are listed in Table II. Fig. 6.

Decomposed power flow analyzing result of a three-port dc auto.

Fig. 6(b) and (c) shows the decomposed power flow analyzing result of operating cases 2 and 3 for the three-port dc autotransformer. D. Dimensioning of the Power Rating of VSCs From the Decomposed Power Flow Analysis For case 1, the two ac power components for VSC1, VSC3, and VSC5 are in the same direction; therefore, power of VSC1, VSC3, and VSC5 in this case reach the maximum values. Power rating of VSC1, VSC3, and VSC5 can therefore be dimensioned as 150, 343.75, and 150 MW. For cases 2 and 3, the two ac power components for VSC2 and VSC4 are in the same direction; therefore, power of VSC2 and VSC4 in these operating cases reaches the maximum values. Power ratings of VSC2 and VSC4 are the same and dimensioned

IV. DIRECT POWER FLOW ANALYSIS OF MULTIPORT DC–DC AUTOTRANSFORMER A. Direct Power Flow Analysis The decomposed power flow analysis is able to indicate the flow of each component of the dc power. However, it is not mathematically rigorous. For a four-port test dc autotransformer with its rated dc power and dc voltages listed in Table IV, there exist lots of operating cases. It is complex to get intuitive decomposed power flow diagram as shown in Fig. 6 to dimension power rating of each VSC. A direct power flow analysis is therefore proposed in this section. Fig. 7 shows the general diagram for direct power flow analysis of a four-port dc autotransformer. Denote the exported dc power from E1 , E2 , and E3 as P1 , P2 , and P3 . The output dc currents of E1 , E2 , and E3 are therefore P1 /E1 , P2 /E2 , and P3 /E3 . The dc current injecting into E4 is therefore (P1 + P2 + P3 )/E4 . From Kirchhoff’s current law, dc current

LIN et al.: MULTIPORT DC–DC AUTOTRANSFORMER FOR INTERCONNECTING MULTIPLE HIGH-VOLTAGE DC SYSTEMS AT LOW COST

TABLE II RATED DC VOLTAGES AND DC POWER OF A THREE-PORT TEST SYSTEM E1 ±250

E2 ±320

E3 ±400

P1 d c 500

P2 d c 1000

±250

TABLE III RATED DC VOLTAGES AND DC POWER OF EACH OF THE VSC IN THE THREE-PORT TEST SYSTEM VSC

E d c (kV)

P d c (MW)

VSC1 VSC2 VSC3 VSC4 VSC5 Total

80 70 500 70 80 /

150 65.625 343.75 65.625 150 775

P1 d c

P2 d c

P3 d c

P4 d c

±320

±400

±500

700

1000

1300

2000

      E1 E 1 E1 E1 E1 = 1− − − P1+ P2 + P3 .(23) E4 E2 E4 E3 E4

|P2 | ≤ P2N

(24)

|P3 | ≤ P3N (16)

iVSC2

P1 + P2 + P3 P3 = − E4 E3

(17)

iVSC3 =

P1 + P2 + P3 P3 P2 − − E4 E3 E2

(18)

iVSC4 =

P1 + P2 + P3 P3 P2 P1 − − − . E4 E3 E2 E1

(19)

The power rectified by VSC1–VSC4 is therefore calculated as E4 − E 3 E4 − E 3 = (P1 + P2 + P3 )(20) 2 2E4

−PVSC4 = −iVSC4 E1   P1 + P2 + P3 P3 P2 P1 = −E1 − − − E4 E3 E2 E1

E3

|P1 | ≤ P1N

iVSC1

E2 − E1 E2 − E 1 PVSC3 = iVSC3 = 2 2   P1 + P 2 + P 3 P3 P2 − − E4 E3 E2   E2 − E1 E2 − E 1 E2 − E 1 P1 − − P2 = 2E4 2E2 2E4   E2 − E1 E2 − E 1 − − P3 2E3 2E4

E3

Equations (20)–(23) subject to the following conditions:

P1 + P2 + P3 = E4

E3 − E2 E3 − E 2 = PVSC2 = iVSC2 2 2   P1 + P 2 + P 3 P3 − E4 E3  E3 − E2 E3 − E 2 E3 − E 2 P1 + P2 − = 2E4 2E4 2E3  E3 − E 2 − P3 2E4

E2

B. Dimensioning Power Rating Using Direct Power Flow Analysis

flowing through VSC1–VSC4 is

PVSC1 = iVSC1

TABLE IV RATED DC VOLTAGES AND DC POWER OF A FOUR-PORT TEST SYSTEM E1

P3 d c −1500

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|P1 + P2 + P3 | ≤ P4N

(25)

where P1N , P2N , P3N , and P4N are, respectively, the maximum exported/imported power of E1 , E2 , E3 , and E4 . For (20), the coefficients before P1 , P2 , and P3 are all positive values. Therefore, when |P1 + P2 + P3 | = P4N , PVSC1 reaches the maximum value. For (21), if P1 and P2 are in the same direction, P3 of the opposite direction, and in the meantime (25) is satisfied, PVSC2 reaches its maximum value. For (22), if P2 and P3 are in the same direction, P1 of the opposite direction and (25) is satisfied, PVSC3 reaches its maximum value. For (23), if P1 , P2 , and P3 are of the same direction and the larger the coefficient, the higher the values of P1 , P2 or P3 , PVSC4 reaches its maximum value. C. Case Study of Dimensioning Power Rating Using Direct Power Flow Analysis Substitute the rated dc voltages of Table IV into (20)–(23), we have

(21)

PVSC1 = 0.1(P1 + P2 + P3 )

(26)

PVSC2 = 0.08(P1 + P2 ) − 0.02P3

(27)

PVSC3 = 0.07P1 − 0.039375P2 − 0.0175P3

(28)

−PVSC4 = 0.5P1 + 0.28125P2 + 0.125P3 .

(22)

(29)

For (26), if P1 + P2 + P3 = 2000 MW, PVSC1 reaches its maximum value of 200 MW. For (27), if P1 = 700 MW, P2 = 1000 MW, and P3 = −1300 MW, PVSC2 reaches its maximum value of 162 MW. For (28), if P1 = 700 MW, P2 = −1000 MW, and P3 = −1300 MW, PVSC3 reaches its maximum value of 132.125 MW. For (29), if P1 = 700 MW, P2 = 1000 MW, and P3 = 300 MW, PVSC4 reaches its maximum value of 668.75 MW.

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TABLE V RATED DC VOLTAGES AND DC POWER OF EACH OF THE VSC IN THE FOUR-PORT TEST SYSTEM VSC VSC1 VSC2 VSC3 VSC4 VSC5 VSC6 VSC7 Total (dc auto) Total (Conventional)

E d c (kV)

P d c (MW)

100 80 70 500 70 80 100 / /

200 162 132.125 668.75 132.125 162 200 1657 5000

The design results of the four-port test dc auto are listed in Table V. A total of 5000 MW power converter is required for a four-port conventional dc–ac–dc technology while only 1657 MW power converter is required for the multiport dc–dc autotransformer technology. The total required power converter for the multiport dc auto is only 33% of the conventional dc– ac–dc technology. D. Cost and Loss Comparison With the Conventional Multiport DC–AC–DC System Power loss in the multiport dc–ac–dc and multiport dc–dc autotransformer is mainly composed by the losses at the MMC and losses at the transformer/phase reactor. Losses of MMC are mainly composed by valve conduction loss, valve switching loss, and arm inductor conduction. Losses of the transformer are mainly composed by the winding conduction loss and core loss. Losses of the phasor reactor are mainly composed by winding conduction loss as air core instead of iron core inductor will be used. According to the research results of Luth et al. [16], power loss ratio of a MMC converter, the transformer loss, and the phasor reactor loss are typically 0.48%, 0.48%, and 0.41% at 50 Hz. For the test three-port dc auto with its power flow shown in Fig. 5, the rightmost third and fourth columns of Table I compare the power loss ratio of the multiport dc–dc autotransformer and the conventional multiport dc–ac–dc technology. Only the operating cases 1 and 2 are analyzed as cases 3 and 4 are duality cases of cases 1 and 2. For the three-port dc–dc autotransformer, the VSC3 has the highest power rating. To reduce the cost of ac transformers, VSC3 is connected to the ac common bus through phasor reactor while the other VSCs are connected to the ac common bus through ac transformers. For the three-port dc–ac–dc system, the VSC interfacing the ±400 kV dc grid has the highest power rating. It is connected

V. CONTROL OF THE MULTIPORT DC–DC AUTOTRANSFORMER A. Control of the Common Bus AC Voltage AC voltage of the ac common bus of the multiport dc auto needs to be controlled to enable stable operating of the multiport dc auto. For the three-port dc–dc autotransformer shown in Fig. 2, VSC1 and VSC5 are used to control the common ac-bus voltage since they are interfacing E3 which has the highest voltage and power ratings. VSC3 is used to control the dc output power of E1 while VSC2 and VSC4 are used to control the dc output power of E2 . Alternatively, other control modes can be used, such as using VSC3 to control the ac voltage u or using VSC2 and VSC4 to control u.

(|PVSC1 | + |PVSC2 | + |PVSC4 | + |PVSC5 |)(0.48 + 0.48) + (|PVSC3 |)(0.48 + 0.41) 1500 (|Pdc1 | + |Pdc2 |)(0.48 + 0.48) + (|Pdc3 |)(0.48 + 0.41) = 1500

κauto = κdc−ac−dc

to the ac common bus through phasor reactor while VSCs interfacing the ±250 and ±320 kV dc grids are connected to the ac common bus through ac transformers. In Table I, Pdc1 , Pdc2 , and Pdc3 are, respectively, the output dc power of E1 , E2 , and E3 , which are rectified/inverted by the VSCs in the multiport dc–ac–dc. PVSC1 –PVSC5 are the inverted power of VSC1–VSC5 in the dc autotransformer. We can see from the rightmost third and fourth columns of Table I that power loss ratio of the multiport dc auto is significantly lower than multiport dc–ac–dc, typically only 20% of the conventional dc–ac–dc technology for the three-port test dc-auto with its parameters shown in Table II. Power loss ratio of the multiport dc autotransformer and dc– ac–dc is, respectively, calculated by equation (30) and (31) as shown on the bottom of the page. Where 1500 is the rated transferred power of the multiport dc–dc converter. For a test three-port conventional dc–ac–dc with rated dc power of each port shown in Table II, a total of 3000 MW power converters are required to enable each port freely interchange power with each other port. While as listed in Table III, the overall required power converters in the three-port dc auto is only 775 MW. According to the estimated price disclosed in [31]–[33], price of each 1 GW ac/dc VSC is 110 M€. Therefore, a total of 330 M€ is required for the conventional dc–ac–dc technology while only 85.3 M€ is required for the three-port dc autotransformer technology. It should be noted that the previous cost comparison is a rough comparison, as it does not consider the number of VSCs but only consider the power rating of the VSCs. Nevertheless, the rough cost comparison indicates that the multiport dc auto technology is promising to significantly reduce the cost of conventional multiport dc–ac–dc.

(30) (31)

LIN et al.: MULTIPORT DC–DC AUTOTRANSFORMER FOR INTERCONNECTING MULTIPLE HIGH-VOLTAGE DC SYSTEMS AT LOW COST

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Fig. 9 shows the control diagram of VSC3. VSC3 is used to control the dc output power of E1 . In Fig. 9, Pdcpu 1 is the output dc power of E1 in per unit values. Id3 and Iq 3 are the dq components of the ac current iac3 . Iq ref 3 is set to zero to reduce the reactive power circulating of VSC3. VSC2 and VSC4 are installed with similar dc power controller as Fig. 9.

Fig. 8.

Fig. 9.

C. System Reliability During Failure of a Converter

Control diagram of VSC1.

Diagram of dc power controller.

With the dc voltage drop on the dc lines neglected, dynamics of the ac link of VSC1 is   E3 − E 2 d Md1 k1 = Ucd1 = R1 + L1 Id1 − ωo LIq 1 + Ud 2 dt   E3 − E 2 d k1 = Ucq 1 = R1 + L1 Mq 1 Iq 1 + ωo LId1 + Uq 2 dt (32) where Ud and Uq are the d and q components of the ac-bus voltage u. Ucd1 and Ucq 1 are the output ac voltage of VSC1 in the dq frame when reflected to the Bus side of the transformer. Id1 and Iq 1 are the dq components of the ac current iac1 , k1 is the turn ratio of the transformer, Md1 and Mq 1 are the dq modulation indexes of VSC1. R1 and L1 are, respectively, the resistance and leakage inductor of the ac transformer when reflecting to the common ac-bus side. Measuring points of the currents and voltages are shown in Fig. 2. Equation (32) indicates Ud can be increased by increasing Md1 while Uq can be increased by increasing Mq 1 . Fig. 8 shows the control diagram of VSC1. The subscript “pu” denotes variables are in per unit; the subscript “1” denotes VSC1. A voltage-controlled oscillator is used to provide reference angle for generating firing pulses of VSC1. To ensure secure operating of the VSCs, inner current control loop is also added in Fig. 8. B. Control of the DC Power Taking the three-port dc auto shown in Fig. 2 as an example, if the d component of iac2 is kept constant, iVSC2 is kept constant. Since idc1 = iVSC3 –iVSC2 , if iVSC3 is increased, idc1 can be increased therefore dc output power of E1 can be increased. Since E1 iVSC3 = 1.5Ud Id3 , by increasing Id3 , idc1 can be increased, the output dc power of E1 can therefore be increased.

Since all the converters are connected in series in the multiport dc auto, reliability issues arises if any of the converter fails. This section takes the three-port dc auto shown in Fig. 2 as an example to analyze the impact of tripping one converter on the operation of the remaining converters. The analysis will be confirmed by simulation in Section VI-D. If VSC1 or VSC5 fail, the remaining converters VSC2–VSC4 form a two-port dc–dc autotransformer (as shown in Fig. 5) that interconnects the dc grid E1 and the dc grid E2 . VSC3 can be used to control the ac voltage of the common ac bus while VSC2 and VSC4 can be used to control the transferred dc power between E1 and E2 (alternatively, VSC2 and VSC4 control the voltage of the common ac bus and VSC3 control the transferred dc power). Operation of the remaining converters in case of failure at VSC1 and VSC5 will not be affected. If VSC2 or VSC4 fail, VSC2 need to be bypassed from the multiport dc auto to provide dc current path between E1 and E3 . The dc grid E2 should also be disconnected from the multiport dc auto. After bypassing VSC2 and VSC4, the dc voltage difference between E3 and E1 are applied at VSC1 and VSC5 which exceeds the voltage rating of VSC1 and VSC5. Therefore, to enable VSC1 and VSC5 remain operation in case that VSC2 and VSC4 are unavailable, more submodules should be added in VSC1 and VSC5 to increase the voltage ratings of VSC1 and VSC5 from (E3 –E2 )/2 to (E3 –E1 )/2. Those additional submodules operate in bypass state in normal operation and are switched in when VSC2 and VSC4 are at fault. The additional submodules will increase the cost of the multiport dc auto but the overall cost of the multiport dc auto will still be competitive compared with conventional multiport dc–ac–dc. As in the conventional multiport dc–ac–dc, dc voltage ratings of VSC1 and VSC5 should be as high as E3 /2 while it is only (E3 –E1 )/2 in the multiport dc auto. If VSC3 fails, the VSC1 and VSC5 can be viewed as CON1 and CON3 in the two-port dc auto shown in Fig. 5. The serial connection of VSC2, E1 and VSC4 can be viewed as CON2 in Fig. 5. VSC1 and VSC5 can be used to maintain the ac voltage of the common ac bus while VSC2 and VSC4 are used to control the transferred dc power between E2 and E1 . Alternatively, control functions of these VSCs can be swapped. From the previous analysis, we can see that the most severe condition is that VSC2 and VSC4 are at fault which requires the voltage ratings of VSC1 and VSC5 to be increased in the design stage. Fault at VSC1, VSC5 or VSC3 will not significantly affect the normal operation of the remaining converters of the multiport dc auto.

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In practical operation, MMC will be preferred to construct the VSCs in the multiport dc auto. The MMC could be designed with high reliability by use of redundant power modules [30] so as to reduce the failure rate of the multiport dc auto. VI. SIMULATION VERIFICATIONS Simulations are carried in PSCAD/EMTDC to verify the technical feasibility of the multiport dc–dc autotransformer. Both the three-port test system and the four-port test system are simulated. DC power rating and dc voltage rating of the three-port and four-port systems are, respectively, listed in Tables II and IV where typical power and voltage ratings for dc system at HVDC levels are selected [29]. Each of the VSC is modeled using detailed equivalent models of MMC presented in [34] and [35]. Number of voltage levels of the three-port test dc auto for VSC1, VSC2, and VSC3 are, respectively, 51, 45, and 313 to make the rated submodule voltage close to 1.6 kV. Submodule capacitors and arm inductors are dimensioned according to B¨arnklau et al. [36]. A. E1 Power Flow Reverse of the Three-Port Test System Fig. 10 shows the simulation result of the three-port dc–dc autotransformer. E1 and E2 are used to control their respective dc power while E3 acts as the power balance port. From 0.2 to 0.6 s, output dc power orders of E1 and E2 are, respectively, increased from 0 to 500 MW and from 0 to 1000 MW. From 1.0 to 1.4 s, output dc power order of E1 is reversed from 500 to −500 MW, and power order of E2 remains unchanged. Fig. 10(a) shows the measured exported dc power of E1 and E2 and imported dc power of E3 ; we can see that the measured dc power follows their power orders. Fig. 10(b) shows the inverted ac power of the five VSCs in the three-port dc auto. With E1 and E2 exporting 500 and 1000 MW and E3 importing 1500 MW dc power, the measured inverted ac power of the VSCs is PVSC3 = 368 MW, PVSC2 = PVSC4 = −18.9 MW, PVSC1 = PVSC5 = −166 MW. The thetheory = 343.75 MW, oretical values shown in Fig. 6(a) are PVSC3 theory theory theory theory = PVSC5 = PVSC2 = PVSC4 = −21.875 MW, and PVSC1 −150 MW. The measured values are very close to the theoretical values. The difference is mainly caused by the inconsistency of the dc voltages. In the theoretical analysis, Vdc1 , Vdc2 , and Vdc3 are assumed to be equal to their rated values. While as shown in Fig. 10(c), the dc terminal voltages of the VSCs deviate from their rated values. We can also see from Fig. 10(a) and (b) that when the total dc power is 3000 MW, the total ac power of the five VSCs is 740 MW (368 + 18.9 ∗ 2 + 166 ∗ 2). Only 25% of the transferred dc power needs ac/dc converting. Power loss of the multiport dc–dc autotransformer is therefore significantly lower than the conventional multiport dc–ac–dc technology. There are oscillations at the dc power and dc voltages shown Fig. 10(a) and (c). Fig. 10(d)–(g) shows the waveform of the common bus ac voltage and the output current of VSC1–VSC3 at steady state during 0.8–0.9 s. Currents of VSC4 and VSC5 are not shown as they are almost the same as the currents of

Fig. 10. Simulation result of E 1 reverses its power flow in the three-port dc auto, (a) dc power, (b) ac power, (c) dc voltages, (d) Common bus ac voltage (u), (e) waveform of ia c 1 , (f) waveform of ia c 2 , (g) waveform of ia c 3 , and (h) THD of the common bus ac voltage and the currents i1 –i3 .

LIN et al.: MULTIPORT DC–DC AUTOTRANSFORMER FOR INTERCONNECTING MULTIPLE HIGH-VOLTAGE DC SYSTEMS AT LOW COST

Fig. 11. Simulation result of E 2 reverses its power flow in the three-port dc auto: (a) dc power and (b) ac power.

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Fig. 12. Simulation result of both E 1 and E 2 reverses their power flow in the three-port dc auto: (a) output dc power of each of the dc systems and (b) inverted ac power of each of the VSC.

VSC1 and VSC2. Measuring points of these signals are shown in Fig. 2. Fig. 10(d)–(g) shows that the voltages and currents are very close to sinusoidal waveforms. Fig. 10(f) summarizes the total harmonic distortion (THD) of the common ac-bus voltage and the ac currents. We can see that the THD of u, iac2 , and iac3 are well below 1% and the THD of iac1 is below 3%. Overall harmonic distortion at the ac line of the multiport dc–dc autotransformer is low. The oscillations shown in Fig. 10(a) and (c) might be caused by dc-side interactions and will be addressed in future work. B. E2 Power Flow Reverse of the Three-Port Test System Fig. 11 shows the simulation result with E2 reverses its dc power order during 1.0–1.4 s. We can see from Fig. 11(a) and (b) that the three-port dc–dc auto operates stably during E2 reversing its dc power. With E1 exporting 500 MW dc power, E2 importing 1000 MW dc power and E3 exporting 500 MW dc power, the total transferred dc power is 2000 MW while the total power of the five VSCs is only (47.8 ∗ 2 + 41 + 68.5 ∗ 2) = 274 MW. Only 14% of the transferred dc power needs ac/dc converting. C. E3 Power Flow Reverse of the Three-Port Test System Fig. 12 shows simulation result with both E1 and E2 reverse their dc power orders during 1.0–1.4 s. We can see from Fig. 12(a) and (b) that the three-port dc–dc autotransformer operates stably during such large power transfer reversal. D. Response to Failure of a Converter Fig. 13 shows system response to tripping VSC1 and VSC5 in the test three-port dc auto. Assume VSC1 and VSC5 are at fault at 1.0 s, firing pulses of all the insulated-gate bipolar transistors of VSC1 and VSC5 are blocked at 1.0 s. Fig. 13(a) and (b), respectively, shows the exported/imported dc power of

Fig. 13. System response to tripping of VSC1 and VSC5 in the test three-port dc auto: (a) dc power and (b) ac power.

each dc grid and the inverted power of each of the VSC. Before VSC1 and VSC5 subject to fault, both E1 and E2 are exporting 500 MW dc power while E3 is importing 1000 MW dc power. VSC3 is used to control the common bus ac voltage. Fig. 13(a) shows that the dc power imported by E3 drops to zero when VSC1 and VSC5 are tripped. E2 is able restore prefault power transfer capability within 100 ms after tripping VSC1 and VSC5. DC power of E1 automatically changes its direction to keep power balance of the dc auto. Fig. 13(b) shows the inverted power by each VSC. The power inverted by VSC1 and VSC5 (Pac1,5 ) drops to zero once VSC1 and VSC5 are tripped. Theoretical value of the power inverted by VSC3 after 1 s is 500 ∗ (1–250/320) = 109 MW, which matches the simulation result of Fig. 13(b). Fig. 14 shows system response to tripping of VSC3 at 1.0 s. Assume VSC3 is at fault at 1.0 s; all the firing pulses of VSC3 are then blocked at 1.001 s. E1 and E2 are, respectively, exporting

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Fig. 14. System response to tripping of VSC3 in the three-port dc auto: (a) dc power and (b) ac power.

500 and 1000 MW dc power before tripping VSC3 while E3 is importing 1500 MW dc power before 1.0 s. After tripping VSC3, VSC1 and VSC5 are used to control the common bus ac voltage while VSC2 and VSC4 are used to control the transferred dc power of E2 . Fig. 14 indicates that E2 is able to restore prefault power transfer capability after tripping VSC3. The dc power exported by E2 flows into both E1 and E3 . In such condition, one portion of the dc power exported by E2 is first inverted by VSC2 and VSC4 and then rectified by VSC1 and VSC5 which is then injected into E3 , a second portion of the dc power of E2 is also transferred to E3 through the direct electrical connection formed by the dc voltage E2 and the dc current of VSC1 and VSC5, a third portion of dc power of E2 is transferred to E1 through the direct electrical connection formed by the dc voltage E1 and the dc current of VSC2 and VSC4. Fig. 14(b) validates that VSC1 and VSC5 operate in rectifier mode after 1 s, VSC2 and VSC4 operate in inverter mode. The simulation result of Figs. 13 and 14 validate that the multiport is able to achieve high reliability. Fault at a single converter will not take down the entire system. The response to tripping of VSC2 and VSC4 is similar to the response of VSC1 and VSC5 except that it requires the bypassing of the additional submodules in normal operation and inserting the additional submodules once VSC2 and VSC4 are tripped to improve the voltage rating of VSC1 and VSC5. Bypassing and inserting additional submodules can be achieved using the existing technologies in the literature [30]. E. Simulation of the Four-Port Test System Figs. 15 and 16 show the simulation result of the four-port test dc–dc autotransformer. Parameters of the four-port dc auto are listed in Tables IV and V. Fig. 15 shows the output dc power of each of the dc systems. E1 , E2 , and E3 are exporting 700, 1000, and −1300 MW dc power in steady state during the period of 0.5–1.5 s, E4 acts as

Fig. 15. DC power of the four-port dc auto: (a) output dc power of E 1 , (b) output dc power of E 2 , (c) output dc power of E 3 , and (d) output dc power of E4 .

Fig. 16.

Total absolute dc power and ac power of the four-port dc auto.

the power balancing port. During 1.5–1.9 s, dc power order of E2 is reversed. We can see from Fig. 15(a) and (c) that dc power of E1 and E3 remain unchanged during the power reversal of E2 . Fig. 15(b) shows that dc power order of E2 follows its power order.

LIN et al.: MULTIPORT DC–DC AUTOTRANSFORMER FOR INTERCONNECTING MULTIPLE HIGH-VOLTAGE DC SYSTEMS AT LOW COST

Fig. 16 shows the total dc power and the total ac power of the seven VSCs. It is interesting to note from Fig. 16 that during 0.5–1.5 s, the total dc power is 3366 MW while the total ac power of the seven VSCs is 970 MW. With power reversal of E2 , the total dc power increases up to 4660 MW while the total ac power even reduces to 590 MW. Operational power loss of the multiport dc–dc autotransformer is in the order of 10% of the conventional multiport dc–ac–dc technology. VII. CONCLUSION This paper proposes a multiport dc–dc autotransformer technology that is able to interconnect multiple dc systems at low cost. In the test three-port dc–dc autotransformer, a total of 775 MW power converters are required to enable any mode of power transfer between the interconnected dc systems while a total of 3000 MW power converters are required for the conventional multiport dc–ac–dc technology. In the test four-port dc–dc autotransformer, a total of 1657 MW power converters are required to enable any mode of power transfer between the four interconnected dc systems while a total of 5000 MW power converter are required for the conventional dc–ac–dc technology. The multiport dc–dc autotransformer is able to reduce the total used power converters to approximately 30% of the conventional dc–ac–dc technology. Cost and operational power losses of the multiport dc–dc autotransformer are therefore significantly lower than the conventional dc–ac–dc technology. The multiport dc–dc autotransformer shows promising prospects for interconnecting multiple HVDC systems in the future dc power grid. REFERENCES [1] D. Van Hertem and M. Ghandhari, “Multi-terminal VSC HVDC for the European Supergrid: Obstacles,” Renewable Sustainable Energy Rev., vol. 14, no. 9, pp. 3156–3163, Dec. 2010. [2] N. Ahmed, A. Haider, D. Van Hertem, L. Zhang, and H. P. Nee, “Prospects and challenges of future HVDC super grids with modular multilevel converters,” in Proc. 14th Eur. Conf. Power Electron. Appl., 2011, pp. 1–10. [3] V. Akhmatov, M. Callavik, C. M. Franck, S. E. Rye, T. Ahndorf, M. K. Bucher, H. Muller, F. Schettler, and R. Wiget, “Technical guidelines and prestandardization work for first HVDC grids,” IEEE Trans. Power Del., vol. 29, no. 1, pp. 327–335, Feb. 2014. [4] D. Jovcic, K. Linden, D. Van Hartem, and J. P. Taisne, “Feasibility of DC transmission Networks,” in Proc. 2nd IEEE PES Int. Conf. Exhib. Innov. Smart Grid Technol., Manchester, Dec. 2011, pp. 1–8. [5] C. M. Franck, “HVDC circuit breakers: A review identifying future research needs,” IEEE Trans. Power Del., vol. 26, no. 3, pp. 998–1007, Apr. 2011. [6] D. Huang, Y. Shu, J. Ruan, and Y. Hu, “Ultra high voltage transmission in China: Developments, current status and future prospects,” Proc. IEEE, vol. 97, no. 3, pp. 555–589, Mar. 2009. [7] N. Flourentzou, V. G. Agelidis, and G. D. Demetriades, “VSC-based HVDC power transmission systems: An overview,” IEEE Trans. Power Electron., vol. 24, no. 3, pp. 592–602, Mar. 2009. [8] R. L. Koropatnick. (2012, Mar.). HVDC Projects Listing [Online]. Available: http://www.ece.uidaho.edu/hvdcfacts/ [9] C. D. Barker, C. D. Davidson, D. R. Trainer, and R. S. Whitehouse, “Requirements of DC-DC converters to facilitate large DC grids,” in Proc. CIGRE Conf., 2012, pp. 1–10. [10] S. P. Engel, M. Stieneker, N. Soltau, S. Rabiee, H. Stagge, and R. W. De Doncker, “Comparison of the modular multilevel dc converter and the dual-active bridge converter for power conversion in HVDC and MVDC grids,” IEEE Trans. Power Electron., vol. 30, no. 1, pp. 124–137, Jan. 2015.

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Weixing Lin (S’11–M’13) received the B.Eng. and Ph.D. degrees in electrical engineering from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 2008 and 2014, respectively. He was a visiting Ph.D. student at the Cardiff University, U.K., from December 2011 to June 2012. He is currently a Postdoctoral Research Fellow at the University of Aberdeen, Aberdeen, U.K. and a Research Fellow at the HUST. His research interests lie in HVDC, high-power dc–dc converter, high power dc hub, dc grids and wind power.

Jinyu Wen (M’10) received the B.Eng. and Ph.D. degrees from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 1992 and 1998, respectively, both in electrical engineering. He was a Visiting Scholar from 1996 to 1997 and from 2002 to 2003 at the University of Liverpool, U.K. In 2003, he joined the HUST where he is currently a Professor. His current research interests include smart grid, renewable energy, energy storage, FACTS, HVDC and power system operation and control.

Shijie Cheng (M’86–SM’87–F’11) received the B.Eng. degree from Xi’an Jiaotong University, Xi’an, China, in 1967, the M.Sc. degree from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 1981, and the Ph.D. degree from the University of Calgary, Calgary, AB, Canada, in 1986, all in electrical engineering. He has been a Professor at HUST since 1991. His research interests include power system control, stability analysis, application of artificial intelligence, and energy storage. Dr. Cheng has been a Fellow of the Chinese Academy of Sciences since 2007.