IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005 427 VSC Transmission Operating Under Unbalanced AC Conditions—Analysis and Control Design Lie Xu, Member, IEEE, Bjarne R. Andersen, Senior Member, IEEE, and Phillip Cartwright Abstract—This paper presents an analysis and a new control design of a voltage-source converter (VSC) transmission system operating under unbalanced network conditions. The system is analyzed in the positive and negative synchronous reference frames. The proposed control strategy contains a main controller and an auxiliary controller. The main controller is implemented in the positive d–q frame using decoupling control without involving positive/negative-sequence decomposition. The auxiliary controller is implemented in the negative-sequence d–q frame using cross-coupling control of negative-sequence current. Simulation results using the SIMULINK power system blockset show good performance of the proposed control strategy for a 300-MW 300-kV dc VSC transmission system during both balanced conditions and unbalanced conditions as may be caused by a solid single-phase-to-ground fault. Index Terms—Control design, converters, modeling, power transmission, unbalance. NOMENCLATURE , , , , , , , , Network voltage. Fundamental frequency voltage of converter output. Source current. AC side inductance, resistance. DC side capacitance. Source voltage angular frequency. Modulation index. AC active, reactive power inputs. DC side voltage, current, power. Superscripts Positive, negative d-q reference frame. Reference value for controller. Subscripts Stationary – axis. Synchronous d–q axis. Positive, negative components Manuscript received April 29, 2003. Paper no. TPWRD-00193-2003. L. Xu was with ALSTOM T&D Ltd., Power Electronic Activities, Stafford, ST17 4LN U.K. He is now with the School of Electrical and Electronic Engineering, Queen’s University of Belfast, Belfast, BT9 5AH U.K. (e-mail: l.xu@ee.qub.ac.uk). B. R. Andersen was with ALSTOM T&D Ltd., Power Electronic Activities, Stafford, ST17 4LN U.K. He is now with Andersen Power Electronic Solutions Ltd. Stafford, ST16 1BW U.K. (e-mail: Bjarne@andersenPES.com). P. Cartwright was with ALSTOM T&D Ltd., Power Electronic Activities, Stafford, ST17 4LN U.K. He is now with Areva T&D Technology Centre, Stafford, ST17 4LN U.K. (e-mail: phill.cartwright@areva-td.com). Digital Object Identifier 10.1109/TPWRD.2004.835032 I. INTRODUCTION H Vdc schemes employing line-commutated, current source converters with thyristors have been widely used for power transmission and its control strategies have been well established. On the other hand, voltage-source converter (VSC) transmission using state-of-the-art insulated-gate bipolar transistor (IGBT) technology has attracted increasing attention and a number of installations are now in operation. The principle characteristics of VSC transmission are that it needs no external voltage source for commutation, that it can independently control the reactive power flow at each ac network, and that reactive power control is independent of the active power control. These features make VSC transmission attractive for connection of weak ac systems, island networks, and renewable sources to a main grid. However, VSC transmission does have high power loss and high cost compared to conventional HVdc systems [1]. To take full advantages of VSC transmission and to enable it to compete with conventional HVdc, a number of advances in technology are required. One such requirement is the ability to operate in severe unbalanced network conditions. Reference [2] presents an equivalent continuous-time averaged state-space model of a VSC transmission system and a control system based on decoupling control. This control strategy can be applied only to balanced network conditions. References [3] and [4] study STATCOM control under unbalanced network conditions, and separate loops for the positive- and negative-sequence components are used. A similar approach is used for controlling a VSC feeding an unbalanced load [5]. In [6], the control principles are used to control a pulsewidth-modulated (PWM) rectifier taking into account unbalanced network conditions. However, within a VSC transmission system, it is necessary to consider the interaction of at least two ac networks and this makes more demands on dynamic response. Simply separating the controller into positive- and negative-sequence loops as used in [3]–[6] may not achieve satisfactory performance due to the delays introduced by decomposing the positive- and negative-sequence components of the voltage and current. This paper presents an analysis and a new control strategy for a VSC transmission system under balanced and unbalanced network conditions. The VSC transmission system under balanced and unbalanced condition is analyzed first. The control design for balanced condition is briefly outlined and then the principles of the proposed approach for unbalanced network are described. Finally, simulation results are provided to demonstrate the feasibility of the proposed controller. 0885-8977/$20.00 © 2005 IEEE 428 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005 Fig. 1. Schematic diagram of the VSC transmission system. Fig. 2. Simplified circuits of one end of the VSC transmission system: (a) AC side. (b) DC side. II. ANALYSIS OF VSC TRANSMISSION SYSTEM The schematic diagram of a typical VSC transmission scheme is shown in Fig. 1. The simplified equivalent circuits on the ac and dc sides are shown in Fig. 2. where and lation indexes at - and -axis. A. Balanced Condition Detailed model of a VSC transmission scheme under balanced network conditions has been studied in [2]; therefore, only a brief description is given here. As no negative-sequence components exist when the network is balanced, the voltage/current variables in this subsection are all positive-sequence components expressed in the positive-sequence reference frame. Referring to Fig. 2, the system on the ac side can be expressed in the synchronous d–q reference frame, where the d-axis is fixed to the source voltage , as [2] and [7] (1) where Fig. 3. Relationships between the (dq) reference frames. . Using the power-balancing equation, the dc side system of one end as shown in Fig. 2(b) is expressed as (2) reference frame and the (dq) and are the modu- B. Unbalanced Condition Assuming no zero-sequence component, the three-phase voltage and current may be decomposed into positive- and negative-sequence components when the network is unbalanced. In reference frame, the three-phase voltages and the stationary currents are decomposed into positive- and negative-sequence components as (5) where represents either voltage or current and and are the respective phase shift for positive- and negative-sequence components. There are various methods which can be used to separate the positive- and negative-sequence components. One technique is to delay the input signal by a quarter of the fundamental frequency period as shown in the following equation [8]: (3) Assuming an ideal converter model, the ac and dc side systems can be expressed as (4) (6) The positive- and negative-sequence components in the stationary reference frame are then transformed into and reference frames rotating at angular speeds of and , respectively. Fig. 3 shows the spatial relationship of the three reference frames. XU et al.: VSC TRANSMISSION OPERATING UNDER UNBALANCED AC CONDITIONS—ANALYSIS AND CONTROL DESIGN According to Fig. 3, the transformation between reference frames is given by and (7) and Therefore, in the be expressed as 429 not square [7]. One way to overcome this difficulty is to consider the model in (4) and divide the control into two separate loops—an inner fast current loop and an outer slow dc voltage loop. The interaction between the two loops is avoided by adequately separating their respective dynamics [2], [7]–[9]. The auxiliary inputs are defined as follows: reference frames, (1) can (11) The current and can be controlled independently by and , respectively. Furthermore, acting upon the inputs by using integral control, the tracking errors will be minimized. Therefore, the controller is designed as follows: (8) (12) The active and reactive power inputs at the point of common coupling (PCC) are expressed as [6] where and are the proportional and integral gains of the current controller. and are given by Therefore, the control variable (9a) where , , , and are given by (13) (9b) Therefore, using the power-balancing equation, the dc side equation for the unbalanced condition can be expressed as (10) now is given by (9a) and (9b). where Thus, (8) and (10) represent the ac and dc side system model for one end of a VSC transmission scheme under unbalanced network conditions. Similar to the current loop, the controller for the dc voltage loop is designed as (14) and are the proportional and integral gains of the where dc voltage regulator. is then The control input of the d-axis current reference derived as (15) III. CONTROL DESIGN In this section, the control design for the balanced condition will be briefly described first and then the proposed design for the unbalanced condition will be provided. A. Balanced Condition The system model represented by (4) is nonlinear because of the existence of multiplication terms between the state variables ) [2], [7]. ( , ) and the input ( , The operation of the VSC transmission scheme requires the state variables and to follow varying reference points. In also has to be maintained at a addition, the dc voltage level set value. However, the model has only two independent inputs and . Hence, the exact feedback linearization technique is not applicable since the corresponding decoupling matrix is B. Unbalanced Condition As the model shown in (8) indicates, the inner current loop is normally separated into two controllers (i.e., a positive-seframe and a negative-sequence current controller in the quence current controller in the frame [3], [4]). Each controller uses (12) and (13) to achieve dynamic tracking of the positive/negative-sequence current references. and The positive and negative current references are generated according to various control objectives and they and are normally generated according to the requirement of . For the transmission scheme, it may be preferred to eliminate second harmonic power input to (or output from) the converter such that there will be no second-order harmonic on the dc side. Therefore, according to (9b), the power oscillation terms 430 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005 and need to be zero. It should be noted that (9b) represents the active and reactive power seen from the transformer primary side (PCC); therefore, (9b) needs to be modified to take into account the influence of the transformer leakage inductance as Therefore, in the is expressed as frame, the system represented by (1) (18) (16) . where The and can then be calculated according to the values of , , , and . The issues associated with this conventional approach of controlling the positive- and negative-sequence currents are of the following. • Good performance of this control strategy is based on the accurate decoupling of the d-q component and the removal of the impact of the network voltage. However, as the process of extracting the positive- and negative-sequence components (both current and voltage) involves considerable time delay, the system cannot be decoupled under transient conditions. Therefore, the system performance is degraded and the stability of the system is reduced. • If the active power is generated from an outer dc voltage control loop based on the controller expressed in (15), any second-order harmonic in the dc voltage or current will result in second-order harmonic in the active power or the positive current reference . This reference indicates actually contains negative-sequence current components. Therefore, the two sets of positive/negative-sequence controllers interact with each other and, thus, the performance is less satisfactory. In order to overcome the problems highlighted, a new control strategy is proposed in this paper. The strategy is to have two current controllers, namely a main controller and an auxiliary controller. The main controller is implemented in the frame which rotates at an angular speed of . The controller is designed using the same principles as shown in (12) and (13). However, it does not involve any positive- and negative-seand as used in the conventional apquence separation of proach. The auxiliary controller is specially designed for controlling the negative-sequence current and is implemented in the frame. In order to avoid the problem associated with inadequate decoupling, the so-called “cross coupling control” is used for the auxiliary controller [10]–[12]. The design of these two controllers is discussed below. According to Fig. 3 and (8), the current and voltage in the frame can be expressed as (17) where and refer to the converter outputs controlled by the main and auxiliary controllers, respectively. Using decoupling control described in (13) and without involving any positive- and negative-sequence decomposition, is controlled as (19) where is given by (20) As previously described, may contain negative-sequence components and it is expressed as (21) represents the negative-sequence components in where the current references of the main controller. For simplicity, is assumed to be zero for the following analysis and its impact will be described later. Substituting (17), (19), and (20) into (18), and splitting into a positive-sequence subsystem and a negative-sequence subsystem yields (22) (23) Equation (22) represents the dynamics of the positive-sequence current components and appropriate selection of and of the main controller can give good control of the system. Alternatively, (23) gives the dynamics of the negative-sequence current with the auxiliary controller. Without causing significant impact on the system dynamic performance, (23) can be simplified by neglecting the integral term as (24) XU et al.: VSC TRANSMISSION OPERATING UNDER UNBALANCED AC CONDITIONS—ANALYSIS AND CONTROL DESIGN 431 Fig. 4. One terminal of the simulated VSC transmission scheme. In the reference frame, extracting the negative-sequence current components and using the so-called cross is given by coupling control [9], [10], TABLE I LIST OF PARAMETERS OF THE SYSTEM STUDIED (25) Substituting (25) into (24) and transforming it into the frequency domain, the dynamics of negative-sequence currents are then given by (26) where represents in the reference frame. Consequently, there will be an extra term on the right-hand side of (26) and it is given by Equation (25) indicates that the negative-sequence currents follow a second-order system. In reality because of the use of PI controllers, the system is no longer a second-order system. However, the existence of the integral part does not cause significant difference on the system dynamic performance, but it does reduce the steady-state error of the current controller. As , according to (26), and follow their respective references and the interaction between the negative-sequence d- and q-axis currents is small. which was previously neNow consider the impact of glected. Please note which is the negative component contained in the current reference of the main controller while is the negative-sequence current reference for the auxiliary controller. Taking into account , an extra term on the right side of (24) appears and this term is given as (28) where (27) Comparing (28) to (26), it can be seen that all terms on the right-hand side of (28) tend to zero. This indicates that the influence of is rejected by the auxiliary controller. Therefore, with the combination of the two controllers, both the positive- and negative-sequence currents are controlled precisely. The d–q positive and negative current references are generated using the same approach as previously described. IV. SIMULATION RESULTS A VSC transmission system employing the aforementioned control principle was simulated in SIMULINK. Fig. 4 shows one terminal of the simulated system. Four-level Foch converters were used in this study which leads to reduced power loss and voltage harmonic contents [1]. The parameters of the simulated system are listed in Table I. 432 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005 Fig. 5. Simulation results under balanced conditions. (a) DC voltage controller d–q current references and responses. (b) Power controller d–q current references and responses. (c) Active power inputs at the two ends. (d) Main dc and floating capacitor voltages. An ac voltage controller, which may be implemented by controlling the reactive power, is not included in the system. Instead, the model simply uses q-axis current order to directly give reactive power reference. The two converters were implemented with one converter controlling the dc voltage (namely, the dc voltage controller) and the other controlling the active power (namely, the power controller). The location of the two controllers is independent of the power transfer direction. Therefore, the dc voltage controller can operate as a rectifier or an inverter and the same can be applied to the power controller. As the aim of this study is to develop a suitable control strategy, the energization sequence of the converter is not studied here. It is assumed that the main dc capacitor was initially charged at 300 kV and the floating capacitors and were charged at 200 and 100 kV, respectively, prior to the deblock of both converter stations. First, system operation under balanced network conditions is tested with active and reactive power variations. Fig. 5 shows the simulation results of the current references and responses for the two converters. Both converters were deblocked at a time of 0.05 s and then various active power orders were set at the power controller (at a rate of 100 MW/20 ms) and q-axis current orders were set for both ends of the scheme. As can be seen from Fig. 5, the system responses are satisfactory and the main dc and the floating capacitor voltages are well controlled under transient conditions. Unbalanced conditions were simulated using a solid single-phase-to-ground fault applied directly at the transformer primary side. A fault on each side of the converters was studied with active power flow in either direction. During the simulation, faults were applied at 0.4 s and cleared at 0.6 s. Before the fault, the transmitted power is 200 MW. The negative-sequence currents were controlled to ensure clean active power input/output to the converter, (i.e., no second-order dc power oscillation). The maximum converter current was set at 2 kA and the positive-sequence d-axis cur- XU et al.: VSC TRANSMISSION OPERATING UNDER UNBALANCED AC CONDITIONS—ANALYSIS AND CONTROL DESIGN 433 Fig. 6. Simulation results under single-phase-to-ground fault on the power controller side. (a) DC voltage controller d–q current references and responses. (b) Power controller positive-sequence d–q current references and responses. (c) Power controller negative-sequence d–q current references and responses. (d) Active power inputs measured at the PCC and converter side of the power controller. (e) AC voltage THD on both sides. (f) Main dc and floating capacitor voltages. 434 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005 rent is automatically limited to ensure the overall current is within this range. Fig. 6 shows the simulation results under single-phase-toground fault on the power controller side when the power controller operates as an inverter. The performance when the power controller operated as a rectifier is very similar to those shown in Fig. 5 and is not shown due to space limitations. Fig. 6(a) shows the d–q current reference and response of the dc voltage controller while the positive- and negative-sequence current references and responses of the power controller are shown in Fig. 6(b) and (c). It can be seen that under the single-phase fault condition, both the positive- and negative-sequence currents are well controlled. Fig. 6(d) shows the power measured at the transformer primary (PCC) and secondary (converter) sides, respectively. As can be seen, the output power from converter does not contain second harmonic while the power measured at the transformer primary side does contain second harmonic due to the transformer leakage inductance. The common bus ac voltages and their THD of the two ends are shown in Fig. 6(e), respectively. It can be seen, apart from transient, that the THDs for both ends are below 2% even during the fault. The main dc and floating capacitor voltages for both ends are shown in Fig. 6(f). It can be seen that the dc is regulated at its nominal value with little second-order harmonics even under single-phase fault conditions. During the whole operating period, the floating capacitor voltage is well balanced. The increase of the floating capacitor voltage ripple at the power controller side is due to the increase of the converter current (i.e., the converter is operated at its current limit of 2 kA during the fault). Simulation results when single-phase-to-ground fault applied to the dc voltage controller side have shown similar performance as those depicted in Fig. 6. [3] S. Chen, G. Joos, and L. T. Moran, “Dynamic performance of PWM STATCOM’s operating under unbalanced and fault conditions in distribution systems,” in Proc. IEEE Power Eng. Soc. Winter Meeting, 2001, pp. 950–955. [4] C. Hochgraf and R. H. Lasseter, “STATCOM controls for operation with unbalanced voltage,” IEEE Trans. Power Del., vol. 13, no. 2, pp. 538–544, Apr. 1998. [5] C. B. Jacobina, M. B. de R. Correa, R. F. Pinheiro, E. R. C. da Silva, and A. M. N. Lima, “Modeling and control of unbalanced three-phase systems containing PWM converters,” IEEE Trans. Ind. Appl., vol. 37, no. 6, pp. 1807–1816, Nov./Dec. 2001. [6] P. Rioual, H. Pouliquen, and J. Louis, “Regulation of a PWM rectifier in the unbalanced network state using a generalized model,” IEEE Trans. Power Electron., vol. 11, no. 3, pp. 495–502, May 1996. [7] C. Cshauder and H. Mehta, “Vector analysis and control of advanced static VAR compensator,” Proc. Inst. Elect. Eng., Elect. Power Applicat., vol. 140, no. 4, pp. 299–306, Jul. 1993. [8] J. Svensson and A. Sannino, “Active filtering of supply voltage with series-connected voltage source converter,” Eur. Power Electron. Drives J., vol. 12, no. 1, pp. 19–25, Feb. 2002. [9] N. Mendalek, K. Al-Haddad, L. A. Dessaint, and F. Fnaiech, “Nonlinear control strategy applied to a shunt active power filter,” in Proc. IEEE Power Electron. Specialist Conf., 2001, pp. 1871–1882. [10] Q. Yu, S. D. Round, L. E. Norum, and T. M. Undeland, “Dynamic control of a unified power flow controller,” in Proc. IEEE Power Electronics Specialist Conf., 1996, pp. 508–514. [11] H. Fujita, Y. Watanabe, and H. Akagi, “Control and analysis of a unified power flow controller,” IEEE Trans. Power Electron., vol. 14, no. 6, pp. 1021–1027, Nov. 1999. [12] L. Xu and V. G. Agelidis, “A flying capacitor multilevel PWM converter based UPFC,” Proc. Inst. Elect. Eng., Electr. Power Applicat., vol. 149, no. 4, pp. 304–310, Jul. 2002. V. CONCLUSION A VSC transmission system operated under unbalanced ac conditions has been analyzed in this paper. A new control design for improving VSC transmission system performances during unbalanced network conditions has been proposed. The proposed approach uses two sets of controller (i.e., a main controller and an auxiliary controller). The main controller is implemented in the positive-sequence d–q frame using decoupling without getting involved in positive- and negative-sequence decomposition. Alternatively, the auxiliary controller is implemented in the negative-sequence d–q frame with cross coupling control of the negative-sequence current. Simulation results have shown good performance of the proposed system under balanced conditions and unbalanced fault conditions. REFERENCES [1] B. R. Andersen, L. Xu, P. Horton, and P. Cartwright, “Topology for VSC transmission,” Inst. Elect. Eng. Power Eng. J., vol. 16, no. 3, pp. 142–150, Jun. 2002. [2] J. L. Thomas, S. Poullain, and A. Benchaib, “Analysis of a robust DC-bus voltage control system for a VSC transmission scheme,” in Proc. 7th AC/DC Transmission Conf., Nov. 2001. Lie Xu (M’03) received the B.Sc. degree in electrical and electronic engineering from Zhejiang University, Hangzhou, China, in 1993, and the Ph.D. degree in electrical and electronic engineering from the University of Sheffield, Sheffield, U.K., in 1999. Currently, he is with the School of Electrical and Electronic Engineering, Queen’s University of Belfast, Belfast, U.K. Previous to this, he was with ALSTOM T&D Ltd., Power Electronic Activities (PEA), Stafford, U.K. He was with the Centre for Economic Renewable Power Delivery (CERPD), University of Glasgow, Glasgow, U.K., from 1999 to 2000. His main interests are power electronics, renewable energy, and application of power electronics to power systems. Bjarne R. Andersen (SM’02) was born in Copenhagen, Denmark, in 1948. He received the M.Sc. degree in electrical power engineering and the Ph.D. degree in high-voltage technique from the Technical University of Denmark, Copenhagen, Denmark. He is now with Andersen Power Electronic Solutions Ltd. Stafford. Previously, he was Special Projects Director with ALSTOM T&D Ltd., Power Electronic Activities (PEA), Stafford, U.K., where he spent most of his career working on HVdc, SVC, and flexible ac transmission systems (FACTS). Dr. Andersen is a Fellow of the IEE, U.K. He is a member of IEEE Working Group I5 and I8 of the Substation Committee. He is the Convenor of CIGRE Working Group B4-37 VSC Transmission and the Regular Member for U.K. of Study Committee B4. Phillip Cartwright received the B.Eng. (Hons.) degree in electrical engineering from Staffordshire University, Stafford, U.K., in 1995, and is currently pursuing the Ph.D. degree at the University of Manchester Institute of Science and Technology, Manchester, U.K. Currently, he is with Areva T&D Technology Centre, Stafford. Previously, he was with Alstom T&D Ltd., Power Electronic Activities, Stafford, where he contributed to the development, design, implementation, and testing of several HVdc systems. His main research interests include doubly fed induction machines using VSCs and their application within wind farm applications.