Comparative Analysis of Control Strategies for Modular Multilevel Converters

Transcription

1 IEEE PEDS 2011, Singapore, 5-8 December 2011 Comparative Analysis of Control Strategies for Modular Multilevel Converters A. Lachichi 1, Member, IEEE, L. Harnefors 2, Senior Member, IEEE 1 ABB Corporate Research Centre, SE Västerås, Sweden 2 ABB Power Systems/HVDC, SE Ludvika, Sweden amel.lachichi@se.abb.com Abstract-Performances analysis of a modular multilevel converter using two different control strategies is presented. The first approach uses a voltage control with a feedback loop on each individual cell to assure cell s voltage balancing. Nonetheless, this latter can be affected by the total cell s voltage ripple if not compensated. As a consequence, low frequencies are injected in the phase output voltage. To overcome this drawback, the voltage references are modified accordingly to compensate for the voltage ripple and reject low frequencies. A circulating current control is necessary in this approach to reduce harmonics contents in the arm s current. The second approach uses the energy as an image of the state of the system to assure the voltage balancing between the cells. In this method, even though there is no need to use a circulating current controller, the arm s currents are exempt of the 2 nd harmonic. Simulation results are presented to ascertain the operation of the system under steady and unsteady state conditions. e v NOMENCLATURE phase output voltage with respect to the dc-link mid-point i c circulating current i v phase line output current i vp/n positive/negative-arm converter current L v, R v inductance and resistance of the arm s inductor N Number of cells per arm / positive/negative-arm total capacitor voltage u d DC bus voltage u vp/n positive/negative-arm voltage difference of energy between the arm of one leg total energy of one leg / positive/negative-arm total energy α c control-loop bandwidth of the ac output current controller α cc control-loop bandwidth of the circulating current controller α f low-pass-filter bandwidth of phase output voltage α fc low-pass-filter bandwidth of the circulating current ξ p/n positive/negative-arm averaged switching function ξ p/ni positive/negative-arm switching function of the i th cell I. INTRODUCTION Nowadays, in order to meet high voltage and current level requirements, the use of either semiconductors with high blocking voltage capability or a series connection of semiconductors are among the choices available for the traditional two levels VSC. For high-power and powerquality demanding applications, multilevel converters are considered as the state-of-art power conversion systems. Different multilevel converter topologies have found their way into the industry. However operational issues have limited the use of those topologies with higher level [1, 2]. This gave rise to the development of new converter topologies such as the modular multilevel converter [3]--[5]. This latter offers interesting performances with design properties and costs that differ from traditional multilevel converter topologies. The modular multilevel converter has not yet reached a certain level of maturity. Intensive research activities are carried out on the topic focusing on all aspects of the system: protection, modulation approaches as well as control strategies. Research works published so far have proved that the harmonics contents of the arm s current not only play a crucial role on the design of the converter s components (capacitors, inductors and switches) but as well influence deeply the stability of the system. This inherent drawback has prompted many attempts to find a better solution for harmonics elimination [6]--[10]. The aim of this work is to highlight effects of two control strategies on the performance and stability of the modular multilevel converter (MMC) topology prior to prototyping. After presenting the topology under study, the dynamic equations governing the behavior of the converter are derived. Two control strategies in conjunction with their modulation and voltage balancing algorithm are presented. In the first approach, though not explicitly detailed, a phase-shifted PWM modulation technique is used. The control approach considers the state variables of the converter. It is mainly based on a separate voltage control of each individual cell through a feedback loop. Accuracy on the dynamics and on the measurements of the cell s voltage becomes crucial. Moreover, in some circumstances, the converter is affected by stability problems mainly caused by the capacitor cell s ripple [11]. To overcome this drawback, the modulation references are modified accordingly to /11/$ IEEE 538

2 compensate the voltage ripple of the cells and to get a better stability of the system. However, in this method, the harmonics content in the arm s current, if not reduced can lead as well to instability. A circulating current control is considered to reduce the second harmonic component. Clearly, this method requires more hardware for implementation. An interesting and quite a new approach consists of considering the dynamic of the MMC as energytransformation blocks and controlling their energy exchanges. This control technique can be found in [12, 13]. The open loop approach is considered in the paper. The basic idea is to consider the energy variation describing the dynamics behavior of the system. The open loop approach is based on the estimation of the total energy of one leg as well as the energy balance between two arms of the same leg. A direct modulation is considered in this case where the average reference voltage is set to be equal to the modulated voltage waveform [14]. However, in order to avoid processing the duty cycle and storing the result in a look-up table, the average reference voltage is compared to just one triangular signal, given all the switching instants of the converter. The circulating current is not controlled but it converges to the steady state dc-component eliminating hence the negative effects of the second harmonic component on the system. Simulations results for both approaches are presented and compared. II. TOPOLOGY DESCRIPTION AND OPERATION PRINCIPLE Fig. 1 illustrates one leg of the MMC topology. The arm consists of one inductor in series with a string of N seriesconnected identical cells. Those latter consist of a dc capacitor and two controllable switches with their antiparallel diodes. A detailed model which captures all effects that are likely to be significant for the analysis is generally speaking difficult to handle and work with. For control objectives of the converter, an averaged model assuming an infinite switching frequency, an infinite number of cells per arm and a voltage balancing between the cells is considered. That is, the switching functions can be varied from 0 to 1 and hence be averaged as / / (1) Applying Kirchhoff s circuit laws to each arm, the behavior of the system can be described by the following (2) (3) Fig. 1. Modular Multilevel topology. One leg consisting of 2N cells (Left). Basic cell of the converter (Right). where u cp/n are defined to be the inserted positive/negative arm s voltage. By adding (2) and (3) one obtains the governing equation of the circulating current i c (4) By subtracting (2) and (3) one obtains the governing equation of the phase line output current i v (5) where 2 and 2 are the output phase equivalent inductance and resistance respectively. u v and u c are the differential voltage seen by the converter at its input and the voltage that drives the circulating current respectively. They are expressed as Due to the particular internal dynamics of the modular multilevel converter, the design of the control is aiming first to guarantee system stability rather than to achieve the fastest response to load variations III. CONTROL STRATEGIES Unavoidable circulating current flows through the arms due to capacitors voltage ripple. The harmonic spectrum of the arm s current shows a strong 2 nd harmonic component content. If not reduced to a minimum acceptable value, unnecessary high rating switches would be used but most importantly stability of the system would be lost, though other phenomena are proven to influence the stability. (6) 539

3 In the following, two control strategies are compared, each one dealing differently with the circulating current and the balancing of the cell s capacitor voltage. For both approaches, it is worth pointing out that the ac output current control is achieved through a proportional current controller with a feedforward voltage and a dq coupling elimination term [15]. The implementation of the current controller is achieved by the following control law (7) Bold writing represents a space vector. The second and third term of (7) is the added decoupling term and the feedforward term of the low pass filtered of the output phase voltage respectively. Note that the ac current controller forms the inner loop of the overall system controller. As such, it must have the widest bandwidth in the system and must have a nearly zero steadystate error which is satisfied in this case. A. Current-voltage control In this method, step by step solutions are combined to achieve stability of the system leading to a cascaded control structure. However, because the state variables are used current tracking and disturbances rejection are more or less easy to achieve separately. The voltage drop across the inductance L v and the resistance R v are neglected, though it has been observed that if the resistance tends to zero the system may become unstable. If one assumes that the dc bus voltage is maintained constant, the voltage across each arm could be defined by the following Fig. 2. (a) positive arm voltage u vp -blue-, inserted capacitors voltage u cp - black-. (b) output voltage harmonic spectrum. u d = 320 kv, N=40, C c = 700 μf, L v= 60.4 mh. Substituting (8) in (4) yields to (8) (9) As already mentioned, the circulating current contains a dc component and an ac component of twice the fundamental frequency. It is desired to limit as much as possible this ac component which is achieved using a dedicated current controller. The control law is given by (10) Moreover, to assure the balancing task, the cells voltage are measured and fed-back. However, using a circulating current controller and a feedback controller are not enough to assure a stable operating system. It has been observed that the total capacitors voltage ripple has a significant effect on the quality of the phase output waveforms in term of harmonic contents. Fig. 3. (a) positive arm voltage u vp -blue-, inserted capacitor voltage u cp - black-. (b) output voltage harmonic spectrum. u d = 320 kv, N=40, C c = 700 μf, L v= 60.4 mh. As depicted in Fig. 2 (a), the arm s voltage is more or less distorted when the waveform hits the total capacitors voltage. 540

4 That is, undesired low frequencies are seen in the output voltage as illustrated in Figure 2 (b). Those frequencies are close to the fundamental frequency and hence are difficult to filter. If the ripples are not compensated, the output current would considerably be distorted. Besides, though not explicitly shown in this particular example, the cells voltage may diverge. To compensate for the low frequency harmonics, the modulation references are accordingly modified to reject the low frequencies. This is achieved by adding a term to the voltage reference that would correct each capacitor s cell voltage ripple. Figure 3 shows how the waveforms are improved by rejecting the low frequencies. Sideband harmonics appear around the effective switching frequency of the converter. As expected, this is due to the modified modulation references. B. Energies control (open loop control) Rather than modifying the modulation references to compensate for the capacitor voltages ripple, the total capacitors voltages are instead controlled through the control of the energy exchange of each arm. With this in mind, the effectiveness of this method to solve the above-mentioned issues is now explained. This is achieved by processing the total energy of one leg as well as the difference of energy between two arms of the same leg as given by the following (11) 2 2 (15) Firstly, let us assume that the circulating current is exempt from the second harmonic component and that it converges to its mean value I c0. By equating (4) to zero and hence setting u c equal to RI c0, solution of (15) yield to a complete definition of the modulation references. If the capacitors cells are charged enough to maintain the dc bus voltage at the desired level ±u d, the total capacitors voltage lies above the arm s voltage as shown in Fig. 4 (a). The harmonic spectrum of the output voltage (Fig. 4 (b)) shows no injection of low frequencies due to the capacitors voltage ripple that would eventually distort the phase output current. Note the peak level around 4.5 khz in the harmonic spectrum of the output voltage. This comes from the carrier used to process the switching instants of each cells. u vp,u cp [kv] t [s] This scheme is known as an open loop control [13]. The time derivative of the stored energy is equal to the input power arm which yields to / / / (12) Interestingly, the inserted voltages u cp/n can be expressed in term of u c as Substituting (13) in (12) yields to (13) (14) Differentiating (11) and substituting (14) for each derivative variables yield to Fig. 4. (a) positive arm voltage u vp -blue-, total capacitors voltage u cp -black-. (b) output voltage harmonic spectrum. u d = 320 kv, N=40, C c = 700 μf, L v= 60.4 mh. In this example, the peak to peak total capacitors voltage is reduced by about 60% compared to the previous control method. Clearly, this allows reducing the size of the capacitor. In order to assess the balancing method, different initial voltages conditions are set for the total capacitors voltage of each arm. For the positive arm, an initial voltage equal to 640 kv is chosen whereas a voltage of 300 kv is set for the negative arm. As depicted in Fig. 5, the total capacitor voltage reaches its mean value after 300 ms. The time response of the system is relatively slow with a high 541

5 overshoot, though improvement of the system s dynamics can be achieved by connecting virtual resistors to the system t [s] Fig. 5. Positive-arm total capacitors voltage u cp (black). Negative-arm total capacitors voltage u cn (red). u d = 320 kv, N=40, C c = 700 μf, L v= 60.4 mh. [9] M. Akagi, Classification, Terminology and Application of the Modular Multilevel Cascade Converter (MMCC), in Proc. IPEC [10] M. Hagiwara, H. Akagi, Control and Experiment of Pulsewidth- Modulated Modular Multilevel Converters, IEEE Trans. On Power Elec., Vol. 24, No. 7, pp , [11] S. Kouro et al, Multicarrier PWM With DC-Link Ripple Feedforward Compensation for Multilevel Inverters, IEEE Trans. On Power Elec. Vol. 23, No. 1, Jan [12] A. Antonopoulos et al, On Dynamics and Voltage Control of the Modular Multilevel Converter, in Proc. EPE [13] L. Ängquist et al, Inner Control of Modular Multilevel Converters -An Approach using Open-loop Estimation of Stored Energy, in Proc. IPEC [14] G. Holmes, T. A. Lipo, Pulse Width Modulation for Power Converters, ISBN , [15] L. Harnefors and H.-P. Nee, Model-based current control of ac machines using the internal model control method, IEEE Trans. Ind. Appl., vol. 34, no. 1, pp , Jan./Feb IV. CONCLUSION Two control approaches have been presented in the paper to operate the modular multilevel converter. Interestingly, phenomena proper to the converter that would lead to instability are solved differently by either compensating the voltage ripple if the state variables are controlled or by controlling the total capacitors voltage via the energy of the system. The first method relies on accurate measurements of the cells voltage which may be seen as a disadvantage compared to the second approach where the variables as estimated. Moreover, the energy control approach showed reduction of the voltage ripple of about 60 % which will help to reduce the requirements of the total installed energy for operation. REFERENCES [1] Rodriguez et al, Multilevel Converters: An Enabling Technology for High Power Transmission Invited paper [2] S. Kouro et al, Recent Advances and Industrial Applications of Multilevel Converters, IEEE Trans. On Ind. Elec., Vol. 57, No. 8, Aug [3] A. Lesnicar, R. Marquardt, A new modular voltage source inverter topology, in Proc. EPE, [4] A. Lesnicar, R. Marquardt, An Innovative Modular Multilevel Converter Topology Suitable for a Wide Power Range, PowerTec, [5] M. Glinka, R. Marquardt, A New Single Phase AC/AC-Multilevel Converter For Traction Vehicles Operating On AC Line Voltage, in Proc. PEDS, [6] Q. Tu et al, Reduced Switching-Frequency Modulation and Circulating Current Suppression for Modular Multilevel Converters, Accepted paper to IEEE Trans. On Power delivery. [7] F. Munch et al, Modeling and Current Control of Modular Multilevel Converters Considering Actuator and Sensor Delays, in Proc. IECON, [8] M. Hagiwara et al, Theoretical Analysis and Control of the Modular Multilevel Cascade Converter Based on Double-Star Chopper-Cells (MMCC-DSCC), in Proc. IPEC