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3rd The International Conference on Renewable Energy Research and Applications 19-22 Oct 2014 Milwakuee-USA Modular multilevel converters with integrated batteries energy storage A. Lachichi ABB Corporate Research Centre, SE-721 78 Västerås, Sweden [email protected] Abstract—This paper presents the analysis of the modular multilevel converter with integrated batteries energy storage and highlights the influence of the power injected to the grid from the batteries or vice versa on the capacitors’ voltage balancing. The control objective of the converter is to maintain a balance between the arms. By redefining the circulating current in order to compensate for reactive power and rebalance the ac grid voltage asymmetries, it is shown through simulation results that the current injected by the batteries does not introduce any unbalance to the converter. Keywords—Batteries energy converter; STATCOM/BESS storage; modular multilevel NOMENCLATURE Cc Cell capacitance. iBp/n,I positive/negative-arm current injected to/from the battery of the ith cell. ic circulating current when batteries are not connected to the cells. icB circulating current with batteries connected to the cells. iv phase line output current. ip/n positive/negative-arm converter current. Lv arm inductance. m modulation index. N Number of cells per arm. Pac ac active power. PB Batteries power. Pdc dc power. Rv arm’s resistance. S apparent power. ucm common mode injection voltage. ucp/n positive/negative-arm inserted capacitor voltage. positive/negative-arm total available capacitor voltage. / ud dc bus voltage. uv differential voltage. uvp/n positive/negative-arm voltage. W difference of energy between the arms of one leg. W total energy of one leg. W / positive/negative-arm total energy. positive/negative-arm averaged switching function. p/n positive/negative-arm switching function of the ith cell. p/ni phase shift of the fundamental line output current with respect to the fundamental output voltage. fundamental angular frequency. ICRERA 2014 p i cm n v phase shift of the fundamental line output current positive sequence with respect to the fundamental output voltage positive sequence. phase shift of the fundamental output common mode voltage with respect to the fundamental output voltage positive sequence. phase shift of the fundamental output voltage negative sequence with respect to the fundamental output voltage positive sequence. I. INTRODUCTION The integration of batteries energy storage into a STATCOM is largely used to tackle different gridtransmission problems by providing additional active power support to the grid. For instance, transient stability and subsynchronous oscillation damping are improved [1], and phase jump as well as magnitude fluctuation are reduced [2]. Many studies have been carried out to find the best approach to connect batteries energy storage into the STATCOM converter that would optimize not only the size of the batteries but as well would be a cost effective solution. In [3], the authors highlight the advantages and disadvantages of connecting batteries energy storage either in the cascaded converter or the diode-clamped converter, while in [4], a sensitive analysis is carried out in order to highlight influence of the choice of the topology and the network voltage level on the losses. Multilevel cascaded converters have made it possible to integrate batteries energy storage units into the cell of the topology [5-7]. One of the main benefits of this layout is undoubtedly the possibility to integrate and adjust the required active power since each battery unit can operate at different power level, while maintaining a three-phase balanced line-toline voltage. Moreover, due to its success in HVDC application, modular multilevel converters are now proposed as a solution to integrate batteries energy storage into the cell as exemplified in [8] for solar application. It is demonstrated in [9] that modular multilevel converters have internal dynamics which define the behavior of the sum of all capacitor voltages in one converter arm and the circulating current which flows between the arms. This inherent circulating current constitutes a degree of freedom that can be used in a Statcom/BESS system to compensate the reactive power and to rebalance the ac grid voltage asymmetries by 3rd The International Conference on Renewable Energy Research and Applications providing the required active power from the batteries to the grid. Dynamics of the converter indicate as well the presence of harmonics components in the arm’s current. Even though it is possible to reduce the predominant second harmonic component with the appropriate control strategy, an interface that would act as a buffer is necessary between the cell of the converter and the batteries where they are connected to. This adds to the cost of the overall of the converter. Besides, the arm’s current oscillates at the fundamental frequency which could severely damage the batteries if this current is let to flow into them. This paper details the analysis of the modular multilevel converter with batteries energy storage units integrated into the cells and addresses the problem of imbalance in the phaseleg of a StatCom/BESS system. Firstly, the dynamics of the converter are presented by taking into account the power injected from the batteries to the ac grid or vice versa in order to define the circulating current in steady-state operation of the converter and show the influence of the batteries’ current upon the capacitors’ voltage balance and the energy balance between the phase-arms of the converter. Then the circulating current is redefined for ac voltage grid asymmetries. The method used relies on injecting a common mode voltage to rebalance the ac grid. Finally, a case study is presented to ascertain the main findings. II. CIRCUIT DYNAMICS The modular multilevel converter is conceptually composed of two traditional cascaded multilevel converters, stacked one over the other with the middle point forming the output phase of the converter. As illustrated in Figure 1(a), where the basic structure of a single phase-leg of an N-level multilevel converter is shown, the cascaded converter connected to the positive/negative pole forms the positive/negative arm. Each arm is formed by an array of a series-connection of single-phase inverters referred as cells. Inductors are included within each arm for protection purpose, etc. Figure 1(b) depicts a simplified circuit diagram of an individual cell considered for this analysis. It is composed of one leg with two IGBTs and their anti-parallel diodes. The voltage ucp/ni across each capacitor is usually fixed. Both IGBTs operate in a complementary manner. Moreover, the cell is said to be either inserted if the upper IGBT is turned on or the cell is said to be bypassed if the upper IGBT is turned off. These imply that the cell can insert or bypass its capacitor to the total array of the capacitors of the converter leg, synthesizing hence the multilevel waveform. In the particular case where both IGBTs are turned off, the cell is said to be blocked and the current flows through the diodes (and through the capacitor if the latter is to be charged). This particular case is not considered in this analysis. Batteries energy storage are connected to the cell via an interface. For the sake of generality, the batteries and the interface are modeled as a current source that injects/absorbs a current to/from the ac grid, regardless of the interface’s structure as shown in Figure 1(b). The influence of batteries’ characteristics on the performance of the converter is postponed to future papers. ICRERA 2014 19-22 Oct 2014 Milwakuee-USA A. Circuit dynamics In this section dynamics equations governing the behavior of the M2LC with batteries energy storage connected to the cell are derived. According to the sign’s convention adopted in Figure 1, the ac output current is defined as = (1) where ip and in are the positive and negative arm converter current. Fig. 1. (a) Phase-leg of the modular multilevel converter. (b) Integrated batteries energy storage into the cell - equivalent model. A circulating current containing dc and ac components flows through the arms due to the voltage ripple of the capacitors. It maintains the capacitors’ voltage between the arms balanced. In STATCOM operation of the M2LC, since a dc voltage between the arms is created, this circulating current is still present for the same previously stated purpose [10]. In order to highlight the power exchange from/to the batteries energy storage, we will differentiate between the circulating current with and without the energy storage. The current that flows in the positive/negative arm is hence defined as = = + + + (2) , , (3) where ic is the circulating current that flows between the arms when batteries are not connected to the cells. iBp,i and iBn,i are the positive and the negative-arm current injected to/from the battery connected to the ith cell. N-j is the number of cells with batteries energy storage connected to them. Note that j could be equal to zero meaning that batteries are connected to all cells of the arm. 3rd The International Conference on Renewable Energy Research and Applications By adding (2) and (3), a new circulating current can be defined. It takes into account the active power exchanged between the ac grid and the batteries. It is expressed as = +( + )= (4) The dynamics of the arm’s currents are given by = = (5) , + (6) , By adding (5) and (6), we obtain the governing equation of the circulating current icB , = , , = , (12) = B. Control strategy The main purpose of the open loop control is to find an expression of / which defines the insertion indices np/n in (9). The method is based on the evaluation of the energy stored in each arm which makes the control open looped [9]. The time derivative of the stored energy in one arm is equal to the input power of the corresponding arm which yields / (7) By subtracting (5) and (6), we obtain the governing equation of the output current iv (8) where = and = are the output phase equivalent inductance and resistance respectively. It is worth mentioning that, though the converter is intended to operate in a STATCOM mode, the dc-grid voltage is maintained constant thanks to the capacitors’ cell voltage regulation. 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 internal control objectives of the converter that aim to maintain an energy balance between the arms, an averaged model is used with the following assumptions that hold up satisfactory as demonstrated in [11] An infinite switching frequency is assumed. An infinite number of cells per arm is assumed. = / = / / (9) The dynamics equations governing the circulating current and the ac output current are hence rewritten as = = (10) (11) where uv and uc are the voltage that drives the ac output current and the circulating current respectively. They are expressed as ICRERA 2014 / / (13) / (14) On another hand, the energy stored in one arm is expressed as = / Differentiating (14) and substituting the result in (13) yields / = / (15) cos (16) / The expression of the inserted capacitors’ voltage for each arm can be deduced from (12). However, to simplify the analysis they can be defined as = = + cos (17) For the positive arm, substituting (2) and (16) into (15) yields = + + ( + ( cos ) (18) cos ) (19) + (20) For the negative arm, substituting (3) and (17) into (15) yields The voltage balancing between the cells is always assured. With these assumptions, by inserting the required number of cells, the inserted voltage ucp/n in each arm varies from 0 to / , and is given by 19-22 Oct 2014 Milwakuee-USA = + The open loop control relies on processing the energy stored in one leg and the difference of energy between the positive and negative arm. Hence by adding and then subtracting (18) and (19), we obtain =2 = + 2 cos + cos cos + + cos (21) Two cases are considered hereafter depending on whether the ac grid voltages are balanced or not. The aim of the analysis is to highlight the influence of the batteries on the capacitors’ voltage balance and the energy balance between the phase arms. Henceforth, the expression of the circulating 3rd The International Conference on Renewable Energy Research and Applications current that will achieve the control objective for both cases is derived. Case A Let us assume that the output phase voltage and current are quasi-sinusoids, though the output phase current is controlled using a feedforward controller. They are given by = = cos ) In the particular case of ac grid unbalance the ac current is not anymore split equally between the arms. This leads to a circulating current containing a dc component and an ac component that oscillates at the fundamental frequency. It can be defined as = (23) Substituting (23) in (20) and rearranging the terms yields =2 + (cos(2 + + (25) cos (26) The circulating current is hence given by = cos (27) Case B In this case, we shall define the circulating current under asymmetrical ac grid conditions that will rebalance the unbalanced ac voltages. Moreover, the development of the algorithm relies as well on the injection of a common ac voltage that oscillates at the fundamental frequency as presented in [12] for the cascaded converter. The converter phase voltage are hence redefined as cos( )+ cos( + )+ cos( + (28) Similarly, the converter phase current are redefined as = ICRERA 2014 cos + cos( + ) (29) = ) ( where = = When batteries are providing an active power to the grid, there is a small reduction in the reactive power supply due to the quadratic relation between the active and the reactive power. Hence, the first term in (26) would theoretically be different from zero. Note that even when batteries are disconnected, the circulating current should be different from zero in order to allow a power exchange between the arms. Hence, for a STATCOM operation of the M2LC, a small amount of active power should be provided especially when the converter is absorbing reactive power. = , ) ( and it is given (31) ) The common mode voltage is determined by considering the total phase-leg average power of each phase. It is expressed as = or using the notation icB, it is defined as = = , (24) = (30) For phase a, we found the expression of In order to have a stable operation of the converter, i.e., the capacitor’s voltages remain balanced, the constants in (21) and (24) should be zeroed. It appears from (21) that iBp should be equal to iBn which means that the number of batteries energy rooms connected in the positive arm should be equal to the number of batteries energy rooms connected in the negative arm. Hence, we should always satisfy the following = cos by cos ) + cos ) + Note that during ac grid asymmetry, the circulating current is defined for each phase-leg depending on the difference of power in one phase-leg . (22) cos( 19-22 Oct 2014 Milwakuee-USA cos 2 ) sin( ) and tan( + cos( ), = cos( cos sin + + 4 3 + + 2 cos sin )= sin + + 4 3 + sin( ) III. CASE STUDY To ascertain the feasibility of the study, a model of the M2LC with batteries units integrated in each cell has been implemented in PSCAD with the parameters shown in Table I. TABLE I. S PECIFICATION OF THE SIMULATED SYSTEM Apparent power Batteries energy storage power Grid voltage DC-link voltage Cell capacitance Nominal cell voltage Number of cells per arm 60 MVA 35 MW 30 kV ±50kV 2.5 mF 2.5 kV 40 Figure 2 depicts the voltage across each cell when batteries are injecting active power to the grid at t=0.5s. The capacitors’ voltage are kept well balanced and are not influenced by the current injected from the batteries. The current that is injected by each battery is around 100 A, and it is reflected in the circulating current as shown in Figure 3. The value of the discharge current has been chosen in such a way that the batteries are discharged in roughly 30 min. Figure 4 depicts the active and reactive power for this case. Similar figures are obtained when batteries are being charged at t=1.6s. In this particular case, the active power flows from the ac grid to the batteries. Figure 5 depicts the voltage across each cell where the voltage is being adjusted. Figure 6 shows the circulating current which reflects the 3rd The International Conference on Renewable Energy Research and Applications charging current of a battery room, fixed to 50 A in the simulation. Figure 7 shows the active and reactive power for the charging mode. P [MW] 2 5 0 -2 1.2 4 1.3 1.4 1.5 1.6 t [s] 1.7 1.8 1.9 2 1.3 1.4 1.5 1.6 t [s] 1.7 1.8 1.9 2 -55 Q [Mvar] ucp,i [kV] 19-22 Oct 2014 Milwakuee-USA 3 -60 -65 1.2 2 1 0.3 0.4 0.5 0.6 0.7 Figure 7. Charging mode. Active power (top). Reactive power (bottom). 0.8 t [s] Fig. 2. Discharging mode. Voltage across the cells (positive arm). 200 100 ic [A] 0 -100 -200 -300 0.2 0.3 0.4 0.5 0.6 t [s] 0.7 0.8 0.9 1 IV. CONCLUSION In this analysis, we have focused on exploring the capability of the modular multilevel converter with integrated batteries energy storage through deriving the circulating current expression to compensate for reactive power and to rebalance the ac grid voltage asymmetries. Simulation results showed that batteries can be charged or discharged without introducing any unbalance to the converter provided that the same number of batteries’ units is connected to the positive and negative arm. The capability of the converter to rebalance the ac grid during asymmetric ac grid conditions is postponed to future papers. Fig. 3. Discharging mode. Circulating current for a discharge current of 100A. REFERENCES P [MW] 0 [1] -2 -4 0.2 0.3 0.4 0.5 0.6 t [s] 0.7 0.8 0.9 1 0.3 0.4 0.5 0.6 t [s] 0.7 0.8 0.9 1 Q [Mvar] -50 -60 -70 0.2 Fig. 4. Discharging mode. Active power (top). Reactive power (bottom). 4 ucp,i [kV] 3.5 3 2.5 2 1.5 1 1.4 1.45 1.5 1.55 1.6 t [s] 1.65 1.7 1.75 Fig. 5. Charging mode. Voltage across the cells (positive arm). 150 ic [A] 100 50 0 -50 1.2 1.4 1.6 1.8 2 2.2 t [s] Fig. 6. Charging mode.Circulating current for a charge current of 50 A. ICRERA 2014 Z. Yang,et al, ‘Integration of a StatCom and Battery Energy Storage’, IEEE TRANSACTIONS ON POWER SYS., VOL. 16, NO. 2, MAY 2001 pp. 254/60 [2] H. Xie, et al, ‘Active power compensation of voltage source converters with energy storage capacitors’, in Proc. 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Maharjan et al, ‘Fault-Tolerant Operation of a Battery-EnergyStorage System Based on a Multilevel Cascade PWM Converter With Star Configuration’, IEEE Trans. On Power Elec., Vol. 25, No. 9, pp. 2386-96, Sep 2010. [8] M. A. Perez et al, ‘Modular Multilevel Converter with Integrated Storage for Solar Photovoltaic applications’, IECON 2013. [9] A. Antonopoulos et al, ‘On Dynamics and Voltage Control of the Modular Multilevel Converter’, EPE 2009. [10] S. Du, et al, ‘A Study on DC Voltage Control for Chopper-Cell-Based Modular Multilevel Converters in D-STATCOM Application’, IEEE Trans. ON Power Del., VOL. 28, NO. 4, pp. 2030/38, Oct 2013. [11] A. Lachichi, et al, ‘Comparative Analysis of Control Strategies for Modular Multilevel Converters’, PEDS 2011. [12] R. E. Betz et al, ‘Using a Cascaded H-Bridge STATCOM for Rebalancing Unbalanced Voltages’, 7th international Conference on Power Electronics, Oct. 2007.