/$ IEEE

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 55, NO. 10, OCTOBER 2008 1061 UPS Parallel Balanced Operation Without Explicit Estimation of Reactive Power A Simpler Scheme Edgar Campos Furtado, Luis Antônio Aguirre, and Leonardo A. B. Tôrres Abstract A novel scheme of the well-known technique for parallel operation of uninterruptible power supply systems, namely frequency and voltage droop control method, is presented. The innovation relies on active power estimation, together with the use of a piecewise-continuous nonlinear function, in order to eliminate the need for costly cascaded low-pass filters usually employed to estimate the reactive power. Moreover, the whole scheme is derived in the time domain on a state-space approach. As a consequence, models that are lower order and more amenable to nonlinear analysis are obtained. Simulated results for two UPS parallel operation connected to a resistive load are presented. The results indicate that the novel technique leads to a proper load sharing. Index Terms Droop method, uninterruptible power supply (UPS) system, parallel operation. I. INTRODUCTION I N RECENT YEARS, the development of uninterruptible power supply systems have matured, mainly motivated by the increased number of critical loads (e.g., air traffic control and life support equipment) and industrial applications [1], [2]. In order to supply continuous power to such loads with reliability and good quality, a system composed of various uninterruptible power supplies (multi-ups) operating in parallel is recommended, since it also increases the power capability of the overall system [3] [5]. The stabilization of a multi-ups parallel system can be realized using control interconnections, by wire, among all of the units, or by measuring only local variables without extra interconnections, which is usually called wireless control. The first approach is based on exchanging some information, e.g., the UPS output current, to provide a proper load sharing [6], [7]. However, this approach decreases the reliability, since any failure on the control connection could lead to overall system failure. The second approach is often based on the droop method [8], in which local variables, such as the UPS output current and line voltage, are used to estimate the active and the reactive power delivered to the load, which are subsequently employed to adjust the frequency and voltage of an internal UPS reference signal. However, to successfully apply the droop method, several tradeoffs must be observed, as pointed out in [9] and [10], mainly concerning the frequency and voltage regulations and Manuscript received August 27, 2007; revised March 14, 2008. Current version published October 15, 2008. This work was supported in part by CNPq and CAPES. This paper was recommended by Associate Editor C. Nwankpa. The authors are with the Laboratório de Modelagem, Análise e Controle de Sistemas Não-Lineares, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, Minas Gerais, Brazil (e-mail: edgar.furtado@gmail.com; aguirre@cpdee.ufmg.br; torres@cpdee.ufmg.br). Digital Object Identifier 10.1109/TCSII.2008.926800 the dynamical performance. The dynamics of the multi-ups system parallel operation, based on the droop control method, is highly dependent on the power estimation algorithm and on the specific coefficients of the curves relating active power to frequency variation and reactive power to output voltage amplitude variation [11]. Methods often used for power calculation were proposed in [8] and [12], which are based on filtering instantaneous power delivered by the UPS. As a result, modeling becomes a complex task. The aim of this paper is to present a novel scheme of the droop control method, without explicit estimation of the reactive power. The concept of generalized active power is introduced, from which the estimated reactive power can be obtained through the use of a nonlinear piecewise-continuous function and the knowledge of the instantaneous power. The novel scheme is compared with common alternatives that rely on the use of various low-pass filters and phase estimators [11], [12]. Simulation results indicate that the proposed implementation is indeed adequate to synchronize two UPS systems connected to a resistive load. Moreover, the novel scheme exhibits good synchronization times, and it seems to be less complex than those observed in usual implementations. This work is organized as follows. In Section II, the parallel operation of the multi-ups system via droop control method is reviewed. In Section III, the UPS modeling is presented, which also presents the novel technique to estimate the powers. Numerical results of power estimations and offline parallel operation between two identical are provided. Conclusions are given in Section V. II. WIRELESS PARALLEL OPERATION The wireless parallel operation of a multi-ups system assumes that only local variables are accessible for control: usually the current and voltage supplied by the UPS. From such variables, sinusoidal reference signals are generated in each UPS, according to the so-called droop method [8]. The stable parallel operation of multi-ups systems in this case is attained when differences in output voltages, generated by each UPS unit, vanish, which leads to proper load sharing by equal distribution of the demanded power among UPS units. In the droop method, the following relations between active power and frequency, and between reactive power and voltage, are used to guarantee stable operation of interconnected UPS [8]: (1) (2) where and are the active power and reactive power, respectively, and are the output voltage frequency and ampli- 1549-7747/$25.00 2008 IEEE

1062 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 55, NO. 10, OCTOBER 2008 Fig. 1. Circuit representation of an inverter. tude at no load condition, and and are slopes that must be adjusted to ensure stable operation. Equations (1) and (2) reveal that there is unavoidable drift from nominal conditions when or, in steady state. Moreover, the dynamical performance and stability are both highly dependent on power calculations from measured data, which usually employ two or more low-pass filters and phase estimators [11], [12]. A. Inverter Model III. MODELING THE UPS As shown in Fig. 1, in the UPS model, it was considered the existence of a typical single-phase inverter, represented by a dc power source, followed by a PWM inverter providing the signal, based on the reference signal. The PWM inverter output signal is comprised by a fundamental component and accompanying harmonics. Control design technique for dc ac PWM inverter can be found in [13]. Moreover, the UPS contains an LC low-pass filter at the output formed by,, and, together with a coupling inductor. This coupling inductor is essential to guarantee stable operation when (1) and (2) are implemented, as observed in [11]. The line connection between inverter and load is represented by the resistance. Usually, the PWM switching frequency is several orders of magnitude higher than the cutoff frequency of the low-pass filter represented by the LC combination (Fig. 1), and therefore the contribution of the harmonic parcel on the output voltage can be ignored, such that. B. Power Calculation Block To implement the strategy represented by (1) and (2), the active power and the reactive power supplied by the UPS must be somehow estimated. One way to estimate the active power delivered by the UPS unit is by low-pass filtering the instantaneous output power, such that where is viewed as a generalized active power signal, represents the instantaneous power, and is the associated low-pass filter cutoff angular frequency. On the other hand, commonly used methods for reactive (3) Fig. 2. Block diagram of three power calculation algorithms. (a) Method 1. (b) Method 2. power estimation are based on the output current and line voltage measurements [8], [12]. Two of them are exemplified in Fig. 2(a) and (b). As can be seen from the figure, such methods use two or more low-pass filters ( LPF blocks) and phase estimators (the block denoted by ), where the output voltage is taken as the reference for phase calculations. Models obtained from such methods seem to be more complex, rendering the nonlinear stability analysis cumbersome. Despite this, it is interesting to note that the reactive power can be obtained directly from instantaneous power and active power. From classical electrical circuit theory for sinusoidal steady-state response, it is possible to show that the reactive power can be expressed as If one substitutes, in (4), by, in (3) and ensures that the denominator in the above expression will never be zero by approximating the cosecant function by a bounded mapping, then it is possible to estimate the reactive power relying solely on and, without adding extra low-pass filters. A very similar idea will be used in the droop control method, as presented in Section III-C, to suggest a major complexity reduction in the control implementation. C. UPS Control Block In light of the above-mentioned approximations, (1) and (2) can be rewritten as (4) (5) (6)

FURTADO et al.: UPS PARALLEL BALANCED OPERATION WITHOUT EXPLICIT ESTIMATION OF REACTIVE POWER A SIMPLER SCHEME 1063 TABLE I PARAMETERS OF THE UPS MODEL AND THE LOAD Fig. 3. Block diagram of the UPS modeled by (8). The sinusoidal reference signal is obtained from (5) and (6) by multiplying both sides of (6) by, which yields Fig. 4. Transient response for the frequency of u : (-) method 1 [Fig. 2(a)]; (-) for both method 2 [Fig. 2(b)] and for the proposed one, since the estimation procedure is the same. (7) The function is the reference signal, where,,, and from (1). The singularity in can be artificially removed through the substitution of by a constant, with, and, every time that. This approximation results in a modified reference signal, denoted by, which is more amenable to digital implementation. It is important to point out that such an approximation does not contribute with harmonic distortion in the load voltage, since, for and, the THD values of the reference signals were approximately 0.034%. To control the output voltage such that it follows the reference (Fig. 1), the inductor current and the capacitor voltage are measured as feedback variables, as shown in Fig. 3. An inner current loop provides current limiting, acting together with a proportional-plus-integral (PI ) voltage control loop that regulates the output voltage. The model in the time domain for a single-phase UPS, following the above description, can be written as where are represented in Fig. 3, is the output of the PI block,, and. The other parameters are: ; ; ; (8) ; ; is the PWM signal generation gain, which is considered as a unit gain; and and are the PI controller parameters. It is interesting to note that, if one considers a static relation between output voltage and current, (8) can be rewritten as a Lur e system [14], [15]. In the case of resistive load, the reference signal will become dependent on and, since and, and the UPS model yields IV. NUMERICAL RESULTS Here, the main points of the UPS model (9) are illustrated by means of two simulated cases. In the first case, a fixed UPS scheme was tested for different power calculation methods. In the second case, two UPS parallel operations connected to a resistive load are investigated. A. Comparison of Power Calculation Methods Consider the UPS scheme shown in Fig. 3. The parameters for the PI controller, the inverter, and the droop curves are listed in Table I. The time evolution of the reference signal frequency, obtained by implementing the droop method using different strategies to estimate the active and reactive powers, together with the (9)

1064 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 55, NO. 10, OCTOBER 2008 Fig. 6. Structure of coupling between two UPS. Fig. 5. Transient response for u. (a) (-) Method 1 and (-) method 2. (b) Method 3 (-) before and (-) after filtering. strategy presented above, is shown in Fig. 4. The dynamical performance of each technique is quite similar. However, method 1 is more complex to implement in practice. On the other hand, the amplitude transient response, which depends on the estimated reactive power, is clearly different for each strategy, as can be seen in Fig. 5(a) and (b), although the settling time is similar for all of the schemes. The transient regime for the proposed method [Fig. 5(b)] is characterized by abrupt variations located near the singularities points of the function. However, filtering this signal with a low-pass filter (just for comparison purposes and not in the strategy implementation), the resulting time-series indicates that the amplitude settles down to a final value close to that exhibited by the other schemes. In practice, one expects that these abrupt variations are naturally filtered out by the limited bandwidth of the UPS internal controlled inverter (PI controller plus LC low-pass filter). B. Parallel Operation of Two Identical UPS Consider two identical UPS (Fig. 6) described by (9), which together or not, have to supply a resistive load. The coupled system can be modeled by Fig. 7. Coupling between two UPS. (a) Load variation. (b) Active power. (c) Reactive power. (10) (11)

FURTADO et al.: UPS PARALLEL BALANCED OPERATION WITHOUT EXPLICIT ESTIMATION OF REACTIVE POWER A SIMPLER SCHEME 1065 As a result, the control scheme has low complexity, both for modeling and for computational implementation. Simulated results reveal that all of the power calculation methods attain the same steady-state regime. In the proposed strategy, it was observed that high variations occur in the estimated reactive power signal, but this seems to be immaterial for single and parallel operation. In addition, parallel operation results show that the proposed scheme can attain stable sharing of active power between 2 UPS units during resistive load variations. Fig. 8. Output current of the UPS between 2:2 t 2:4 sfor: (-) UPS1 and (-) UPS2. From (10) and (11), it is clear that increasing the number of UPS will affect the load voltage, since it depends on the currents supplied by each UPS. However, in the control scheme proposed, such a variable is measured, which means that the structure of control will not be affected by the number of UPS operating in parallel. Fig. 7 presents the time evolution of two UPSs operating in parallel. Such units make use of the control scheme proposed and described in Section III-C. For s, only UPS 1 supplies energy to the load, whose value varies at s from 4 to 8.At s, UPS 2 is connected to the circuit starting the parallel operation with UPS 1. As can be seen in Fig. 7(b), the active power is properly divided between the UPS. At s, the load changes to 6, and the coupled multi-ups system continues to suitably share the active power delivered to the load. Fig. 7(c) shows the reactive power associate with one of the UPS. Very high variations are observed when changes occur in the coupled system. Such variations are nonetheless artifacts produced by the use of the piecewise-continuous nonlinear function, during the instantaneous reactive power signal estimation. This conclusion can be reinforced by observing that the output current of each the UPS is free from these effects, as shown in Fig. 8. An interesting observation is that, in the case of nonlinear loads it is pointed out in the literature that the droop method, in its original form, does not have an appropriate response for nonlinear loads due to the incapability of sharing appropriately current harmonics. Depending on the value of such harmonics, the power could not be balanced. However, the technique proposed in this paper could be effective in such cases because there is no explicit calculation of reactive power and, on the other hand, the instantaneous power is used to balance the system. V. CONCLUSION This work presented a time-domain state-space model of a single-phase UPS unit. The model proposed (8) is fifth order and was obtained based on a new power calculation method, which requires just one low-pass filter and a nonlinear static function to estimate both active and reactive powers. ACKNOWLEDGMENT The authors would like to thank P. Cortizo for the critical reading of an early version of this paper. REFERENCES [1] S. B. Bekiarov and A. Emadi, Uninterruptible power supplies: Classification, operation, dynamics, andcontrol, in Proc. Appl. Power Electron. Conf. Expo. APEC, Mar. 2002, vol. 1, pp. 597 604. [2] C.-C Yeh and M. D. Manjrekar, A reconfigurable uninterruptible power supply system for multiple power quality applications, in Proc. Appl. Power Electron. Conf. Expo. APEC, Mar. 2005, vol. 3, pp. 1824 1830. [3] T. Kawabata and S. Higashino, Parallel operation of voltage source inverters, IEEE Trans. Ind. Appl., vol. 24, no. 2, pp. 281 287, Mar./ Apr. 1988. [4] M. C. Chandorkar, D. M. Divan, and R. Adapa, Control of parallel connected inverters in standalone AC supply systems, IEEE Trans. Ind. Appl., vol. 29, pp. 136 143, Jan./Feb. 1993. [5] X. Sun, L.-K. Wong, Y.-S. Lee, and D. Xu, Design and analysis of an optimal controller for parallel multi-inverter systems, IEEE Trans. Circuits Syst. II, Express Briefs, vol. 52, no. 1, pp. 56 61, Jan. 2006. [6] J. F. Chen and C. L. Chu, Combination voltage-controlled and current-controlled PWM inverters forups parallel operation, IEEE Trans. Power Electron., vol. 10, pp. 547 558, 5, Sep. 1995. [7] Y. J. Cheng and K. Kenneth, A novel communication strategy for decentralized control of paralleled multi-invertersystems, IEEE Trans. Power Electron., vol. 21, no. 4, pp. 148 156, Jan. 2006. [8] A. Tuladhar, H. J. J. Unger, and K. Mauch, Parallel operation of single phase inverter modules with no control interconnections, in Proc. Appl. Power Electron. Conf. Expo. APEC, 1997, vol. 1, pp. 94 100. [9] X. Sun, Y. S. Lee, and D. Xu, Modeling, analysis, and implementation of parallel multi-inverter systemswith instantaneous average-current-sharing scheme, IEEE Trans. Power Electron., vol. 18, no. 3, pp. 844 856, May 2003. [10] J. M. Guerrero, L. G. Vicuna, J. Matas, M. Castilla, and J. Miret, Output impedance design of parallel-connected UPS inverters with wirelessload-sharing control, IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1126 1135, Aug. 2005. [11] E. A. A. Coelho, P. C. Cortizo, and P. F. D. Garcia, Small-signal stability for parallel-connected inverters in stand-alone acsupply systems, IEEE Trans. Ind. Appl., vol. 38, no. 2, pp. 533 542, Apr. 2002. [12] J. M. Guerrero, L. G. d. Vicuña, J. Matas, and J. Miret, Steady-state invariant-frequency control of parallel redundant uninterruptiblepower supplies, in Proc. Ind. Electron. Conf. IECON, Nov. 2002, vol. 1, pp. 274 277. [13] Y. Ye, K. Zhou, B. Zhang, D. Wang, and J. Wang, High-performance repetitive control of PWM DC-AC converters with real-time phase-lead fir filter, IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 8, pp. 768 772, Aug. 2006. [14] L. O. Chua, Nonlinear circuits, IEEE Trans. Circuits Syst., vol. CAS-31, no. 1, pp. 69 87, Jan. 1984. [15] M. Vidyasagar, Nonlinear Systems Analysis. Philadelphia, PA: SIAM, 2002.