IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER

Transcription

1 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER A Wireless Controller to Enhance Dynamic Performance of Parallel Inverters in Distributed Generation Systems Josep M. Guerrero, Member, IEEE, Luis García de Vicuña, José Matas, Miguel Castilla, and Jaume Miret, Member, IEEE Abstract This paper presents a novel control strategy for parallel inverters of distributed generation units in an ac distribution system. The proposed control technique, based on the droop control method, uses only locally measurable feedback signals. This method is usually applied to achieve good active and reactive power sharing when communication between the inverters is difficult due to its physical location. However, the conventional voltage and frequency droop methods of achieving load sharing have a slow and oscillating transient response. Moreover, there is no possibility to modify the transient response without the loss of power sharing precision or output-voltage and frequency accuracy. In this work, a great improvement in transient response is achieved by introducing power derivative-integral terms into a conventional droop scheme. Hence, better controllability of the system is obtained and, consequently, proper transient performance can be achieved. In addition, an instantaneous current control loop is also included in the novel controller to ensure proper sharing of harmonic components when supplying nonlinear loads. Simulation and experimental results are presented to prove the validity of this approach, which shows excellent performance as opposed to the conventional one. Index Terms Distributed generation (DG), droop control method, nonlinear loads. I. INTRODUCTION DISTRIBUTED generation (DG) systems are presented as a suitable form to offer high reliable electrical power supply [1]. The concept is particularly interesting when different kinds of energy resources are available, such as photovoltaic panels, fuel cells, or speed wind turbines [2], [3]. Most part of these resources need power electronic interfaces to make up local ac grids [4], [5]. This way, inverters or ac-to-ac converters are connected to an ac common bus with the aim to share properly the disperse loads connected to the local grid [6]. In addition, every unit must be able to operate independently when communication is too difficult due to the long distance between its connection points [7]. In this sense, several control techniques have been proposed without control wire interconnections based on Manuscript received July 16, 2003; revised June 3, This paper was presented in part at PESC 03, Acapulco, México, June 15 19, This work was supported by the Spanish Ministry of Science and Technology under CICYT DPI C Recommended by Associate Editor I. Gadoura. The authors are with the Departament d Enginyeria de Sistemes, Automàtica i Informàtica Industrial, Departament d Enginyeria Electrònica, Universidad Politécnica de Cataluña, Barcelona, Spain ( josep.m.guerrero@upc.es). Digital Object Identifier /TPEL the droop method [8] [11]. To achieve good power sharing, the control loop makes tight adjustments over the output voltage frequency and amplitude of the inverter, in order to compensate the active and reactive power unbalances [12]. This concept steams from the power system theory, in which a generator connected to the utility mains drops its frequency when the power required increases [13]. In the literature, there are many control schemes based on the droop method to share linear loads [14]. Nevertheless, nowadays the proliferation of nonlinear loads has become a problem, because the units must both share harmonic current and to balance active and reactive power. In [15], a controller was proposed to share nonlinear loads by adjusting the output voltage bandwidth with the delivered harmonic power. However, this technique has two main limitations: the controller uses an algorithm which is too complicated to calculate the harmonic current content, and the harmonic current sharing is achieved at the expense of reducing the stability of the system. Recently, novel control loops that adjust the output impedance of the units by adding virtual resistors [16] or reactors [17] have been included in the droop method, with the purpose to share the harmonic current content properly. In another approach [18], every single term of the harmonic current is used to produce a proportional droop in the corresponding harmonic voltage term, which is added to the output-voltage reference. Nevertheless, the control approaches mentioned above have an inherent tradeoff between voltage regulation and power sharing. Besides, the droop method exhibits slow dynamic response, since it requires low-pass filters with a reduced bandwidth to calculate the average value of the active and reactive power [19]. Then, the stability and the dynamics of the whole system are strongly influenced by the characteristics of these filters and by the value of the droop coefficients, which are bounded by the maximum allowed deviations of the output voltage amplitude and frequency. In this paper, we propose a novel control scheme that is able to improve the transient response of parallel-connected inverters without using communication signals. A wireless controller was developed, by adding a supplemental transient droop characteristic to the conventional static droop approach, which improves the paralleled-system dynamics. The novel droop function ensures both steady-state objectives and a good transient performance. Simulation and experimental results are reported, confirming the validity of this control technique /04$ IEEE

2 1206 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004 Fig. 3. Static droop characteristics P 0! and Q 0 E. Fig. 1. Distributed generation units connected in parallel to a common ac bus. Fig. 2. Equivalent circuit of an inverter connected to a bus. II. REVIEW OF THE CONVENTIONAL DROOP METHOD Fig. 1 shows a DG system made up of different kind of resources, such as solar panels, fuel cells, and speed wind turbines. As mentioned previously, every resource needs an electric power interface to transfer energy to the common bus. We can model every unit as an inverter connected to the common bus through a decoupling impedance, as shown in Fig. 2. Usually the inverter output impedance is highly inductive, and, hence, the active and reactive powers drawn to the bus can be expressed as [13] where is the output reactance of an inverter, is the phase angle between the output voltage of the inverter and the voltage of the common bus, and and are the amplitude of the output voltage of the inverter and the load voltage, respectively. From the above equations, it can be derived that the active power is predominately dependent on the power angle, while the reactive power mostly depends on the output-voltage amplitude. Consequently, most of the wireless-control of paralleled-inverters uses the conventional droop method, which introduces the following droops in the amplitude and the frequency of the inverter output voltage (1) (2) (3) (4) being and the output voltage angular frequency and amplitude at no load, and and are the droop coefficients for the frequency and amplitude, respectively. It is well known that if droop coefficients are increased, then good power sharing is achieved at the expense of degrading the Fig. 4. Tradeoff between frequency deviation and active power sharing (droop coefficient m >m). voltage regulation [15], which can be acceptable if, for instance, the frequency and amplitude deviations are mostly at 2% and 5%, respectively (see Figs. 3 and 4). The inherent tradeoff of this scheme restricts the mentioned coefficients, which can be a serious limitation in terms of transient response, power sharing accuracy, and system stability [19]. On the other hand, to carry out the droop functions expressed by (3) and (4), it is necessary to calculate the average value over one line-cycle of the output active and reactive instantaneous power. This can be implemented by means of low-pass filters with a smaller bandwidth than that of the closed-loop inverter. Consequently, the power calculation filters and droop coefficients determine, to a large extent, the dynamics and the stability of the paralleled-inverters [19]. Damping and oscillatory phenomena of phase shift difference could cause instabilities and a large transient circulating current that can overload and damage the units. In conclusion, the conventional droop method has several intrinsic problems related to its limited transient response, since the system dynamics depends on the power-calculation filter characteristics, the droop coefficients, and the output impedance. These parameters are determined by the line-frequency, the maximum allowed frequency and amplitude deviations, and the nominal output power. Thus, by using the conventional droop method, the inverter dynamics cannot be independently controlled. III. PROPOSED CONTROL TECHNIQUE In this paper, we will try to overcome the above limitations and to synthesize a novel control strategy without communication wires that could be appropriate for a high-performance

3 GUERRERO et al.: WIRELESS CONTROLLER 1207 voltage proportionally to the time-derivative of the fundamental output-current. On the other hand, in order to share harmonic current content, without increasing output-voltage THD too much, the resistive-impedance should be achieved. Hence, a high pass filter can easily carry out both behaviors. Note that the gain and the pole value of this filter must be carefully chosen. The proper design of this output impedance can reduce, to a large extent, the line-impedance impact over the power sharing accuracy. Fig. 5. Block diagram of the proposed controller. DG electrical ac interface system. To improve the dynamics of the system, the following novel droop-based control scheme is proposed: where is the derivative coefficient of the reactive power ;,, and are the integral, proportional, and derivative coefficients of the active power. Note that if we take into account that, the steady-state voltage and the frequency droops coincide exactly with those obtained with the conventional method, expressed by (3) and (4). The proposed control scheme allows us to modify the transient response, act on the control coefficients, and, at the same time, keep the static droop characteristic. Also, it minimizes the transient circulating current among the units and further improves the dynamic performance of the whole system. In fact, the coefficients and fix the steady-state droop function while,, and are selected to guarantee stability and good transient response. (5) (6) V. SMALL-SIGNAL MODELING To analyze the stability and the transient response, a smallsignal model of the parallel-inverter system is proposed. An objective of the above controllers is to avoid the existence of a circulating current among the inverters. Hence, this current can be an interesting variable to investigate; however, it is a fast and oscillating variable, which can complicate the analysis of the system. To facilitate this analysis, from Fig. 2, the envelope signal of the current drawn to the bus can be found By taking the usual approximations,, and, we can derive where is a small variation of the phase difference. As it can be seen, the envelope of is proportional to the power angle. Consequently, a small-signal analysis is proposed to obtain the dynamics of taking into account the well-known infinite bus approximation [13], [19]. First, we must take into account the expression of the lowpass filters, shown in Fig. 5, which averages the instantaneous active and reactive power values. By using (1) and (2), and modeling the low-pass filters as a first-order system, it yields to (7) (8) IV. CONTROLLER IMPLEMENTATION Fig. 5 depicts the block diagram of the proposed controller. The average active power can be obtained by multiplying the inverter output voltage by the inverter output current, and by filtering the product using a low-pass filter. In a similar way, the average reactive power is obtained, but in this case the output voltage must be delayed 90. In order to adjust the output voltage phase, (5) is implemented, which corresponds to a PID controller applied over the average active power signal. The output-voltage amplitude is regulated by using the conventional droop method with the inclusion of the reactive power derivative term [see (6)]. Finally, the output impedance of the inverter can be emulated by means of a high-pass filter to share linear and nonlinear loads [20]. In this case, an additional faster loop is added to program the output impedance. On the one hand, inductive output impedance can be implemented by dropping the output (9) (10) where denotes perturbed values, capital letters mean equilibrium point values, and is the cut-off angular frequency of the low-pass filters, which must be fixed over one decade below from frequency mains. Second, by perturbing (5) (6) and using (9) (10), we obtain (11) (12)

4 1208 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004 Finally, substituting (12) into (11), it can be found where,, and are (13) Using (13), the stability of the closed-loop system can be evaluated, and a desired transient response can be selected following a linear three-order dynamics. From the values of,, and coefficients, it can be seen that the proposed controller endows superior controllability of the dynamics as opposed to the conventional approach, in which,, and. VI. DESIGN METHODOLOGY In order to properly select the coefficients of the loadsharing controller, we propose a design methodology. First, the coefficients and can be chosen as in the conventional droop method to ensure steady state control objectives [15] as follows: Fig. 6. Root locus diagrams for (a) 0 m 10, m =51 10 and (b) 0 m 10, m = TABLE I PARAMETERS OF THE WIRELESS LOAD-SHARING CONTROL (14) (15) where and are the maximum active and reactive powers that can be delivered by the inverter and and are the maximum frequency and amplitude output-voltage deviations allowed (see Fig. 3). Hence, these two parameters can be fixed by the designer taking into account the tradeoff between the power sharing accuracy and the frequency and amplitude deviation. Second, the coefficients,, and are chosen in order to adjust the transient response, and ensuring system stability. In this sense, the analysis of the eigenvalues of (13) through several root locus plots as a function of these parameters is presented. Fig. 6(a) and (b) show the root locus plots using the parameters listed in Table I, and considering a variation of the coef-

5 GUERRERO et al.: WIRELESS CONTROLLER 1209 Fig. 7. Family of root locus diagrams for n =0, 5110, and 10. (a) 0 m 10 and (b) 0 m 10. ficients and from zero to. Notice that this system has three roots: two conjugated poles ( and ) and a real pole. The arrows indicate the evolution of the corresponding pole when the coefficient increases. As Fig. 6(a) shows, with the increasing of, the conjugated poles tend to go far away from the imaginary axis splitting as two real poles, while the single pole is attracted toward the origin, becoming the dominant root. Thus, the system behavior can be approximated as a first order system but it turns slower. Fig. 6(b) shows that when increasing, the complex poles become dominant, resulting in a near second order behavior. Since in both cases the poles remain in the left half -plane, the system is stable in the range of concern. Fig. 7 illustrates the low sensibility of over the system dynamics, through three superimposed root locus plots considering the same variations as in Fig. 6. Due to the small variation in the root locus, this parameter can be previously fixed or finally adjusted for fine tuning purposes. Fig. 8 depicts two family of root locus considering a wider variation of and coefficients, which allow us to identify Fig. 8. Family of root locus diagrams (n =5110 ): (a) m =0, 5110, 10110, and for 010 m 10 and (b) m = , ,0,5 1 10, , and for 0 m 10. stable and unstable behaviors. Note that, in this case, when and have positive values the system is stable. It can be seen that there is a small range of negative values of in which the system remains stable. Out of this range, the system becomes unstable (see shadowed area). In a practical design, and coefficients should be chosen to obtain the desired transient response specifications, taking into account the well-known tradeoff design between an over-damping fast response or a slower first order dynamics. VII. SIMULATION AND EXPERIMENTAL RESULTS The conventional droop method (3) (4) and the proposed control scheme (5) (6) were simulated with the parameters listed in Table I and the scheme shown in Fig. 9 for a two-inverter paralleled system in order to compare its outstanding features. Coefficients and were chosen taking into account the tradeoff between the power sharing accuracy and the voltage regulation, while,, and were selected to

6 1210 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004 Fig. 9. Parallel operation of two inverters. Fig. 11. Dynamic response of the phase difference between inverters, at variations of (a) m and (b) m. Fig. 10. Transient response of circulating current and its approximated envelope deduced from (8): (a) conventional droop method and (b) proposed control method. ensure stability and a good transient response as explained in the previous section. Fig. 10 shows the startup circulating current and its approximated envelope deduced from (8), using the conventional droop method and the proposed control, respectively. These results confirm that the proposed controller achieves a better dynamic response than that of the classical droop method approach. Note that in spite of the initial current peak due to the initial phaseerror between inverters, a faster transient response, better dynamic performance, and less circulating current are achieved with the proposed control solution. Fig. 11 shows startup waveforms of the phase difference between the inverters for different values of the coefficients of the proposed controller, which proves that the transient response of the system can be easily modified with these parameters. Fig. 11(a) depicts that the transient behavior turns slower and less damped when increasing, due to the fact that the real pole becomes dominant, as shown Fig. 6(a). Fig. 11(b) shows the tendency to obtain a more oscillatory response when increasing, since it attracts the conjugated poles toward the imaginary axis, as can be seen in Fig. 6(b). Combining these two degrees of freedom with the tight adjust of, we can obtain a better dynamic performance than in the conventional droop method, since using the conventional one the transient response can not be adjusted without change and values. Two 1-kVA single-phase inverter units were built and tested in order to show the validity of the proposed approach. Each inverter consisted of a single-phase insulated gate bipolar transistor (IGBT) full-bridge with a switching frequency of 20 khz and an output filter, with the following parameters: mh, F, V, and V Hz. The controllers of these inverters were based on three loops: an inner current-loop, an outer PI controller that ensures voltage regulation [21], and the load-sharing controller, based on (5) and (6). The last controller was implemented by means of a TMS320LF2407A, fixed-point 40-MHz digital signal processor (DSP) from Texas Instruments (see Fig. 12), using the parameters listed in Table I. The DSP-controller also includes a PLL block in order to synchronize the inverter with the common bus. When this occurs, the static bypass switch is turned on, and the droop-based control is initiated.

7 GUERRERO et al.: WIRELESS CONTROLLER 1211 Fig. 12. Power stage and controller of a single unit. (a) (a) (b) (b) Fig. 13. Transient response of the circulating current (X-axis: 5 A/div, Y-axis: 100 ms/div): (a) conventional droop method and (b) proposed control method. Fig. 14. Transient response of the active power P (X-axis: 500 W/div, Y-axis: 200 ms/div): (a) conventional droop method and (b) proposed control method. The dynamic performance of the parallel system is experimentally evaluated in case of connecting inverter #2 when the inverter #1 is supplying all the power required by the load. Fig. 13 shows the circulating-current using the (a) conventional droop method and (b) the one proposed. Fig. 14 depicts the active power transient behavior for both control schemes. These results show an overall improvement in the dynamic response of the proposed control solution. The second experimental test consists in supplying a nonlinear load by means of the two parallel inverter systems. Fig. 15

8 1212 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004 (b) Fig. 15. Steady-state waveforms supplying a nonlinear load: (a) load voltage and current (X-axis: 5 ms/div, Y-axis: 150 V/div, 10 A/div) and (b) output current of the two units (X-axis: 10 ms/div, Y-axis: 10 A/div). (a) shows the load voltage and current, and the output current of the two units. As it can be seen, the load sharing capability is very good, even when supplying nonlinear loads. VIII. CONCLUSION In this paper, a novel load-sharing controller for parallel inverters has been proposed. Based on the droop method, the controller avoids the use of control wire interconnections. In a sharp contrast with the conventional droop method, the presented controller is able to modify the dynamic response of the paralleled system by correctly tuning control gain parameters. Simulation and experimental results show that the dynamic response is significantly improved, highlighting the possibilities of the proposed approach for inverters in DG systems, when several units must be connected to a common ac bus with a proper transient response. Linear and nonlinear loads can be correctly supplied by the parallel system using the proposed control solution. ACKNOWLEDGMENT The authors would like to thank J. Barri, R. Ciurans, D. Montesinos, and A. Sabé, Salicrú Electronics, for their help with the experimental verification. REFERENCES [1] R. H. Lasseter et al., White paper on integration of distributed energy resources. The CERTS microgrid concept, in Consort. Electric Reliability Technology Solutions, 2002, pp [2] K. Ro and S. Rahman, Two-loop controller for maximizing performance of a grid-connected photovoltaic-fuel cell hybrid power plant, IEEE Trans. Energy Conv., vol. EC-13, pp , Sept [3] R. H. Lasseter and P. Piagi, Providing premium power through distributed resources, in Proc. IEEE 33rd Hawaii Int. Conf. System Sciences (HICSS 00), 2000, pp [4] S. R. Wall, Performance of inverter interfaced distributed generation, in Proc. IEEE/PES-Transmission and Distribution Conf. Expo., 2001, pp [5] C. Wekesa and T. Ohnishi, Utility interactive AC module photovoltaic system with frequency tracking and active power filter capabilities, in Proc. IEEE-PCC 02 Conf., 2002, pp [6] J. Liang, T. C. Green, G. Weiss, and Q.-C. Zhong, Evaluation of repetitive control for power quality improvement of distributed generation, in Proc. IEEE-PESC 02 Conf., 2002, pp [7] S. Barsi, M. Ceraolo, P. Pelachi, and D. Poli, Control techniques of dispersed generators to improve the continuity of electricity supply, in Proc. IEEE PES 02 Winter Meeting, 2002, pp [8] R. H. Lasseter, Microgrids, in Proc. IEEE PES 02 Winter Meeting, 2002, pp [9] C.-C. Hua, K.-A. Liao, and J.-R. Lin, Parallel operation of inverters for distributed photovoltaic power supply system, in Proc. IEEE PESC 02 Conf., 2002, pp [10] J. Sachau and A. Engler, Static and rotating grid formation for modularly expandable island grids, in Proc. EPE 99 Conf., Laussane, Frane, 1999, pp [11] H. Matthias and S. Helmut, Control of a three phase inverter feeding an unbalanced load and operating in parallel with other power sources, in Proc. EPE-PEMC 02 Conf., 2002, pp [12] T. Kawabata and S. Higashino, Parallel operation of voltage source inverters, IEEE Trans. Ind. Applicat., vol. IA-24, pp , Mar./Apr [13] A. R. Bergen, Power Systems Analysis. Englewood Cliffs, NJ: Prentice-Hall, [14] M. C. Chandorkar and D. M. Divan, Control of parallel connected inverters in standalone AC supply system, IEEE Trans. Ind. Applicat., vol. IA-29, pp , Jan./Feb [15] A. Tuladhar, H. Jin, T. Unger, and K. Mauch, Parallel operation of single phase inverter modules with no control interconnections, in Proc. IEEE-APEC 97 Conf., 1997, pp [16] S. J. Chiang, C. Y. Yen, and K. T. Chang, A multimodule parallelable series-connected PWM voltage regulator, IEEE Trans. Ind. Electron., vol. 48, pp , June [17] A. Engler, Control of parallel operating battery inverters, PV Hybrid Power Syst., [18] U. Borup, F. Blaabjerg, and P. N. Enjeti, Sharing of nonlinear load in parallel-connected three-phase converters, IEEE Trans. Ind. Applicat., vol. 37, pp , Nov./Dec [19] E. A. A. Coelho, P. Cabaleiro, and P. F. Donoso, Small signal stability for single phase inverter connected to stiff AC system, in Proc. IEEE- IAS 99 Annu. Meeting, 1999, pp [20] J. M. Guerrero, L. García de Vicuña, J. Matas, and J. Miret, Steady-state invariant-frequency control of parallel redundant uninterruptible power supplies, in Proc. IEEE-IECON 02 Conf., 2002, pp [21] H. Wu, D. Lin, D. Zhang, K. Yao, and J. Zhang, A current-mode control technique with instantaneous inductor-current feedback for UPS inverters, in Proc. IEEE APEC 99 Conf., 1999, pp Josep M. Guerrero (S 01 M 03) received the B.S. degree in telecommunication engineering, the M.S. degree in electronic engineering, and the Ph.D. degree from Polytechnic University of Catalunya, Barcelona, Spain, in 1997, 2000, and 2003, respectively. Since 1998, he has been an Assistant Professor in the Department of Automatic Control Systems and Computer Engineering, Polytechnic University of Catalunya, where he teaches digital signal processing, control theory, and microprocessors. His research interests include DSP-based control, uninterruptible power supplies, and distributed power systems. Dr. Guerrero is an Associate Editor with the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and is listed in the International Who s Who in the World and Who s Who in Science and Engineering.

9 GUERRERO et al.: WIRELESS CONTROLLER 1213 Luis García de Vicuña received the Ingeniero de Telecomunicación and Dr.Ing. degrees from the Polytechnic University of Catalunya, Barcelona, Spain, in 1980 and 1990, respectively, and the Dr.Sci. degree from the Université Paul Sabatier, Toulouse, France, in From 1980 to 1982, he was an Engineer with Control Applications Company. He is currently an Associate Professor in the Department of Electronic Engineering, Polytechnic University of Catalunya, where he teaches power electronics. His research interests include power electronics modeling, simulation and control, active power filtering, and high-power-factor ac/dc conversion. Miguel Castilla received the M.S. and Ph.D. degrees in telecommunication engineering from the Polytechnic University of Catalunya, Barcelona, Spain, in 1995 and 1998, respectively. Since 2002, he has been an Associate Professor in the Department of Electronic Engineering, Polytechnic University of Catalunya, where he teaches analog circuits and power electronics. His research interests are in the areas of modeling, simulation, and control of dc-to-dc power converters and high-power-factor rectifiers. José Matas received the B.S., M.S., and Ph.D. degrees in telecommunication engineering from the Polytechnic University of Catalunya, Barcelona, Spain, in 1988, 1996, and 2003, respectively. Since 1997, he has been an Associate Professor in the Department of Electronic Engineering, Polytechnic University of Catalunya. His research interests include power-factor-correction circuits, distributed power systems, and nonlinear control. Jaume Miret (M 98) received the B.S. degree in telecommunications and the M.S. degree in electronics from the Polytechnic University of Catalunya, Barcelona, Spain, in 1992 and 1999, respectively, where he is currently pursuing the Ph.D. degree. Since 1993, he has been an Assistant Professor at the Polytechnic University of Catalunya. His research interests include dc-to-ac converters, active power filters, and digital control.