IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 37, NO. 6, NOVEMBER/DECEMBER 2001 1817 Sharing of Nonlinear Load in Parallel-Connected Three-Phase Converters Uffe Borup, Member, IEEE, Frede Blaabjerg, Senior Member, IEEE, and Prasad N. Enjeti, Fellow, IEEE Abstract—In this paper, a new control method is presented which enables equal sharing of linear and nonlinear loads in three-phase power converters connected in parallel, without com- munication between the converters. The paper focuses on solving the problem that arises when two converters with harmonic compensation are connected in parallel. Without the new solution, they are normally not able to distinguish the harmonic currents that flow to the load and harmonic currents that circulate between the converters. Analysis and experimental results on two 90-kVA 400-Hz converters in parallel are presented. The results show that both linear and nonlinear loads can be shared equally by the proposed concept. Index Terms—Control, ground power units, nonlinear loads, paralleling, power converters. I. INTRODUCTION I N MANY CASES, it can be favorable to connect power con- verters in parallel. This could be in systems with high reli- ability requirements, e.g., in radar power supplies, in UPS sys- tems, or in 400-Hz ground power where a low demand factor is expected, so that the totally installed converter rating is min- imized. Special precautions must be prepared in order to make the converters share the common load equally. This is due to the nonphysical relation between output power and frequency in a solid-state converter (the frequency is controlled by a crystal). The problem of sharing harmonic currents is similar to the problem of sharing active and reactive power in power con- verters. The main control target is to insure that the units in par- allel share the common load. Active power, reactive power, and harmonic powers have to be shared equally. The conventional approach to parallel solid-state power converters requires interconnections between the converters to achieve balanced load sharing [1]–[5], for example, by having a voltage-controlled “master” unit and several current-con- trolled “slave” units. However, a configuration based on the master/slave principle is not redundant due to the dependency of the master unit. Paper IPCSD 01–020, presented at the 2000 IEEE Applied Power Electronics Conference and Exposition, New Orleans, LA, February 6–10, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the In- dustrial Power Converter Committee of the IEEE Industry Applications Society. Manuscript submitted for review April 1, 2000 and released for publication July 23, 2001. U. Borup is with AXA Power, DK-5270 Odense, Denmark (e-mail: uffe.borup@ieee.org). F. Blaabjerg is with the Institute of Energy Technology, Aalborg University, DK-9220 Aalborg East, Denmark (e-mail: fbl@iet.auc.dk). P. N. Enjeti is with the Department of Electrical Engineering, Texas A&M University, College Station, TX 77843-3128 USA (e-mail: p.enjeti@ieee.org). Publisher Item Identifier S 0093-9994(01)09708-0. To achieve true redundancy, all units should be able to op- erate independently. This matter has been discussed in [6]–[8]. Linear balanced loads can be shared equally by using droop co- efficients that make the frequency and the voltage amplitude proportional to the active and reactive power, respectively. The principle of sharing load by droop coefficients is well estab- lished in the utility business. In [9] and [10], a new control scheme was presented where nonlinear load can be shared equally in single-phase uninter- ruptible power supply (UPS) systems by adjusting the gain of the voltage controller proportional to the amount of har- monic VA that is delivered. This is practical at a fundamental frequency of 60 Hz and with a low VA rating. In a 400-Hz high-VA system [16], the switching frequency is limited due to losses and switching delays. The losses and switching delays limit the bandwidth of the control loop, so that the controller is not able to control harmonic voltages with a linear propor- tional-integral-derivative (PID)-type feedback controller. In high-power converters, harmonics can be damped by artifi- cial control that actively controls each harmonic to a low value. The harmonic compensation can be achieved by different ap- proaches [11]–[13]. This paper presents a load-sharing technique that will share harmonic currents among converters equipped with active com- pensation for harmonic distortion without mutual communica- tion. In the following section, the fundamental theory of con- necting ac power units in parallel will be described. The prin- ciple of sharing linear balanced load is adapted from the utility control theory. Then, the concept will be developed to apply for harmonics as well. Finally, simulations and tests show the value of the presented concept applied on the fifth harmonic in two 90-kVA 400-Hz ground power units (GPUs) connected in par- allel. II. SHARING OF LINEAR LOAD Consider two solid-state three-phase power converters con- nected to a linear load through a pure inductance as shown in Fig. 1. The complex powers delivered from converter 1 and con- verter 2 to the load are then given by (1) where apparent power vector of converter ; active power of converter ; reactive power of converter ; output current vector of converter ; voltage vector of the point of common connection. 0093–9994/01$10.00 © 2001 IEEE