The paper presents a new approach to positive and negative sequence current vector control of a grid connected three-phase three-wire power electronic converter operating under grid voltage imbalance conditions. The concept utilizes representation of unbalanced converter current in the new coordinates frame in which the current vector components are constant. The nonlinear trigonometric transformation of two-dimensional current vector components from the stationary frame to the new frame is found on-line depending on the reference current asymmetry. The presented concept of new coordinates utilization allows implementation of proportional-integral terms as current regulators without the use of resonant terms and without the use of the measured current symmetrical sequences decomposition. The paper presents the theoretical approach, simulation results, as well as laboratory tests results.
- AC–DC power conversion
- Current control
- Clarke’s transformation
- Park’s transformation
Fig. 1. Scheme of the power circuit of a three-phase power electronic converter operating with unbalanced grid voltage.
EXPECTED SIMULATION RESULTS:
Fig. 2. Simulation results showing the new trigonometric transformation properties in the case in which the asymmetry factor is out of the dead-zone.
Fig. 3. Simulation results showing the new trigonometric transformation properties in the case in which the asymmetry factor crosses the dead-zone
Fig. 4. Simulation results showing the reference vector hodograph in the case in which the asymmetry factor crosses the dead-zone.
Fig. 5. Simulation results presenting three-phase grid voltage (a), and three-phase unbalanced current for DSFR control with notch filters (b), DSFR control with positive and negative sequence decoupling (c), oscillatory terms based current controllers (d), and proposed current control method (e) during reference step change of the converter current imbalance.
Fig. 6. Simulation results presenting operation of the grid power converter with the new transformations application for the case of grid voltage imbalance compensation and fundamental positive sequence component sag compensation (0-0.05s – initial state, 0.05-0.3s – no load operation with imbalance and sag compensation, 0.3-0.5s – imbalance and sag compensation with simultaneous dc bus feeding from external source by 26kW of power (inverter operation mode).
The paper presents a new transformation of unbalanced three-phase signals to the oblique non-Cartesian frame in which the obtained signals in the new frame have equal amplitudes and are shifted by despite three-phase signals imbalance. Thus in a new frame the vector is seen as balanced. Transformed next to the rotating frame using Park’s transformation the vector components are constant. The proposed transformation from stationary to new frame and next from to the frame was used in the voltage oriented vector control of a three-phase grid converter.
The new transformation parameters can be relatively simply found based on reference positive and negative sequence current vector components, making it possible to obtain any imbalance of converter current depending on the outer control loops referencing current vector components.
The method has a limitation in a narrow range of current asymmetries, where the magnitude of positive sequence vector is close to the magnitude of the negative sequence vector, therefore a dead-zone is implemented to avoid converter operation in this narrow range. Simulation and experimental results show that the method works in a stable manner even when crossing the dead-zone. Simulation and experimental tests were done with disabled outer control loops of dc and ac voltage (so with arbitrarily referenced positive and negative sequence components) and with enabled outer control loops. In both cases the results are satisfactory.
 VDE–AR–N 4120: Technical requirements for the connection and operation of customer installations to the high–voltage network VDE, Jan. 2015, Germany.
 M. M. Baggu, B. H. Chowdhury and J. W. Kimball, “Comparison of Advanced Control Techniques for Grid Side Converter of Doubly-Fed Induction Generator Back-to-Back Converters to Improve Power Quality Performance During Unbalanced Voltage Dips,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 2, June 2015, pp. 516-524.
 W. Liu, F. Blaabjerg, D. Zhou and S. Chou, “Modified Instantaneous Power Control with Phase Compensation and Current-limited Function under Unbalanced Grid Faults,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 3, June 2021, pp. 2896 – 2906.
 Y. Du, X. Lu, H. Tu, J. Wang and S. Lukic, “Dynamic Microgrids With Self-Organized Grid-Forming Inverters in Unbalanced Distribution Feeders,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 2, June 2020, pp. 1097-1107.
 A. Mora, R. Cárdenas, M. Urrutia, M. Espinoza and M. Díaz, “A Vector Control Strategy to Eliminate Active Power Oscillations in Four-Leg Grid-Connected Converters Under Unbalanced Voltages,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 2, June 2020, pp. 1728-1738.