This article discusses the mathematical relationship between the grid-voltage-modulated-directpower-control (GVM-DPC) and the vector-current-control (VCC) for three-phase voltage-source-converters (VSCs). It reveals that the GVM-DPC is equivalent to the VCC at the steady-state, yet presents a superior transient performance by removing the need of phase-locked loop (PLL). That means the GVM-DPC solves the disadvantage of conventional DPC such as poor steady-state performance. Moreover, the GVM-DPC will reduce the computational burden in comparison with the VCC due to the absence of Park transformation and PLL. Consequently, we can expect that the GVM-DPC method has a good capability of plug-and-play for the VSC. Finally, the experiment results match the theoretical expectations closely. Index Terms Direct power control, vector current control, voltage source converters, phase-locked loop. I. INTRODUCTION OF CONTROL OF GRID-CONNECTED VOLTAGE-SOURCE CONVERTERS Voltage source converter (VSC) is widely used in the application of smart grid, flexible AC transmission systems, and renewable energy sources (e.g., wind and solar) [1]-[6]. Various control methods are researched for VSC to improve its performance, stability, and robustness [7].

A novel grid voltage modulated direct power control (GVM-DPC) strategy for a grid-connected voltage source converter is proposed to control the instantaneous active and reactive powers directly. The GVM-DPC method consists of a nonlinear GVM controller, a conventional controller (feedforward and PI feedback), and nonlinear damping. The proposed control strategy shows a relationship between DPC and voltage-oriented control methods designed in d-q frame. The main advantage is that the proposed method makes the system be a linear time-invariant system, which enables us to apply various control methods easily. The GVM-DPC guarantees not only the convergence rate but also the steady-state performance of the system. Moreover, it is ensured that the closed-loop system is exponentially stable. Finally, simulation and experimental results using a 2.2-kVA VSC are provided to validate the tracking performance and robustness of the proposed control architecture. In addition, the total harmonic distortion of the current is 1.9% which is much less than the requirement for grid operation. Index Terms-Direct power control, DC-AC power converters, linear time-invariant system, exponentially stable.

In this paper, we design a voltage modulated direct power control (VM-DPC) for a three-phase voltage source inverter (VSI) connected to a weak grid, where the PLL system may make the system unstable if the conventional vector current control (VCC) method is applied. Compared with the conventional VCC method, the main advantage of the proposed VM-DPC method is that the PLL system is eliminated. Moreover, in order to inject the rated real power to the weak grid, the VSI system should generate some certain amount of reactive power as well. An eigenvalues based analysis shows the system with the proposed method tracks its desired dynamics in the certain operating range. Both simulation and experimental results match the theoretical expectations closely. Index Terms-Voltage source inverter, voltage modulated direct power control (VM-DPC), vector current controller, weak grid, stable system.

We propose a vector current control derived from direct power control (VCC-DPC) for a three-phase voltage source inverter (VSI) in the synchronous rotating frame through instantaneous real and reactive powers. The proposed VCC-DPC method has the same control structure as the conventional VCC except for the coordinate transformation, since we obtain the d-q axes currents model of VSI without using Park transformation and the PLL system. Consequently, the proposed method has the same property as the conventional VCC if the PLL extracts the phase angle of the grid voltage correctly. However, with the consideration of the slow dynamics of the PLL, the proposed method has an enhanced dynamical performance feature compared with the conventional VCC. Moreover, it has another benefit that the reduction of the computational burden could be expected since there is no Park transformation and the PLL in the controller implementation. We can guarantee that the closed-loop system with the proposed method is exponentially stable in the operating range. Finally, both simulation and experimental results using a 15-kW-inverter system match the theoretical expectations closely. Index Terms-Voltage source inverter, vector current controller, instantaneous real and reactive powers, exponentially stable.

In practical microgrids, the inhomogeneous initial values are widely appeared due to soft-starting operation. If traditional model order reduction approaches are applied, the inputoutput maps error between the original system and reducedorder system is large. To address this problem, this paper proposes a reduced-order aggregate model based on balanced truncation approach to provide the preprocessing approach for the real-time simulation of large-scale converters with inhomogeneous initial conditions in DC microgrid. Firstly, the standard linear time-invariant model with inhomogeneous initial conditions is established through non-leader multiagents concept. To end this, it is convenient for scholars to build complex system modeling with switched topology. Furthermore, the full system is divided into two components, i.e., the unforced component with nontrivial initial conditions and forced component with null initial conditions. Moreover, this paper presents an aggregated approach that involves independent reducing component responses and combining reducing component responses. Based on this, the input-output maps error is reduced. Then, the approximated error estimate of the reduced-order aggregate model regarding large-scale converters in DC microgrid is first provided, which provides prior knowledge and theoretical basis for DC microgrid designers. Finally, the simulation results illustrate the accuracy of the proposed approach.