TY - JOUR

T1 - The Equilibrium Points and Stability of Grid-Connected Synchronverters

AU - Lorenzetti, Pietro

AU - Kustanovich, Zeev

AU - Shivratri, Shivprasad

AU - Weiss, George

N1 - Publisher Copyright:
© 1969-2012 IEEE.

PY - 2022/3/1

Y1 - 2022/3/1

N2 - Virtual synchronous machines are inverters with a control algorithm that causes them to behave towards the power grid like synchronous generators. A popular way to realize such inverters are synchronverters. Their control algorithm has evolved over time, but all the different formulations in the literature share the same 'basic control algorithm'. We investigate the equilibrium points and the stability of a synchronverter described by this basic algorithm, when connected to an infinite bus. We formulate a fifth order model for a grid-connected synchronverter and derive a necessary and sufficient condition for the existence of equilibrium points. We show that the set of equilibrium points with positive field current is a two-dimensional manifold that can be parametrized by the corresponding pair (P,Q), where P is the active power and Q is the reactive power. This parametrization has several surprizing geometric properties, for instance, the prime mover torque, the power angle and the field current can be seen directly as distances or angles in the (P,Q) plane. In addition, the stable equilibrium points correspond to a subset of a certain angular sector in the (P,Q) plane. Thus, we can predict the stable operating range of a synchronverter from its parameters and from the grid voltage and frequency. Our stability result is based on the intrinsic two time scales property of the system, using tools from singular perturbation theory. We illustrate our theoretical results with two numerical examples.

AB - Virtual synchronous machines are inverters with a control algorithm that causes them to behave towards the power grid like synchronous generators. A popular way to realize such inverters are synchronverters. Their control algorithm has evolved over time, but all the different formulations in the literature share the same 'basic control algorithm'. We investigate the equilibrium points and the stability of a synchronverter described by this basic algorithm, when connected to an infinite bus. We formulate a fifth order model for a grid-connected synchronverter and derive a necessary and sufficient condition for the existence of equilibrium points. We show that the set of equilibrium points with positive field current is a two-dimensional manifold that can be parametrized by the corresponding pair (P,Q), where P is the active power and Q is the reactive power. This parametrization has several surprizing geometric properties, for instance, the prime mover torque, the power angle and the field current can be seen directly as distances or angles in the (P,Q) plane. In addition, the stable equilibrium points correspond to a subset of a certain angular sector in the (P,Q) plane. Thus, we can predict the stable operating range of a synchronverter from its parameters and from the grid voltage and frequency. Our stability result is based on the intrinsic two time scales property of the system, using tools from singular perturbation theory. We illustrate our theoretical results with two numerical examples.

KW - Park transformation

KW - Virtual synchronous machine

KW - frequency droop

KW - inverter

KW - saturating integrator

KW - singular perturbation method

KW - synchronverter

KW - voltage droop

UR - http://www.scopus.com/inward/record.url?scp=85111604884&partnerID=8YFLogxK

U2 - 10.1109/TPWRS.2021.3097954

DO - 10.1109/TPWRS.2021.3097954

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AN - SCOPUS:85111604884

SN - 0885-8950

VL - 37

SP - 1184

EP - 1197

JO - IEEE Transactions on Power Systems

JF - IEEE Transactions on Power Systems

IS - 2

ER -