On the Solution of Equilibrium Points of Power Systems With Penetration of Power Electronics Considering Converter Limitation

Abstract

Increasing penetration of power electronics is changing the understanding of modern power systems. In particular, current saturation of converters leads to multiple equilibrium points for both normal and short-circuit conditions. This paper aims to identify equilibrium points in power systems with penetration of power electronics. First, a steady-state model of power systems considering the power electronics operation is presented. Then, a general methodology is developed to obtain equilibrium points including all possible combinations of converter current saturation states. A system of equations is defined for each combination and is solved considering the possibility to have single or multiple solutions. This methodology is suitable for steady-state analysis in normal operation and during short-circuit scenarios. Test systems with Voltage Source Converters are used to validate the presented methodology.

Grid Equivalent Representation of Power Systems With Penetration of Power Electronics

“…The required input information of this algorithm includes the admittance matrix Y, constraint equations modeling power electronics and non-power electronics elements H, the output impedance magnitudes, z out , and angles, θ z . In particular, the VSC equivalent model, which associates a specific control mode and various potential current-saturated states, are included in the set of constrains H as detailed in [30], [31].…”

“…In particular, the equivalent model of power converters, which involves a specific control mode and various potential current-saturation states, is included in the system formulation. Then, the system equilibrium point that satisfies all converters' operation limits can be identified by either going through all possible combinations of converters' current-saturation states [30], [31] or testing only selected combinations iteratively for a more efficient calculation [32], [33]. The previous studies are based on the formulation of the complete studied system.…”

“…Next, the U-I characteristic of a VSC operated in gridforming (GF) mode is shown in example 2. The GF converter is analyzed with an instantaneous current-limiter [35] following the equivalent model expressed in [30]. The VSC in unsaturated state (USS) regulates both the output voltage magnitude and angle at the reference values.…”

“…The external system can be modeled following the generic formulation (which is expressed in [33] with a three-phase expression and in [30], [31] with a single-phase expression) such that:…”

“…The current injection at bus 1 is composed of the Thévenin equivalent current i th−f , which is defined by h 1−f , and the VSC current injection i vsc−f , which is defined by h 2−f . The Thévenin equivalent current is the same for the three combinations, while the VSC current injection will be modified following the VSC equivalent model in PQ mode presented in [30]. Then, the vector of current injection constraints, H f , is defined for each combination f as:…”