The Application of Vector Fitting to Eigenvalue-Based Harmonic Stability Analysis

Abstract

Abstract-Participation factor analysis is an interesting feature of the eigenvalue-based stability analysis in a power system, which enables the developers to identify the problematic elements in a multi-vendor project like in an offshore wind power plant. However, this method needs a full state space model of the elements that is not always possible to have in a competitive world due to confidentiality. In this paper, by using an identification method, the state space models for power converters are extracted from the provided data by the suppliers. Some uncertainties in the identification process are also discussed and solutions are proposed, and in the end the results are verified by time domain simulations for linear and nonlinear cases with different complexities, no matter which domain (phase or dq) is used.

Oscillation Suppression Method by Two Notch Filters for Parallel Inverters under Weak Grid Conditions

“…From Equation (3), it can be assumed that the grid voltage is stable in the absence of the inverter, and the inverter will be stable if the grid impedance is zero. Nevertheless, when the grid impedance is not negligible, the system will be stable only if the impedance ratio K satisfies the Nyquist criterion in Reference [12]. In other words, the system will be stable, only if the Nyquist curve of the impedance ratio does not surround (−1, j0).…”

“…The first is the eigenvalue-based analysis [11], which is usually utilized to evaluate the system's stability. The eigenvalue-based stability analysis studies the eigenvalues of a system's state space model matrix, which requires the physical features and control parameters in the system [12]. The second one is the impedance-based stability criteria [13,14], which is well built to adjudicate the system stability.…”

Improving the Impedance-Based Stability Criterion by Using the Vector Fitting Method

“…The eigenvalues can be obtained by an analytical evaluation of the whole system [13] or by approximating the driving point impedance, which is indeed the equivalent impedance of that node as a frequency response, into state equations using the Vector Fitting method [11], [12]. However, the former leads to a very complicated study and it also needs analytical models of all components that might not be available due to the confidentiality or difficulty in the modeling [14]- [16]. The latter can also not identify the problematic subsystem because it only measures the driving point impedance.…”

“…However, in the design phase the system designer might have some unstable cases, which cannot be predicted by this method. The Vector Fitting method has recently been used for finding a state-space model for the components, whose parameters/structures are unknown due to either the confidentiality or difficulty in the modeling [16]. The Component Connection Method (CCM) is afterwards used to find the overall state-space model of the entire system.…”

“…This is the case for the terminal characteristics of Wind Turbine Generators or frequency domain models of cables and transformers. In [16] the entire system is modelled in detail and all dynamics of the system can be studied, whereas in this paper the system is studied from a node and in the end a reduced model of the system will be obtained. Multiple uses of the VF are avoided by doing this and the errors in the final results could be kept below a certain limit and identification is also less time-consuming.…”