Frequency‐coupled impedance model‐based sub‐synchronous interaction analysis for direct‐drive wind turbines connected to a weak AC grid

Abstract

Recently, emerging sub-synchronous oscillation (SSO) issues caused by the interaction between power electronic converters and weak AC grids have provoked serious stability concerns. Impedance-based modelling approaches have been widely employed for stability analysis of such interactions. In this study, a sequence-domain frequency-coupled impedance model (FCIM) and the corresponding stability criterion are proposed. First, a fast identification method of the FCIM is proposed, in which the impedance-frequency curves of the FCIMs at multiple frequencies are measured, followed by identification of their transfer function models. Next, the proposed method is applied to model a practical system, where a SSO event once occurred due to the interactions between direct-drive wind turbines and a weak AC grid. The individual FCIMs of wind turbine generators, steam turbine generators and static var generator in this system are derived. After that, an aggregated FCIM is formed by combining the FCIMs without extra coordinate transformation. Then, the aggregated FCIM-based stability analysis is carried out to investigate the interaction between the wind farms and weak AC grids. In the end, the results of FCIM-based stability analysis are verified by time-domain simulations.

Oscillation suppression strategy for modular multi‐level converter grid‐connected system based on virtual damping in modulation link

“…Many oscillation accidents at home and abroad show that there is frequency coupling phenomenon when the interconnection system containing AC and DC power electronic equipment oscillates [25, 26]. Ignoring the frequency coupling effect for stability analysis may lead to inaccurate analysis results [27].…”

Black-Box Impedance Prediction of Grid-Tied VSCs Under Variable Operating Conditions

“…iii) Next we solve the homogeneous linear equations (27). Obviously, ρ 1 and ρ 2 are linearly independent, which means that the dimension of the vector space of solutions of ( 27) is at least 2.…”

“…s Superscript, the variable in the system dq frame c Superscript, the variable in the controller dq frame θ Phase of the synchronization control part ∆θ Angle mismatch between the controller and system dq frames V dc Voltage of direct-current bus P , P in Output active power and input active power i d,q dand q-axis components current e d,q dand q-axis components internal potential I d,q Steady values of the dand q-axis components current V d , q Steady values of the dand q-axis components voltage L f , R The filter inductance and resistance of the VSC e abc The potential of the VSC V tabc ,i abc The three-phase voltages and currents at the point of common coupling V t ,e t The voltage amplitude of V tabc and e abc T ∆θ Coordinate transformation matrix in (1) f d,qin ,f d,qid The intermediate variables in (7) f d,qvn ,f d,qvd The intermediate variables in (7) f i , f v The intermediate variables in (8) f d,qθ The intermediate variables in (8) VOLUME 4, 2016 g i , g v The intermediate variables in (9) Z The impedance matrix, including Z dd ,Z dq ,Z qd ,Z qq ∆ gv The intermediate variables in (12) a kn ,b kn The all coefficients in (13) x The operating point vector in (15) a k ,b k The system parameters in (15) A 0 ,A ij The intermediate variables in (16) Σ 1−4 The intermediate variables in (20) m 1,2 ,ρ 1,2 The intermediate variables in (23) M 1 The intermediate variables in (27) p n ,q n The intermediate variables in (29) p,q,k,h The intermediate variables in (30) K 1,2 ,H 1,2 The intermediate variables in (32) R,R r The intermediate variables in (33) and its real part C The DC capacitance of VSC r The number of operaing points Q Output reactive power ω 0 Fundamental frequency of the system k p,ip Proportional and integral coefficients of PI controller in the power flow control K p,q Gain coefficients of the basic droop control k p,iv Proportional and integral coefficient of PI controller in the basic droop control D p,q ,J Gain coefficient of the virtual synchronous generator control N f The number of disturbance frequencies in Equ. Due to increasing pressure of environmental protection and energy resource, a great quantity of solar and wind powers with the form of distributed sources have been connected to grid recently [1], and meanwhile the traditional power system has being gradually transformed into a semiconducting power system (also called power-electronic-based power system) [2]- [5].…”

“…The major limitation of the latter method is that it is still a graybox method, on the assumption that the control structure of VSC should include PLL. Recently, Liu et al [27] further proposed a sequence-domain frequency-coupled impedance model (FCIM) with the corresponding stability criterion, and well studied the problem of subsynchronous oscillation caused by interaction between power electronic equipment and weak AC grids. This article will extend the NDAM in the sequence domain [26] to the dq domain and make some great improvements by applying it to a VSC under an arbitrary control structure and completely black-box conditions.…”

Impact of Fixed/Variable Speed Hydro, Wind, and Photovoltaic on Sub-Synchronous Torsional Oscillation—A Review

“…The following shown in Figure 6 is the impedance model of doubly-fed induction machine (DFIM) connected to grid for SSO Study. The sequence-domain frequency-coupled impedance model (FCIM) looks at the SSO that can happen between weak AC grids and direct-drive wind turbines [80]. Initially, a fast identification approach for the FCIM is developed to measure the FCIM's impedancefrequency curves.…”