Small-signal Dynamic Equivalence And Oscillation Stability Analysis Of A Wind Power Collecting Network

In recent years,several oscillation incidents have been reported to happen in practical wind power integrated power systems(WPIPSs)globally,which seriously impact the safe and stable operation of the power system and is one of the main bottlenecks to the accomplishment of the friendly integration of the wind power generation.Researches up to date show that the oscillation instability of the WPIPS is mostly caused by the unfavorable dynamic interactions between the electrical equipment in the system and the interaction process usually involves the participation of the dynamics of the converter control systems of the wind turbine generators(WTGs).In a large-scale wind power collecting network,the number of the WTGs is huge and the order of the model of a wind farm is high.Besides,the coupling between the WTGs and the WTGs with the external AC power system is complex,making it hard to clarify the characteristics and impacts of dynamic interactions in the WPIPS.Thus at present,the mechanism for the oscillations in the WPIPS is not yet completely clear.And reasonable and effective equivalent modeling of the wind farm is the basis for the in-depth study of the mechanism for and main influencing factors of the oscillations caused by the dynamic interactions in the system.Therefore,in this dissertation,a series of research work is carried out around the small-signal dynamic equivalence and oscillation stability analysis of the wind power collecting networks,where the subsynchronous oscillations are mainly focused on.The main research work and contributions of this dissertation are listed as follows.(1)The small-signal dynamic equivalent model of a grid-connected wind farm(GCWF)is derived and the impact of the number of the WTGs on its oscillation stability is studied under the condition that the WTGs inside the wind farm are approximately of the same linearized model and symmetrically connected to the external AC power system.Firstly,the linearized model of the GCWF with N WTGs is decoupled into N independent equivalent subsystems(ESs)by introducing a variable transformation.The first(N-1)ESs consist of a WTG being connected to an infinite bus and thus reflect the internal dynamics of the GCWF.The Nth ES consists of a WTG being connected the external AC power system and it reflects the overall dynamic output characteristics of the GCWF.Secondly,based on the Nth ES,the single-machine equivalent model of the GCWF is established.According to the form of the equivalent model,it is found that as the number of the WTGs increases,the strength of the connection between the equivalent model and the AC grid weakens,which may induce the risk of loss of the oscillation stability of the GCWF.Finally,the single-machine equivalent model mentioned above is extended and applied to the dynamic equivalence of a power system with multi wind farms or groups of WTGs integrated.The equivalent model established is simple to use and can effectively reflect the oscillation characteristics of the original system when a disturbance occurs with the computational burden effectively reduced.(2)On the basis of(1),the decoupling representation of the GCWF is derived with complex network structures being taken into consideration and the impact of the change of the network structure,parameters and number of the WTGs on the oscillation stability of the GCWF is discussed.Firstly,a network reactance matrix of the GCWF is defined from its node impedance matrix.The equivalent decomposition of the linearized model of the GCWF is derived by introducing a variable transformation based on the basic methodology of modal analysis and the similar diagonal transformation of the network reactance matrix.For a GCWF with N WTGs,the linearized model of it can be decoupled into N ESs,each of which consists of a single WTG being connected to the external AC power system.Secondly,with reference to the concepts of mode shape,controllability and observability in the modal analysis theory,the mode shape,controllability and observability of an ES are defined and the relationship between the dynamics of the ESs and the WTGs in the original wind farm is established.Finally,based on the ESs,the impact of the change of the network structure,parameters and the number of the WTGs on the oscillation stability of the GCWF is studied.It is found that as the reactance of the wind power transmission line,the overall electrical distance of the power collecting network inside the wind farm or the number of the WTGs increase,the strength of the connection between the WTG and the AC grid in the ESs weakens,which may induce the risk of loss of the oscillation stability of the GCWF.Besides,a reduced-order modal computation method for the small-signal stability examination of a wind farm in the planning stage is proposed based on the ESs.(3)Based on the definition of the mode shape,controllability and observability of the ESs in(2),the reasons for and conditions under which that the WTGs inside a wind farm can exhibit identical dynamic characteristics to the external AC power system and the overall dynamic output characteristics of the GCWF can be reflected by one WTG under the effect of an external disturbance are studied.Thus a preliminary theoretical foundation for the research of the small-signal dynamic equivalence of the GCWF is laid.Then the dynamic equivalent model of a wind farm is established based on the model of the ESs considering different prerequisites.(4)Taking the small-signal stability of a GCWF with direct drive permanent magnet wind turbine generators(PMSGs)dominated by the dynamics of the phase-locked loops(PLLs)as an example,the stability limit of the GCWF is derived based on the ESs.Based on the analytical solution obtained,the impact of the change of network structure,parameters and the number of the PMSGs on the oscillation stability of the GCWF is studied and the mechanism for the oscillation instability of the wind farm induced by the dynamics of the PLLs under the condition of weak grid connection is revealed.It is indicated that as the reactance of the wind power transmission line,the overall electrical distance of the power collecting network inside the wind farm,the steady-state active power output of the PMSG and the integral coefficient of the PLL increases,the small-signal stability of the grid-connected PMSG wind farm dominated by the dynamics of the PLLs decreases.