Modal Frequency In Renewable-Integrated Power Systems:Definition,analysis And Control

As one of the three basic elements of the sinusoidal signal,frequency is a essential feature of AC voltage,and maintaining system frequency within a certain range is also a basic requirement of the AC power grid.However,as synchronous generators(SGs)are extensively replaced by renewables,the inertia and frequency regulation capacity of the power system decrease,accompanied by larger frequency response fluctuations,which jeopardize the frequency stability of power systems.Recently,a number of major blackout events over the world are caused by frequency collapse,exposing the deficiencies in the analysis and control of power system frequency response.Modern bulk power systems are featured in large spatial scales and a huge number of generation devices,which are of various types and complex dynamics.The system frequency response is related to the network topology and device dynamics of the entire power system.So the order of the frequency response is very high,which makes it difficult to be analyzed.Therefore,it is challenging to scientifically cognize the system frequency response,and quantify the frequency stability.Further,the current frequency control of renewables is usually a simple imitation of SGs.How to use the high controllability of power electronic converters to optimally support the system frequency is also worth exploring.To this end,based on the concept of modal frequency,this dissertation investigated the definition,analysis method,and control strategy of frequency in renewable-integrated power systems.The main contributions of this dissertation are summarized as follows.1)In terms of the definition of the frequency of renewable-integrated power systems,a frequency response recognition and analysis method based on modal frequency(including common-mode frequency(CMF)and differential-mode frequency(DMF))is proposed.Frequency stability analysis usually focuses on the global frequency of the power system.While the frequency response of each bus shows a consistent trend,there are also distribution differences.In order to scientifically cognize the consistency and differentiation of the frequency response,firstly,the frequency response model of the renewableintegrated power system is established.Then the frequency response is decomposed according to the spectral decomposition of the system return-difference matrix,which leads to the modal frequencies,including the CMF and the DMFs.Among them,the CMF is consistent over the system,which represents the global frequency.It reveals that the essential reason for the consistency of the frequency response is the rotation invariance of the power flow with respsect to phase angle.Besides,the expression of the CMF demonstrates that generators and disturbances have different weights on the global frequency depending on their locations,which phenomenon cannot be captured by traditional methods.On the other hand,the DMF reflects the synchronization process between devices and it is the source of the frequency distribution difference.This method reveals the influence mechanism of voltage dynamics on the system frequency response,and helps to deepen the understanding of the frequency dynamic process.2)In terms of the analysis of the CMF,a model simplification method based on a unified transfer function structure(UTFS)is proposed,then frequency strength indices which quantify the frequency nadir and the average rate of change are established.To calculate the CMF,it is necessary to sum the frequency input-active power output transfer functions of all devices.Besides,the expression of the revised CMF includes a system-wide coupling term.So it is difficult to analyze the frequency trajectory and quantify the system frequency strength.To this end,the UTFS is proposed to characterize the frequency-active power response of the generation device.The frequency regulation dynamics of various types of devices are approximately described by three forms,so the order of the system will not increase after the superposition of the UTFSs.In addition,a decoupling method is proposed for the voltage coupling term.According to the property of the power flow Jacobian matrix,the system-wide high-order coupling terms can be decomposed into several local low-order ones,which can also be simplified into unified structures.The simplified CMF has only two orders,whose trajectory can be analyzed.Then,two indices,termed frequency drop depth coefficients and slope coefficients are proposed to quantify the frequency nadir and the average rate of change of frequency(Ro Co F).The expressions of the indices are simple,which helps to intuitively understand the impact of device-level frequency regulations on the system-level frequency response,and reveals the equivalence of increasing inertia or damping(fast primary frequency regulation)to improve the frequency nadir and average Ro Co F.3)In terms of the analysis of the DMF,it is proposed to approximately characterize the DMF by the frequency components based on the quadratic eigenvalue problem(QEP),and the nodal modal inertia index is established to analyze the DMF distribution differences.In a heterogeneous system,the DMF obtained based on the spectral decomposition of the return-difference matrix cannot obtain the explicit expression,which makes it difficult to be analyzed.To this end,generation devices are firstly approximated by the UTFSs.After that,the system is a second-order system with n degrees of freedom,and its frequency response can be decomposed into n second-order components based on the method of the QEP.It is demonstrated that when the system is homogeneous or weakly heterogeneous,the QEP frequency components are completely consistent or very close to the modal frequencies.Besides,the former frequency components can be accurately analyzed,so they can be used to approximately investigated the DMF.Furthermore,by analogy with the relationship between the Ro Co F and the SG inertia,the nodal modal inertia is defined.The index is closely related to the position of disturbance and observation,and it can be used to analyze the distribution difference of DMF.In particular,there exist certain buses where the differential modal inertia tends to infinity and the corresponding DMF response is close to zero.Moreover,the amplitude of the DMF gradually increases away from these buses.These buses can be referred to as centers of differential mode oscillations.4)In the control design of renewable supporting CMF,the optimal control problem considering multiple frequency objectives is established,and corresponding approximate optimal control structures are analyzed.Currently,the guiding ideology of frequency regulation design of renewables is usually to simply imitate the SGs,without making full use of their flexibility.There are few literatures on the optimal frequency supporting control of renewables.To this end,firstly,the optimal control problem of renewable under the energy constraint is established,and the general property of optimal control is analyzed.Secondly,frequency characteristics such as frequency nadir,maximum Ro Co F,the integral of the square of frequency deviation and Ro Co F are taken as the optimization objectives,and the optimal frequency and active power trajectories are solved by theoretical analysis or numerical algorithm.Moreover,approximate optimal control structures are analyzed.It is found that,compared with the rest of the selected objective functions,the obtained optimal frequency response is more satisfactory when the optimization objective is the weighted sum of integrals of the square of frequency deviation and Ro Co F.Further study shows that this optimal control is similar to the combination of virtual inertia and droop control,which shows the rationality of adopting this kind of control in practical engineering.