Inter-harmonics in multi-terminal VSC-based HVDC systems

Multi-terminal voltage sourced converter(VSC)-based high voltage direct current (HVDC) system composes of a number of VSCs connected to an HVDC grid (or dc grid).The dc grid is often configured by cable interconnections between converter stations,thus imposing resonance issues affecting harmonic interaction in the system.Based on the harmonic transfer characteristics of VSC and HVDC systems,the appearance and the interaction of inter-harmonics in the multi-terminal VSC-based HVDC system are analyzed.Simulation models are built and implemented using SimPowerSystems in MATLAB.The simulation results show that,a series of inter-harmonics are produced and tend to be dominant in low-frequency range.Especially in the dc grid,the inter-harmonic transfer can be magnified due to inter-harmonic resonances.The complex resonance issues in the dc grid are investigated in combination with interaction through the VSC,it is beneficial to harmonic filter designs as well as other harmonic mitigation methods.

Linear Support Vector Machine Based Inter-harmonic Modeling and Parameter Estimation

There are often system. The high measure many inter-harmonics in power t accuracy of inter-harmonics order, amplitude and initial phase is needed. A new approach is presented for inter-harmonic modeling and parameter estimation based on linear support vector machine （SVM）. Firstly, parameter estimation of linear model is realized based on standard linear SVM. Then, interharmonic model is transformed to a linear model according to trigonometric functions. The approach obtains order of inter-harmonic model with windowed Blackman-Tukey （BT） spectrum analysis, and gets number and frequency of harmonics. Finally, the linear SVM is applied to estimate the inter-harmonic parameters, amplitude and initial phase. The simulation results show that the proposed approach has high precision and good antinoise. The accuracy of three parameters are all higher than 98%.

Cross-spectral root-min-norm algorithm for harmonics analysis in electric power system

To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root-min-norm algorithm was described,but it is susceptive to noises with unstable performance in different SNRs.So the modified root-min-norm algorithm based on cross-spectral estimation was proposed,utilizing cross-correlation matrix and independence of different Gaussian noise series.Lots of simulation experiments were carried out to test performance of the algorithm in different conditions,and its statistical characteristics was presented.Simulation results show that the modified algorithm can efficiently suppress influence of the noises,and has high frequency resolution,high precision and high stability,and it is much superior to the classic DFT method.

Impacts of subsynchronous and supersynchronous frequency components on synchrophasor measurements

Phasor measurement units(PMU) are playing an increasingly important role in power system dynamic security monitoring and control. However, the wide-area deployments of the renewable energy sources and the high voltage direct current(HVDC) transmission bring a large number of inter-harmonics to the power grid, which may result in further power system security problems. The impacts of inter-harmonics on synchrophasor measurements are revealed. This paper derives the phasor expressions of the signal, which contains the fundamental component and the inter-harmonics. It is found that the inter-harmonics will lead to the subsynchronous oscillation of the phasor measurements. The frequency transmutation principle between the harmonic and the phasor oscillation is revealed. Then, the field PMU data recorded during a subsynchronous oscillation, which occurred in an area of China with a high concentration of wind farms and HVDC transmission lines, are studied. A geographical wiring diagram with the subsynchronous oscillation distribution depicts the severe consequences of the inter-harmonics. In addition, the correctness of the theoretical derivation and the possibility of the inter-harmonics monitoring are verified.

Effect of Multiple Models of Closed-loop Transfer Functions on Inter-harmonic Oscillation Characteristics of Grid-connected PMSG

Establishing a suitable closed-loop transfer function model for the grid-connected PMSG system is the key basis in performing inter-harmonic characteristics analysis.Multiple closed-loop transfer functions can be constructed when different components of the converter controller are taken into account.However,the effect of different components of the converter controller on inter-harmonic stability analysis is not clear.In this paper,the complete transfer function,considering different loops,is first given.Based on the complete closed-loop transfer function,the DC-link,PLL and voltage forward-feed are removed step by step to derive different closed-loop transfer functions.The inter-harmonic related poles of different closed-loop transfer functions are further calculated to analyze the effect of closedloop transfer functions on inter-harmonic characteristics analysis.Finally,by performing time domain simulation,the correctness of the theoretical analysis results is verified.The results show that under the conditions of a weak AC system,each loop of the converter control system will reduce the stability of the interharmonic in the sub-synchronous frequency range and influence the inter-harmonic oscillation frequency.The transfer function needs to consider the influence of each loop to accurately calculate the inter-harmonic stability of the system.