Double-sided Frequency-Domain Modeling And Advanced Control Technologies Of Current Loop In High-power Converters With Low Carrier Ratio

With the development of industrial traction,transportation,power grid equipment and other industries,large-capacity converters have more and more urgent application needs and broader market prospects.In order to improve the system conversion efficiency and expand the scope of industrial application,large capacity converters are developing towards higher power capacity and higher voltage grade.The increase of rated capacity means the increase of system loss,which becomes the core factor restricting the safe operation of the converters.Therefore,high capacity converters usually adopt low-carrier-ratio modulation strategy in order to reduce the switching frequency of the power devices and therefore reduce the operating loss of the system.However,the low-carrier-ratio condition increases the control delay of the converter,which inevitably threatens the stability of the control loop.Among them,the current loop is the internal control loop with the fastest frequency response of the converter,and its stability is most affected by the control delay.In order to improve the stability of the current loop of the low-carrier-ratio converters,a series of improved control methods for the three-phase symmetric and the three-phase asymmetric current loop are proposed in this paper based on the stability criterion in frequency domain and using double-sided frequency domain modeling as the analysis method,which effectively expands the stable operation range of the low-carrier-ratio converters.Firstly,the modeling error function of classical frequency-domain method is established for three-phase symmetrical current loop,and the quantitative influence of low carrier ratio on stability is analyzed by using double-sided frequency-domain model.Based on the theoretical assumption of complete decoupling of dq axes,classical frequency-domain modeling will introduce non-negligible modeling errors under low-carrier-ratio conditions,which severely affects the stability margin of the current loop.The negative correlation between the modeling error function and carrier ratio is concluded by deducing the quantitative relationship between the modeling error function and carrier ratio,which illustrates the limitations of classical frequency domain modeling method.On the other hand,the double-sided frequency-domain model of the current loop is derived from the complex transfer function,and the stability margin of the current loop is analyzed by using the double-sided frequency-domain Bode plot.The positive correlation between the stability margin of the current loop and the carrier ratio is obtained by means of the double-sided frequency domain model,and the positive effect of the delay compensation angle on enhancing the stability of the current loop is explained.Secondly,the vector angle PI control method is proposed for the three-phase symmetrical current loop.It can be seen from the double-sided frequency domain model that the control delay caused by the low-carrier-ratio makes the open loop complex transfer function of the current loop show the characteristics of asymmetry in the frequency domain,and the stability margin is reflected in the asymmetry between the positive and negative frequency bands of the phase margin.The existing phase margin compensator can enhance the stability of the current loop to some extent by shifting the phase characteristics,but does not change the sum of the phase margin in the positive and negative bands.By introducing two additional vector angle control parameters,the vector angle PI controller proposed in this paper can increase the sum of phase margin in positive and negative frequency bands,thus further enlarging the low-carrier-ratio operating range of current loop.The mathematical derivation shows that the existing phase shift compensator can be regarded as a special case of the vector angle PI controller.The stability margin of the vector angle PI controller is superior to the phase shift compensator,and both of them are superior to the classical PI controller.Thirdly,a double-sided frequency-domain modeling method based on the characteristic loci of transfer function matrix is proposed for three-phase asymmetric current loops.The transfer function matrix can be used to accurately describe the model of asymmetric current loops,and the generalized Nyquist criterion determines the stability by the position relation between the characteristic loci of the transfer function matrix and the point(-1,0)on the complex plane.The stability and stability margin of the current loop can be reflected more intuitively by using the double-sided frequency domain Bode plot of characteristic loci.Through mathematical analysis,it is found that there is a universal symmetrical feature in frequency domain between the two characteristic loci,and it is proved that the complex transfer function describing the symmetric current loop can be regarded as a characteristic locus of the transfer function matrix,thus revealing the relationship between them.Time-domain simulation shows that the double-sided frequentdomain model of characteristic characteristic loci can effectively determine the stability of asymmetric current loops with low carrier ratio.Finally,a matrix vector angle PR control method is proposed for three phase asymmetric current loops.Both the characteristic locus describing the asymmetric current loop and the complex transfer function describing the symmetric current loop have the characteristics of asymmetry in the positive and negative frequency bands in the double-sided frequency domain model,which is reflected in the difference of phase margin in the positive and negative frequency bands in the stability margin.By using the matrix diagonal tool,the phase shift compensator suitable for symmetric current loops can be extended to the asymmetric current loops.The matrix phase shift compensator can be formed,and the stability margin of the asymmetric current loops can be improved by equalizing the phase margin of the positive and negative frequency bands of the characteristic loci.Furthermore,the vector angle PI controller suitable for symmetric current loops is extended to matrix vector angle PR controller suitable for stationary asymmetric current loops.By introducing two vector angle control parameters,the sum of phase margin in positive and negative frequency bands can be increased,and the low carrier ratio operating range of asymmetric converters can be extended.The main conclusions in this paper are verified by experiments on a five-level converter prototype system.