This paper presents an interesting method for the calculation of bus voltage transients in an electric power system. The method is specifically intended for application to distribution and subtransniission networks. The transient bus voltages are calculated during the application of large industrial loads. In this sense, the calculation is a power quality assessment. In particular, the case of load currents which are electronically switched may be analyzed. The essence of the method is the Fourier transform of Ohm's law. The fast Fourier transform is used in order to give computational efficiency. An interesting method for obtaining the Fourier transform of the bus transfer impedance, Z,j(w), is developed from the theory of parallel n-port networks. Two approximations are found for the calculation of this transfer impedance and one of these is found to be applicable to the cited problem. Examples are used to illustrate the calculation of bus voltage transients and harmonic content. Although the latter is not a transient, harmonic voltages may be calculated by the proposed method under certain circumstances. The main application illustrated is that of a transient which has dynamics which occur in a time interval of similar order as the period of the power frequency (i.e., 1/60 sec for a 60 Hz system). With the advent of power electronic switches, this type of transient is a serious reality at distribution power levels.
The frequency response of an electrical networkConsider a multi-port electric network of n+l busses with voltages at each bus measured from a given reference bus as vl(t), vz(t), . * ,vn(t). Also consider injection currents at the busses with return path through the reference bus. These currents are il(t), i2(t), * ,in(t). Under most circumstances of practical interest, these voltages and currents possess a two-sided Fourier transform, for example,Consider further that the electrical network is decomposed into two networks labeled SE and SH which are characterized as follows: the SE network contains only resistances and inductances and therefore this network is modelled as W -W 89 WM 101-7 PWRD by the IEEE Transmission and Distribution Committee of the IEEE Power Engineering Society f o r presentation a t the IEEE/PES A paper recommended and approvedwhere VSE(t) and iSE(t) are n-dimensional vectors of the bus voltages and currents using one system bus as a reference. Similarly, let the SH network contain only conductances and capacitances. The SH network is modelled asThe terms RSE, LSE, GSH, and CSH are n by n matrices which exist and are non-singular when the SE and SH networks are connected. The reference bus must be connected to each system bus. The Fourier transform of Equations (1) and (2) areFrom these equations one collects terms and recognizes familiar expressions,vSH(w) = (GSH +jWCSH)-llSH(w) * Figure 1 shows a pictorial of the network decomposition.
Figure 1. Distribution network decomposed into SE and SH networksThe SE network is the series portion of the network and the SH is the shunt ...
