Relationship for Electric Network Between Internal Voltage Amplitude/Frequency Stimulation and Active/Reactive Power Response and Its Characteristics Analysis

The process, in which the internal voltage with time-varying amplitude and frequency (A/F) regulated by equipment generates the electric network's terminal power variations, plays a critical role in the system dynamic. For the system dynamic analysis, the relationship between the time-varying A/F and the power response, as well as its characteristics, is required. However, this subject has yet to be emphasized and thoroughly studied due to insufficient attention to the fact that the frequency is time-varying. In traditional power system analysis, since the network's time constant is often fast enough compared to synchronous generators, the electric network is generally depicted by the static relationship with the assumption of constant frequency, although it is not consistent with the practice of frequency time-varying. Moreover, in the present renewable generation scenario, the fast A/F dynamics of internal voltages can impact the power response, and further the system dynamics. So that adequate investigations around the electric network's power response in relation to the time-varying A/F are more urgent. Motivated by these considerations, this paper studies the network's original relationship between the internal voltage's A/F stimulation and the active/reactive power response, which contains the oscillatory integral problem in math. By using the method of integration by parts, an explicit expression of this relationship is given. Further, a simplified relationship is presented to help understand the dynamic characteristics of the network. Several unusual observations, including the composition and consumption on the line of the active/reactive power in relation to the time-varying A/F, are obtained.