Small Signal Stability Analysis of Distribution Networks with Electric Springs

Abstract

This paper presents small signal stability analysis of distribution networks with electric springs (ESs) installed at the customer supply points. The focus is on ESs with reactive compensation only. Vector control of ES with reactive compensation is reported for the first time to ensure compatibility with the standard stability models of other components such as the interface inverter of distributed generators (DGs). A linearized state-space model of the distribution network with multiple ESs is developed which is extendible to include inverter-interfaced DGs, energy storage, active loads etc. The impact of distance of an ES from the substation, proximity between adjacent ESs and the R/X ratio of the network on the small signal stability of the system is analyzed and compared against the case with equivalent DG inverters. The collective operation of ESs is validated through simulation study on a standard distribution network.

Stability of Isolated Microgrids With Renewable Generation and Smart Loads

“…The stability problem in [18] was mainly associated with the dynamics of the filter components leading to relatively high frequency (hundreds or thousands of Hz) instability which is fundamentally different in nature from the low frequency oscillatory stability problem studied in this paper. Moreover, a smart load configuration with only the series converter in its voltage compensator was considered in [18] which has limited flexibility [2], [5]. Hence, the stability analysis presented in [18] needs to be extended to include the dynamics of the shunt converter and the DC link and then apply it in the context of IMG to analyse the role of SLs in low frequency dynamics.…”

“…The linearized state space model (LSSM) of an IMG with CDGs in grid-forming mode [12] is extended to include a SL with a series-shunt converter as described earlier in Section II. The LSSM of the SeC of the SL is adopted from [18] while the CDGs and the line segments are modelled using equations (10)−(41), (50)−(51) from [12]. Hence, only the LSSMs of the ShC of the SL, the DC link and the voltagedependent load are presented here due to space restriction.…”

“…The individual LSSM of ShC, DC link and the voltagedependedent load (described above) together with LSSM of CDGs, line segments [12] and SeC [18] are stacked up to form the overall state (A), input (B), output (C) and transfer (D) matrices. The algebraic relations between the elements is captured through a matrix L T by matching the inputs and outputs of each LSSM.…”

“…In [18], dynamics of the control loops of SL has been considered for stability analysis of power networks, in general but not specifically for IMGs. The stability problem in [18] was mainly associated with the dynamics of the filter components leading to relatively high frequency (hundreds or thousands of Hz) instability which is fundamentally different in nature from the low frequency oscillatory stability problem studied in this paper. Moreover, a smart load configuration with only the series converter in its voltage compensator was considered in [18] which has limited flexibility [2], [5].…”

“…Moreover, a smart load configuration with only the series converter in its voltage compensator was considered in [18] which has limited flexibility [2], [5]. Hence, the stability analysis presented in [18] needs to be extended to include the dynamics of the shunt converter and the DC link and then apply it in the context of IMG to analyse the role of SLs in low frequency dynamics. This is what motivates this paper.…”