School of Engineering, University of Applied Sciences of Western Switzerland HES-SO, Sion, Switzerland.
Institute of Theoretical Physics, EPFL, Lausanne, Switzerland.
PLoS One. 2019 Mar 21;14(3):e0213550. doi: 10.1371/journal.pone.0213550. eCollection 2019.
Conventional generators in power grids are steadily substituted with new renewable sources of electric power. The latter are connected to the grid via inverters and as such have little, if any rotational inertia. The resulting reduction of total inertia raises important issues of power grid stability, especially over short-time scales. With the motivation in mind to investigate how inertia reduction influences the transient dynamics following a fault in a large-scale electric power grid, we have constructed a model of the high voltage synchronous grid of continental Europe. To assess grid stability and resilience against disturbance, we numerically investigate frequency deviations as well as rates of change of frequency (RoCoF) following abrupt power losses. The magnitude of RoCoF's and frequency deviations strongly depend on the fault location, and we find the largest effects for faults located on the support of the slowest mode-the Fiedler mode-of the network Laplacian matrix. This mode essentially vanishes over Belgium, Eastern France, Western Germany, northern Italy and Switzerland. Buses inside these regions are only weakly affected by faults occuring outside. Conversely, faults inside these regions have only a local effect and disturb only weakly outside buses. Following this observation, we reduce rotational inertia through three different procedures by either (i) reducing inertia on the Fiedler mode, (ii) reducing inertia homogeneously and (iii) reducing inertia outside the Fiedler mode. We find that procedure (iii) has little effect on disturbance propagation, while procedure (i) leads to the strongest increase of RoCoF and frequency deviations. This shows that, beyond absorbing frequency disturbances following nearby faults, inertia also mitigates frequency disturbances from distant power losses, provided both the fault and the inertia are located on the support of the slowest modes of the grid Laplacian. These results for our model of the European transmission grid are corroborated by numerical investigations on the ERCOT transmission grid.
传统电网中的发电机正在被新型可再生电力源逐步取代。后者通过逆变器连接到电网，因此几乎没有旋转惯性。总惯量的减少带来了电网稳定性的重要问题，尤其是在短时间尺度上。为了研究惯性减少如何影响大型电网故障后的暂态动力学，我们构建了一个欧洲大陆高压同步电网的模型。为了评估电网稳定性和对干扰的恢复能力，我们通过数值方法研究了突然功率损失后频率偏差和频率变化率（RoCoF）。RoCoF 和频率偏差的幅度强烈依赖于故障位置，我们发现位于网络拉普拉斯矩阵最慢模式——菲德勒模式——支撑上的故障影响最大。该模式在比利时、法国东部、德国西部、意大利北部和瑞士基本上消失了。这些地区内的母线受到位于该地区外的故障的影响较小。相反，这些地区内的故障只有局部影响，对外区母线的干扰较弱。根据这一观察结果，我们通过三种不同的方法来减少旋转惯性，分别是（i）减少菲德勒模式上的惯性，（ii）均匀减少惯性，（iii）减少菲德勒模式之外的惯性。我们发现，方法（iii）对干扰传播的影响很小，而方法（i）导致 RoCoF 和频率偏差的最大增加。这表明，惯性不仅在吸收附近故障后的频率干扰方面，而且在减轻来自遥远功率损失的频率干扰方面也具有作用，前提是故障和惯性都位于电网拉普拉斯矩阵的最慢模式的支撑上。我们对欧洲传输电网模型的这些结果得到了对 ERCOT 传输电网的数值研究的证实。
