Decentralization can hinder frequency synchronization in power grids through multiple phase transitions

Abstract

Decarbonization is rapidly increasing the penetration of inverter-based renewables and other low-capacity generators, intensifying concerns about frequency synchronization in increasingly decentralized power grids. A common heuristic from Kuramoto onset theory and homogeneous parameter swing-equation models is that distributing generation across many smaller units reduces the effective heterogeneity of nodal injections (natural frequencies) and lowers the coupling required for synchronization. Here, using a second-order Kuramoto model, we investigate how decentralization affects frequency synchronization when inertia and damping scale with power generation and consumption. We find that decentralization does not always lower the critical frequency synchronization threshold. Instead, increasing decentralization can induce a non-monotonic dependence of the critical coupling strength and lead to a double phase transition in frequency synchronization. These behaviors remain robust under asymmetric inertia between consumers and generators. Even when empirical power-generation and power-consumption distributions are considered, a region in which the critical threshold remains nearly constant is observed as decentralization increases. Our results demonstrate that decentralization can give rise to complex collective dynamics and caution against assuming that decentralization alone ensures improved frequency synchronization.

Figures (3)

• Figure 1: Frequency order parameter $F$ as a function of the degree of decentralization $p$ and the coupling strength $\lambda$. For each value of $p$, simulations are performed by sweeping $\lambda$. All results are averaged over 100 independent realizations. (a) Forward process with $\alpha = 0.5$ and $\beta = 0.1$. (b) Backward process with $\alpha = 0.5$ and $\beta = 0.1$. (c) Forward process with $\alpha = 0.5$ and $\beta = 0.5$.
• Figure 2: Forward process with $\alpha = 0.5$, $\beta = 0.1$, $p = 19/32$, and $\Delta\lambda = 0.5$. (a) Frequency order parameter $F$ as a function of $\lambda$. Results are averaged over 1,000 independent realizations. (b--e) Time-averaged frequencies of all 1,024 nodes in the stationary state for a single realization at each value of $\lambda$. The nodes are ordered from lower to higher time-averaged frequency. (b) $\lambda = 5.0$, (c) $\lambda = 6.0$, (d) $\lambda = 8.5$, (e) $\lambda = 11.0$.
• Figure 3: (a) Frequency order parameter $F$ as a function of the degree of decentralization $p$ and the coupling strength $\lambda$ in the forward process with $\alpha_c = 0.05$, $\beta_c = 0.05$, $\alpha_g = 0.5$, and $\beta_g = 0.1$. (b) Distribution of rated power outputs of $30,757$ photovoltaic panels in the United Kingdom. (c) Distribution of power consumption of $5,567$ households in London. Consumption data are sampled at three randomly chosen time points between November 2011 and February 2014. (d) Frequency order parameter $F$ as a function of the degree of decentralization $p$ and the coupling strength $\lambda$ in the forward process with $\alpha = 0.5$ and $\beta = 0.1$, using the empirical power-generation and power-consumption distributions shown in (b) and (c). (a, d) For each value of $p$, simulations are performed by sweeping $\lambda$, and all results are averaged over 100 independent realizations.