Wenqi Cui

In January 2023, the City of Pasadena, CA, USA, set a goal to provide 100% of the city’s electricity from carbon-free resources by 2030. In this article, we describe some challenges in the path toward 100% carbon-free electricity in Pasadena and potential mitigation strategies. Through an ongoing collaboration between the city’s municipal utility and Caltech, these real-world considerations are formalized as system models and optimization programs. In particular, we focus on the planning of distributed solar photovoltaic (PV) power in the Pasadena distribution system as one step toward the decarbonization goal. We discuss the following questions: 1) What are the grid impacts from widespread and distributed PV adoption? 2) What is the maximum PV hosting capacity while ensuring safe operations? 3) What are potential infrastructure upgrades to mitigate the impact of large-scale PV adoption?

The increasing integration of renewable energy resources into power grids has led to time-varying system inertia and consequent degradation in frequency dynamics. A promising solution to alleviate performance degradation is using power electronics interfaced energy resources, such as renewable generators and battery energy storage for primary frequency control, by adjusting their power output set-points in response to frequency deviations. However, designing a frequency controller under time-varying inertia is challenging. Specifically, the stability or optimality of controllers designed for time-invariant systems can be compromised once applied to a time-varying system. We model the frequency dynamics under time-varying inertia as a nonlinear switching system, where the frequency dynamics under each mode are described by the nonlinear swing equations and different modes represent different inertia levels. We identify a key controller structure, named Neural Proportional-Integral (Neural-PI) controller, that guarantees exponential input-to-state stability for each mode. To further improve performance, we present an online event-triggered switching algorithm to select the most suitable controller from a set of Neural-PI controllers, each optimized for specific inertia levels. Simulations on the IEEE 39-bus system validate the effectiveness of the proposed online switching control method with stability guarantees and optimized performance for frequency control under time-varying inertia.

Deep reinforcement learning approaches are becoming appealing for the design of nonlinear controllers for voltage control problems, but the lack of stability guarantees hinders their deployment in real-world scenarios. This paper constructs a decentralized RL-based controller for inverter-based real-time voltage control in distribution systems. It features two components: a transient control policy and a steady-state performance optimizer. The transient policy is parameterized as a neural network, and the steady-state optimizer represents the gradient of the long-term operating cost function. The two parts are synthesized through a safe gradient flow framework, which prevents the violation of reactive power capacity constraints. We prove that if the output of the transient controller is bounded and monotonically decreasing with respect to its input, then the closed-loop system is asymptotically stable and converges to the optimal steady-state solution. We demonstrate the effectiveness of our method by conducting experiments with IEEE 13-bus and 123-bus distribution system test feeders.

The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits after various potential faults. However, current numerical solvers of DAEs are often too slow for real-time system operations. In addition, detailed system parameters are often not exactly known. Machine learning approaches have been proposed to reduce the computational efforts, but existing methods generally suffer from overfitting and failures to predict unstable behaviors. This paper proposes a novel framework to predict power system transients by learning in the frequency domain. The intuition is that although the system behavior is complex in the time domain, there are relatively few dominant modes in the frequency domain. Therefore, we learn to predict by constructing neural networks with Fourier transform and filtering layers. System topology and fault information are encoded by taking a multi-dimensional Fourier transform, allowing us to leverage the fact that the trajectories are sparse both in time and spatial frequencies. We show that the proposed approach does not need detailed system parameters, greatly speeds up prediction computations and is highly accurate for different fault types.

Frequency control plays a pivotal role in reliable power system operations. It is conventionally performed in a hierarchical way that first rapidly stabilizes the frequency deviations and then slowly recovers the nominal frequency. However, as the generation mix shifts from synchronous generators to renewable resources, power systems experience larger and faster frequency fluctuations due to the loss of inertia, which adversely impacts the frequency stability. This has motivated active research in algorithms that jointly address frequency degradation and economic efficiency in a fast timescale, among which the distributed averaging-based integral (DAI) control is a notable one that sets controllable power injections directly proportional to the integrals of frequency deviation and economic inefficiency signals. Nevertheless, DAI does not typically consider the transient performance of the system following power disturbances and has been restricted to quadratic operational cost functions. This paper aims to leverage nonlinear optimal controllers to simultaneously achieve optimal transient frequency control and find the most economic power dispatch for frequency restoration. To this end, we integrate reinforcement learning (RL) to the classic DAI, which results in RL-DAI control. Specifically, we use RL to learn a neural network-based control policy mapping from the integral variables of DAI to the controllable power injections which provides optimal transient frequency control, while DAI inherently ensures the frequency restoration and optimal economic dispatch. Compared to existing methods, we provide provable guarantees on the stability of the learned controllers and extend the set of allowable cost functions to a much larger class. Simulations on the 39-bus New England system illustrate our results.

Power distribution systems are becoming much more active with increased penetration of distributed energy resources. Because of the intermittent nature of these resources, the stability of distribution systems under large disturbances and time-varying conditions is becoming a key issue in practical operations. Because the transmission lines in distribution systems are lossy, standard approaches in power system stability analysis do not readily apply. In this letter, the stability of lossy distribution systems is certified by breaking the network into subsystems. By looking at the equilibrium-independent passivity of each subsystem, the stability of the whole network is implied by the diagonal stability of the interconnection matrix. This analysis scales to large networked systems with time-varying equilibria. The proposed method gracefully extrapolates between lossless and lossy systems, and provides a simple yet effective approach to optimize control efforts with guaranteed stability regions. Case studies verify that the proposed method is much less conservative than existing approaches.

As more inverter-connected renewable resources are integrated into the grid, frequency stability may degrade because of the reduction in mechanical inertia and damping. A common approach to mitigate this degradation in performance is to use the power electronic interfaces of the renewable resources for primary frequency control. Since inverter-connected resources can realize almost arbitrary responses to frequency changes, they are not limited to reproducing the linear droop behaviors. To fully leverage their capabilities, reinforcement learning (RL) has emerged as a popular method to design nonlinear controllers to optimize a host of objective functions. Because both inverter-connected resources and synchronous generators would be significant part of the grid in the near and intermediate future, the learned controller of the former should be stabilizing with respect to the nonlinear dynamics of the latter. To overcome this challenge, we explicitly engineer the structure of neural network--based controllers such that they guarantee system stability by construction, through the use of a Lyapunov function. A recurrent neural network architecture is used to efficiently train the controllers. The resulting controllers only use local information and outperform optimal linear droop as well as other state-of-the-art learning approaches.