Pseudo-gradient Based Local Voltage Control in Distribution Networks

Voltage regulation is critical for power grids. However, it has become a much more challenging problem as distributed energy resources (DERs) such as photovoltaic and wind generators are increasingly deployed, causing rapid voltage fluctuations beyond what can be handled by the traditional voltage regulation methods. In this paper, motivated by two previously proposed inverter-based local volt/var control algorithms, we propose a pseudo-gradient based voltage control algorithm for the distribution network that does not constrain the allowable control functions and has low implementation complexity. We characterize the convergence of the proposed voltage control scheme, and compare it against the two previous algorithms in terms of the convergence condition as well as the convergence rate

Branch Flow Model: Relaxations and Convexification—Part II

We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results

Branch Flow Model: Relaxations and Convexification (Parts I, II)

We propose a branch flow model for the anal- ysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.Comment: A preliminary and abridged version has appeared in IEEE CDC, December 201

ResOT: Resource-Efficient Oblique Trees for Neural Signal Classification

Classifiers that can be implemented on chip with minimal computational and memory resources are essential for edge computing in emerging applications such as medical and IoT devices. This paper introduces a machine learning model based on oblique decision trees to enable resource-efficient classification on a neural implant. By integrating model compression with probabilistic routing and implementing cost-aware learning, our proposed model could significantly reduce the memory and hardware cost compared to state-of-the-art models, while maintaining the classification accuracy. We trained the resource-efficient oblique tree with power-efficient regularization (ResOT-PE) on three neural classification tasks to evaluate the performance, memory, and hardware requirements. On seizure detection task, we were able to reduce the model size by 3.4X and the feature extraction cost by 14.6X compared to the ensemble of boosted trees, using the intracranial EEG from 10 epilepsy patients. In a second experiment, we tested the ResOT-PE model on tremor detection for Parkinson's disease, using the local field potentials from 12 patients implanted with a deep-brain stimulation (DBS) device. We achieved a comparable classification performance as the state-of-the-art boosted tree ensemble, while reducing the model size and feature extraction cost by 10.6X and 6.8X, respectively. We also tested on a 6-class finger movement detection task using ECoG recordings from 9 subjects, reducing the model size by 17.6X and feature computation cost by 5.1X. The proposed model can enable a low-power and memory-efficient implementation of classifiers for real-time neurological disease detection and motor decoding

Reverse and Forward Engineering of Local Voltage Control in Distribution Networks

The increasing penetration of renewable and distributed energy resources in distribution networks calls for real-time and distributed voltage control. In this paper we investigate local Volt/VAR control with a general class of control functions, and show that the power system dynamics with non-incremental local voltage control can be seen as a distributed algorithm for solving a well-defined optimization problem (reverse engineering). The reverse engineering further reveals a fundamental limitation of the non-incremental voltage control: the convergence condition is restrictive and prevents better voltage regulation at equilibrium. This motivates us to design two incremental local voltage control schemes based on the subgradient and pseudo-gradient algorithms respectively for solving the same optimization problem (forward engineering). The new control schemes decouple the dynamical property from the equilibrium property, and have much less restrictive convergence conditions. This work presents another step towards developing a new foundation - network dynamics as optimization algorithms - for distributed real-time control and optimization of future power networks

Optimization and Control of Power Flow in Distribution Networks

Climate change is arguably the most critical issue facing our generation and the next. As we move towards a sustainable future, the grid is rapidly evolving with the integration of more and more renewable energy resources and the emergence of electric vehicles. In particular, large scale adoption of residential and commercial solar photovoltaics (PV) plants is completely changing the traditional slowly-varying unidirectional power flow nature of distribution systems. High share of intermittent renewables pose several technical challenges, including voltage and frequency control. But along with these challenges, renewable generators also bring with them millions of new DC-AC inverter controllers each year. These fast power electronic devices can provide an unprecedented opportunity to increase energy efficiency and improve power quality, if combined with well-designed inverter control algorithms. The main goal of this dissertation is to develop scalable power flow optimization and control methods that achieve system-wide efficiency, reliability, and robustness for power distribution networks of future with high penetration of distributed inverter-based renewable generators. Proposed solutions to power flow control problems in the literature range from fully centralized to fully local ones. In this thesis, we will focus on the two ends of this spectrum. In the first half of this thesis (chapters 2 and 3), we seek optimal solutions to voltage control problems provided a centralized architecture with complete information. These solutions are particularly important for better understanding the overall system behavior and can serve as a benchmark to compare the performance of other control methods against. To this end, we first propose a branch flow model (BFM) for the analysis and optimization of radial and meshed networks. This model leads to a new approach to solve optimal power flow (OPF) problems using a two step relaxation procedure, which has proven to be both reliable and computationally efficient in dealing with the non-convexity of power flow equations in radial and weakly-meshed distribution networks. We will then apply the results to fast time- scale inverter var control problem and evaluate the performance on real-world circuits in Southern California Edison’s service territory. The second half (chapters 4 and 5), however, is dedicated to study local control approaches, as they are the only options available for immediate implementation on today’s distribution networks that lack sufficient monitoring and communication infrastructure. In particular, we will follow a reverse and forward engineering approach to study the recently proposed piecewise linear volt/var control curves. It is the aim of this dissertation to tackle some key problems in these two areas and contribute by providing rigorous theoretical basis for future work.</p

Branch flow model: Relaxations and convexification

We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results