Engineering topics
Cortes, Jorge
Publications and source records attributed to Cortes, Jorge.
Chapter 7: Learning Stable Local Volt/Var Controllers in Distribution Grids
This chapter describes a framework to synthesize provably stable local Volt/Var controllers for distributed energy resources (DERs) in power distribution grids (DGs). The goal is to control the reactive power injections of DERs to improve the system performance as quantified by a generic optimal reactive power flow (ORPF) problem. To achieve this, we jointly design for each DER the control function, which prescribes the reactive power update rule, and the equilibrium function, which approximates the ORPF solutions from local measurements of voltages and powers. We provide conditions on the equilibrium functions and the control parameters ensuring the stability of the closed-loop system. In particular, we discuss the trade-offs between each set of conditions accounting for practical considerations, like fully exploiting the DERs' generation capabilities and reducing the optimality gap. These conditions are then translated into learning constraints on the neural networks' parameters that are enforced in the training phase. We validate our framework with numerical simulations on the IEEE 37-bus network and through a comparison with an optimized version of standard piece wise linear control rules.
Unsupervised Learning for Equitable DER Control: Preprint
In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.
Constraints on OPF Surrogates for Learning Stable Local Volt/Var Controllers
We consider the problem of learning local Volt/Var controllers in distribution grids (DGs). Our approach starts from learning separable surrogates that take both local voltages and reactive powers as arguments and predict the reactive power setpoints that approximate optimal power flow (OPF) solutions. We propose an incremental control algorithm and identify two different sets of slope conditions on the local surrogates such that the network is collectively steered toward desired configurations asymptotically. Our results reveal the trade-offs between each set of conditions, with coupled voltage-power slope constraints allowing an arbitrary shape of surrogate functions but risking limitations on exploiting generation capabilities, and reactive power slope constraints taking full advantage of generation capabilities but constraining the shape of surrogate functions. AC power flow simulations on the IEEE 37-bus feeder illustrate their guaranteed stability properties and respective advantages in two DG scenarios.
Gramian-Based Characterization of Network Vulnerability to Nodal Impulse Inputs: Preprint
Impulsive inputs applied at influential nodes of a network system may result in undesirable behavior and degrade performance. This paper proposes the notion of vulnerability matrix (VM) to characterize the effect of impulse inputs on a network following either discrete-time or continuous-time dynamics. The VM describes the first-order effects of impulse inputs on edge flows and is based on the controllability Gramian. We provide explicit expressions for the elements of the vulnerability matrix for the class of directed line networks in terms of the edge weights. Simulations validate our results and highlight the utility of the proposed metric in capturing the transient effects of nodal impulse inputs on edge flows.
Learning Local Volt/VAR Controllers Toward Efficient Network Operation with Stability Guarantees: Preprint
This paper considers the problem of voltage regulation in distribution network. The primary motivation is to keep voltages within pre-assigned operating limits by commanding the reactive power output of distributed energy resources (DERs) deployed in the grid. We develop a framework for developing local Volt/Var control that comprises of two main steps. In the first, exploiting historical data and for each DER, we learn a function representing desirable equilibrium points for the power network. These points approximate solutions of an Optimal Power Flow problem. In the second, we propose a control scheme for steering the network towards these favorable configurations. Theoretical conditions are derived to formally guarantee the stability of the developed control scheme and numerical simulations illustrate the effectiveness of the proposed approach.
Enabling DER Participation in Frequency Regulation Markets
Distributed energy resources (DERs) are playing an increasing role in ancillary services for the bulk grid, particularly in frequency regulation. In this article, we propose a framework for collections of DERs, combined to form microgrids and controlled by aggregators, to participate in frequency regulation markets. Our approach covers both the identification of bids for the market clearing stage and the mechanisms for the real-time allocation of the regulation signal. The proposed framework is hierarchical, consisting of a top layer and a bottom layer. The top layer consists of the aggregators communicating in a distributed fashion to optimally disaggregate the regulation signal requested by the system operator. The bottom layer consists of the DERs inside each microgrid whose power levels are adjusted so that the tie line power matches the output of the corresponding aggregator in the top layer. The coordination at the top layer requires the knowledge of cost functions, ramp rates, and capacity bounds of the aggregators. We develop meaningful abstractions for these quantities respecting the power flow constraints and taking into account the load uncertainties and propose a provably correct distributed algorithm for optimal disaggregation of regulation signals among the microgrids.
Agent-Supervisor Coordination for Decentralized Event-Triggered Optimization
This letter proposes decentralized resource-aware coordination schemes for solving network optimization problems defined by objective functions that combine locally evaluable costs with network-wide coupling components. These methods are well suited for a group of supervised agents trying to solve an optimization problem under mild coordination requirements. Each agent has information on its local cost and coordinates with the network supervisor for information about the coupling term of the cost. The proposed approach is feedback-based and asynchronous by design, guarantees anytime feasibility, and ensures the asymptotic convergence of the network state to the desired optimizer. Numerical simulations on a power system example illustrate our results.
Virtual-Voltage Partition-Based Approach to Optimal Transmission Switching
This article deals with optimal transmission switching (OTS) problems involving binary decisions about network topology and nonconvex power flow constraints. We adopt a semidefinite programming formulation for the optimal power flow (OPF) problem that, however, remains nonconvex due to the presence of discrete variables and bilinear products between the decision variables. To tackle the latter, we introduce a physically inspired, virtual-voltage approximation that leads to provable lower and upper bounds on the solution of the original problem. To deal with the exponential complexity caused by the discrete variables, we introduce a graph partition-based algorithm that breaks the problem into several parallel mixed-integer subproblems of smaller size. Simulations on the IEEE bus test cases demonstrate the high degree of accuracy and affordable computational requirements of our approach.