Hosting capacity is defined as the level of penetration that a particular technology can connect to a distribution network without causing power quality problems. In this work, we study the impact of solar photovoltaics (PV) on voltage rise. In most cases, the locations and sizes of the PV are not known in advance, so hosting capacity must be considered as a random variable. Most hosting capacity methods study the problem considering a large number of scenarios, many of which provide little additional information. We overcome this problem by studying only cases where voltage constraints are active, with results illustrating a reduction in the number of scenarios required by an order of magnitude. A linear power flow model is utilised for this task, showing excellent performance. The hosting capacity is finally studied as a function of the number of generators connected, demonstrating that assumptions about the penetration level will have a large impact on the conclusions drawn for a given network.
This paper presents a method to obtain a convex inner approximation that aims to improve the feasibility of optimal power flow (OPF) models in distribution feeders. For a resistive distribution network, both real and reactive power effect the node voltages and this makes it necessary to consider both when formulating the OPF problem. Inaccuracy in linearized OPF models may lead to under and over voltages when dispatching flexible demand, at scale, in response to whole-sale market or grid conditions. In order to guarantee feasibility, this paper obtains an inner convex set in which the dispatch…
Interconnection studies for distributed energy resources (DERs) can currently take months since they entail simulating a large number of power flow scenarios. If DERs are to be actively controlled, probabilistic hosting capacity analysis (PHCA) studies become more time-consuming since they require solving multiple optimal power flow (OPF) tasks. PHCA is expedited here by leveraging the powerful tool of multiparametric programming (MPP). Using an approximate grid model, optimal DER setpoints are decided by a quadratic program, which depends on analysis and uncertain parameters in a possibly non…
The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time properties of this model. Our analysis focuses on the system of two fluid queueing links in series. The upstream link has a constant capacity (saturation rate) and an infinite buffer size. The downstream link has a stochastic capacity and a finite buffer size. Queue spillback occurs when the the downstream link is full. We derive a necessary condition and a sufficien…
We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface that splits the state space into action and inaction regions. We then show that a solution of the MFG of capacity expansion induces approximate Nash equilibria for the $N$-player games with approximation error $\varepsilon$ going to zero as $N$ tends to…
The distribution optimal power flow (D-OPF) models have gained attention in recent years to optimally operate acentrally-managed distribution grid. On account of nonconvex formulation that is difficult to solve, several relaxation methods have been proposed; the exactness of the solutions obtained from the relaxed models, however, remain a concern. In this paper, we identify one such problem related to radial distribution feeder where second-order cone program (SOCP) relaxation does not yield a solution that is feasible with respect to the original nonlinear OPF model. Specifically, we formula…
We propose stochastic optimization methodologies for a staffing and capacity planning problem arising from home care practice. Specifically, we consider the perspective of a home care agency that must decide the number of caregivers to hire (staffing) and the allocation of hired caregivers to different types of services (capacity planning) in each day within a specified planning horizon. The objective is to minimize the total cost associated with staffing (i.e., employment), capacity allocation, over-staffing, and under-staffing. We propose two-stage stochastic programming (SP) and distributio…
This paper presents a market-based optimization framework wherein Aggregators can compete for nodal capacity across a distribution feeder and guarantee that allocated flexible capacity cannot cause overloads or congestion. This mechanism, thus, allows Aggregators with allocated capacity to pursue a number of services at the whole-sale market level to maximize revenue of flexible resources. Based on Aggregator bids of capacity (MW) and network access price ($/MW), the distribution system operator (DSO) formulates an optimization problem that prioritizes capacity to the different Aggregators acr…
In this paper, we discuss the relationships between capacity of control in entropy theory and intrinsic properties in control theory for a class of finite dimensional stochastic dynamical systems described by a linear stochastic differential equations driven by mixed fractional Brownian motion with delay in control. Stochastic dynamical systems can be described as an information channel between the space of control signals and the state space. We study this control to state information capacity of this channel in continuous time. We turned out that, the capacity of control depends on the time …
This paper addresses the energy management of a grid-connected photovoltaic plant coupled with a battery energy storage device, within the capacity firming specifications of the French Energy Regulatory Commission. The paper contributions are positioned in the continuity of the studies adopting stochastic models for optimizing the bids of renewable energy sources in a day-ahead market by considering a storage device. The proposed deterministic and stochastic approaches are optimization problems formulated as quadratic problems with linear constraints. The case study is a real microgrid with PV…
This paper applies the N-block PCPM algorithm to solve multi-scale multi-stage stochastic programs, with the application to electricity capacity expansion models. Numerical results show that the proposed simplified N-block PCPM algorithm, along with the hybrid decomposition method, exhibits much better scalability for solving the resulting deterministic, large-scale block-separable optimization problem when compared with the ADMM algorithm and the PHA algorithm. The superiority of the algorithm's scalability is attributed to the two key features of the algorithm design: first, the proposed hyb…
This paper considers the problem of stabilizing a discrete-time non-linear stochastic system over a finite capacity noiseless channel. Our focus is on systems which decompose into a stable and unstable component, and the stability notion considered is asymptotic ergodicity of the $\mathbb{R}^N$-valued state process. We establish a necessary lower bound on channel capacity for the existence of a coding and control policy which renders the closed-loop system stochastically stable. In the literature, it has been established that under technical assumptions, the channel capacity must not be smalle…
This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the \textit{here and now} variables which represent the capacity of the network. The main contribution is a heuristic approach which involves the formulation of the problem as a mean-field game. Every agent in the mean-field game has control over its own primal-dual dynamics and seeks consensus with neighboring agents according to a communication topology. We obtain theoretical results concerning the existence of a mean-field equilibrium. Mo…
A stochastic programming approach for dynamic allocation of bed capacity and assignment of patients to collaborating hospitals during pandemic outbreaks
This paper studies a stochastic congested location problem in the network of a service system that consists of facilities to be established in a finite number of candidate locations. Population zones allocated to each open service facility together creates a stream of demand that follows a Poisson process and may cause congestion at the facility. The service time at each facility is stochastic and depends on the service capacity and follows a general distribution that can differ for each facility. The service capacity is selected from a given (bounded or unbounded) interval. The objective of o…
Modular and Mobile Capacity Planning for Hyperconnected Supply Chain Networks
H.Milton Stewart School for Industrial & Systems Engineering, Georgia Institute of Technology（佐治亚理工学院工业与系统工程系）；The Centre of Excellence for Supply Chain Innovation & Transportation, Kedge Business School（凯致商学院供应链创新与运输卓越中心）
We consider a general class of dynamic resource allocation problems within a stochastic optimal control framework. This class of problems arises in a wide variety of applications, each of which intrinsically involves resources of different types and demand with uncertainty and/or variability. The goal involves dynamically allocating capacity for every resource type in order to serve the uncertain/variable demand, modeled as Brownian motion, and maximize the discounted expected net-benefit over an infinite time horizon based on the rewards and costs associated with the different resource types,…
This paper proposes a strategy to size a grid-connected photovoltaic plant coupled with a battery energy storage device within the \textit{capacity firming} specifications of the French Energy Regulatory Commission. In this context, the sizing problem is challenging due to the two-phase engagement control with a day-ahead nomination and an intraday control to minimize deviations from the planning. The two-phase engagement control is modeled with deterministic and stochastic approaches. The optimization problems are formulated as mixed-integer quadratic problems, using a Gaussian copula methodo…
Ride-pooling, which accommodates multiple passenger requests in a single trip, has the potential to significantly increase fleet utilization in shared mobility platforms. The ride-pooling assignment problem finds optimal co-riders to maximize the total utility or profit on a shareability graph, a hypergraph representing the matching compatibility between available vehicles and pending requests. With mixed fleets due to the introduction of automated or premium vehicles, fleet sizing and relocation decisions should be made before the requests are revealed. Due to the immense size of the underlyi…
The large shares of wind power generation in electricity markets motivate higher levels of operating reserves. However, current reserve sizing practices fail to account for important topological aspects that might hinder their deployment, thus resulting in high operating costs. Zonal reserve procurement mitigates such inefficiencies, however, the way the zones are defined is still open to interpretation. This paper challenges the efficiency of predetermined zonal setups that neglect the location of stochastic power production in the system, as well as the availability, cost and accessibility o…
Optimal Policies for Simultaneous Energy Consumption and Ancillary Service Provision for Flexible Loads under Stochastic Prices and No Capacity Reservation Constraint
One of the primary challenges in large-scale distributed learning stems from stringent communication constraints. While several recent works address this challenge for static optimization problems, sequential decision-making under uncertainty has remained much less explored in this regard. Motivated by this gap, we introduce a new linear stochastic bandit formulation over a bit-constrained channel. Specifically, in our setup, an agent interacting with an environment transmits encoded estimates of an unknown model parameter to a server over a communication channel of finite capacity. The goal o…
