## Section: New Results

### Distributed network control and smart-grids

** 1.**** Distributed Control of Thermostatically Controlled Loads: Kullback-Leibler Optimal Control in Continuous Time** [20]
The paper develops distributed control techniques to obtain grid services from flexible loads. The Individual Perspective Design (IPD) for local (load level) control is extended to piecewise deterministic and diffusion models for thermostatically controlled load models. The IPD design is formulated as an infinite horizon average reward optimal control problem, in which the reward function contains a term that uses relative entropy rate to model deviation from nominal dynamics. In the piecewise deterministic model, the optimal solution is obtained via the solution to an eigenfunction problem, similar to what is obtained in prior work. For a jump diffusion model this simple structure is absent. The structure for the optimal solution is obtained, which suggests an ODE technique for computation that is likely far more efficient than policy-or value-iteration.

** 2.**** Optimal Control of Dynamic Bipartite Matching Models** [23]
A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a stochastic process. Matched pairs leave the system and the others wait in the queues, which induces a holding cost. We model this problem as a Markov Decision Process and study the discounted cost and the average cost case. We first consider a model with two types of supply and two types of demand items with an N-shaped matching graph. For linear cost function, we prove that an optimal matching policy gives priority to the end edges of the matching graph and is of threshold type for the diagonal edge. In addition, for the average cost problem, we compute the optimal threshold value. According to our numerical experiments, threshold-type policies perform also very well for more general bipartite graphs.

** 3.**** Kullback-Leibler-Quadratic Optimal Control of Flexible Power Demand** [24]
A new stochastic control methodology is introduced for distributed control, motivated by the goal of creating virtual energy storage from flexible electric loads, i.e. Demand Dispatch. In recent work, the authors have introduced Kullback-Leibler-Quadratic (KLQ) optimal control as a stochastic control methodology for Markovian models. This paper develops KLQ theory and demonstrates its applicability to demand dispatch. In one formulation of the design, the grid balancing authority simply broadcasts the desired tracking signal, and the heterogeneous population of loads ramps power consumption up and down to accurately track the signal. Analysis of the Lagrangian dual of the KLQ optimization problem leads to a menu of solution options, and expressions of the gradient and Hessian suitable for Monte-Carlo-based optimization. Numerical results illustrate these theoretical results.

** 4.**** Bike sharing systems: a new incentive rebalancing method based on spatial outliers detection** [8]
Since its launch, Velib' (the Bike Sharing System-BSS-in Paris) has emerged in the Parisian landscape and has been a model for similar systems in many cities. A major problem with BSS is the stations' heterogeneity caused by the attractivity of some stations located in particular areas. In this paper, we focus on spatial outliers defined as stations having a behavior significantly different from their neighboring stations. First, we propose an improved version of Moran scatterplot to exploit the similarity between neighbors, and we test it on a real dataset issued from Velib' system to identify outliers. Then, we design a new method that globally improves the resources' availability in bike stations by adapting the users' trips to the resources' availability. Results show that with a partial collaboration of the users or a limitation to the rush hours, the proposed method enhances significantly the resources' availability in Velib' system.

** 5.**** Stochastic Battery
Operations using Deep Neural Networks** [25]
In this paper, we introduce a scenario-based optimal control framework to account for the forecast uncertainty in battery arbitrage problems. Due to the uncertainty of prices and variations of forecast errors, it is challenging for battery operators to design profitable strategies in electricity markets. Without any explicit assumption or model for electricity price forecasts' uncertainties, we generate future price scenarios via a data-driven, learning-based approach. By aiding the predictive control with such scenarios representing possible realizations of future markets, our proposed real-time controller seeks the optimal charge/discharge levels to maximize profits. Simulation results on a case-study of California-based batteries and prices show that our proposed method can bring higher profits for different battery parameters.

** 6.**** Aggregate capacity for TCLs providing virtual energy storage with cycling constraints** [26]
The coordination of thermostatically controlled loads (TCLs) is challenging due to the need to meet individual loads quality of service (QoS), such as indoor temperature constraints. Since these loads are usually on/off type, cycling rate is one of their QoS metrics; frequent cycling between on and off states is detrimental to them. While significant prior work has been done on the coordination of air conditioning TCLs, the question of cycling QoS has not been investigated in a principled manner. In this work we propose a method to characterize aggregate capacity of a collection of air conditioning TCLs that respects the loads cycling rate constraints (maximum number of cycles in a given time period). The development is done within the framework of randomized local control in which a load makes on/off decisions probabilistically. This characterization allows us to propose a reference planning problem to generate feasible reference trajectories for the ensemble that respect cycling constraints. The reference planning problem manifests itself in the form a Nonlinear Programming problem (NLP), that can be efficiently solved. Our proposed method is compared to previous methods in the literature that do not enforce aggregate cycling. Enforcing individual cycling constraint without taking that into account in reference generation leads to poor reference tracking.

** 7.**** Optimal Storage Arbitrage under Net Metering using Linear Programming** [29]
We formulate the optimal energy arbitrage problem for a piecewise linear cost function for energy storage devices using linear programming (LP). The LP formulation is based on the equivalent minimization of the epigraph. This formulation considers ramping and capacity constraints, charging and discharging efficiency losses of the storage, inelastic consumer load and local renewable generation in presence of net-metering which facilitates selling of energy to the grid and incentivizes consumers to install renewable generation and energy storage. We consider the case where the consumer loads, electricity prices, and renewable generations at different instances are uncertain. These uncertain quantities are predicted using an Auto-Regressive Moving Average (ARMA) model and used in a model predictive control (MPC) framework to obtain the arbitrage decision at each instance. In numerical results we present the sensitivity analysis of storage performing arbitrage with varying ramping batteries and different ratio of selling and buying price of electricity.

** 8.**** Energy Storage in
Madeira, Portugal: Co-optimizing for Arbitrage, Self-Sufficiency,
Peak Shaving and Energy Backup** [30]
Energy storage applications are explored from a prosumer (consumers with generation) perspective for the island of Madeira in Portugal. These applications could also be relevant to other power networks. We formulate a convex co-optimization problem for performing arbitrage under zero feed-in tariff, increasing self-sufficiency by increasing self-consumption of locally generated renewable energy, provide peak shaving and act as a backup power source during anticipated and scheduled power outages. Using real data from Madeira we perform short and long timescale simulations in order to select end-user contract which maximizes their gains considering storage degradation based on operational cycles. We observe energy storage ramping capability decides peak shaving potential, fast ramping batteries can significantly reduce peak demand charge. The numerical experiment indicates that storage providing backup does not significantly reduce gains performing arbitrage and peak demand shaving. Furthermore, we also use AutoRegressive Moving Average (ARMA) forecasting along with Model Predic-tive Control (MPC) for real-time implementation of the proposed optimization problem in the presence of uncertainty.

** 9.**** Sensitivity to
forecast errors in energy storage arbitrage for residential
consumers** [34]
With the massive deployment of distributed energy resources, there has been an increase in the number of end consumers that own photovoltaic panels and storage systems. The optimal use of such storage when facing Time of Use (ToU) prices is directly related to the quality of the load and generation forecasts as well as the algorithm that controls the battery. The sensitivity of such control to different forecasts techniques is studied in this paper. It is shown that good and bad forecasts can result in losses in particularly bad days. Nevertheless, it is observed that performing Model Predictive Control with a simple forecast that is representative of the pasts can be profitable under different price and battery scenarios. We use real data from Pecan Street and ToU price levels with different buying and selling price for the numerical experiments.

** 10.**** Sizing and Profitability of Energy Storage for Prosumers in Madeira, Portugal** [47]
This paper proposes a framework to select the best-suited battery for co-optimizing for peak demand shaving, energy arbitrage and increase self-sufficiency in the context of power network in Madeira, Portugal. Feed-in-tariff for electricity network in Madeira is zero, which implies consumers with excess production should locally consume the excess generation rather than wasting it. Further, the power network operator applies a peak power contract for consumers which imposes an upper bound on the peak power seen by the power grid interfaced by energy meter. We investigate the value of storage in Madeira, using four different types of prosumers, categorized based on the relationship between their inelastic load and renewable generation. We observe that the marginal increase in the value of storage deteriorates with increase in size and ramping capabilities. We propose the use of profit per cycle per unit of battery capacity and expected payback period as indices for selecting the best-suited storage parameters to ensure profitability. This mechanism takes into account the consumption and generation patterns, profit, storage degradation, and cycle and calendar life of the battery. We also propose the inclusion of a friction coefficient in the original co-optimization formulation to increase the value of storage by reducing the operational cycles and eliminate low returning transactions.

** 11.**** Arbitrage with Power Factor Correction using Energy Storage** [48]
The importance of reactive power compensation for power factor (PF) correction will significantly increase with the large-scale integration of distributed generation interfaced via inverters producing only active power. In this work, we focus on co-optimizing energy storage for performing energy arbitrage as well as local power factor corrections. The joint optimization problem is non-convex, but can be solved efficiently using a McCormick relaxation along with penalty-based schemes. Using numerical simulations on real data and realistic storage profiles, we show that energy storage can correct PF locally without reducing arbitrage gains. It is observed that active and reactive power control is largely decoupled in nature for performing arbitrage and PF correction (PFC). Furthermore, we consider a stochastic online formulation of the problem with uncertain load, renewable and pricing profiles. We develop a model predictive control based storage control policy using ARMA forecast for the uncertainty. Using numerical simulations we observe that PFC is primarily governed by the size of the converter and therefore, look-ahead in time in the online setting does not affect PFC noticeably. However, arbitrage gains are more sensitive to uncertainty for batteries with faster ramp rates compared to slow ramping batteries.

** 12.**** A Utility Optimization
Approach to Network Cache Design** [11]
In any caching system, the admission and eviction policies determine which contents are added and removed from a cache when a miss occurs. Usually, these policies are devised so as to mitigate staleness and increase the hit probability. Nonetheless, the utility of having a high hit probability can vary across contents. This occurs, for instance, when service level agreements must be met, or if certain contents are more difficult to obtain than others. In this paper, we propose utility-driven caching, where we associate with each content a utility, which is a function of the corresponding content hit probability. We formulate optimization problems where the objectives are to maximize the sum of utilities over all contents. These problems differ according to the stringency of the cache capacity constraint. Our framework enables us to reverse engineer classical replacement policies such as LRU and FIFO, by computing the utility functions that they maximize. We also develop online algorithms that can be used by service providers to implement various caching policies based on arbitrary utility functions.

** 13.**** Rapid Mixing of Dynamic Graphs with Local Evolution Rules** [15]
Dynamic graphs arise naturally in many contexts. In peer-to-peer networks, for instance, a participating peer may replace an existing connection with one neighbor by a new connection with a neighbor of that neighbor. Several such local rewiring rules have been proposed to ensure that peer-to-peer networks achieve good connectivity properties (e.g. high expansion) at equilibrium. However, the question of whether there exists such a rule that converges rapidly to equilibrium has remained open. In this work, we provide an affirmative answer: we exhibit a local rewiring rule that converges to equilibrium after each participating node has undergone only a number of changes that is at most poly-logarithmic in the system size. As a byproduct, we derive new results for random walks on graphs, bounding the spread of their law throughout the transient phase, i.e. prior to mixing. These rely on an extension of Cheeger's inequality, based on generalized isoperimetric constants, and may be of independent interest.