Dariush Fooladivanda

Joint Resource Allocation and User Association for Heterogeneous Wireless Cellular Networks

We propose a unified static framework to study the interplay of user association and resource allocation in heterogeneous cellular networks. This framework allows us to compare the performance of three channel allocation strategies: Orthogonal deployment, Co-channel deployment, and Partially Shared deployment. We have formulated joint optimization problems that are non-convex integer programs, are NP-hard, and hence it is difficult to efficiently obtain exact solutions. We have, therefore, developed techniques to obtain upper bounds on the systems performance. We show that these upper bounds are tight by comparing them to feasible solutions. We have used these upper bounds as benchmarks to quantify how well different user association rules and resource allocation schemes perform. Our numerical results indicate that significant gains in throughput are achievable for heterogeneous networks if the right combination of user association and resource allocation is used. Noting the significant impact of the association rule on the performance, we propose a simple association rule that performs much better than all existing user association rules.

Joint channel allocation and user association for heterogeneous wireless cellular networks

We study the engineering of heterogeneous cellular networks composed of a macrocell and some picocells by investigating the interplay of different network processes and parameters such as channel allocation, user association and reuse pattern (to control inter-cell interference between picocells). We formulate a joint association, channel allocation, and inter-cell interference management problem that relies on very few assumptions. This problem turns out to be an Integer Non-Linear program that is NP-hard. However, its structure is such that we can solve it exactly for relatively large size systems. We use optimal solutions as benchmarks to understand how different simple association schemes perform. Our results show the critical impact of the association rules on system performance and shows the interplay of the different processes and parameters. We believe that these insights will help design online association schemes in the future.

Confliction of the Convexity and Metric Properties in f-Divergences

We prove that the Variational distance (and its positive multiples) is the only f-divergence that satisfies both the identity of indiscernibles and the triangle inequality. Therefore it is the unique f-divergence which serves as a metric. This point is interpreted as a fundamental confliction of the convexity for f(x) with the metric properties for its associated f-divergence. Therefore, we relax the convexity of f(x) and replace it with other constraints to create new metrics.

Energy Storage and Regulation: An Analysis

Electric system operators rely on regulation services to match the total system supply to the total system load in quasi real-time. The regulation contractual framework requires that a regulation unit declares its regulation parameters at the beginning of the contract, the operator guarantees that the regulation signals will be within the range of these parameters, and the regulation unit is rewarded proportionally to what it declares and what it supplies. We study how this service can be provided by a unit with a non-ideal storage. We consider two broad classes of storage technologies characterized by different state of charge evolution equations, namely batteries and flywheels. We first focus on a single contract, and obtain formulas for the upward and downward regulation parameters that a unit with either a battery or a flywheel should declare to the operator to maximize its reward. We then focus on a multiple contract setting and show how to analytically quantify the reward that such a unit could obtain in successive contracts. We quantify this reward using bounds and expectation, and compare our analytical results with those obtained from a dataset of real-world regulation signals. Finally, we provide engineering insights by comparing different storage technologies in terms of potential rewards for different contract durations and parameters.

Optimal pump scheduling and water flow in water distribution networks

This paper focuses on the optimal operation of water distribution networks. We model water distribution networks using physical and hydraulic constraints, and formulate a joint pump scheduling and water flow problem using the hydraulic characteristics of variable speed pumps. The optimal pump scheduling and water flow problem is a mixed integer nonlinear program. This problem is generally non-convex, and hence NP-hard. We propose a second-order cone relaxation for this problem, and analytically show that the proposed relaxation is exact for a wide class of water network topologies. The proposed problem is a mixed integer nonlinear program with a linear objective function and quadratic constraints. This problem can be solved with a commercial solver such as CPLEX. Finally, we consider a real-world water network, and demonstrate the effectiveness of the proposed relaxation in computing the optimal pump schedules and water flows.

An analysis of energy storage and regulation

We focus on a region whose power system is controlled by an operator that relies on a regulation service to balance the total system supply to the total system load in quasi real-time. We consider the existing contractual framework in which a regulation unit declares its regulation parameters at the beginning of the contract, the operator guarantees that the regulation signals will be within the range of these parameters, and the regulation unit is rewarded proportionally to what it declares. Our purpose is twofold. We first want to obtain formulas for the regulation parameters that a unit with non-ideal storage should declare to the operator given its state of charge at the beginning of a contract. Second, we want to analytically quantify, ahead of time, the reward that such a unit could obtain in successive contracts by performing this regulation service. Since the state of charge at the beginning of a contract depends on what happened in the previous contract and, hence, is a random variable, we quantify this reward analytically using bounds and expectation. We then provide engineering insights by applying our results to three specific energy storage technologies that are often considered as candidates for regulation. In particular, we show the impact of the storage parameters and the length of one contract on the potential reward over a given period.

Energy-Optimal Pump Scheduling and Water Flow

This paper focuses on the optimal operation of water supply networks. We model water supply networks using hydraulic constraints, and formulate a joint optimal pump scheduling and water flow problem (OWF) using the hydraulic characteristics of variable speed pumps. OWF is a mixed-integer nonlinear program. This problem is nonconvex, and hence NP-hard. To compute an exact solution of OWF, we first focus on the feasibility region of OWF, and propose a mixed-integer second-order cone relaxation for the feasibility region of OWF. We prove that the proposed relaxation is exact for several relevant network topologies. We then focus on the objective function in OWF, and show that for some energy metrics, OWF can be transformed into a mixed-integer second-order cone program. Furthermore, we propose an ADMM-based algorithm to compute suboptimal solutions to OWF and lower bounds on the optimal value of the objective in OWF when the objective function is nonconvex. Finally, we consider a real-world water network, and demonstrate the effectiveness of the proposed relaxation in computing the optimal pump schedules and water flows.

Secure state estimation for nonlinear power systems under cyber attacks

This paper focuses on securely estimating the state of a nonlinear dynamical system from a set of corrupted measurements. In particular, we consider a wide class of nonlinear systems, and propose a technique which enables us to perform secure state estimation for such nonlinear systems. We then provide guarantees on the achievable state estimation error against arbitrary corruptions, and analytically characterize the number of errors that can be perfectly corrected by a decoder. To illustrate how the proposed nonlinear estimation approach can be applied to practical systems, we focus on secure estimation for the wide area control of an interconnected power system under cyber-physical attacks and communication failures, and propose a secure estimator for the power system. Finally, we numerically show that the proposed secure estimation algorithm enables us to reconstruct the attack signals accurately.

Allocating Sensors and Actuators via Optimal Estimation and Control

We consider the problem of planning the location and size of sensors and actuators to achieve optimal dynamic performance. Using basic results from control and convex optimization, we formulate mixed-integer semidefinite programs for the actuator placement and sizing to obtain the linear quadratic regulator with the lowest cost, and the sensor placement to obtain the Kalman filter with the lowest error. The two formulations are nearly identical due to the duality of optimal linear control and estimation. We also pose similar problems in terms of observability and controllability, which result in smaller mixed-integer semidefinite programs. Since the mixed-integer semidefinite programing is not yet a mature technology, we also use greedy heuristics in conjunction with continuous semidefinite programming. The approach is demonstrated on two modern applications from power systems: the placement and sizing of energy storage for regulation and the placement of phasor measurement units for estimation.

Secure State Estimation and Control for Cyber Security of the Nonlinear Power Systems

We focus on securely estimating the state of a nonlinear dynamical system from a set of corrupted measurements for two classes of nonlinear systems, and propose a technique that enables us to perform secure state estimation for those systems. We then illustrate how the proposed nonlinear secure state estimation technique can be used to perform estimation in the cyber layer of interconnected power systems under cyber-physical attacks and communication failures. In particular, we focus on an interconnected power system comprised of several synchronous generators, transmission lines, loads, and energy storage units, and propose a secure estimator that allows us to securely estimate the dynamic states of the power network. Finally, we numerically demonstrate the effectiveness of the proposed secure estimation algorithm, and show that the algorithm enables the cyber layer to accurately reconstruct the attack signals.