Centralized Optimization Problem Research Articles

Confidence Level Optimization of DG Piecewise Affine Controllers in Distribution Grids

Distributed generators (DGs) reactive powers are controlled to mitigate voltage overshoots in distribution grids with stochastic power production and consumption. Classical DGs controllers may embed piecewise affine laws with dead-band terms. Their settings are usually tuned using a decentralized method which uses local data and optimizes only the DG node behavior. It is shown that when short-term forecasts of stochastic powers are Gaussian and the grid model is assumed to be linear, nodes voltages can either be approximated by Gaussian or sums of truncated Gaussian variables. In the latter case, the voltages probability density functions (pdf) that are needed to compute the overvoltage risks or DG control effort are less straightforward than for normal distributions. These pdf are used into a centralized optimization problem which tunes all DGs control parameters. The objectives consist in maximizing the confidence levels for which voltages and powers remain in prescribed domains and minimizing voltage variances and DG efforts. Simulations on a real distribution grid model show that the truncated Gaussian representation is relevant and that control parameters can easily be updated even when extra DGs are added to the grid. The DG reactive power can be reduced down to 50% or node voltages variances can be reduced down to 30%.

Distributed Real-Time Economic Dispatch in Smart Grids: A State-Based Potential Game Approach

In this paper, a distributed optimization algorithm based on state-based potential game (SPG) is proposed for the real-time economic dispatch (RTED) problem in smart grids. Under the DC power flow approximation, we formulate the RTED with coupled operational constraints as a centralized optimization problem (C-RTED). By treating each node in the grid as an agent, we convert the C-RTED into an SPG by augmenting its objective function in the designed game with a local augmented Lagrange-like function, leading to a distributed algorithm for solving the C-RTED problem. We reveal that the stationary-state Nash equilibrium of the SPG exactly identifies the global optimum of the constrained C-RTED problem. The proposed algorithm is capable of handling both equality and inequality constraints in complicated forms, and can be further simplified to entail lower communication burden. Simulations on the IEEE 9-, 39-, and 118-bus systems confirm that the algorithm can quickly converge to the global optimum even under unreliable communication and plug-and-play operations.

Electric Vehicle Scheduling Strategy in Residential Demand Response Programs With Neighbor Connection

As smart grid enablers, demand response programs for household purposes have been in highlight recently. This paper presents a detailed structure of a household user, which is capable of energy transactions among consumer and load-serving entity. The proposed household model comprises several assets including nonshiftable appliances, shiftable appliances, and electric vehicle (EV). The EV can further contribute to the vehicle-to-home and vehicle-to-grid type of connections that can reduce the household electricity payments with their bilateral energy transactions. The day-ahead dynamic prices are superimposed with peak power limiting approach to prevent the formation of new peaks. The energy transaction among neighbor enhances the reduction in daily energy payments and flexibility among users. The centralized optimization problem is formulated as mixed integer linear programming problem. The validity of the proposed system can be proven by performance evaluation of simulation results.

Distributed Lagrangian Method for Tie-Line Scheduling in Power Grids under Uncertainty

System operators (SOs) manage the grid and its assets in different parts (areas) of an interconnected power network. One would ideally seek to co-optimize the grid assets across multiple areas by solving a centralized optimization problem. Gathering the dispatch cost structures and the network constraints from all areas for a centralized solution remains difficult due to technical, historical, and sometimes legal barriers. Motivated by the need for a distributed solution architecture for multi-area power systems, we propose a distributed Lagrangian algorithm in this paper.We establish convergence rates for our algorithm that solves the deterministic tie-line scheduling problem as well as its robust variant (with policy space approximations). Our algorithm does not need any form of central coordination. We illustrate its efficacy on IEEE test systems.

Scalability through Decentralization: A Robust Control Approach for the Energy Management of a Building Community

Recent studies in the literature have shown that cooperative energy management of an aggregation of buildings may lead to substantial energy savings. These approaches typically assume the existence of a central operator that is capable of formulating and solving, within a reasonable amount of time, a centralized optimization problem. However, this requirement may be unrealizable in cases of large scale districts, and it also fails to address privacy concerns of the building occupants. In this paper, we deal with these issues by proposing a decentralized control scheme which only requires the individual buildings to communicate bounds on their energy demands. The proposed method partly alleviates concerns on privacy since this limited communication scheme does not reveal the exact characteristics of the energy usage within each building. In addition, it enables a distributed computation of the solution, making our method highly scalable. We demonstrate through a numerical study the efficacy of the proposed approach, which leads to solutions that closely approximate those obtained by the centralized formulation only at a fraction of the computational effort.

Distributed QoS Based Robust Transmission Design for MISO Wiretap Channel with Cooperative Jamming

A communication network that consists of a transmitter, a legitimate receiver, an eavesdropper and several friendly helpers is considered. Both the transmitter and the helpers are equipped with multiple antennas while the legitimate receiver or the eavesdropper has one antenna. The transmitter and the helpers have the channel state information to the legitimate receiver. The channels to the eavesdropper are partially known and modeled with uncertainty ellipsoids. The transmitter applies maximum ratio transmission to the legitimate receiver. The helpers generate interference to degrade the receiving performance of the eavesdropper. The transmit power of the helpers is optimized with the worst-case secrecy rate requirement as the Quality of Service constraint. Based on robust convex optimization, a centralized optimization problem is developed for the helpers to generate interference efficiently with minimum total transmit power. A distributed algorithm is developed which scales well with a large number of helpers.

Energy Trading in the Smart Grid: A Distributed Game-Theoretic Approach

In this paper, we propose both a centralized solution and a distributed game-theoretic approach to solve the problem of energy trading in the smart grid. In particular, we consider a number of geographically distributed consumers that need to buy energy from the neighboring users who have a surplus stored energy to meet their local demands. While buyers minimize their energy bill by buying energy at prices lower than that of the grid, sellers can make pro?t by selling the extra stored energy, which could have been acquired from affordable renewable resources. Buying energy from neighboring users also helps in reducing the stress on the main grid, which decreases electricity prices and protects the environment. We ?rst formulate the energy trading problem as a centralized optimization problem. Then, we propose a distributed solution based on the game theory that requires each user to merely apply its best response strategy to the current state of the system. Buyers play the game by deciding how much energy to be bought from each seller in order to minimize their energy bill taking into account different constraints tied to the grid infrastructure. Extensive simulations con?rm the effectiveness of the proposed approach in terms of energy bill savings, convergence in acceptable times, and fairness to its users.

Distributed Optimization Framework for Energy Management of Multiple Smart Homes With Distributed Energy Resources

This paper proposes a distributed optimization algorithm for scheduling the energy consumption of multiple smart homes with distributed energy resources. In the proposed approach, the centralized optimization problem for home energy management is decomposed into a two-level optimization problem, corresponding to the local home energy management system (LHEMS) at the first level and the global home energy management system (GHEMS) at the second level. The controllable household appliances (e.g., air conditioner and washing machine) are scheduled in the LHEMS within the consumer’s preferred appliance scheduling and comfort level, while the energy storage system and power trading between households are scheduled in the GHEMS. In the simulation study, the proposed distributed algorithm shows almost equivalent performance to the centralized algorithm in terms of the electricity cost and the consumer’s comfort level. The impact of different network topologies on the proposed algorithm is also analyzed, and the result provides insight into the selection of the optimal network configuration in view of the consumer’s electricity cost saving.

Fair Flow Control and Fairness Evaluation in Computer Networks and Systems

Fairness is an important property of computer networks and systems. In a wide range of these systems such as distributed multi-hop wireless networks, multihomed networks, and cloud computing, each user may be allocated a number of system resources; this resembles a many-to-many relationship between the sets of users and resources, which raises the problem of system-wide fair resource allocation. In this paper, we assume that each user/node can be allocated a number of resources, which could be either in its neighborhood or far from it. As a key difference with previous works and through incorporating the concept of “flow”, we model near/far resources allocated to nodes. To attain fair flow control in such systems, first we model this situation by introducing a new multi-server system called multi-ring , in which a server that represents a resource, can serve only a subset of either neighboring or far nodes in the system. Then, we define a centralized optimization problem to attain weighted proportional fairness among all nodes meaning that the sum of allocated capacities from all servers to each node (while considering its flow) is fair. We evaluate fairness properties of multi-ring networks and provide conditions on system parameters under which a system can have a fair resource allocation. Moreover, we present a distributed method to attain fairness in distributed environments, and its stability/convergence is evaluated by non-linear discrete dynamical systems. We present conditions under which the system is stable, and through numerical analysis, we show how to obtain stable system parameters for large systems. The effectiveness of the presented method is studied through extensive numerical evaluation. Results show the success of our method in attaining fairness for various topologies and system parameters, and confirm our stability analysis. A number of systems with fairness issues are also studied as potential applications of our model.

Study of centralized and distributed coordination of power injection in multi-TSO HVDC grid with large off-shore wind integration

This paper studies centralized and distributed schemes for the coordination of power injection in an HVDC grid connected to large wind generation. This coordination of power injection aims to keep the power balanced within the HVDC grid especially during large wind disturbances. Furthermore, the coordination tries to follow the converters’ schedules set by the connecting AC-TSOs every 15-min. This schedule comes from an overall combined AC/DC economic dispatch calculation with lower resolution compared to this coordination. In this paper, the coordination of power injection has been formulated as a non-linear constrained optimization problem for the centralized architecture. Next, the centralized optimization problem is decomposed to sub-problems using the Auxiliary Problem Principle (APP) method for the distributed architecture. This distributed optimization problem is solved by exchanging the required information between the AC TSOs. These two different approaches have been evaluated for a 5-terminal HVDC grid. Furthermore, a sensitivity analysis has been carried out to find the optimal updating rate of power injection set-points. The result shows that the more frequent updating of power injection coordination in the centralized architecture improves the generation reserves in each AC area.

A game-theory analysis of charging stations selection by EV drivers

We address the problem of Electric Vehicle (EV) drivers’ assistance through Intelligent Transportation System (ITS). Drivers of EVs that are low in battery may ask a navigation service for advice on which charging station to use and which route to take. A rational driver will follow the received advice, provided there is no better choice i.e., in game-theory terms, if such advice corresponds to a Nash-equilibrium strategy. Thus, we model the problem as a game: first we propose a congestion game, then a game with congestion-averse utilities, both admitting at least one pure-strategy Nash equilibrium. The former represents a practical scenario with a high level of realism, although at a high computational price. The latter neglects some features of the real-world scenario but it exhibits very low complexity, and is shown to provide results that, on average, differ by 16% from those obtained with the former approach. Furthermore, when drivers value the trip time most, the average per-EV performance yielded by the Nash equilibria and the one attained by solving a centralized optimization problem that minimizes the EV trip time differ by 15% at most. This is an important result, as minimizing this quantity implies reduced road traffic congestion and energy consumption, as well as higher user satisfaction.

LP-Based Covering Games with Low Price of Anarchy

We design a new class of vertex and set cover games, where the price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs. This is in contrast to all previously studied covering games, where the price of anarchy grows linearly with the size of the game. Both the game design and the price of anarchy results are based on structural properties of the linear programming relaxations. For linear costs we also exhibit simple best response dynamics that converge to Nash equilibria in linear time.

On Feasibility, Stability and Performance in Distributed Model Predictive Control

In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm small. In this technical note, we present a stopping condition to such distributed solution algorithms that is based on a novel adaptive constraint tightening approach. The stopping condition guarantees feasibility of the optimization problem and stability and a prespecified performance of the closed-loop system.

Jamming-Aware Traffic Allocation for Multiple-Path Routing Using Portfolio Selection against DDOS

Multiple-path routing protocols allow data source node to distribute the total traffic among available paths. We consider the problem of jamming-aware source routing in which the source node performs traffic allocation based on empirical jamming statistics at individual network nodes. We formulate this traffic allocation as a lossy network flow optimization problem using portfolio selection theory. This centralized optimization problem can be solved using a distributed algorithm based on decomposition in NUM. Along with this Network based attacks have become a serious threat to the critical information infrastructure. There are many security attacks in MANET e.g. DDOS. The effect of DDOS leads to routing load, packet drop rate, end to end delay in network. So considering these parameters we build secure IDS to detect such attack and block it. Identifying the source of the attackers is necessary to correlate the incoming and outgoing flows or connections. To resist attempts at correlation, the attacker may encrypt or otherwise manipulate the connection traffic. Timing based correlation approaches are subject to timing perturbations that may be deliberately introduced by the attacker at stepping stones. So watermark-based correlation scheme is proposed which is designed specifically to be robust against timing perturbations. Unlike most previous timing based correlation approaches, our watermark-.based approach is active in that it embeds a unique watermark into the encrypted flows by slightly adjusting the timing of selected packets.

Optimal charging and discharging for multiple PHEVs with demand side management in vehicle-to-building

Plug-in hybrid electric vehicles (PHEVs) will be widely used in future transportation systems to reduce oil fuel consumption. Therefore, the electrical energy demand will be increased due to the charging of a large number of vehicles. Without intelligent control strategies, the charging process can easily overload the electricity grid at peak hours. In this paper, we consider a smart charging and discharging process for multiple PHEVs in a building's garage to optimize the energy consumption profile of the building. We formulate a centralized optimization problem in which the building controller or planner aims to minimize the square Euclidean distance between the instantaneous energy demand and the average demand of the building by controlling the charging and discharging schedules of PHEVs (or ‘users’). The PHEVs' batteries will be charged during low-demand periods and discharged during high-demand periods in order to reduce the peak load of the building. In a decentralized system, we design an energy cost-sharing model and apply a non-cooperative approach to formulate an energy charging and discharging scheduling game, in which the players are the users, their strategies are the battery charging and discharging schedules, and the utility function of each user is defined as the negative total energy payment to the building. Based on the game theory setup, we also propose a distributed algorithm in which each PHEV independently selects its best strategy to maximize the utility function. The PHEVs update the building planner with their energy charging and discharging schedules. We also show that the PHEV owners will have an incentive to participate in the energy charging and discharging game. Simulation results verify that the proposed distributed algorithm will minimize the peak load and the total energy cost simultaneously.

Jamming-Aware Traffic Allocation for Multiple-Path Routing Using Portfolio Selection

Multiple-path source routing protocols allow a data source node to distribute the total traffic among available paths. In this paper, we consider the problem of jamming-aware source routing in which the source node performs traffic allocation based on empirical jamming statistics at individual network nodes. We formulate this traffic allocation as a lossy network flow optimization problem using portfolio selection theory from financial statistics. We show that in multisource networks, this centralized optimization problem can be solved using a distributed algorithm based on decomposition in network utility maximization (NUM). We demonstrate the network's ability to estimate the impact of jamming and incorporate these estimates into the traffic allocation problem. Finally, we simulate the achievable throughput using our proposed traffic allocation method in several scenarios.

Research of Inventory Routing Problem Based on Combination Auction

The Inventory Routing Problem, once taken as a centralized optimization problem, integrated the inventory management and vehicle routing simultaneously, which leads IRP with distributed feature. The components were mapped into agents and coordinated by combination auction to generate the optimal delivery strategy. An experiment was conducted to show the distributed approach of multi-agent system might solve the centralized problems.

Distributed subchannel assignment in a two-hop network

This paper studies distributed subchannel allocation in a two-hop network comprising multiple source nodes, one multi-channel relay node and one destination node. The underlying subchannel allocation problem in a relay network, when posed as a centralized allocation problem, is formulated as a three-dimensional assignment problem. Distributed subchannel allocation is studied using noncooperative game theory. A sequential game model is formulated where in first stage source nodes opportunistically select their transmission resources after which in second stage a channel-aware relay node assigns the resources in a way that maximizes the sum of utilities at the destination node. The subchannel allocation game is a potential game, possessing an implicit joint objective (potential) of the players. Numerical examples illustrate the performance of opportunistic channel allocation in an OFDMA system. Using the sequential scheme, noncooperative allocation in first link implies performance similar to that obtained by solving two consecutive assignment problems, first optimizing the allocation of subchannels in source-relay link and second in relay-destination link. Auction-based solutions to noncooperative subchannel allocation, both with fixed and variable transmit power, are presented to obtain approximate solutions to the underlying centralized resource optimization problems.

Delay Robustness of Nonlinear Internet Congestion Control Schemes

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Several nonlinear Internet congestion control schemes have been proposed in the previous years based on primal and dual decompositions of convex yet centralized optimization problems that describe the bandwidth allocation problem. This design methodology uses (sub)gradient methods for the design of node/link dynamics and guarantees nominal functionality for arbitrary system sizes. In this technical note we analyze the robustness of such nonlinear schemes to the presence of multiple, non-commensurate (heterogeneous) communication delays. </para>

Resource Allocation in Cognitive Radio Networks: A Comparison Between Game Theory Based and Heuristic Approaches

Cognitive Radio (CR) approach can be considered as a promising and suitable solution to solve in an efficient and flexible way the increasing and continuous demand of services and radio resources. This paper shows the potential benefits of the adoption of a cognitive radio strategy to the coexistence problem. Two different approaches have been considered: the first one is based on the Game Theory while the second one is formalized as a constrained maximum search and represent the optimum solution. The Game theory approach, suitable for a distributed implementation, provides performances comparable to the heuristic one which is a centralized optimization problem. The paper analyzes the performances of both approaches in terms of secondary rates and spectral efficiency provided by the secondary system.