Convex Approximation Algorithm for AC/DC Distribution Network With Energy Router

The optimal operation model of AC/DC distribution network with energy router (ER) is essentially a nonconvex nonlinear programming (NLP) problem. In order to improve the feasibility of solving the model, a convex approximation algorithm is proposed in this work. The steady-state model of ER is developed with considering the loss characteristics and multiport coordinated control strategy. It is embedded in the optimization formulations of AC/DC network as basic operating equations. Then, using second-order cone relaxation technology, the power flow equations of AC and DC distribution networks are convexly relaxed. On this basis, the highly nonlinear operating model of ER is linearized by introducing a successive approximation approach. Therefore, the original NLP problem is transformed into the convex programming problem and the solution efficiency is improved. Meanwhile, an iterative solution algorithm is developed to ensure the accuracy of the convex approximation approach. Simulation results verify the feasibility and efficiency of the proposed algorithm.

Energy-Efficient Power Allocation in Non-Linear Energy Harvesting Multiple Relay Systems

In this paper, to maximize the energy efficiency (EE) in the two-hop multi-relay cooperative decoding and forwarding (DF) system for simultaneous wireless information and power transmission (SWIPT), an optimal power allocation algorithm is proposed, in which the relay energy harvesting (EH) adopts a nonlinear model. Under the constraints, including energy causality, the minimum transmission quality of information and the total transmission power at the relays, an optimization problem is constructed to jointly optimize the transmit power and power-splitting (PS) ratios of multiple relays. Although this problem is a nonlinear fractional programming problem, an iterative algorithm is developed to obtain the optimal power allocation. In particular, the joint power allocation at multiple relays is first decoupled into a single relay power allocation, and then single-relay power allocation is performed by the Dinkelbach iteration algorithm, which can be proven that it is a convex programming problem. Its closed form solutions for different polylines of EH models are obtained by using mathematical methods, such as monotonicity, Lagrange multipliers, the KKT condition and the Cardan formula. The simulation results show the superiority of the power allocation algorithm proposed in this paper in terms of EE.

An Analytical Model for 5G Network Resource Sharing with Flexible SLA-Oriented Slice Isolation

Network slicing is a novel key technology in 5G networks which permits to provide a multitude of heterogeneous communication services over a common network infrastructure while satisfying strict Quality of Service (QoS) requirements. Since radio spectrum resources are inherently scarce, the slicing of the radio access network should rely on a flexible resource sharing policy that provides efficient resource usage, fairness and slice isolation. In this article, we propose such a policy for bandwidth-greedy communication services. The policy implies a convex programming problem and is formalized to allow for session-level stochastic modeling. We developed a multi-class service system with service rates obtained as a solution to the optimization problem, a Markovian Arrival Process and state-dependent preemptive priorities. We use matrix-analytic methods to find the steady state distribution of the resulting continuous-time Markov chain and the expressions for important performance metrics, such as data rates. Numerical analysis illustrates the efficiency of the proposed slicing scheme compared to the complete sharing and complete partitioning policies, showing that our approach leads to a data rate about the double of that obtained under complete partitioning for the analyzed scenario.

Integrated Heat and Electricity Dispatch for District Heating Networks with Constant Mass Flow: A Generalized Phasor Method

Using thermal inertia in district heating systems (DHSs) to improve the dispatch flexibility and economy of integrated heat and electricity systems (IHESs) is a research hotspot and difficulty. In most existing studies, the partial differential equations (PDEs) of thermal inertia are approximated by discrete-time models, making it difficult to accurately describe the continuous dynamic processes. In this paper, we propose a novel generalized phasor method (GPM) for thermal inertia in DHSs with constant mass flow. Based on the analytical solution of the PDEs and the Fourier transform, the intractable PDEs are transformed into a series of complex algebraic equations represented by phasors. The GPM has higher accuracy compared to traditional discrete models because it is essentially a continuous model in the time domain. Then, we present a different representation of an integrated heat and electricity dispatch (IHED) model combining a DHS model in phasor form and a traditional electrical power system model. The IHED model is a convex programming problem and can be easily solved. The effectiveness of the proposed GPM and dispatch model is verified in three test systems. Compared with traditional methods for modeling the thermal inertia, the proposed GPM is more accurate.

Integrated Heat and Electricity Dispatch for District Heating Networks with Constant Mass Flow: A Generalized Phasor Method

Using thermal inertia in district heating systems (DHSs) to improve the dispatch flexibility and economy of integrated heat and electricity systems (IHESs) is a research hotspot and difficulty. In most existing studies, the partial differential equations (PDEs) of thermal inertia are approximated by discrete-time models, making it difficult to accurately describe the continuous dynamic processes. In this paper, we propose a novel generalized phasor method (GPM) for thermal inertia in DHSs with constant mass flow. Based on the analytical solution of the PDEs and the Fourier transform, the intractable PDEs are transformed into a series of complex algebraic equations represented by phasors. The GPM has higher accuracy compared to traditional discrete models because it is essentially a continuous model in the time domain. Then, we present a different representation of an integrated heat and electricity dispatch (IHED) model combining a DHS model in phasor form and a traditional electrical power system model. The IHED model is a convex programming problem and can be easily solved. The effectiveness of the proposed GPM and dispatch model is verified in three test systems. Compared with traditional methods for modeling the thermal inertia, the proposed GPM is more accurate.

Integrated Heat and Electricity Dispatch for District Heating Networks with Constant Mass Flow: A Generalized Phasor Method

Using thermal inertia in district heating systems (DHSs) to improve the dispatch flexibility and economy of integrated heat and electricity systems (IHESs) is a research hotspot and difficulty. In most existing studies, the partial differential equations (PDEs) of thermal inertia are approximated by discrete-time models, making it difficult to accurately describe the continuous dynamic processes. In this paper, we propose a novel generalized phasor method (GPM) for thermal inertia in DHSs with constant mass flow. Based on the analytical solution of the PDEs and the Fourier transform, the intractable PDEs are transformed into a series of complex algebraic equations represented by phasors. The GPM has higher accuracy compared to traditional discrete models because it is essentially a continuous model in the time domain. Then, we present a different representation of an integrated heat and electricity dispatch (IHED) model combining a DHS model in phasor form and a traditional electrical power system model. The IHED model is a convex programming problem and can be easily solved. The effectiveness of the proposed GPM and dispatch model is verified in three test systems. Compared with traditional methods for modeling the thermal inertia, the proposed GPM is more accurate.

Optimality and duality in nonsmooth vector optimization with non-convex feasible set

For a convex programming problem, the Karush-Kuhn-Tucker (KKT) conditions are necessary and sufficient for optimality under suitable constraint qualification. Recently, Suneja et al proved KKT optimality conditions for a differentiable vector optimization problem over cones in which they replaced the cone-convexity of constraint function by convexity of feasible set and assumed the objective function to be cone-pseudoconvex. In this paper, we have considered a nonsmooth vector optimization problem over cones and proved KKT type sufficient optimality conditions by replacing convexity of feasible set with the weaker condition considered by Ho and assuming the objective function to be generalized nonsmooth cone-pseudoconvex. Also, a Mond-Weir type dual is formulated and various duality results are established in the modified setting.

Decentralized Optimization of Electricity-Natural Gas Flow Considering Dynamic Characteristics of Networks

The interconnection of power and natural gas systems can improve the flexibility of system operation and the capacity of renewable energy consumption. It is necessary to consider the interaction between both, and carry out collaborative optimization of energy flow. For space-time related line packs, this paper studies the optimal multi-energy flow (OMEF) model of an integrated electricity-gas system, taking into account the dynamic characteristics of a natural gas system. Besides, in order to avoid the problem of large data collection in centralized algorithms and consider the characteristics of decentralized autonomous decision-making for each subsystem, this paper proposes a decentralized algorithm for the OMEF problem. This algorithm transforms the original non-convex OMEF problem into an iterative convex programming problem through penalty convex-concave procedure (PCCP), and then, uses the alternating direction method of multipliers (ADMM) algorithm at each iteration of PCCP to develop a decentralized collaborative optimization of power flow and natural gas flow. Finally, numerical simulations verify the effectiveness and accuracy of the algorithm proposed in this paper, and analyze the effects of dynamic characteristics of networks on system operation.

A Proximal Alternating Direction Method of Multipliers with a Substitution Procedure

In this paper, we considers the separable convex programming problem with linear constraints. Its objective function is the sum of m individual blocks with nonoverlapping variables and each block consists of two functions: one is smooth convex and the other one is convex. For the general case m≥3, we present a gradient-based alternating direction method of multipliers with a substitution. For the proposed algorithm, we prove its convergence via the analytic framework of contractive-type methods and derive a worst-case O1/t convergence rate in nonergodic sense. Finally, some preliminary numerical results are reported to support the efficiency of the proposed algorithm.

Optimality and duality for nonsmooth semi-infinite E-convex multi-objective programming with support functions

In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak and strong duality theorems under various generalized E-convexity assumptions.