Second-order Cone Programming Approximation Research Articles

Assessing the impact of inertia and reactive power constraints in generation expansion planning

On the path towards power systems with high renewable penetrations and ultimately carbon-neutral, more and more synchronous generation is being displaced by variable renewable generation that does not currently provide system inertia nor reactive power support. This could create serious issues of power system stability in the near future, and countries with high renewable penetrations such as Ireland are already facing these challenges. Therefore, this paper aims at answering the questions of whether and how explicitly including inertia and reactive power constraints in generation expansion planning would affect the optimal capacity mix of the power system of the future. Towards this end, we propose the novel Low-carbon Expansion Generation Optimization model, which explicitly accounts for: unit commitment constraints, Rate of Change of Frequency inertia requirements and virtual inertia provision, and, a second-order cone programming approximation of the AC power flow, accounting for reactive power constraints. An illustrative case study underlines that disregarding inertia and reactive power constraints in generation expansion planning can result in additional system cost, system infeasibilities, a distortion of optimal resource allocation and inability to reach established policy goals.

Joint chance constrained shortest path problem with Copula theory

In this paper, we investigate the constrained shortest path problem where the arc resources of the problem are dependent normally distributed random variables. A model is presented to maximize the probability of all constraints, while not exceeding a certain amount. We assume that the rows of the constraint matrix are dependent, so we use a marginal distribution of the Copula functions, instead of the distribution functions and the dependency is driven by an appropriate Archimedean Copula. Then, we transform the joint chance-constrained problems into deterministic problems of second-order cone programming. This is a new approach where considers the dependency between resource consumptions and connects Copulas to stochastic resource constrained shortest path problem (SRCSPP). The results indicate that the effect of marginal probability levels is considerable. Moreover, the linear relaxation of SRCSPP is generally not convex; thus we can use lower and upper bounds of the second-order cone programming approximation to solve the relaxation problem. The experimental results show that the SRCSPP with Copula theory can achieve efficient performance.

Maximum probability shortest path problem

The maximum probability shortest path problem involves the constrained shortest path problem in a given graph where the arcs resources are independent normally distributed random variables. We maximize the probability that all resource constraints are jointly satisfied while the path cost does not exceed a given threshold. We use a second-order cone programming approximation for solving the continuous relaxation problem. In order to solve this stochastic combinatorial problem, a branch-and-bound algorithm is proposed, and numerical examples on randomly generated instances are given.

Efficient Beamforming in Cognitive Radio Multicast Transmission

The optimal beamforming problems for cognitive multicast transmission are quadratic nonconvex optimization problems. The standard approach is to convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation and later employ randomization techniques for solution search. However, in many cases, this approach brings solutions that are far from the optimal ones. We consider the problem of minimizing the total power transmitted by the antenna array subject to quality-of-service (QoS) at the secondary receivers and interference constraints at the primary receivers. It is shown that this problem, which is known to be nonconvex NP-hard, can be approximated by a convex second-order cone programming (SOCP) problem. Then, an iterative algorithm in which the SOCP approximation is successively improved is presented. Simulation results demonstrate the superior performance of the proposed approach in terms of total transmitted power and feasibility, together with a reduced computational complexity, as compared to the existing ones, for both the perfect and imperfect channel state information (CSI) cases. It is further shown that the proposed approach can be used to address the max-min fairness (MMF) based beamforming problem.

Sum Rate Optimization in Multiuser Cognitive Radio Networks

In multiuser cognitive radio (CR) networks, we address the problem of joint transmit beamforming (BF) and power control (PC) for secondary users (SUs) when they are allowed to transmit simultaneously with primary users (PUs). The objective is to optimize the network sum rate under the interference constraints of PUs, which is a nonconvex problem. Iterative dual subgradient (IDuSuG) algorithm is proposed by iteratively performing BF and PC to optimize the sum rate, among which minimum mean square error (MMSE) or virtual power-weighed projection (VIP2) is used to design beamformers and subgradient method is used to control the power. VIP2 algorithm is devised for the case in which the interference caused by MMSE beamformer exceeds the threshold. Moreover, channel uncertainty due to lack of cooperation is considered. A closed-form worst-case expression is derived, with which the uncertainty optimization problem is transformed into a certain one. A robust algorithm based on IDuSuG is provided by modifying updates in iterative process. Furthermore, second-order cone programming approximation (SOCPA) method is proposed as another robust algorithm. Typical network models are approximated to SOCP problems and solved by interior-point method. Finally the network sum rates for different PU and SU numbers are assessed for both certainty and uncertainty channel models by simulation.