Optimal allocation of static var compensator via mixed integer conic programming

This paper introduces a smart coordinated allocation of distributed generation (DG) units, shunt-connected capacitors (SC), and static VAR compensators (SVC) for power loss minimization. The problem is formulated as a mixed-integer non-linear programming and is solved using a BONMIN solver embedded in General Algebraic Modeling System (GAMS). The proposed method’s evaluation was performed on the IEEE 33-bus test system, where three cases were discussed. GAMS/BONMIN was used to find optimal locations and power outputs of DGs in the first case. Simulation results, in this case, showed that losses were reduced by 48.42% with one DG unit, 58.58% with two DG units, and 65.44% with three optimally allocated DG units. In the second case, the proposed method was used to coordinate DGs and SCs, while in the third case, coordinated allocation of DG and SVC was investigated. The results showed that SC/SVC coordination further reduces active power losses. With three SCs allocated, the reduction in the active power losses was 93.5% compared to the base case, and 82.18% compared to losses in the case where only 3 DGs are connected, while in the case of three SVC allocated, it was 93.85% compared to the base case, and 82.21% compared to the case where 3 DGs are connected. The second and third cases also showed that the coordination of SC/SVC leads to an improved voltage profile, where the bus voltages are close to the acceptable range, and voltage fluctuation is significantly reduced. The comparison between different non-linear programming solvers embedded in GAMS for solving optimal power flow was also presented.

The placement of FACTS devices in a power network is of great importance to ensure the utilization of the full potential of the transmission network. In this study firstly, a static VAr compensators (SVCs) are placed optimally in a power network by taking into consideration the generation costs of both active and reactive power and the cost of the SVCs. The optimal power flow (OPF) and the genetic algorithm (GA) based optimization procedure are employed to solve the problem of optimal allocation of SVCs. Secondly, a small disturbance stability study is performed in order to investigate how installing the SVCs with additional control loops at such locations could contribute to system small disturbance stability. The study demonstrated that the optimal allocation of SVCs is a cost effective measure since the installed SVCs reduce overall generation costs and additionally contribute to the enhancement of the security of the transmission network by improving the damping of electromechanical oscillations.

Second-order conic programming model for load restoration considering uncertainty of load increment based on information gap decision theory

Multi-stage active management of renewable-rich power distribution network to promote the renewable energy consumption and mitigate the system uncertainty

Recent research shows that non-convex AC OPF problem can be recast as a convex Semidefinite (SD) problem or Second Order Cone Programming (SOCP) problem. This paper presents a stochastic SOCP OPF (SSOCP-OPF) model for power systems connected to the wind farms. This is performed by reformulating the original non-convex OPF problem using more practical parameters of the power system. Finally, we obtain a convex optimization problem through some well-known approximations and an exact relaxation incorporating the stochastic nature of wind power. One of the advantage of convex SOCP problems, which are a general form of linear problems, is that they can be efficiently solved through Interior Point Methods (IPMs). The proposed OPF model takes advantage of both DC-OPF models (solution efficiency) and full AC-OPF models (solution accuracy). As an application of SSOCP-OPF model, we study the impact of wind power uncertainty on the transmission loss in the power systems. To evaluate the proposed stochastic model modified IEEE 30-bus test system is used. The optimization problem is coded in GAMS platform and solved using its embedded interior point optimizer MOSEK.

The Sharpe ratio is a measure based on the theory of mean variance, it is the measure of the performance of a portfolio when the risk can be measured through the standard deviation. This paper suggests a Sharpe-ratio portfolio solution using a second order cone programming (SOCP). We use the penalty-regularized method to represent the nonlinear portfolio problem. We present a computationally tractable way to determining the Sharpe-ratio portfolio. A Markov chain structure is employed to represent the underlying asset price process. In order to determine the optimal portfolio in Markov chains, a new hybrid optimization programming method for SOCP is proposed. The suggested method’s efficiency and efficacy are demonstrated using a numerical example.

Flexible alternating current transmission systems (FACTS) are power electronics-based static controllers which control the transmission network parameters to improve system performance. They are used to solve various power system problems which include; voltage stability, voltage deviation and power losses. However, these devices need to be optimized to achieve desired results. This paper presents the application of firefly algorithm (FA) to optimize Static Var Compensator (SVC) and Static Synchronous Compensator (STATCOM) for voltage profile improvement and power loss minimization on IEEE 14 bus system. The results showed that the active and reactive power losses were minimized by 8.7 and 10.1%, respectively with FA optimized SVC and 10.7 and 14.7%, respectively with FA optimized STATCOM. Therefore, the optimal allocation of SVC and STATCOM improve the performance of the network which indicates the effectiveness of FA in optimizing SVC and STATCOM.KeywordsFACTSSTATCOMSVCFAVoltage magnitudePower loss

Flexible AC transmission systems (FACTS) technology is widely adopted and utilized to maintain the performance of power systems. However, the improvements of power system performance achieved by FACTS devices depend on the right sizing and allocation of such devices. For technical and economic considerations, a FACTS device's location and size should be selected very carefully in order to maximize its benefits to the power system. In this paper, the sizing and location of a static VAR compensator (SVC) are optimally determined using a new optimization technique called lightning attachment procedure optimization (LAPO). The optimal allocation of the SVC is determined regarding the improvement of voltage deviation index and the reduction of total active power losses. The system is optimized in two cases: once without SVC installation in order to find out the optimal settings of the system that achieve the objective functions, and another time with SVC installation to determine its optimum sizes and locations by which the required objective functions are achieved. Then the system performance is analyzed after optimization with and without SVC devices to show the impact of the optimum sizing and location of the SVC on the system. The study is validated using the standard IEEE 30-bus system, while the developed LAPO is performed by MATLAB M-Files and the system performance analysis in different cases is performed by NEPLAN software.

This paper investigates a joint optimization design method for beamforming and power allocation to improve the energy efficiency (EE) of a multicell MIMO downlink system considering the effect of channel estimation errors. The channel state information (CSI) imperfections can be well modeled with the power for training sequence. Assuming that both base stations and users are equipped with multiple antennas, this research focuses on the joint optimization of the beamforming vectors and the power allocation ratio between training sequence power and transmit data in order to maximize the EE under power constraints. A robust alternating optimization based on iterative algorithm to solve this problem which is in a nonconvex fractional form is proposed. First, the fractional problem is transformed into a linear form using the Dinkelbach method. The sumrate maximization problem is, then, replaced by the sum-MSE minimization problem by applying weighted mean square error minimization (WMMSE) method. Finally, the expectation taken over the distribution of the channels can be approximated using the sample average approximation (SAA) and the problem can be solved by computing a second order cone programming (SOCP). The robustness and effectiveness of the proposed method are validated by the simulation results.

Purpose – This paper aims to find an objects representation scheme with high precision and to compute the objects’ separation distance effectively in final analysis. Proximity queries have been used widely in robot trajectory planning, automatic assembly planning, virtual surgery and many other applications. The core of proximity query is the precise computation of (minimum) separation distance in narrow phase, and specific object representation scheme corresponds to different methods of separation distance computation. Design/methodology/approach – In this paper, a second-order cone programming (SOCP)-based (minimum) separation distance computation algorithm was proposed. It treats convex superquadrics, descriptive primitives of complex object as the study objects. The separation distance between two convex superquadrics was written as a general nonlinear programming (NLP) problem with superquadric constraints and then transformed into an SOCP problem with the method of conic formulation of superquadric constraints. Finally, a primal-dual interior point method embedded in MOSEK was used for solving the SOCP problem. Findings – The proposed algorithm achieved exact separation distance computation between convex superquadrics, with a relative error of 10-6. It is particularly suitable for proximity queries in narrow phase of static collision detection algorithms. Further, the proposed algorithm achieved continuous collision detection between rectilinear translation superquadrics. Originality/value – The proposed algorithm in narrow phase of static collision detection algorithms makes objects’ separation distance effectively computed. Proximity queries are easy and more accurate to perform in this way.

A directional constant beamwidth (DCB) beamforming algorithm is introduced, which keeps the beamwidth unchanged when the mainlobe is steered to a large range of angles. The algorithm is based on the optimization theory that minimizing the sidelobe level subjects to the minimum mean square error between the designed mainlobe under all directions and the corresponding reference mainlobe. The introduced algorithm can be written in the form of second order cone programming (SOCP) and can be solved by some certain matlab toolboxes. It is shown by simulation that the new algorithm can form the directional constant beamwidth beampattern effectively under the designed mainlobe direction from -60° to +60°.

A thinned irregular tiled array synthesis approach is proposed for 5G base station array design. To fit the needs of multiusers, different sizes of vertical tiles with thinned elements ae considered. The tiling configuration and excitations are optimized to achieve high gain, low sidelobes, and wide-angle scanning simultaneously. A mixed integer second-order cone programming (MISOCP) model is obtained from convexity analysis and transformation. Besides, a generalized Benders decomposition algorithm is built to decouple the complex original problem into mixed integer linear programming (MILP) master problems and convex second-order cone programming (SOCP) subproblems, which is used to solve the large-scale problems efficiently. Irregular partition optimization is based on full-wave simulations of regular finite arrays. The joint effects of active VSWR and radiation patterns are considered to reduce the mismatch between element simulations and final performances. Numerical results show that the 5G array synthesized by the proposed approach is superior to those reported by the state-of-the-art methods in terms of both E- and H-plane scans and the number of T/R modules.

Locating the position of a remote node on a wireless network is becoming more relevant, as we move forward in the Internet of things and in autonomous vehicles. This paper proposes a new system to implement the location of remote nodes. A new prototype Android application has been developed to collect real measurements and to study the performance of several smartphone’s sensors and location algorithms, including an innovative one, based on the second order cone programming (SOCP) relaxation. The application collects the WiFi access points information and the terminal location. An internal odometry module developed for the prototype is used when Android’s service is unavailable. This paper compares the performance of existing location estimators given in closed form, an existing SOCP one, and the new SOCP location estimator proposed, which has reduced complexity. An algorithm to merge measurements from non-identical terminals is also proposed. Cooperative and terminal stand-alone operations are compared, showing a higher performance for SOCP-based ones, that are capable of estimating the path loss exponent and the transmission power. The heterogeneous terminals were also used in the tests. Our results show that the accurate positioning of static remote entities can be achieved using a single smartphone. On the other hand, the accurate real-time positioning of the mobile terminal is provided when three or more scattered terminal nodes cooperate sharing the samples taken synchronously.

We investigate in this paper the generalized trust region subproblem (GTRS) of minimizing a general quadratic objective function subject to a general quadratic inequality constraint. By applying a simultaneous block diagonalization approach, we obtain a congruent canonical form for the symmetric matrices in both the objective and constraint functions. By exploiting the block separability of the canonical form, we show that all GTRSs with an optimal value bounded from below are second order cone programming (SOCP) representable. Our result generalizes the recent work of Ben-Tal and Hertog (Math. Program. 143(1-2):1-29, 2014), which establishes the SOCP representability of the GTRS under the assumption of the simultaneous diagonalizability of the two matrices in the objective and constraint functions. Compared with the state-of-the-art approach to reformulate the GTRS as a semi-definite programming problem, our SOCP reformulation delivers a much faster solution algorithm. We further extend our method to two variants of the GTRS in which the inequality constraint is replaced by either an equality constraint or an interval constraint. Our methods also enable us to obtain simplified versions of the classical S-lemma, the S-lemma with equality, and the S-lemma with interval bounds.

Active lateral earth pressure of geosynthetic-reinforced retaining walls with inherently anisotropic frictional backfills subjected to strip footing loading