Post-contingency Corrective Control for Integrated Electricity-Gas Systems based on Convex Hull

The interdependency between power and natural gas is so tight, especially where natural gas extraction is economical. Therefore, co-expansion planning is imperative for having efficient systems with minimum cost. In this paper, multistage stochastic co-expansion planning power and natural gas systems is presented. Natural gas load flow (NGLF) is modeled with the Weymouth equation, a non-linear and non-convex problem. In order to overcome the non-convexity of the problem, mixed-integer second-order cone programming (MISOCP) is utilized to solve NGLF. Furthermore, linepack constraints are added to exploit the natural gas stored in the pipeline for co-expansion planning, mainly at the transmission level where voluminous pipelines are used and linepack is noticeable. Natural gas storage is considered in the model to alleviate operational and investment costs. Decreasing the investment and operational costs of co-expansion planning is the objective of the model. Investment decisions can be taken more than once so that investment costs can be divided into the whole planning horizon to avoid an enormous budget at the beginning of the planning horizon. Power and natural gas load growth are taken into account as long-term uncertainties. The proposed model is applied in a real case of southwestern Iran. The results determine that by implementing the proposed model, the investment and operational costs decrease 6.3% and 14%, respectively.

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.

This paper studies the complex energy coupling relationship of unbalanced power distribution network integrated with the natural gas distribution system. An Alternating Direction Method of Multipliers (ADMM) based decentralized solution approach is proposed to achieve the multi-period synergistic operation of the power distribution and natural gas distribution networks. A bi-level solution strategy is used to solve the power distribution subsystem problem, where level-1 is the linearized version of three-phase optimal load flow and level-2 solves the convex nonlinear problem. The level-1 problem helps to determine the status of voltage control devices whereas the level-2 problem obtains the optimal and feasible solution of the optimal load flow problem. The non-convexities present in the integrated energy system are dealt with the Second Order Cone Programming (SOCP) and Quadratic Relaxation (QR). The purposed solution procedure is validated using IEEE 13-bus distribution system integrated with 6-bus natural gas network. The numerical results corroborate the applicability of the proposed approach to minimize the operation cost of the integrated energy system.

Considering the increased interactions between power grids and natural gas grids, this study presents a chance‐constrained maintenance scheduling model for integrated gas‐electric grids with wind energy integration. Given the uncertainties of wind power, the loss of wind power probability is modelled as a chance constraint, ensuring the high utilisation of wind power. To overcome the adversities caused by the non‐linear and non‐convex models of natural gas systems, a piecewise linear approximation method is employed to transform the non‐linear models into a group of mixed integer linear models. A big‐M formulation method is used to construct inequality constraints for lines/pipelines to be under maintenance. In addition, unit commitment is also coordinated to achieve the best maintenance strategies. The proposed chance‐constrained stochastic programming model is converted into an equivalent deterministic programming model via a strong extended formulation for the sample average approximation by leveraging the star‐inequalities. Several tests on a four‐node natural gas system with a six‐bus power system and a 20‐node natural gas system with a modified IEEE 118‐bus power system demonstrate the effectiveness of the proposed model.

The power to gas (P2G) technology can realize the large-scale storage of electric energy in the form of natural gas, so that the power system and the natural gas system have the ability to flow energy, and the degree of coupling between the power system and the natural gas system is deepened. As the coupling between the power system and the natural gas system continues to increase, an integrated energy system (IES) with the power grid as the core has emerged. However, under uncertain conditions, the current planning methods still cannot guarantee the optimal interests of each manufacturer, so a collaborative planning method for gas-electric systems based on non-cooperative game theory is proposed. With each energy unit and electricity and gas network companies as independent interest groups, and with the maximum annual net income as the optimization goal, establishing a comprehensive non-combination of wind turbines, gas turbines, electric-to-gas turbines, transmission lines and natural gas pipelines in the gas-electric integrated system linear programming model. Aiming at the uncertainty of wind power and load, an improved two-stage robust optimization method is proposed. Finally, the modified IEEE 39-node power system and 20-node natural gas system gas-electric network verify the application value of the model and algorithm.

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.

With the increasing interactions between natural gas systems (NGS) and power systems, component failures in one system may propagate to the other one, threatening reliable operation of the whole system. Due to neglect of such cross-sectorial failure propagation in integrated electricity-gas systems (IEGSs), traditional economy-oriented reserve expansion models may lead to unreasonable planning results. In order to address this, an innovative reserve expansion model is proposed to determine the allocation of energy production components through the harmonization between costs and reliability. First, novel multifactor-influenced reliability indices are defined considering synthetic effects of multiple uncertainties, including failure propagation, load uncertainties and generation failures. In reliability index formulation, contribution of failure propagation on system reliability is analytically expressed. To avoid high computational complexity, the fuzzy set theory is combined with conventional methods, e.g., Monte-Carlo simulation technique to reduce numerous contingency states. Sampled contingency states are aggregated into several clusters represented by a fuzzy number. To effectively solve the planning model, a decomposition approach is introduced and applied to decompose the original problem into a master problem and two correlated reliability sub-problems. Numerical studies show the proposed model can plan reasonable reserves to guarantee reliability levels of IEGSs considering failure propagation.

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°.

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

The joint operation of natural gas system and power system is an important direction of energy system integration. In this paper, the unit combination modeling method of integrated gas-electric energy system is studied, and the operation constraints such as output, climbing and duration considering unit startup and shutdown state are established. The matrix balance model of power system and natural gas system is established. Based on the generation transfer distribution factor, the tie line security constraints are proposed, and the simplified method of gas electric coupling model of gas turbine based on the piecewise linearization method is proposed. Finally, 6-node power system and 6-node natural gas system are used to build an integrated gas electric energy system. Taking the economic cost optimization as the optimization goal, it is verified that the unit combination constraint in this paper can effectively optimize the unit operation dispatching in the combined system.

The interdependence between natural gas and electric power systems is becoming increasingly tight, as the share of natural gas-fired units increases. Within this context, this paper addresses the coordinated expansion planning of natural gas and power systems. We analyze the tradeoff of building natural gas-related facilities (e.g., natural gas pipelines and natural gas-fired generation units) versus electric-power-related facilities (e.g., transmission lines and other generation units). We use a two-stage stochastic optimization model that provides an appropriate balance between accuracy and computational tractability and represents uncertainty pertaining to electricity and natural gas demands. We show the importance of representing uncertainty by computing the value of stochastic solution, which is significant. We analyze the functioning of the model through a small example and a case study based on the IEEE 118-bus system. Computational results confirm the need for detailed representation of both the natural gas and power systems to achieve investment decisions that are well coordinated and optimal.

This paper proposes an optimal day-ahead optimization schedule for gas-electric integrated energy system (IES) considering the bi-directional energy flow. The hourly topology of electric power system (EPS), natural gas system (NGS), energy hubs (EH) integrated power to gas (P2G) unit, are modeled to minimize the day-ahead operation cost of IES. Then, a second-order cone programming (SOCP) method is utilized to solve the optimization problem, which is actually a mixed integer nonconvex and nonlinear programming issue. Besides, cutting planes are added to ensure the exactness of the global optimal solution. Finally, simulation results demonstrate that the proposed optimization schedule can provide a safe, effective and economical day-ahead scheduling scheme for gas-electric IES.