Chance Constrained Scheduling and Pricing for Multi-Service Battery Energy Storage

Exact solution approaches for integer linear generalized maximum multiplicative programs through the lens of multi-objective optimization

A mixed-integer second order cone program (MISOCP) formulation is proposed for solving Markowitz’s asset portfolio construction problem under a cardinality constraint. Compared with a standard alternative big-M linearly constrained formulation, our reformulation is solved significantly faster using state-of-the-art integer programming solvers. We consider learning methods that are based on the MISCOP formulation: cardinality-constrained Markowitz (CCM) solves the MISCOP for a given cardinality k and training set data of asset returns. We also find reinforcing evidence for factor model theory in the selection of factors to form optimal CCM portfolios. For large datasets in the absence of a hard-cardinality constraint, we propose a method (CCM-R) that is based on the continuous relaxation of our MISCOP, where k selected by rolling time window validation. In predictive performance experiments, based on historical stock exchange data, our learning methods usually outperform a competing extension of the Markowitz model that penalizes the L1 norm of asset weights.

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.

We consider a continuous multi-facility location-allocation problem that aims to minimize the sum of weighted farthest Euclidean distances between (closed convex) polygonal and/or circular demand regions, and facilities they are assigned to. We show that the single facility version of the problem has a straightforward second-order cone programming formulation and can therefore be efficiently solved to optimality. To solve large size instances, we adapt a multi-dimensional direct search descent algorithm to our problem which is not guaranteed to find the optimal solution. In a special case with circular and rectangular demand regions, this algorithm, if converges, finds the optimal solution. We also apply a simple subgradient method to the problem. Furthermore, we review the algorithms proposed for the problem in the literature and compare all these algorithms in terms of both solution quality and time. Finally, we consider the multi-facility version of the problem and model it as a mixed integer second-order cone programming problem. As this formulation is weak, we use the alternate location-allocation heuristic to solve large size instances.

This paper proposes a coordinated active–reactive power optimization model for an active distribution network with energy storage systems, where the active and reactive resources are handled simultaneously. The model aims to minimize the power losses, the operation cost, and the voltage deviation of the distribution network. In particular, the reactive power capabilities of distributed generators and energy storage systems are fully utilized to minimize power losses and improve voltage profiles. The uncertainties pertaining to the forecasted values of renewable energy sources are modelled by scenario-based stochastic programming. The second-order cone programming relaxation method is used to deal with the nonlinear power flow constraints and transform the original mixed integer nonlinear programming problem into a tractable mixed integer second-order cone programming model, thus the difficulty of problem solving is significantly reduced. The 33-bus and 69-bus distribution networks are used to demonstrate the effectiveness of the proposed approach. Simulation results show that the proposed coordinated optimization approach helps improve the economic operation for active distribution network while improving the system security significantly.

A two-stage stochastic programming approach is pursued to optimally place and size photovoltaic (PV) inverters in a radial distribution network under solar irradiance and load uncertainties. First-stage variables include binary PV unit placement as well as continuous real and apparent power capacities of the inverters. Second-stage decisions comprise reactive power compensation, power flows, and nodal voltages, which are determined adaptive to the uncertainty. The objective is to minimize installation cost and expected thermal losses on the network. The optimization problem is formulated as a mixed-integer second-order cone program and is tested on a practical distribution network.

Controlled islanding plays an essential role in preventing the blackout of power systems. Although there are several studies on this topic in the past, no enough attention is paid to the uncertainty brought by renewable energy sources (RESs) that may cause unpredictable unbalanced power and the observability of power systems after islanding that is essential for back-up black-start measures. Therefore, a novel controlled islanding model based on mixed-integer second-order cone and chance-constrained programming (MISOCCP) is proposed to address these issues. First, the uncertainty of RESs is characterized by their possibility distribution models with chance constraints, and the requirements, e. g., system observ-ability, for rapid back-up black-start measures are also considered. Then, a law of large numbers (LLN) based method is employed for converting the chance constraints into deterministic ones and reformulating the non-convex model into convex one. Finally, case studies on the revised IEEE 39-bus and 118-bus power systems as well as the comparisons among different models are given to demonstrate the effectiveness of the proposed model. The results show that the proposed model can result in less unbalanced power and better observability after islanding compared with other models.

Mixed integer second-order cone programming formulations for variable selection in linear regression

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.

Resilient operation of multi-energy industrial park based on integrated hydrogen-electricity-heat microgrids

Local distribution resources, such as distributed generations (DGs), energy storage systems, and some renewable energy resources, can be interconnected for service restoration in distribution systems and operate as an island after extreme events. High penetration of renewable energy resources makes it difficult to make decisions on restoration strategies because the power injections become uncertain. This paper proposes a chance-constrained program with relaxed second-order cone constraints (SOCC) to formulate the critical load restoration problem. The joint probability density function of power outputs of PVs and WTs is represented by a Gaussian mixture model (GMM). Using the sample average approximation method, an approximate analytical form of the chance constraints is proposed, which transforms the probabilistic program to a deterministic mixed-integer second-order cone program (MISOCP). The MISOCP can be solved by off-the-shelf optimization solvers. The effectiveness of the proposed method is validated by the simulation of the IEEE 33-node test system.

The problem of reconfiguration for active distribution systems is formulated as a stochastic mixed-integer second-order conic programming (MISOCP) model that simultaneously considers the minimization of energy power losses and CO2 emissions. The solution of the model determines the optimal radial topology, the operation of switchable capacitor banks, and the operation of dispatchable and non dispatchable distributed generators. A stochastic scenario-based model is considered to handle uncertainties in load behavior, solar irradiation, and energy prices. The optimal solution of this model can be reached with a commercial solver; however, this is not computationally efficient. To tackle this issue a novel methodology which explores the efficiency of classical optimization techniques and heuristic based on neighborhood structures, referred as matheuristic algorithm is proposed. In this algorithm. the neighborhood search is carried out using the solution of reduced MISOCP models that are obtained from the original formulation of the problem. Numerical experiments are performed using several systems to compare the performance of the proposed matheuristic against the direct solution by the commercial solver CPLEX. Results demonstrate the superiority of the proposed methodology solving the problem for large-scale systems.

Chance-constrained model predictive control for drinking water networks

Currently, a huge amount of cargo is transported via containers by liner shipping companies. Under stochastic demand, repacking operations and carbon reduction, which may lead to an increase in effectiveness and environmental improvement, have been rarely considered in previous literature. In this paper, we investigate a container transshipment route scheduling problem with repacking operations under stochastic demand and environmental protection. The problem is a combinatorial optimization problem. Lacking historical data, a chance-constrained programming model is proposed to minimize the total operating and environment-related costs. We choose two distribution-free approaches, i.e., approximation based in Markov’s Inequality and Mixed Integer Second-Order Conic Program to approximate the chance constraints. As the loses induced by unfulfilled demand are not taken into account in the above model, a scenario-based model is developed considering the loses. Risk-neutral model may provide solutions that perform poorly while considering uncertainty. To incorporate decision makers’ perspectives, therefore, we also propose a risk-averse model adopting a risk aversion measure called Conditional Value-at-Risk to meet different preferences. Finally, we conduct computational experiments based on real data to compare the performances of the modeling methods and illustrate the impacts by testing different risk levels and confidence levels.

Hybrid AC/DC distribution network (HADDN) will be the development trend of smart grid. This paper presents an optimal operation method for hybrid AC/DC distribution network to achieve safe and economic operation, in the case of uncertain renewable energy (RES) output and load demand. The proposed model is formulated based on a novel two-stage robust model. The first stage of the model optimizes the work states of the on-load tap changers (OLTC), capacitor banks (CBs) and energy storages (ESs) at one cycle. The second stage of the model optimizes the AC/DC converter stations (CSs) output to suppress the overvoltage problem and further reduce the operating cost by using corrective control policy. Furthermore, this paper adopts an ambiguity set to represent uncertainties of RESs and load demand, which makes the model less conservative and also shortens the model solving time. Then, the proposed model can be converted into the mixed integer second-order cone programming (MISCOP) problem, which can be solved by the delayed column-and-constraint generation algorithm. Finally, case study shows that this method can effectively realize safe and economic operation of the HADDN, which is obviously superior to other mainstream methods in reducing operation cost and restraining overvoltage problem.