Optimization Approaches for Electricity Generation Expansion Planning Under Uncertainty

In this dissertation, we study the long-term electricity infrastructure investment planning problems in the electrical power system. These long-term capacity expansion planning problems aim at making the most effective and efficient investment decisions on both thermal and wind power generation units. One of our research focuses are uncertainty modeling in these long-term decision-making problems in power systems, because power systems\u27 infrastructures require a large amount of investments, and need to stay in operation for a long time and accommodate many different scenarios in the future. The uncertainties we are addressing in this dissertation mainly include demands, electricity prices, investment and maintenance costs of power generation units. To address these future uncertainties in the decision-making process, this dissertation adopts two different optimization approaches: decision-dependent stochastic programming and adaptive robust optimization. In the decision-dependent stochastic programming approach, we consider the electricity prices and generation units\u27 investment and maintenance costs being endogenous uncertainties, and then design probability distribution functions of decision variables and input parameters based on well-established econometric theories, such as the discrete-choice theory and the economy-of-scale mechanism. In the adaptive robust optimization approach, we focus on finding the multistage adaptive robust solutions using affine policies while considering uncertain intervals of future demands. This dissertation mainly includes three research projects. The study of each project consists of two main parts, the formulation of its mathematical model and the development of solution algorithms for the model. This first problem concerns a large-scale investment problem on both thermal and wind power generation from an integrated angle without modeling all operational details. In this problem, we take a multistage decision-dependent stochastic programming approach while assuming uncertain electricity prices. We use a quasi-exact solution approach to solve this multistage stochastic nonlinear program. Numerical results show both computational efficient of the solutions approach and benefits of using our decision-dependent model over traditional stochastic programming models. The second problem concerns the long-term investment planning with detailed models of real-time operations. We also take a multistage decision-dependent stochastic programming approach to address endogenous uncertainties such as generation units\u27 investment and maintenance costs. However, the detailed modeling of operations makes the problem a bilevel optimization problem. We then transform it to a Mathematic Program with Equilibrium Constraints (MPEC) problem. We design an efficient algorithm based on Dantzig-Wolfe decomposition to solve this multistage stochastic MPEC problem. The last problem concerns a multistage adaptive investment planning problem while considering uncertain future demand at various locations. To solve this multi-level optimization problem, we take advantage of affine policies to transform it to a single-level optimization problem. Our numerical examples show the benefits of using this multistage adaptive robust planning model over both traditional stochastic programming and single-level robust optimization approaches. Based on numerical studies in the three projects, we conclude that our approaches provide effective and efficient modeling and computational tools for advanced power systems\u27 expansion planning

Generation Expansion Planning with Large Amounts of Wind Power via Decision-Dependent Stochastic Programming

Power generation expansion planning needs to deal with future uncertainties carefully, given that the invested generation assets will be in operation for a long time. Many stochastic programming models have been proposed to tackle this challenge. However, most previous works assume predetermined future uncertainties (i.e., fixed random outcomes with given probabilities). In several recent studies of generation assets\u27 planning (e.g., thermal versus renewable), new findings show that the investment decisions could affect the future uncertainties as well. To this end, this paper proposes a multistage decision-dependent stochastic optimization model for long-term large-scale generation expansion planning, where large amounts of wind power are involved. In the decision-dependent model, the future uncertainties are not only affecting but also affected by the current decisions. In particular, the probability distribution function is determined by not only input parameters but also decision variables. To deal with the nonlinear constraints in our model, a quasi-exact solution approach is then introduced to reformulate the multistage stochastic investment model to a mixed-integer linear programming model. The wind penetration, investment decisions, and the optimality of the decision-dependent model are evaluated in a series of multistage case studies. The results show that the proposed decision-dependent model provides effective optimization solutions for long-term generation expansion planning

A Multistage Decision-Dependent Stochastic Bilevel Programming Approach For Power Generation Investment Expansion Planning

In this article, we study the long-term power generation investment expansion planning problem under uncertainty. We propose a bilevel optimization model that includes an upper-level multistage stochastic expansion planning problem and a collection of lower-level economic dispatch problems. This model seeks for the optimal sizing and siting for both thermal and wind power units to be built to maximize the expected profit for a profit-oriented power generation investor. To address the future uncertainties in the decision-making process, this article employs a decision-dependent stochastic programming approach. In the scenario tree, we calculate the non-stationary transition probabilities based on discrete choice theory and the economies of scale theory in electricity systems. The model is further reformulated as a single-level optimization problem and solved by decomposition algorithms. The investment decisions, computation times, and optimality of the decision-dependent model are evaluated by case studies on IEEE reliability test systems. The results show that the proposed decision-dependent model provides effective investment plans for long-term power generation expansion planning

An Accelerated Extended Cutting Plane Approach With Piecewise Linear Approximations For Signomial Geometric Programming

This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane (ECP) approach integrated with piecewise linear (PWL) approximations to solve the global optimization of SGP problems. In this approach, we separate the feasible regions determined by the constraints into convex and nonconvex ones in the logarithmic domain. In the nonconvex feasible regions, the corresponding constraint functions are converted into mixed integer linear constraints using PWL approximations, while the other constraints with convex feasible regions are handled by the ECP method. We also use pre-processed initial cuts and batched cuts to accelerate the proposed algorithm. Numerical results show that the proposed approach can solve the global optimization of SGP problems efficiently and effectively

1800MHz Microwave Induces p53 and p53-Mediated Caspase-3 Activation Leading to Cell Apoptosis <i>In Vitro</i>

<div><p>Recent studies have reported that exposure of mammalian cells to microwave radiation may have adverse effects such as induction of cell apoptosis. However, the molecular mechanisms underlying microwave induced mammalian cell apoptosis are not fully understood. Here, we report a novel mechanism: exposure to 1800MHz microwave radiation induces p53-dependent cell apoptosis through cytochrome <i>c</i>-mediated caspase-3 activation pathway. We first measured intensity of microwave radiation from several electronic devices with an irradiation detector. Mouse NIH/3T3 and human U-87 MG cells were then used as receivers of 1800MHz electromagnetic radiation (EMR) at a power density of 1209 mW/m². Following EMR exposure, cells were analyzed for viability, intracellular reactive oxygen species (ROS) generation, DNA damage, p53 expression, and caspase-3 activity. Our analysis revealed that EMR exposure significantly decreased viability of NIH/3T3 and U-87 MG cells, and increased caspase-3 activity. ROS burst was observed at 6 h and 48 h in NIH/3T3 cells, while at 3 h in U-87 MG cells. Hoechst 33258 staining and in situ TUNEL assay detected that EMR exposure increased DNA damage, which was significantly restrained in the presence of N-acetyl-L-cysteine (NAC, an antioxidant). Moreover, EMR exposure increased the levels of p53 protein and p53 target gene expression, promoted cytochrome <i>c</i> release from mitochondrion, and increased caspase-3 activity. These events were inhibited by pretreatment with NAC, pifithrin-α (a p53 inhibitor) and caspase inhibitor. Collectively, our findings demonstrate, for the first time, that 1800MHz EMR induces apoptosis-related events such as ROS burst and more oxidative DNA damage, which in turn promote p53-dependent caspase-3 activation through release of cytochrome <i>c</i> from mitochondrion. These findings thus provide new insights into physiological mechanisms underlying microwave-induced cell apoptosis.</p></div

The microwave exposure system.

<p>(A) 1800MHz microwave generator. (B) Antenna in an incubator. The antenna was connected to a microwave generator via a flexible coaxial cable and enclosed in a humidified incubator. Petri dishes were positioned on the top of the antenna and cells in petri dishes were exposed to continuous microwave radiation at 1800MHz 1209 mW/m².</p

Schematic representation of p53 activation of caspase-3 signaling pathway in 1800MHz microwave induced cell apoptosis.

<p>1800MHz microwave activates p53 signaling pathway through enhancing ROS production and DNA damage, p53 further upregulates cytochrome <i>c</i>-mediated caspase-3 activation that leads to cell apoptosis. MW, microwave; NAC, N-acetyl-L-cysteine; ROS, reactive oxygen species.</p

Intensity test of microwave radiation for various electronic devices (peak reading XYZ mode).

<p>Intensity test of microwave radiation for various electronic devices (peak reading XYZ mode).</p

Exposure to 1800MHz microwave induces ROS production in NIH/3T3 and U-87 MG cells.

<p>(A, B) Intracellular ROS production was measured by using DCFH-DA after 1800MHz microwave radiation for the indicated time in NIH/3T3 and U-87 MG cells. (C, D) detection of mitochondrial ROS production by using MitoSOX Red after 1800MHz microwave exposure for 6 hours in NIH/3T3 and U-87 MG cells. The imaging experiments were implemented on a two-photon laser scanning microscope system. DCF, 2’,7’-Dichlorodihydrofluorescin diacetate; mROS, mitochondrial reactive oxygen species; MW, microwave; NAC, N-acetyl-L-cysteine.Scale bars: 10 μm. Data represent mean ± S.D. (n = 3; *P < 0.05 vs. sham group.)</p