Compressed Air Energy Storage-Part I: An Accurate Bi-linear Cavern Model

Compressed air energy storage (CAES) is suitable for large-scale energy storage and can help to increase the penetration of wind power in power systems. A CAES plant consists of compressors, expanders, caverns, and a motor/generator set. Currently used cavern models for CAES are either accurate but highly non-linear or linear but inaccurate. Highly non-linear cavern models cannot be directly utilized in power system optimization problems. In this regard, an accurate bi-linear cavern model for CAES is proposed in this first paper of a two-part series. The charging and discharging processes in a cavern are divided into several virtual states and then the first law of thermodynamics and ideal gas law are used to derive a cavern model, i.e., model for the variation of temperature and pressure in these processes. Thereafter, the heat transfer between the air in the cavern and the cavern wall is considered and integrated into the cavern model. By subsequently eliminating several negligible terms, the cavern model reduces to a bi-linear (linear) model for CAES with multiple (single) time steps. The accuracy of the proposed cavern model is verified via comparison with an accurate non-linear model.Comment: 8 page

Compressed Air Energy Storage-Part II: Application to Power System Unit Commitment

Unit commitment (UC) is one of the most important power system operation problems. To integrate higher penetration of wind power into power systems, more compressed air energy storage (CAES) plants are being built. Existing cavern models for the CAES used in power system optimization problems are not accurate, which may lead to infeasible solutions, e.g., the air pressure in the cavern is outside its operating range. In this regard, an accurate CAES model is proposed for the UC problem based on the accurate bi-linear cavern model proposed in the first paper of this two-part series. The minimum switch time between the charging and discharging processes of CAES is considered. The whole model, i.e., the UC model with an accurate CAES model, is a large-scale mixed integer bi-linear programming problem. To reduce the complexity of the whole model, three strategies are proposed to reduce the number of bi-linear terms without sacrificing accuracy. McCormick relaxation and piecewise linearization are then used to linearize the whole model. To decrease the solution time, a method to obtain an initial solution of the linearized model is proposed. A modified RTS-79 system is used to verify the effectiveness of the whole model and the solution methodology.Comment: 8 page

Perfect State Transfer in Laplacian Quantum Walk

For a graph $G$ and a related symmetric matrix $M$, the continuous-time quantum walk on $G$ relative to $M$ is defined as the unitary matrix $U(t) = \exp(-itM)$, where $t$ varies over the reals. Perfect state transfer occurs between vertices $u$ and $v$ at time $\tau$ if the $(u,v)$-entry of $U(\tau)$ has unit magnitude. This paper studies quantum walks relative to graph Laplacians. Some main observations include the following closure properties for perfect state transfer: (1) If a $n$-vertex graph has perfect state transfer at time $\tau$ relative to the Laplacian, then so does its complement if $n\tau$ is an integer multiple of $2\pi$. As a corollary, the double cone over any $m$-vertex graph has perfect state transfer relative to the Laplacian if and only if $m \equiv 2 \pmod{4}$. This was previously known for a double cone over a clique (S. Bose, A. Casaccino, S. Mancini, S. Severini, Int. J. Quant. Inf., 7:11, 2009). (2) If a graph $G$ has perfect state transfer at time $\tau$ relative to the normalized Laplacian, then so does the weak product $G \times H$ if for any normalized Laplacian eigenvalues $\lambda$ of $G$ and $\mu$ of $H$, we have $\mu(\lambda-1)\tau$ is an integer multiple of $2\pi$. As a corollary, a weak product of $P_{3}$ with an even clique or an odd cube has perfect state transfer relative to the normalized Laplacian. It was known earlier that a weak product of a circulant with odd integer eigenvalues and an even cube or a Cartesian power of $P_{3}$ has perfect state transfer relative to the adjacency matrix. As for negative results, no path with four vertices or more has antipodal perfect state transfer relative to the normalized Laplacian. This almost matches the state of affairs under the adjacency matrix (C. Godsil, Discrete Math., 312:1, 2011).Comment: 26 pages, 5 figures, 1 tabl

Expression of bgt gene in transgenic birch (Betula platyphylla Suk.)

Study on the characteristics of integration and expression is the basis of genetic stability of foreign genes in transgenic trees. To obtain insight into the relationship of transgene copy number and expression level, we screened 22 transgenic birch lines. Southern blot analysis of the transgenic birch plants indicated that the copy number of bgt varies from one to four, of which 18.2% were single copy. Copy number of bgt and gus was different in 68% of transgenic birch plants, indicating that rearrangement or partial deletion appeared in the process of T-DNA integration. Transcriptional expression of bgt gene in transgenic birch plants was analyzed by Northern blot. TGS has been found in two transgenic lines with one and four copies of bgt. The ELISA result showed that the BGT protein expression level in the transgenic birch plants ranged from 0.000 to 0.283% of total soluble protein. In contrary to most studies, this research showed no significant correlation was found between copy number and expression level of bgt gene. Effective resistance of transgenic plants against Lymantria dispar was verified in feeding bioassays with the insects. Bioassays results were mostly consistent with the expression level of BGT insecticidal protein detected by ELISA and Western blot in transgenic birch. The paper showed transgenic birch had the high lethal effect on gypsy moth larvae (L. dispar). The practicality of this work will benefit not only the birch producers, but also the environment worldwide

An Accurate Bilinear Cavern Model for Compressed Air Energy Storage

Compressed air energy storage is suitable for large-scale electrical energy storage, which is important for integrating renewable energy sources into electric power systems. A typical compressed air energy storage plant consists of compressors, expanders, caverns, and a motor/generator set. Current cavern models used for compressed air energy storage are either accurate but highly nonlinear or linear but inaccurate. The application of highly nonlinear cavern models in power system optimization problems renders them computationally challenging to solve. In this regard, an accurate bilinear cavern model for compressed air energy storage is proposed in this paper. The charging and discharging processes in a cavern are divided into several real/virtual states. The first law of thermodynamics and ideal gas law are then utilized to derive a cavern model, i.e., a model for the variation of temperature and pressure in these processes. Thereafter, the heat transfer between the air in the cavern and the cavern wall is considered and integrated into the cavern model. By subsequently eliminating several negligible terms, the cavern model reduces to a bilinear model. The accuracy of the bilinear cavern model is verified via comparison with both an accurate nonlinear model and two sets of field-measured data. The bilinear cavern model can be easily linearized and is then suitable for integration into optimization problems considering compressed air energy storage. This is verified via comparatively solving a self-scheduling problem of compressed air energy storage using different cavern models.Comment: 18 pages, 15 figures, accepted by Applied Energy on March 201

The stability of transgene expression and effect of DNA methylation on post transcriptional gene silencing (PTGS) in birch

In this paper, we selected transgenic birch (Betula platyphylla Suk) plants, which included nonsilencing plants, transcriptional silence plants including TP96, TP74, TP73 and the post-transcriptional silence ones (TP67 and TP72). The transcription of the bgt gene in different tissues and organs were significantly different. The transcriptional level of bgt gene in the different tissues and organs was in the following order: leaf > female flower and male flower > branch bark > phloem > root. The transgenic lines were monitored for foreign gene expression for a long-term period of 8 years during their continuous growth under field conditions. GUS protein expression was not reactivated in the transgene silencing lines TP72 and TP67 when cultured in field conditions for long-term period. Meanwhile, no cases of gene silencing were observed again during the study period in the field conditions. Our results suggest that transgene expression in transgenic birch plants appears to be stable under field conditions. The frequencies of methylated cytosines in the code regions of gus gene was studied. Relation of transgene expression and DNA methylation was analysed. The data of restriction enzyme digestion (HpaII and MspI) indicated that DNA methylation resulted in post transcriptional gene silencing (PTGS) in transgenic birch.Key words: Transgenic birch, DNA methylation, gene silencing

The Vlasov-Poisson-Landau System in Rx3\R^3_x

For the Landau-Poisson system with Coulomb interaction in $\R^3_x$, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close.Comment: 50 page