Search

Linear power flow models are widely used in power system analysis. To control the maximum influence of linearization error on decision making, it is important to evaluate the worst-case linearization error (i.e., the error bound). This letter theoretically derives the error bound of linear power flow models based on the truncation error analysis of Taylor series expansion. A cold-start approach is proposed to restrain the error bound. Case studies show that 1) the proposed error bound is tight and effective and 2) the maximum linearization error can be successfully reduced using the proposed method.

Power electronic devices are important in the modern power system. Control functions and operational characteristics of power electronic devices bring higher nonlinearity and heavier calculation burden to power system analysis, especially in optimization problems. In this article, a general steady-state model of power electronic devices in the AC-DC hybrid grid is proposed, which considers the high voltage direct current (HVDC) connections and the flexible AC transmission systems (FACTS). Power electronic devices are equivalently represented by impedance, transformers, and controlled sources. The linearized steady-state model is derived and then the specific formulation with minimized error is presented. The effectiveness of the proposed method is verified by optimal power flow (OPF) calculation in the IEEE and Polish test systems.

Linear power flow models are widely used in power system analysis because it brings huge computational benefits, especially for power system optimization problems. The improvement of the linearization accuracy is greatly beneficial to the power system operation considering the large amount of power scheduled based on linear power flow models. We find that the linearization error substantially changes with different selections of the variable space. In this paper, we formulate a model to find the linear power flow model with the minimized linearization error based on the optimal selection of the variable space. The expression of the variable space is generalized as a polynomial function. A simplified model of power losses is proposed. The difference between the selection of the variable space and the common hot-start approaches is illustrated. The effectiveness of the proposed linear power flow model is verified by power flow calculation and optimal power flow (OPF) calculation in the IEEE and Polish test systems.

This document presents a more detailed derivation of Eq. (1)-(13) in IEEE letter " Error Bound Restriction of Linear Power Flow Model".

This document presents a more detailed derivation of Eq. (1)-(13) and source files in IEEE letter " Error Bound Restriction of Linear Power Flow Model".

This document presents a more detailed derivation of Eq. (1)-(13) and case data in IEEE letter " Error Bound Restriction of Linear Power Flow Model".

The nonlinearity of the power flow equation is the significant cause of the non-convexity of optimization problems in the power system. The existing linear power flow model is derived based on special mathematical approximation and numerical analysis. In this paper, a method to quantify the linearization error of the power flow equation is proposed. The truncation error of the Taylor series expansion of the power flow equation is studied. The linear power flow models with the independent variable $(v,\theta)$ and $(\pmb{v}^{\mathbf{2}},\theta)$ are compared. The proportion of power loss in high-order components is analyzed. The advantage of $(\pmb{v}^{\mathbf{2}},\theta)$ is demonstrated from a new perspective.

Emerging studies have addressed the role of probiotics in inflammation modulation via modifying gut microbiota. Perturbed gut microbiota is recognized as a pivotal trigger in the pathogenesis of rheumatoid arthritis (RA), and manipulating gut microbiota at the early phase may be helpful to alleviate the disease based on the fact that dysbiosis occurred prior to clinical arthritis. The current study compared the effects of preventive and therapeutic treatment with Bifidobacterium adolescentis on collagen induced arthritis (CIA) in rats. Early B. adolescentis administration before CIA modelling performed better than late B. adolescentis treatment in reducing the clinical symptoms, rebalancing the pro- and anti-inflammatory responses and maintaining the fecal concentration of short chain fatty acids (SCFAs), as well as restoring the intestinal dysbiosis. Preventive B. adolescentis treatment restored the gut microbiota to a normal level while late B. adolescentis fed rats showed clearly different gut microbial profiles. In addition, there were slight discrepancies between early- and late- treatment of B. adolescentis in the production of specific auto-antibodies and tight junction proteins. All those results highlighted that early treatment of probiotics in arthritis might be a better timing for alleviating arthritis.

Recent studies have shed light on the prophylactic effects of Lactobacilli on rheumatoid arthritis (RA). However, the modulatory mechanisms of Lactobacilli remain unclear. The current study evaluated different Lactobacillus species' ability to alleviate arthritis induced by collagen. Rats were intragastrically administered different lactobacilli cocktails two weeks before arthritis induction. The results revealed that the performance of Lactobacillus in relieving arthritis was different for some species. L. reuteri, L. casei, L. rhamnosus and L. fermentum attenuated RA through species-independent pathways that inhibited pro-inflammatory cytokines and anti-CII-antibodies; and through species-dependent immune regulation that was based on rebalancing the intestinal microbiota, and metabolites such as short-chain fatty acids. In particular, L. reuteri and L. casei weaken the Th1 immune response, while L. rhamnosus and L. fermentum impaired Th17 responses. Interestingly, L. plantarum did not alleviate arthritis although it did suppress Th1 and Th17 immune responses, while L. salivarius only delayed the onset of arthritis without influencing the immune response. In conclusion, Lactobacilli protect against collagen-induced-arthritis through both common and individual pathways.

Linear power flow models are widely used in power system analysis. However, finding the linear power flow model with the minimized error is still a difficult task. Actually, the linearization error of the power flow model is influenced by the power flow formulation and the distribution of variables. In this paper, we focus on the linearization of v i v j in the power flow model, which is a major origin of the linearization error. Based on the general linear power flow model, we derive the linearization of v i v j using different formulation of independent variables. The Copula method is used to describe the joint distribution of (v i , v j ). We propose a method to find the optimal Copula function that best fits the actual distribution of the historical data. Finally, an algorithm to obtain the linearization of v i v j with the minimized error is presented. Case studies in the IEEE 118-bus system validate the proposed method.