By Mladen Kezunovic, Sakis Meliopoulos, Vaithianathan Venkatasubramanian, Vijay Vittal (auth.)

This publication illuminates how synchrophasors in attaining the tracking, defense and keep an eye on optimizations essential to extend current energy platforms to help expanding quantities of renewable and disbursed strength assets. The authors describe synchrophasor strategies that could offer operators with higher solution in taking pictures dynamic habit of the ability grid. The ensuing insights aid more suitable real-time choice making within the face of extra iteration and cargo uncertainty, in addition to interruptions as a result of random acts of nature and malicious assaults. Armed with the knowledge during this state-of-the-art source, grid planners and operators could make optimized, versatile, resilient energy platforms a reality.

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**Additional info for Application of Time-Synchronized Measurements in Power System Transmission Networks**

**Sample text**

The chi-square test is applied as follows: Step 1. Compute the state estimate xˆ in the weighted least squares sense. m m i =1 i =1 Step 2. Compute the value ζ = ∑ si2 ( xˆ ) = ∑ ( hi ( xˆ ) − bi σi 2 ). Step 3. “Read” the probability Pr χ 2 ≤ ζ = Pr (ζ , v ) from the chi-square probability distribution function. Step 4. 0 − Pr (ζ , v ). Above probability is the probability that measurements fit the model of the system. This can be also expressed as a confidence level. , data that do not fit the model.

In this book, we will focus on the first approach, which is the most widely used and is introduced next. The weighted least squares solution of the over-determined system above is the vector x, which minimizes the sum of the weighted squares of the components of the residual vector r or the vector of the measurement errors η. Mathematically, this is expressed as follows: m Minimize J = ∑ wi ri 2 = r T Wr = ηT W η, i =1 where wi W the weight for the residual ri, a diagonal matrix, the diagonal elements being the weights wi.

That is, all nonlinearities are moved to the algebraic part of the model through the introduction of additional appropriate state variables. Also note that the nonlinear algebraic equations are of degree no more than two (at most quadratic equations), which is also achieved by the introduction of additional appropriate state variables. Assuming that the dynamic functions vary quadratically within the integration step [t-h, t], and upon quadratic integration [18], the dynamic model of the device is converted into a set of algebraic equations.