Convergence analysis of the triangular-based power flow method for AC distribution grids

<p>This paper addresses the convergence analysis of the triangular-based power flow (PF) method in alternating current radial distribution networks. The PF formulation is made via upper-triangular matrices, which enables finding a general iterative PF formula that does not require admittance matrix calculations. The convergence analysis of this iterative formula is carried out by applying the Banach fixed-point theorem (BFPT), which allows demonstrating that under an adequate voltage profile the triangular-based PF always converges. Numerical validations are made, on the well-known 33 and 69 distribution networks test systems. Gauss-seidel, newton-raphson, and backward/forward PF methods are considered for the sake of comparison. All the simulations are carried out in MATLAB software.</p>

Mathematical Modelling of Twin -T Notch Filter using Floating Admittance Matrix

A novel article presents the RC-notch filter function using the floating admittance matrix approach. The main advantages of the approach underlined the easy implementation and effective computation. The proposed floating admittance matrix (FAM) method is unique, and the same can be used for all types of electronic circuits. This method takes advantage of the partitioning technique for a large network. The sum property of all the elements of any row or any column equal to zero provides the assurance to proceed further for analysis or re-observe the very first equation at the first instant itself. This saves time and energy. The FAM method presented here is so simple that anybody with slight knowledge of electronics but understating the matrix maneuvering can analyze any circuit to derive all types of transfer functions. The mathematical modelling using the FAM method allows the designer to adjust their design at any stage of analysis comfortably. These statements provide compelling reasons for the adoption of the proposed process and demonstrate its benefits.

An Elegant Method of Analysis for the BJT Amplifiers using Floating Admittance Matrix

The Floating Admittance Matrix (FAM) is an elegant, neat, illustrative, and simplified technique for analyzing all configurations of the BJT amplifiers, starting with the maneuvering of the FAM of the phase-splitter circuit. The conventional analysis method requires a small-signal equivalent circuit, and then conventional tools, either KCL, KVL, or Thevenin, Norton, etc., are used for the analysis. The researcher has to guess which conventional tool suites better than the other for any particular circuit, whether active or passive. The proposed technique is equally ell useful for all circuits. In the FAM method, once the device matrix is known rest of the circuit can be embedded in it by inspection. The sum property of this matrix provides a check to know whether FAM has been written correctly to proceed further.

Identification of topology changes in power grids via reduced admittance matrix

Frequent changes in power grid topology bring risks to the stable operation of power systems. It is essential to identify changes in the power grid topology quickly and accurately. This paper presents a novel method named network reduction-based topology change identification (NR-TCI) algorithm to identify topology changes in multi-machine power systems. The proposed algorithm can quickly identify power grid topology changes using only phasor measurement unit (PMU) data sampled during the system’s transient process. The NR-TCI algorithm uses the network order reduction method to reduce the order of a bus admittance matrix and then uses PMU measurement data to estimate the reduced admittance matrix by least square method. Finally, the reduced admittance matrix is adopted to find topological information, and the Sherman–Morrison formula is utilized to identify the topology changes. The effectiveness of the proposed NR-TCI algorithm is verified with a case study of a 3 machine 9 bus system in Matlab. In addition, the influence of PMU sampling frequency on the effectiveness of the proposed algorithm is also studied.

The Lehtinen-Pirjola Method Modified for Efficient Modelling of Geomagnetically Induced Currents in Multiple Voltage Levels of a Power Network

The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirement to model geomagnetically induced currents (GIC) in multiple voltage levels of a power network. The Lehtinen-Pirjola method for modelling GIC is widely used but was developed when the main aim was to model GIC in only the highest voltage level of a power network. Here we present a modification to the Lehtinen-Pirjola (LP) method designed to provide an efficient method for modelling GIC in multiple voltage levels. The LP method calculates the GIC flow to ground from each node. However, with a network involving multiple voltage levels many of the nodes are ungrounded, i.e. have infinite resistance to ground which is numerically inconvenient. The new modified Lehtinen-Pirjola (LPm) method replaces the earthing impedance matrix [Ze] with the corresponding earthing admittance matrix [Ye] in which the ungrounded nodes have zero admittance to ground. This is combined with the network admittance matrix [Yn] to give a combined matrix ([Yn]+[Ye]), which is a sparse symmetric positive definite matrix allowing efficient techniques, such as Cholesky decomposition, to be used to provide the nodal voltages. The nodal voltages are then used to calculate the GIC in the transformer windings and the transmission lines of the power network. The LPm method with Cholesky decomposition also provides an efficient method for calculating GIC at multiple time steps. Finally, the paper shows how software for the LP method can be easily converted to the LPm method and provides examples of calculations using the LPm method.

Lyapunov Analysis of Two Imbalanced Power System Areas

The transient stability is the capability of the system to preserve synchronism while being affected by large disturbances. It is a nonlinear problem that requires a simultaneous solution for many differential equations. Therefore, a thorough analysis is needed to resolve it. In this paper, we present the transient stability for multimachine under different fault cases and to analyze using the Lyapunov function. It serves as an analytical tool to determine the necessary condition to be stable. The system is stable as long as it is contained in the region of attraction. Meanwhile, the swing equation and reduced admittance matrix are used to model the system in three conditions, pre-fault, during the fault, and post-fault. The numerical simulations are conducted to verify that the synchronism can be preserved despite under faults on the transmission lines by achieving the critical clearing time.

Unique Analysis Approach to Bridge-T Network using Floating Admittance Matrix Method”

The RC bridge-T Circuit are sometimes preferred for radio frequency applications as it does not require transformer (inductive coupling). The uses of the resistance-capacitance form of the network permits a wide tuning range. The article aims to develop a band pass filter's mathematical model using the Floating Admittance Matrix (FAM) approach. Both types of RC bridge-T network form the band-pass filters. The use of the conventional methods of analysis such as KCL, KVL, Thevenin's, Norton's depends on its suitability for the type of the particular circuit. The proposed mathematical modeling scheme using the floating admittance matrix approach is unique, and the same can be used for all types of circuits. This method is suitable to use the partitioning technique for large network. The sum property of all the elements of any row or any column equal to zero provides the assurance to proceed further for analysis or re-observe the very first equation. This saves time and energy. The FAM method presented here is so simple that anybody with slight knowledge of electronics but understating the matrix maneuvering, can analyze any circuit to derive all types of its transfer functions. The mathematical modeling using the FAM approach provides leverage to the designer to comfortably adjust their design at any stage of analysis. These statements provide compelling reasons for the adoption of the proposed process and demonstrate its benefits. The theoretically obtained equations meet the expected result for the RC bridge-T network. Its response peaks at the theoretically obtained value of the frequency. The simulated results are in agreement with the topological explanations and expectations.

Mathematical Modelling and Simulation of Band Pass Filters using the Floating Admittance Matrix Method

This article aims to develop a band pass filter's mathematical model using the Floating Admittance Matrix (FAM) method. The use of the conventional methods of analysis based KCL, KVL, Thevenin's, Norton's depends on the type of the particular circuit. The proposed mathematical modeling using the floating admittance matrix method is unique, and the same can be used for all types of circuits. This method uses the partitioning technique for large network. The sum property of all the elements of any row or any column equal to zero provides the assurance to proceed further for analysis or re-observe the very first equation. This saves time and energy. The FAM method presented here is so simple that anybody with slight knowledge of electronics but understating the matrix maneuvering, can analyze any circuit to derive all types of transfer functions. The mathematical modeling using the FAM method provides leverage to the designer to comfortably adjust their design at any stage of analysis. These statements provide compelling reasons for the adoption of the proposed process and demonstrate its benefits