Data Based Linear Power Flow Model Investigation of a Least-Squares Based Approximation
Abstract : Linearization of power flow is an important topic in power system analysis. The computational burden can be greatly reduced under the linear power flow (LPF) model while the model error is the main concern. Therefore, various linear power flow models have been proposed in literature and dedicated to seek better linear models. Many linear power flow models are based on some kind of transformation/simplification/Taylor expansion of AC power flow equations. In this paper, numerical performance and theoretical explanation of the data-based linear power flow model are investigated. The direct least-squares method with complete orthogonal decomposition is designed for addressing collinear data and big data. The resulted linear power flow model is named as least-squares distribution factors (LSDF) and its performance is investigated in cold-start applications. It is found that LSDF is in fact an approximation of the optimal LPF with minimum mean square error. It is also proved that the LSDF can give an accurate estimation of total system losses. Comprehensive numerical testing show that the LSDF can work very well for system with large load variations. The average error of LSDF is only about 1% of the average error of power transfer distribution factor (PTDF) in numerical testing.
? The current injection method (CIM) is based on applying the KCL at each node in the system. The sum of the currents drawn from a node by the loads should be equal to the sum of the currents injected into that node from the rest of the network.
? Using load equivalent current injections, the following general formulation can be reached for a system with nodes (including all the existing phases).
? It is worthwhile mentioning that the unbalance caused by the non-existing phase C at Node 3 contributed significantly to the voltage unbalance, about 5% difference in magnitudes in phases A and B, urging the application of a three-phase analysis.
? The linearization of power flow is beneficial for solving optimization problems because it allows the optimization problems to be transformed into linear programming problems.
? The computational complexity/burden of obtaining the linear power flow model will be greatly reduced when the problem is considered on RS, especially when only infinite number of power flow solutions are included in RS.
? A straightforward way to solve problem is decomposing the problem into main- and sub-problems as and solve them iteratively.
? Non-convex programming problems need to be solved repeatedly during the iterative process.
• A three-phase version of the Newton-Raphson power flow analysis was formulated in complex form.
• Comparing the solution proposed in with the balanced case revealed that this method takes 6 iterations to converge when the maximum tolerance is , while the balanced case takes only 4 iterations to reach the same tolerance.
• A method was proposed in that uses a complex impedance base, as opposed to the conventional magnitude base, to calculate the per-unit impedances.
• A load-stepping technique was proposed in to address the convergence issue of sweepbased methods in heavily loaded feeders.
? On the contrary, there is no slack bus in the calculation of LSDF. This means that the information of all buses is considered, and this is one of the reasons for the high performances of our method.
? The PTDF based formulation is usually regarded as a large-signal sensitive power flow model, but the performance of PTDF is not robust enough as the maximum error of PTDF can reach hundreds of MW in large-scale systems.
? These methods generally show excellent performance around the AC-PF base point, and they are more common in system real-time analysis
? The performance of PTDF is basically in our expectations. Its approximation performance is also very stable, and it can also be applied in system with large perturbations.
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