Online Voltage Stability Assessment for Load Areas Based on the Holomorphic Embedding Method

This paper proposes an online steady-state voltage stability assessment scheme to evaluate the proximity to voltage collapse at each bus of a load area. Using a non-iterative holomorphic embedding method (HEM) with a proposed physical germ solution, an accurate loading limit at each load bus can be calculated based on online state estimation on the entire load area and a measurement-based equivalent for the external system. The HEM employs a power series to calculate an accurate Power-Voltage (P-V) curve at each load bus and accordingly evaluates the voltage stability margin considering load variations in the next period. An adaptive two-stage Pade approximants method is proposed to improve the convergence of the power series for accurate determination of the nose point on the P-V curve with moderate computational burden. The proposed method is illustrated in detail on a 4-bus test system and then demonstrated on a load area of the Northeast Power Coordinating Council (NPCC) 48-geneartor, 140-bus power system.Comment: Revised and Submitted to IEEE Transaction on Power System

A Multi-Dimensional Holomorphic Embedding Method to Solve AC Power Flows

It is well known that closed-form analytical solutions for AC power flow equations do not exist in general. This paper proposes a multi-dimensional holomorphic embedding method (MDHEM) to obtain an explicit approximate analytical AC power-flow solution by finding a physical germ solution and arbitrarily embedding each power, each load or groups of loads with respective scales. Based on the MDHEM, the complete approximate analytical solutions to the power flow equations in the high-dimensional space become achievable, since the voltage vector of each bus can be explicitly expressed by a convergent multivariate power series of all the loads. Unlike the traditional iterative methods for power flow calculation and inaccurate sensitivity analysis method for voltage control, the algebraic variables of a power system in all operating conditions can be prepared offline and evaluated online by only plugging in the values of any operating conditions into the scales of the non-linear multivariate power series. Case studies implemented on the 4-bus test system and the IEEE 14-bus standard system confirm the effectiveness of the proposed method.Comment: Submitted to IEEE Transaction on Power Systems on 14-Mar-2017, Rejected, Revised and Submitted to IEEE Access on 08-Sept-201

Multi-Stage Holomorphic Embedding Method for Calculating the Power-Voltage Curve

The recently proposed non-iterative load flow method, called the holomorphic embedding method, may encounter the precision issue, i.e. nontrivial round-off errors caused by the limit of digits used in computation when calculating the power-voltage (P-V) curve for a heavily loaded power system. This letter proposes a multi-stage scheme to solve such a precision issue and calculate an accurate P-V curve. The scheme is verified on the New Eng-land 39-bus power system and benchmarked with the result from the traditional continuation power flow method.Comment: This manuscript was submitted to IEEE Power Engineering Letters, which contains 2 pages and 4 figures. Minor modifications suggested from the first round review have been addressed and the manuscript has been submitted for the second round revie

Holomorphic Embedded Load-flow Method\u27s Application on Three-phase Distribution System With Unbalanced Wyeconnected Loads

With increasing load and aging grid infrastructure, an accurate study of power flow is very important for operation and planning studies. The study involves a numerical calculation of unknown parameters, such as voltage magnitude, angle, net complex power injection at buses and power flow on branches. The performance of traditional iterative power flow methods, such as Newton-Raphson, depends on initial starting point, does not guarantee solution for heavily loaded, and poor convergence for unbalanced radial power system. Holomorphic load embedding is a non-iterative and deterministic method for finding steady-state solutions of any power system network. The method involves converting voltage parameter at every bus into an embedded parameter (a) where analytic continuation is applied using Pade\u27 approximants. The embedded parameter (a) acts as a well-defined reference for the complex analysis and solution obtained when setting a simple value a is known as Germ Solution, by some texts. Using the values of coefficient of Maclaurin Series, the Holomorphic method can find solutions in the whole complex plane using analytic continuation as it extends the nature offunction beyond the radius of convergence. The holomorphic embedding method has been applied in the past to solve power flow problems in balanced power system models. There are several advantages ofthe iv said method over traditional iterative techniques, such as guaranteed convergence, the existence of solution, and faster calculation for certain cases. The method dives into complex analysis, algebraic curves, Taylor series expansion, Pade\u27 approximants, and solving a linear set of equations. . For simplicity purpose, the networks are often assumed to be balanced with constant power loads. Power flow analysis and its derivatives are performed on a single-phase equivalent of the same system. For bulk systems, the assumption is acceptable as load aggregation balances the loads in each phase to an acceptable level. However, in low-voltage distribution systems, ignoring such parameter could lead to an incorrect solution. In this work, a class of Holomorphic load-flow method is proposed to solve the power flow problem in three-phase distribution systems with unbalanced wye-connected loads