Generator Coherency and Network Partitioning for Dynamic Equivalencing Using Subtractive Clustering Algorithm

Taxonomy of coherency detection and coherency‐based methods for generators grouping and power system partitioning

“…Another point that arises when considering these methods as model‐based is that the linearised models are obtained assuming that the coherent groups of generators are independent of the magnitudes of disturbances. However, as it is shown in [47, 48], the generator grouping can be affected by disturbance severity and location.…”

“…For two real signals, correlation varies from −1 to +1, which means that two perfectly similar signals (that can be associated to rotor angle signals of two coherent generators) have the correlation equal to +1. Considering this fact, the authors in [48, 86–90] used the correlation coefficients of time‐varying signals for assessing the coherency between generators and non‐generating buses, whereas in [91] the correlation between frequency spectrums and in [47] the correlations between real and imaginary parts of the frequency spectrum of swing curves have been used for coherency detection.…”

“…In the first step, the degree of coherency between generators is calculated and, then, in the second step, algorithms such as clustering methods are used to group the generators. Examples of such clustering methods are fuzzy c‐means (FCM) [27, 75, 79, 83, 84], KM [44, 46, 111, 116], k‐harmonic means [117], subtractive clustering [47], partitioning around medoids [78], support vector clustering [73, 74], HC [80, 103], artificial neural network (ANN) [72], growing self‐organising feature maps [104, 115] and multi‐flock‐based approach [76, 77]. As an example, the KM algorithm uses an iterative procedure to place the generators in a predefined number of groups as follows: 1: Initialise c i cluster centres randomly. 2: Determine the membership of each datapoint (bus or generator) with respect to each cluster centre using the equation below: 3: Calculate the cost function defined in (21).…”

“…In such methods, which are all of the measurement‐based type, instead of rotor angles or speed signals, the coherency between generators is assessed using the phase angle or voltage magnitude variation at terminal buses. For example, in [47], after calculating the degree of coherency between buses using the post‐disturbance phase angle variations, subtractive clustering is used to partition the system into areas. The same approach is utilised in [79], where FCM clustering is used to group the buses.…”

Channel Measurements and Modeling at 6 GHz in the Tunnel Environments for 5G Wireless Systems

“…In addition, some important arrival angles are extracted based on subtractive clustering algorithm [51] as shown in Table 5. These parameters presented here can be used for wireless communication system design in indoor environments and can be used for adaptive transmission technologies for 5G wireless network.…”