Power-system dynamic equivalents:coherency recognition via the rate of change of kinetic energy

Abstract

The coherency aggregation method has proved very successful in the determination of dynamic equivalents of sections of a power system, its main drawback being the extensive computation times required to recognise the coherent groups with full-time simulation. The paper demonstrates the advantages of using the new 'rate of change of kinetic energy' method for coherency recognition in relation to other existing methods. A fault is applied on the power system, an approximate critical clearance time is obtained and machine conditions at that stage are used for recognition. Studies in a large power system are reported. Equivalents are obtained and compared with those produced through full simulation and with the method of the singular points. The effect of fault location on the equivalents obtained is reported. The transient responses of the equivalents produced by the different methods are compared with those of the original system. List of symbols RKE = rate of change of kinetic energy P m . = mechanical power of the ith machine P e . = electrical power of the / th machine p = d/dt derivative CJ,-= machine speed 6,-= internal machine angle co 0 = synchronous speed n = number of machines [/] = vector of nodal currents [Y] = admittance matrix [V] = vector of nodal voltages li = complex value of injected current V t = complex value of nodal voltage M t = inertia a t = post fault acceleration of the ith machine

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

“…Sastry and Varaiya in [62] used the linear model of the system as well as decoupled load flow to find the coherency in the system. On the basis of the rate of change of kinetic energy, Rudnick proposed a method in [63], which requires a priori knowledge of the critical clearing time. Wu and Narasimhamurthi [12] also proposed a method for coherency detection using the linear model of the system without solving the swing equations.…”

“…In addition to the above clustering methods, there are also several papers that have used a simple rule to group the generators [40, 42, 63, 82, 88, 89]. On the basis of this rule, if generator i is coherent with generator j and generator k is coherent with generator j , then it follows that generators i and k are coherent.…”

“…steps 2–6, are approximately the same for all of them. Kim et al [40], de Souza and da Silva [42] and Rudnick et al [63], as the only model‐based studies in this class, have used relation error (obtained from Euclidean distance between relation matrices of generators), the difference between angular speed deviation of generators, and rate of change of kinetic energy as coherency measures, respectively, which are all obtained from linearising the system. On the other hand, Kim et al [82] and Aghamohammadi and Tabandeh [89] as measurement‐based methods have used the Euclidean distance between rotor angle variations of generators and the correlation coefficient of the vector of these variations as the coherence measure, respectively.…”

Power systems transient stability indices: an algorithm based on equivalent clusters of coherent generators

“…In [12], the authors determine the coherency for on-line applications, taking the measured velocity of the generators shaft combined with Fourier analysis. Kinetic energy and acceleration [13] and rate of change of kinetic energy [14] have also been used as a coherency criterion. These methods can be classified into two categories: methods that use the solution of the swing equations, with or without linearisation, are more secure but not suitable for on-line applications, and methods that are based on transient energy functions and the equilibrium points are less secure but faster and can be used for on-line operation.…”

Comparative study of clustering techniques for real‐time dynamic model reduction

“…. , g m }, is coherent if their difference in voltage angles is constant over time, i.e., there exists a c ∈ R such that δ g i (t) − δ g j (t) = c for all t ≥ 0 and g i , g j ∈ G. Coherency can be determined using a linearized model around an operating point [21,24] or by analyzing offline simulated dynamics [22]. Either way, it is not capable of capturing real-time operating conditions, which renders the reduced model useless for timely analysis.…”