Criterion to evaluate power system online transient stability based on adjoint system energy function

Abstract

In this paper, a new criterion to quickly evaluate the system transient stability based on wide area measurement system (WAMS) information, energy function method and adjoint power system (APS) model is proposed. APS is a two-dimensionalfirst-order differential equation model, which can be considered as a virtual representation to the real power system. Meaning of APS is first explained by using the one machine infinite bus system. Then, a new criterion based on projection kinetic energy of APS is proposed to determine the transient stability of the original power system with multiple generators. Trajectory prediction method based on curve fitting technique is adopted to accelerate the evaluation process. The proposed method is sufficiently rapid since it does not rely on the network structure, system model, system parameters and the identification of the coherent generator groups. Therefore, it can be utilised for online transient stability assessment based on WAMS. Simulation results on the New England system and one of North China Power System validate the correctness and effectiveness of the proposed method. Nomenclature Minertia constant of OMIB system M i inertia constant of ith generator P mi mechanical power output of ith generator P ei electrical power output of ith generator P e1 electrical power output of the generator in pre-fault P e2 electrical power output of the generator in fault P e3 electrical power output of the generator in post-fault t system time t cl fault clearing time Δt sampling time interval of WAMS α rotor acceleration of OMIB system α i ith rotor acceleration in COI reference δ rotor angle of OMIB system δ re maximum rotor angle of OMIB system in a stable swing δ cr critical rotor angle of OMIB system θ i ith rotor angle in centre of inertia (COI) reference ω rotor speed of OMIB system v i ith rotor speed in COI reference

Sensitivity‐based approach for real‐time evaluation of transient stability of wind turbines interconnected to power grids

“…For any given fault-on trajectory, the reactance terms in (17)- (19) are constant, and as a result, (17) and (19) describe that P max and T max are related to two parameters: the voltage source behind transient reactance and voltage terminal. According to (2) and 5, the sensitivity of TEF for SG and DFIG to P max and T max can be generally presented as follows:…”

“…where ψ i SG and ψ i d f ig are two interim variables that expresses bus voltage or transient emf before reactance. To more simplifying (31), from (1) and (6), it can be written as follows: (32) According to [17], the sensitivity of pω i SG to each dynamic parameter is assumed zero especially in the first steps after the fault occurrence. This is due to the fact that rotor angle can be approximated by second-order Taylor expansion.…”

Augmentation of transient stability margin based on rapid assessment of rate of change of kinetic energy

“…Reinsertion of the brake at this point would limit the increase in the disturbance in angular velocity of the machine. In this case, the brake should be removed at point Br 2 , which is a similar condition to that of the single insertion, given in (13). Using the single machine connected to infinite bus model given in (1), the optimum brake insertion/removal conditions can be proved mathematically as detailed below.…”

“…Recently, a method for the online transient instability detection that is based on a concept called adjoint power system was reported in [13]. This method virtualizes the original system and represents all generators as a unit mass ball rolling on a concave is claimed to be sufficiently rapid and the identification of the coherent generator groups is not a requirement.…”

Partition‐composition method for online detection of interconnected power system transient stability

“…In an n ‐generator power system, the motion of all generators with respect to the centre of inertia (COI) reference can be described as follows [16–18] The motion of the system COI can be written as follows where, θ i = δ i − δ COI , , . δ COI , ω COI and P COI can be calculated as follows …”