Power System Dynamic Equivalents Research Articles

A review of power system dynamic equivalents for transient stability studies

The increasing complexity of interconnected power system has brought challenges to detailed dynamic simulation in terms of computational effort. Therefore, for transient stability assessment, dynamic equivalents of parts of large-scale system are required to capture the electromagnetic transients. This paper presents a review of past research on dynamic equivalencing using coherency-based methods and system identification methods. Future topics are discussed to improve the state-of-art approaches.

Partial Y-Bus Factorization Algorithm for Power System Dynamic Equivalents

This paper presents a partial Y-bus factorization algorithm to reduce the size of a power system model for transient stability analysis. In the proposed approach, steady-state operating conditions for dynamic equivalents are maintained using the traditional Ward admittance method. Fictitious generators are attached at boundary buses to preserve transient behavior following a disturbance. The equivalent dynamic effects from eliminated generators can be maintained by choosing appropriate dynamic parameters of fictitious generators, including machine inertia, transient reactance, and the damping coefficient. Parameters are determined using the idea that the contributions from external generators mostly depend on the network configuration and impedance characterized by the Y-bus matrix. The fictitious generators’ dynamic parameters are determined by conducting partial Y-bus factorization on dynamic parameter matrices. The proposed method’s performance is validated by conducting case studies with the IEEE 118-bus system and a 10,000 synthetic western U.S. power grid model and comparing simulation outcomes between the full system and reduced equivalent models. Simulation comparisons show that the equivalent model maintains high accuracy. The proposed method is promising alternative solution for power system dynamic equivalents.

Heuristic optimization based approach for identification of power system dynamic equivalents

This paper introduces an approach for identification of dynamic equivalent parameters from measured operational dynamic responses associated to different disturbances. To tackle challenges related to optimization problem complexity (i.e., non-linearity of time-domain simulation based fitness calculation, discontinuity, non-convexity, and multimodality), the approach adopts a novel variant of the mean-variance mapping optimization algorithm to pursue efficient and fast search capability. This variant bases on swarm intelligence precepts and employs a multi-parent crossover criterion for offspring creation. Numerical tests performed on the Ecuadorian–Colombian interconnected system, including performance comparisons with other heuristic optimization tools, support the potential of the proposal to provide accurate estimates within a fast convergence rate.

Aggregation of exciter models for constructing power system dynamic equivalents

Constructing a dynamic equivalent for a power system involves several steps: the partition of the system into coherent areas, the coherent area aggregation, and the aggregation of the coherent generators and their control devices. In this paper we investigate the aggregation of exciter models. A trajectory sensitivity method is used to tune the aggregate exciter parameters of the reduced model. The optimal results are used to evaluate the aggregation from the DYNRED program and a weighted MVA method. A three-machine system with one coherent area satisfying the theoretical coherency conditions is used to investigate the impact of the variations of the individual generator, network, and exciter parameters on the aggregate exciter model parameters. The results are then applied to the exciter aggregation of a larger 48-machine system.

モード法による電力系統の新しい縮約論理

Power system dynamic equivalents play an important role in the effort to reduce the computational burden of the transient stability analysis of power systems. This paper proposes a new efficient practical algorithm for forming linear dynamic equivalents for power systems based on modal analysis. The main feature of the proposed method is that the accuracy of the equivalent model is greatly improved by converting a coordinate system representing the subsystem from the R-J coordinate system of the main system to the reference generator D-Q coordinate system of the subsystem. The order reduction is based on aggregation of similar modes and elimination of the inferior modes without significant effect on the frequency response of the subsystem. Thus the equivalent obtained by the proposed method can be used for both steady-state and transient stability analysis studies. To verify the dynamic equivalent performance stability simulation results for a model power system composed of 16 generators also are shown.

Inertial Averaging Aggregation Method for Producing Power System Dynamic Equivalents

ABSTRACT An optimal aggregation problem is formulated in this paper utilizing a performance measure similar to the rms coherency measure for a short simulation interval [18] and a probabilistic step or pulse disturbance restricted to the study system. The form of the optimal equivalent obtained by mini-mizing this performance index is the inertial averaging equivalent found in the present dynamic equivalent package [1 ]. The inertial averaging aggregation method is optimal for simulation of the first swing for dynamic equivalents, where disturbances are restricted to a bus or subregion respectively. Computational results on the 33 bus New England system confirm that the inertial averaging equivalent is more accurate in preserving the first swing but that optimal modal coherent/singular perturbation equivalents are more accurate in simulation beyond 1 second; preservation of load flow; and preservation of eigenvalues from the unreduced model. This Paper justifies the use of inertial averaging for analysis ...

Coherency identification for power system dynamic equivalents

Coherency-based approach to the problem of constructing power system dynamic equivalents has been very successful in applications. The key step in this approach is to identify groups of coherent generators. An analytic study of coherency is conducted. An algebraic characterization of coherency is given. An algorithm, based on the algebraic characterization, to identify coherent groups directly from system data is developed. A physical interpretation of the algebraic characterization of coherency is presented, where the condition for coherency is described in terms of generator inertia constants and their equivalent admittances to the bus of the disturbance.

Structure-preserving model reduction with applications to power system dynamic equivalents

Consider systems that have an intrinsic mathematical representation of the form: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{n}x^{(n)}+ \cdots + A_{0}x = Bu</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x^{(i)}</tex> is the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> th derivative of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x^{(i)}(0)= 0, i = 1, \cdots , n-1</tex> . The matrices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{i}</tex> may possess certain properties. The problem is to construct a reduced model having the same form with corresponding matrices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{A}_{i}</tex> of smaller dimension and possessing the same properties. An algorithm for this structure-preserving model reduction is presented. An algorithm for constructing an approximate reduced model, called <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon</tex> -structure preserving reduced model is also presented, together with the error bounds. The application of the method to power system dynamic equivalents is described.

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

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

Construction of Power System electromechanical Equivalents by Modal Analysis

This paper presents an analytical approch to the construction of power system dynamic equivalents for use in stability calculations and dynamic simulations. The method presented is capable of accurately representing the dynanlical effects of generator field and amortisseur windings, voltage regulators, and speed governors. Experimental evaluation of equivalents constructed by this method is reported in a companion paper.