IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 3, AUGUST 2013 2101 Validation of Equivalent Dynamic Model of Active Distribution Network Cell Jovica V. Milanović, Fellow, IEEE, and Samila Mat Zali, Student Member, IEEE Abstract—Paper presents an equivalent model of an active distri- bution network cell (ADNC) with distributed generation for trans- mission system stability studies. The equivalent model of ADNC comprises a converter-connected generator and a composite load model in parallel. The gray-box approach was chosen as it enables inclusion of prior knowledge about the ADNC structure into the model development, hence making the model more physically rel- evant and intuitive than a black-box or white-box model. The dy- namic equivalent model is presented in a seventh-order nonlinear quasi state space format, developed from the algebraic and dif- ferential equations describing assumed typical components of the ADNC. The developed equivalent model of ADNC was validated through small and large disturbance studies using the modified IEEE nine-bus transmission system model. Index Terms—Active distribution networks, distribution network cell, dynamic equivalent, nonlinear least-square opti- mization. LIST OF SYMBOLS Subscript of motor and generator, respectively. Voltage behind the transient reactance. -axis time constant. Bus voltage. Nominal bus voltage. Angular velocity of rotor. Angular velocity of stator. Angular frequency. Angle between and . Inertia. Reactance. Transient reactance. Mechanical and electrical torque. Manuscript received August 01, 2011; revised January 05, 2012, May 08, 2012, and August 17, 2012; accepted November 06, 2012. Date of publication December 20, 2012; date of current version July 18, 2013. Paper no. TPWRS- 00717-2011. J. V. Milanović is with the School of Electrical and Electronic Engineering, The University of Manchester, Manchester M13 9PL, U.K. (e-mail: mi- lanovic@manchester.ac.uk). S. Mat Zali is with the School of Electrical Systems Engineering, Universiti Malaysia Perlis, Kangar, Perlis, Malaysia (e-mail: samila@unimap.edu.my). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2012.2227844 Excitation voltage. Damping factor. Capacitance. Capacitor dc voltage Capacitor dc current -axis voltage and current at the grid side of converter. -axis voltage and current at the grid side of converter. -axis voltage and current at the generator side of converter. -axis voltage and current at the generator side of converter. I. INTRODUCTION T HE expansion of renewable energy resources and the changed nature (higher participation of power electronic components) of connected system loads has led to progressive changes in the dynamic behavior of power systems, both transmission and distribution. The potential impact of such changes requires development of equivalent dynamic models of parts of or whole distribution networks so that power system operators can appropriately assess their influence on overall power system dynamic behavior without modeling individual components (i.e., components connected at lower voltage levels) of the active distribution network cell (ADNC). Appro- priate dynamic equivalent reduces both the complexity of the model of the distribution network and the computation time required to run a full dynamic simulation. It offers a simple and low-order representation of the system without compromising distribution network dynamic characteristics and behavior as seen by the external grid. The main goal of dynamic equivalent is therefore to replace the actual distribution network model by a simple equivalent model which has similar dynamic characteristics. This is in essence similar to the development of an equivalent load model of the distribution network, with the only difference being higher participation of nonconventional generation technologies, in particular wind and solar. These new technologies (most of which involve a power electronics interface to the ac network) would introduce a dynamic compo- nent into the model, which may not be adequately represented by conventional dynamic load models of the network as these rely to a large extent on representing the dynamic part of the load by an induction motor model. The other issue that 0885-8950/$31.00 © 2012 IEEE