Microgrid is a new power system concept consisting of small-scale distributed energy resources; storage devices and loads. It is necessary to employ a simplified model of microgrid in the simulation of a distribution network integrating large-scale microgrids. Based on the detailed model of the components, an equivalent model of microgrid is proposed in this paper. The equivalent model comprises two parts: namely, equivalent machine component and equivalent static component. Equivalent machine

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... omponent describes the dynamics of synchronous generator, asynchronous wind turbine and induction motor, equivalent static component describes the dynamics of photovoltaic, storage and static load. The trajectory sensitivities of the equivalent model parameters with respect to the output variables are analyzed. The key parameters that play important roles in the dynamics of the output variables of the equivalent model are identified and included in further parameter estimation. Particle Swarm Optimization (PSO) is improved for the parameter estimation of the equivalent model. Simulations are performed in different microgrid operation conditions to evaluate the effectiveness of the equivalent model of microgrid. Microgrid should operate under connected mode most time to take full advantages of distributed generator. Compared with the distribution network, microgrid can be seen as a controlled load or a controlled electric source under this operation mode. In connected mode, the interactions between loads and distributed generations can be ignored, and the microgrid synthesized dynamic characteristics will be considered in the simulation of distribution network. Distributed generation is the basis of microgrid; if the equivalent model of the distributed generation is utilized, dynamic simulation of the microgrid can be simplified. An equivalent model compared with the detailed model of the photovoltaic was discussed in [6] , and the equivalent model could well describe the dynamic characteristics of the photovoltaic under different faults in power grid. The authors of [7, 8] proposed a photovoltaic source dynamic model, the parameters of which were identified based on a least-squares regression-based data processing algorithm. The singular perturbations theory was applied to reduce the model order of the wind farm in [9] , and the dynamics of the reduced-order model matched well with those of the detailed model under different operational conditions. Aggregate modeling and detailed modeling for the transient interaction between a large wind farm and a power system were discussed in [10] , and the aggregate modeling decreased the simulation time without significantly compromising the accuracy in different conditions. In [11, 12] , an equivalent method was proposed for integrating wind power generation system in power flow and transient simulation, the unit plants equivalent method and the multiply equivalent method were used for the power flow calculation and transient dynamics simulation, respectively. A probabilistic clustering concept for aggregate modeling of wind farms was proposed in [13] , the support vector clustering technique was used to cluster wind turbines based on wind farm layout and incoming wind. Due to the short distances of the electric circuits in the microgrid, there is a strong electromagnetic coupling between the electrical components. These characteristics increase the difficulty in the microgrid analysis. A generalized homology equivalence theory based on differential geometry was used for the microgrid equivalent modeling in [14] , and the mathematical analysis of its reduced-order nature was discussed. Parameter estimation method is a very difficult and challenging task in system modeling. Recently, global optimization techniques such as genetic algorithm [15] , evolutionary algorithm [16] and differential evolution [17] have been proposed to solve the parameter estimation problems. Though the genetic algorithm (GA) was employed successfully to solve complex non-linear optimization problems, some deficiencies of GA have been identified in recent research [18] . This degradation in efficiency is apparent when the parameters being optimized are highly correlated and the premature convergence of the GA degrades its performance in terms of reducing the search capability. Particle swarm optimization (PSO) is an evolutionary computation technique in nature motivated by the simulation of social behaviors. In searching the optimal solution of a problem, information of the best position of each individual particle and the best position among the whole swarm are used to direct the searching. Due to the simple concept, easy implementation and quick convergence, nowadays PSO has gained much attention and wide applications in different fields. Authors of papers [19] [20] [21] [22] [23] [24] showed that PSO is a feasible approach to parameter estimation of nonlinear systems. In [19] , PSO was applied in harmonic estimation. A modified PSO was utilized in the maximum power point tracking for the photovoltaic system in [20] . In the field of parameter estimation, PSO-based parameter estimation technique of proton exchange membrane fuel cell models was proposed in [21] , and PSO with quantum was introduced successfully in synchronous generator offline and online parameters estimation problem. Parameter estimation of an induction machine using PSO was shown in [22] , and the dynamic PSO and chaos PSO were better than the standard PSO. PSO was used for jointly estimating both the parameters and states of the lateral flow immunoassay model in [23] . Diffusion particle swarm optimization was proposed to optimize the maximum likelihood function in [24] , and the PSO technique has been shown to provide a good solution to bearing estimation as it alleviates the effects of multi-modality.