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Multistage and decentralized operations of Chapter | 16  437






















             FIGURE 16.16 Dual residuals of sync-ADMM and async-ADMM.






















             FIGURE 16.17 Objective values of sync-ADMM and async-ADMM.

             maximum time lag among the EV agents to be bounded by L max , which in our
             case is set to 5. The minimal number of agents N min in this case is also set to
             5. Figs. 16.15 16.17 show the convergence performance of the asynchronous
             ADMM algorithm compared to the sync version with regard to primal residual,
             dual residual, and the objective value, respectively. Though it takes more steps
             to converge (74 vs 271), asynchronous ADMM can still achieve the system
             optimality with disturbances from the communication and control systems.


             16.6 Conclusion

             In this chapter, we introduce the integration strategies of EVs under micro-
             grid scenarios with the California energy, ancillary service, and DR markets.
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