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• A novel coordination scheme for Wind, PV and battery energy storage systems; • A multiple objective control framework which transforms the control objectives into BESS's set points; • A containment control approach for distributed control of BESS to allow the co-achievement of four objectives; • Finite time convergence of the distributed control is achieved to allow parametric prescription of the convergence time. This paper proposes a finite time containment control scheme to achieve distributed control of a weak grid which is integrated with photovoltaic (PV), wind turbine (WT) and battery energy storage system (BESS). Taking advantage of the containment control in multi-dimensional control, we proposed a multi-objective control scheme of the WT-PV-BESS system in a weak grid, wherein four control objectives are specified, namely, bus voltage regulation, grid frequency control, peak load shaving and economic benefits optimization for the system operator. Firstly, the sizing approach of BESSs to fulfill the operation mission requirements is proposed; meanwhile, the general coordination strategy for the PV, WT and BESS to achieve the demand–supply balance is proposed. Subsequently, the predefined four control objectives are modeled and transferred into the long/short time frame operational constraints of the BESSs. Afterwards, the finite time containment control algorithm is proposed to force the BESSs into achieving containment status within prescribed time. Simulation case studies are conducted on a modified IEEE 9-bus system to show the effectiveness and performance of the proposed scheme. [ABSTRACT FROM AUTHOR]