In this paper, we study a multi-cluster Wireless Powered Communication Network (WPCN) where each cluster of users cooperate with a Cluster Head (CH) and a Hybrid Access Point (HAP). All users are equipped with multiple antennas. This HAP employs beamforming to deliver energy to the users in the downlink phase. The users of each cluster transmit their signals to the HAP and to their CHs in the uplink phase. In the next step the CHs first relay the signals of their cluster users and then transmit their own information to the HAP. We design the Energy Beamforming (EB) matrix, transmit covariance matrices of the users and allocate time slots to energy transfer and cooperation phases by optimizing the max-min and sum throughputs of the network. Our optimization is a non-convex problem which we break it to two non-convex sub-problems and solve them by employing the Alternating Optimization (AO) and the Minorization-Maximization (MM) technique. We recast the resulting sub-problems as a convex Second Order Cone Programming (SOCP) and a Quadratic Constraint Quadratic Programming (QCQP) for the max-min and sum throughput maximization problems, respectively. We take into account the consider imperfect Channel State Information (CSI) and non-linearity in Energy Harvesting (EH) circuits. Using numerical examples, we explore the impact of the proposed cooperation as well as optimal placement of CHs under various setups.