In this paper, we propose centralized and decentralized privacy-preserving and collusion-resistant charging coordination schemes for Energy Storage Units (ESUs). The centralized charging coordination (CCC) scheme is useful where robust communication infrastructure is available that connects ESUs to a charging coordinator (CC), whereas the decentralized charging coordination (DCC) scheme is useful in remote areas and isolated microgrids. In CCC scheme, ESUs acquire tokens to send charging request anonymously to the CC via local aggregators. So, if the CC and the aggregator collude, they cannot identify requests' senders. To prevent linkability attacks, ESUs sends multiple requests with random Time to complete charge (TCC) and state of charge (SoC). Then, the CC compute schedules to maximize the power delivered to ESUs. In DCC scheme, charging is coordinated using a privacy-preserving data aggregation technique. Each ESU selects some ESUs as proxies, and shares a secret mask with each proxy. Then, each ESU adds a mask to its request and encrypts it so by aggregating requests, all masks are nullified and the total demand is known. DCC scheme is secure against collusion attacks due to the masking technique. The results of extensive experiments confirm that our schemes are efficient and secure, and preserve ESUs privacy.