The desire to overcome reliability issues of distributed energy resources (DERs) lead researchers to development of a novel concept named as virtual power plant (VPP). VPPs are supposed to carry out intelligent, secure, and smart energy trading among prosumers, buyers, and generating stations along with providing efficient energy management. Therefore, integrating blockchain in a decentralized VPP network emerged as a new paradigm, and recent experiments over this integration have shown fruitful results. However, this decentralization also suffers with energy management, trust, reliability, and efficiency issues due to the dynamic nature of DERs. In order to overcome this, in this paper, we first work over providing an efficient energy management strategy for VPP to enhance demand response, then we propose an energy oriented trading and block mining protocol and name it as proof of energy market (PoEM). To enhance it further, we integrate differential privacy in PoEM and propose a Private PoEM (PPoEM) model. Collectively, we propose a private decentralized VPP trading model and named it as Virtual Private Trading (VPT) model. We further carry out extensive theoretical analysis and derive step-by-step valuations for market race probability, market stability probability, energy trading expectation, winning state probability, and prospective leading time profit values. Afterwards, we carry out simulation-based experiments of our proposed model. The performance evaluation and theoretical analysis of our VPT model make it one of the most viable models for blockchain based VPP networks as compared to other state-of-the-art works.