Distributed power systems complement centralized grids by coordinating distributed energy resources (DERs) to achieve regional energy self-sufficiency. Scaling such systems raises four persistent challenges: decentralized coordination, fair economic settlement, trustworthy operation, and system optimization, all without a central authority. This paper proposes Proof of Energy (PoE), a blockchain consensus mechanism that addresses these challenges through cryptographically secured, contribution-proportional node selection. In PoE, block generation rights are tied directly to real-world energy contributions, enabling distributed consensus without centralized dispatch. An Energy Contribution Unit (ECU) model is introduced to map heterogeneous energy services onto a unified value metric via scarcity-weighted normalization. A Verifiable Random Function (VRF)-based proposal mechanism then ensures selection probability is strictly proportional to node contribution, preserving fairness and resisting manipulation. Case studies validate PoE across three dimensions: grid coordination, incentive fairness, and optimization efficiency. The result is a cryptographically secured, incentive-compatible framework for decentralized value distribution in energy systems.

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