Quantized Distributed Economic Dispatch for Microgrids: Paillier Encryption–Decryption Scheme

This article is concerned with the secure distributed economic dispatch (DED) problem of microgrids. A quantized distributed optimization algorithm using the Paillier encryption–decryption scheme is developed. This algorithm is designed to optimally coordinate the power outputs of a collection of distributed generators (DGs) in order to meet the total load demand at the lowest generation cost under the DG capacity limits while ensuring communication efficiency and security. First, to facilitate data encryption and reduce data release, a novel dynamic quantization scheme is integrated into the DED algorithm, through which the effects of quantization errors can be eliminated. Next, utilizing matrix norm analysis and mathematical induction, a sufficient condition is provided to demonstrate that the developed DED algorithm converges precisely to the optimal solution under finite quantization levels (and even the three-level quantization using sign transmissions). Moreover, an encryption–decryption scheme is developed based on quantized outputs, which ensures confidential communication by leveraging the homomorphic property of the Paillier cryptosystem. Finally, the effectiveness and superiority of the implemented secure distributed algorithm are confirmed through a simulated example.