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A blockchain consensus mechanism that uses Proof of Solution to optimize energy dispatch and trading


Traditional centralized optimization and management schemes may be incompatible with a changing energy system whose structure is becoming increasingly distributed. This challenge can hopefully be addressed by blockchain. However, existing blockchains have not been well prepared to integrate mathematical optimization, which plays a key role in many energy system applications. Here we propose a blockchain consensus mechanism tailored to support mathematical optimization problems, called Proof of Solution (PoSo). PoSo mimics Proof of Work (PoW) by replacing the meaningless mathematical puzzle in PoW with a meaningful optimization problem. This is inspired by the fact that both the solutions to the puzzle and to an optimization problem are hard to find but easy to verify. We show the security and necessity of PoSo by using PoSo to enable energy dispatch and trading for two integrated energy systems. The results show that compared with existing optimization schemes, PoSo ensures that only the optimal solution is accepted and executed by participants. Further, compared with existing blockchains, PoSo can seamlessly incorporate mathematical optimization and minimize the workload associated with searching and verifying the optimum.

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All prices are NET prices.

Fig. 1: Flow chart of PoSo.
Fig. 2: Schematics of different optimization structures.
Fig. 3: Electricity outputs under the optimal and non-optimal dispatch patterns.

Data availability

The data relevant to system parameters and optimization results of the two IESs are available at and

Code availability

The computational code is available at


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The study is funded by National Natural Science Foundation of China (52077138).

Author information

Authors and Affiliations



S.C., J.P., Z.S. and Q.X. conceived the idea. S.C., J.P. and Z.S. developed the methods. H.M. and Z.S. developed the codes. X.L. and N.Z. provided the data. S.C., Z.Y. and C.K. provided funding. S.C. and H.M. wrote the manuscript. All authors revised the manuscript and responded to reviewer comments.

Corresponding author

Correspondence to Sijie Chen.

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The authors declare no competing interests.

Peer review

Peer review information

Nature Energy thanks Mahmoud Nabil Mahmoud and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Exchanged messages under different optimization schemes considering dishonesty.

a, Centralized. b, Hierarchical. c, Blockchain-as-coordinator. d, PoSo. An honest market operator or delegate lets all communities see a same trading price 639.9 CNY/MWh. A dishonest market operator or delegate, colluding with m1 and m6, sends m5 an electricity price of 292.4 CNY/MWh, 60% lower than that to other communities. By letting m5 see a lowered price and produce less MWh, m1 and m6 can raise the market price (from 639.9 CNY/MWh to 731.0 CNY/MWh) and their sales (see Supplementary Note 4). The supply and demand curves and the finalized trading prices and volumes of m5, m1 & m6, and the other nine communities are shown at the bottom of each sub-figure. Per the supply curves, m5 will sell 334.8 MWh at a price of 292.4 CNY/MWh or 713.2 MWh at a price of 639.9 CNY/MWh. Similarly, the finalized trading price and volume of each other community, whether manipulated or not, are also aligned with its supply or demand curve in each optimization scheme.

Supplementary information

Supplementary Information

Supplementary Figs. 1–2, Tables 1-2 and Notes 1–4.

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Chen, S., Mi, H., Ping, J. et al. A blockchain consensus mechanism that uses Proof of Solution to optimize energy dispatch and trading. Nat Energy 7, 495–502 (2022).

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