Collaborative optimal operation of transmission system with integrated active distribution system and district heating system based on semi-definite programming relaxation method

Highlights: • A collaborative optimal operation model of the transmission system is proposed. • Optimal operation of integrated ADS and DHS is considered. • The coordination between DSO and TSO is considered. • A semi-definite programming relaxation method is introduced to ensure the accuracy. The increasing installment of distributed generations (DGs) and the tight coupling between active distribution system (ADS) and district heating system (DHS) enhance the flexibility of electricity-heat integrated energy system (IES) to participate in the operation of power transmission system. The operation of transmission system will be affected by distribution company (DISCO). In this paper, a collaborative optimal operation model of transmission system is proposed considering the interaction with the district electricity-heat integrated energy systems based on a semi-definite programming relaxation method. The optimal operation problem of ADS is modeled based on AC optimal power flow (ACOPF) with second order cone (SOC) relaxation, and network constraints of DHS are considered. An iterative semi-definite programming relaxation method is utilized to ensure the solution accuracy. The effectiveness of the proposed model on improving the utilization rate of DGs and the economy is verified based on case studies.