Quantum mechanics

Voltage

Linearization

Engineering

Reliability engineering

Power (physics)

Computer science

Active networking

Mathematical optimization

Distributed generation

Computer network

Demand response

Physics

Nonlinear system

AC power

Renewable energy

Mathematics

Karush–Kuhn–Tucker conditions

Electricity

Virtual power plant

Electrical engineering

IEEE Transactions on Sustainable Energy

Virtual power plants (VPPs) have become an effective technique to manage a growing number of flexible resources, which have posed great technical challenges to distribution system operators (DSOs). This article proposes a bi-level programming approach for the collaborative management of an active distribution network (ADN) with multiple VPPs by designing comprehensive prices for active and reactive power. The upper layer aims to minimize the overall operation cost of the ADN considering the system security and economic operation and the interactions among the power market, ADN and VPPs. The lower layer aims to maximize the benefits of each VPP agent considering various flexible resources. Then, the bi-level model is transformed into a tractable single-level problem by using a linearization method, the Karush-Kuhn-Tucker (KKT) optimality conditions, the Fortuny-Amat transformation and the strong duality theorem. Case analyses indicate that the proposed strategy can effectively enhance the system security and improve the system economic performance by introducing reactive power pricing. The implementation effect and superiority of the proposed strategy are profoundly analyzed under different scenarios and conditions, which indicates its promising application value in the industrial field.

Bi-Level Programming for Optimal Operation of an Active Distribution Network With Multiple Virtual Power Plants