An analytical approach is presented to evaluate the impacts of price-sensitive loads on congestion in transmission network. To achieve this aim, the Lagrange multipliers (LMs) of transmission lines' power flow constraints are calculated from independent system operator's social welfare maximisation in which demand-side bidding is considered. It is shown that the LM of each congested line can be decomposed into five components. The first part is a constant value for the specified line, while the next two components are associated to generating units and the last two constitutive parts are related to load service entities (LSEs). The proposed decomposition obtains considerable information regarding the impacts of price-sensitive loads on congestion in transmission network. First, the sensitivity of congestion degree of each congested line to the bidding strategies and maximum price-sensitive demand of LSEs are indicated by weighting coefficients of the last two terms in the decomposed LM. Furthermore, the decomposition of LM to the constitutive components reveals the contribution of each generating unit and LSE to the congestion of corresponding line. The simulation results on a test system confirm the efficiency of the proposed approach.

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