Analysis of Shadow Price of System Power Balance Constraint under Quasi-steady-state Sensitivity

The shadow price of power balance constraint in SCED model represents the marginal cost of slight increase of load, which is of great significance in electricity spot market clearing. Aiming at the problem that the shadow price of system power balance constraint under conventional sensitivity matrix is highly dependent on the selection of reference bus, the systematical analysis of the shadow price of system power balance constraint under quasi-steady-state sensitivity matrix is carried out, which has been reported rarely. In this paper, on the basis of the basic models of optimal clearing and marginal pricing in spot market, the quantitative impact of the reference bus selection on nodal price and the shadow price under conventional sensitivity matrix is analyzed. On this basis, based on the definition and features of quasi-steady-state sensitivity matrix, it is revealed and proved theoretically that the shadow price of system power balance constraint under quasi-steady-state sensitivity is actually the linear weighted average of nodal price at each bus under a certain weight, when ignoring the network loss. The linear weight is just the linear distribution coefficient vector used to form quasi-steady-state sensitivity matrix. Moreover, the expressions of the energy component and congestion component of shadow price are deduced. Finally, a numerical case is given to verify the conclusions put forward.