In IEEE 69-bus test system, the branch from bus 43 to bus 55 is heavily loaded.
Because the reduced branch-bus incidence matrix A retains full column rank, the observability condition is naturally satisfied in the second linear stage of MILP.
Step 1 (forming matrix B and A): Form the constant Jacobian matrix B and the reduced branch-bus incidence matrix A. Step 2 (solving MILP): Solve the MILP (8) by CPLEX software.
The reason for this phenomenon is that both sides of the branch from bus 101 to bus 102 are integrated with wind power injections, which can form a symmetry effect on the branch flow distribution.
Finally, let r i,j be the branch connecting bus b i and bus b j, with x i,j, the reactance of the branch, P i,j, the power 'flowing' from b j to b i (if we neglect power loss on the transmission line, we get P i,j =−P j,i ), and c i,j, the maximum tolerable power on the branch.
For optimal power flow, branch and bus sensitivity for IEEE 14 bus wind-integrated system can be calculated.
The New Canaan branch has bus service in effect, with buses leaving stations 20 minutes before the scheduled train time.
At the same time, an auxiliary measurement vector is defined as {tilde{varvec{z}}} = { U_{i},P_{ij},Q_{ij},P_{i},Q_{i},I_{ij}^{2} } (5 where ( {tilde{varvec{z}}} in R^{m} ) is the auxiliary measurement vector; P ij and Q ij the power flow measurements of branch ij (from bus i to bus j); and ( I_{ij}^{2} ) the square of current magnitude of branch ij (from bus i to bus j).
It is achieved by introducing an auxiliary state vector: {varvec{y}} = { U_{i},K_{ij},L_{ij} } (4 where ( varvec{y} in R^{N + 2b} ) is the auxiliary state vector; N the number of buses; b the number of branches; U i = v i 2 the square of voltage magnitude; and K ij = v i v j cos θ ij and L ij = v i v j sin θ ij the contribution of branch ij (from bus i to bus j) to y.
There's also a branch near the bus and train stations.
