Abstract
This paper addresses the voltage stability margin calculation in medium-voltage distribution networks in the context of exact mathematical modeling. This margin calculation is performed with a second-order cone (SOCP) reformulation of the classical nonlinear non-convex optimal power flow problems. The main idea around the SOCP approximation is to guarantee the global optimal solution via convex optimization, considering as the objective function the λ-coefficient associated with the maximum possible increment of the load consumption at all the nodes. Different simulation cases are considered in one test feeder, described as follows: (i) the distribution network without penetration of distributed generation; (ii) the distribution network with penetration of distributed generation; and (iii) the distribution grid with capacitive compensation. Numerical results in the test system demonstrated the effectiveness of the proposed SOCP approximation to determine the λ-coefficient. In addition, the proposed approximation is compared with nonlinear tools available in the literature. All the simulations are carried out in the MATLAB software with the CVX package and the Gurobi solver.
Highlights
Electrical distribution networks are a sub-component of the power system required for interconnecting end-users with the transmission and sub-transmission systems at the substation points [1]
After the revision of the state-of-the-art, we identify a gap in the literature regarding the voltage stability analysis, which is related to the existence of convex mathematical formulation for voltage stability analysis in AC distribution networks in the optimization context
We can observe that: (i) the injection of active power by distributed generation allows to increment the voltage stability margin about 27.92% respect to the base case (i.e., Case 1 (C1)); and (ii) the injection of reactive power allows to increase the voltage stability margin about 12.11%; its impact is lower when compared with the active power case
Summary
Electrical distribution networks are a sub-component of the power system required for interconnecting end-users with the transmission and sub-transmission systems at the substation points [1]. Its proposed voltage stability index value was calculated at each node of the distribution grid using a modified load flow method for voltage stability analysis. The authors in [9] presented the classical Newton-Raphson method’s extension based on the continuation point for voltage stability analysis in distribution networks Their numerical results showed the efficiency in the 33-nodes test feeder with low-computational effort. For the voltage stability analysis, a second-order cone programming (SOCP) formulation of the nonlinear modified optimal power flow problem in the complex domain is proposed to compute the voltage stability margin (λ-coefficient) in distribution networks. Numerical results in the 33-nodes test feeder demonstrate that the proposed SOCP model reaches the global optimum of the problem compared with multiple nonlinear solvers available in the (GAMS) [16].
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