A Linearized Branch Flow Model Considering Line Shunts for Distribution System and Its Application in Volt/VAr Control

Abstract

With the fast expansion of the power grid and increasing complexity due to modern equipment, power flow models with non-convexity and long computing time are not suitable for network calculation and optimization problems. Therefore, this paper proposes a linearized branch flow model (LBF) considering line shunts (LBFS). The strength of LBF lies in its linear mathematical structure, and hence the convex nature, which is primarily achieved by regarding the apparent power flow as the branch current magnitude. Moreover, the calculation accuracy in nodal voltage magnitude is significantly improved by appropriately modeling line shunt admittances and network equipment like transformers, shunt capacitors and distributed generators (DG). We show the application scope of LBFS by controlling the network voltages through a two-stage stochastic optimization Volt/VAr control (VVC) problem considering DG output uncertainty. Since LBFS results in a linear VVC program, the global solution is guaranteed. Simulations show that VVC framework can optimally dispatch the discrete control devices, viz. substation transformers and shunt capacitors, and also optimize the decision rules for real time reactive power control of DGs. Besides, the computing efficiency is significantly improved compared to traditional VVC methods.

A Linear Distflow Model Considering Line Shunts

“…Four linear models are introduced to test LinDistS's performance: (i) LBFS from [17]; (ii) LPFS from [9]; (iii) A linear branch flow model (LBFMS) is modified through ignoring squared branch current terms, ℓ jk , in [14]; (iv) A linear load flow model (LLFS) is extended to consider line shunts through the modification of the admittance matrix in [21]. According to Table I, LinDistS shows a 80% improvement than LinDist in accuracy of nodal voltage magnitude, which is highly required in large PDS.…”

“…In this case, linear models are highly required for higher efficiency, strong duality and better accuracy in case of reverse power flow. A linear BFM with line shunts (LBFS) is proposed in [17] to replace BFMS considering the effect of reverse power flow, but LBFS shows relatively large errors in branch flow as it regards apparent power flow as current magnitude. Thus, we propose a modified linear Distflow model with line shunts (LinDistS) in this brief with a decent calculation accuracy to address model errors caused by the capacitive susceptance of line shunts.…”

A Linear Distflow Model Considering Line Shunts

“…Four linear models are introduced to test LinDistS's performance: (i) LBFS from [21]; (ii) LPFS from [9]; (iii) A linear branch flow model (LBFMS) is modified through ignoring squared branch current terms, ℓ jk , in [14]; (iv) A linear load flow model (LLFS) is extended to consider line shunts through the modification of the admittance matrix in [22]. According to Table I, LinDistS shows a 80% improvement than LinDist in accuracy of nodal voltage magnitude, which is highly required in large PDS.…”

“…In this case, linear models are highly required for higher efficiency, strong duality and better accuracy in case of reverse power flow. A linear BFM with line shunts (LBFS) is proposed in [17] to replace BFMS considering the effect of reverse power flow, but LBFS shows relatively large errors in branch flow as it regards apparent power flow as current magnitude. Thus, we propose a modified linear Distflow model with line shunts (LinDistS) in this brief with a decent calculation accuracy to address model errors caused by the capacitive susceptance of line shunts.…”

A Linear Distflow Model Considering Line Shunts

“…Four linear models are introduced to test LinDistS's performance: (i) LBFS from [21]; (ii) LPFS from [9]; (iii) A linear branch flow model (LBFMS) is modified through ignoring squared branch current terms, ℓ jk , in [14]; (iv) A linear load flow model (LLFS) is extended to consider line shunts through the modification of the admittance matrix in [22]. According to Table I, LinDistS shows a 80% improvement than LinDist in accuracy of nodal voltage magnitude, which is highly required in large PDS.…”