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An Exact Linearization Method for OLTC of Transformer in Branch Flow Model

Wenchuan Wu, Zhuang Tian, Boming Zhang

arXiv:1606.00941v1eess.SYcs.SY

TL;DR

Branch-flow SOCP-OPF models omit transformers, while introducing nonlinear transformer models makes OPF non-convex. This paper uses binary expansion and big-M constraints to exactly linearize a transformer OLTC model and incorporate it into SOCP-OPF. The method is simulated on an IEEE 33-bus system under different scenarios.

  • Problem

    Branch-flow SOCP-OPF formulations omit transformers, while nonlinear transformer models make the OPF model non-convex.

    Source: §I · p. 1

  • Method

    The paper exactly linearizes the transformer OLTC model with binary expansion and big-M constraints for incorporation into SOCP-OPF.

    Source: §II · pp. 1–2, §IV · p. 2

  • Results

    The proposed method is simulated on an IEEE 33-bus system under different scenarios to demonstrate its effectiveness.

    Source: §IV · p. 2, §III · p. 2

  • Takeaways & Limitations

    The exact linearized transformer model involves few binary variables and can be incorporated into distribution-network SOCP-OPF.

    Source: §IV · p. 2

Abstract

from arXiv · show

The branch flow based optimal power flow(OPF) problem in radianlly operated distribution networks can be exactly relazed to a second order cone programming (SOCP) model without considering transformers. However, the introdution of nonlinear transformer models will make the OPF model non-convex. This paper presents an exact linearized transformer's OLTC model to keep the OPF model convex via binary expanstion scheme and big-M method. Validity of the proposed method is verified using IEEE 33-bus test system.

I. INTRODUCTION

Branch-flow SOCP-OPF formulations omit transformers, although transformers are critical to improving distribution-network voltage profiles. The paper proposes an exact linearized OLTC model for incorporation into SOCP-OPF.

I. INTRODUCTION

  • The branch-flow SOCP-OPF model omits transformers, which are critical to improving voltage profiles in distribution networks.The paper frames OPF as a means to reduce network losses and optimize voltage profiles.Source: §I · p. 1
  • Prior transformer tap-ratio models use approximations or continuous-variable relaxations that may yield suboptimal or infeasible solutions,.Source: §I · p. 1
  • The paper proposes an exact linearized transformer OLTC model for incorporation into the SOCP-OPF model.Source: §I · p. 1

II. LINEARIZATION OF TRANSFORMER’S OLTC MODEL

The section formulates transformer tap changes as discrete variables and linearizes the resulting nonlinear constraints using binary expansion and big-M constraints. The resulting mixed-integer transformer model is incorporated into an SOCP-OPF formulation.

II. LINEARIZATION OF TRANSFORMER’S OLTC MODEL

  • The transformer branch model splits the transformer into an impedance branch and a tap-changer-only branch, with the impedance unchanged from the original branch.Source: §II · p. 1
  • The transformer tap position is an integer variable, with each tap changing the turns ratio by a fixed increment within specified minimum and maximum ratios.Source: §II · p. 1
  • The method replaces products of binary variables and voltage-related variables with linear constraints using a positive large number M.The paper gives constraints for the products involving bus voltage and the transformer tap representation.Source: §II · pp. 1–2
  • Binary expansion and big-M constraints transform the nonlinear transformer constraints into mixed-integer linear constraints.The paper states that the resulting model uses few binary variables and can be incorporated into SOCP-OPF.Source: §II · pp. 1–2
  • The resulting mixed-integer SOCP-OPF minimizes active-power losses and can be solved with software such as CPLEX.Source: §II · p. 2

III. NUMERICAL EXAMPLE

The numerical example tests the proposed OPF on a modified IEEE 33-bus system with transformers and distributed generation. It reports comparisons of power losses and computation time across scenarios and compares the proposed method with an approximate method.

III. NUMERICAL EXAMPLE

  • The modified IEEE 33-bus test places transformers on branches 1-2, 2-19, 3-23, and 6-26, with distributed generation at buses 6, 14, and 29.Transformer turns ratios range from 0.95 to 1.05, and allowable bus voltages range from 0.95 p.u. to 1.05 p.u.Source: §III · p. 2
  • Six scenarios vary the tap increment or fix turns ratios to the scenario 3 results; Table I lists power losses and computation time for the proposed method and the method in.Source: §III · p. 2, Table I · p. 2
  • At a tap increment of 0.005, Table II compares turns ratios and power losses for the proposed exact method and the approximate method in.Source: §III · p. 2, Table II · p. 2

IV. CONCLUSIONS

The conclusion presents an exact linearization of the nonlinear transformer model using binary expansion and the big-M method, and reports simulation on an IEEE 33-bus system under different scenarios.

IV. CONCLUSIONS

  • Binary expansion and the big-M method exactly linearize the nonlinear transformer model using few binary variables, allowing incorporation into distribution-network SOCP-OPF.Source: §IV · p. 2
  • The proposed method is simulated on an IEEE 33-bus system under different scenarios to demonstrate its effectiveness.Source: §IV · p. 2
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