### Abstract

Many problems in power systems depend on parameters, which could be stochastic variables or deterministic system control variables practically, e.g., generation outputs, nodal voltages, etc. Due to the nonlinearity of power systems, the analytical relation between system states and parameters cannot be obtained directly. Using the sampling method to evaluate the influence of parameters on system states is very powerful but time-consuming. One feasible approach is to use polynomial approximations, where the system states are approximately expressed in the form of polynomials in terms of parameters. Galerkin method can be used to identify the approximate solution with high accuracy by solving high-dimensional equations. However, if a large number of parameters are involved, solving these high-dimensional equations becomes a serious challenge. This paper proposes an innovative method for resolving these high-dimensional equations in power systems, which constructs a sequence of decoupled equations to determine the polynomial expansion coefficients. This new approach can provide a local approximation in the form of Taylor expansion at a given operation point. Although the method is general, for simplicity and good readability, we introduce the detailed process in its application to load flow problems. Case studies from 6-, 118-, and 1648-bus system show that the proposed method provides approximation more efficiently than traditional Galerkin method does, and 3-order polynomials can give very accurate results.

Original language | English |
---|---|

Article number | 7728091 |

Pages (from-to) | 3298-3307 |

Number of pages | 10 |

Journal | IEEE Transactions on Power Systems |

Volume | 32 |

Issue number | 4 |

Early online date | 1 Nov 2016 |

DOIs | |

Publication status | Published - Jul 2017 |

### Fingerprint

### Keywords

- Galerkin method
- load flow problems
- parametric problems
- perturbation method
- polynomial approximation

### ASJC Scopus subject areas

- Energy Engineering and Power Technology
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Power Systems*,

*32*(4), 3298-3307. [7728091]. https://doi.org/10.1109/TPWRS.2016.2623820

**A Novel Method of Polynomial Approximation for Parametric Problems in Power Systems.** / Zhou, Yongzhi; Wu, Hao; Gu, Chenghong; Song, Yonghua.

Research output: Contribution to journal › Article

*IEEE Transactions on Power Systems*, vol. 32, no. 4, 7728091, pp. 3298-3307. https://doi.org/10.1109/TPWRS.2016.2623820

}

TY - JOUR

T1 - A Novel Method of Polynomial Approximation for Parametric Problems in Power Systems

AU - Zhou, Yongzhi

AU - Wu, Hao

AU - Gu, Chenghong

AU - Song, Yonghua

PY - 2017/7

Y1 - 2017/7

N2 - Many problems in power systems depend on parameters, which could be stochastic variables or deterministic system control variables practically, e.g., generation outputs, nodal voltages, etc. Due to the nonlinearity of power systems, the analytical relation between system states and parameters cannot be obtained directly. Using the sampling method to evaluate the influence of parameters on system states is very powerful but time-consuming. One feasible approach is to use polynomial approximations, where the system states are approximately expressed in the form of polynomials in terms of parameters. Galerkin method can be used to identify the approximate solution with high accuracy by solving high-dimensional equations. However, if a large number of parameters are involved, solving these high-dimensional equations becomes a serious challenge. This paper proposes an innovative method for resolving these high-dimensional equations in power systems, which constructs a sequence of decoupled equations to determine the polynomial expansion coefficients. This new approach can provide a local approximation in the form of Taylor expansion at a given operation point. Although the method is general, for simplicity and good readability, we introduce the detailed process in its application to load flow problems. Case studies from 6-, 118-, and 1648-bus system show that the proposed method provides approximation more efficiently than traditional Galerkin method does, and 3-order polynomials can give very accurate results.

AB - Many problems in power systems depend on parameters, which could be stochastic variables or deterministic system control variables practically, e.g., generation outputs, nodal voltages, etc. Due to the nonlinearity of power systems, the analytical relation between system states and parameters cannot be obtained directly. Using the sampling method to evaluate the influence of parameters on system states is very powerful but time-consuming. One feasible approach is to use polynomial approximations, where the system states are approximately expressed in the form of polynomials in terms of parameters. Galerkin method can be used to identify the approximate solution with high accuracy by solving high-dimensional equations. However, if a large number of parameters are involved, solving these high-dimensional equations becomes a serious challenge. This paper proposes an innovative method for resolving these high-dimensional equations in power systems, which constructs a sequence of decoupled equations to determine the polynomial expansion coefficients. This new approach can provide a local approximation in the form of Taylor expansion at a given operation point. Although the method is general, for simplicity and good readability, we introduce the detailed process in its application to load flow problems. Case studies from 6-, 118-, and 1648-bus system show that the proposed method provides approximation more efficiently than traditional Galerkin method does, and 3-order polynomials can give very accurate results.

KW - Galerkin method

KW - load flow problems

KW - parametric problems

KW - perturbation method

KW - polynomial approximation

UR - http://www.scopus.com/inward/record.url?scp=85021304829&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1109/TPWRS.2016.2623820

U2 - 10.1109/TPWRS.2016.2623820

DO - 10.1109/TPWRS.2016.2623820

M3 - Article

VL - 32

SP - 3298

EP - 3307

JO - IEEE Transactions on Power Systems

JF - IEEE Transactions on Power Systems

SN - 0885-8950

IS - 4

M1 - 7728091

ER -