### Abstract

Phasor Measurement Units (PMUs) are starting to see increased deployment, enabling accurate measurement of power grid electrical properties to determine system health. Due to the costs associated with PMU acquisition and maintenance, it is practically important to place the minimum number of PMUs in order to achieve system complete observability. In this paper, we consider a variety of optimization models for the PMU placement problem that addresses more realistic assumptions than simple infinite-capacity placement models. Specifically, instead of assuming that a PMU can sense all lines incident to the bus at which it is placed, we impose the more realistic assumption that PMUs have restricted channel capacity, with per-unit cost given as a function of channel capacity. The optimization objective is then to minimize the total cost of placed PMUs, in contrast to their number. Further, we leverage the zero-injection bus properties to reduce the quantity and cost of placed PMUs. In formulating our optimization models, we identify a close relationship between the PMU placement problem (PPP) and a classic combinatorial problem, the set cover problem (SCP). If channel capacity limits are ignored, there is a close relationship between the PPP and the dominating set problem (DSP), a special case of the SCP. Similarly, when measurement redundancy is imposed as a design requirement, there is a close relationship between the PPP and the set multi-cover problem (SMCP), a generalized version of the SCP. These connections to well-studied combinational problems are not well-known in the power systems literature, and can be leveraged to improve solution algorithms. We demonstrate that more realistic, high-fidelity PPP optimization models can be solved to optimality using commercial integer programing solvers such as CPLEX. Specifically, run-times for all test cases, ranging from IEEE 14-bus to 300-bus test systems, are less than a second. This result indicates that the size of system that can be analyzed using state-of-the-art solvers is considerable. Further, our results call into question the need for problem-specific heuristic solution algorithms for the PPP, many of which have been proposed over the past decade. Finally, we analyze cost versus performance tradeoffs using our PPP optimization models on various IEEE test systems.

Original language | English (US) |
---|---|

Journal | Energy Systems |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Dominating set problem
- Integer programming
- Multi-channel PMUs
- PMU placement
- Set cover problem
- Set multi-cover problem

### ASJC Scopus subject areas

- Energy(all)
- Modeling and Simulation
- Economics and Econometrics

### Cite this

**On integer programming models for the multi-channel PMU placement problem and their solution.** / Fan, Neng; Watson, Jean Paul.

Research output: Contribution to journal › Article

*Energy Systems*, vol. 6, no. 1. https://doi.org/10.1007/s12667-014-0132-6

}

TY - JOUR

T1 - On integer programming models for the multi-channel PMU placement problem and their solution

AU - Fan, Neng

AU - Watson, Jean Paul

PY - 2014

Y1 - 2014

N2 - Phasor Measurement Units (PMUs) are starting to see increased deployment, enabling accurate measurement of power grid electrical properties to determine system health. Due to the costs associated with PMU acquisition and maintenance, it is practically important to place the minimum number of PMUs in order to achieve system complete observability. In this paper, we consider a variety of optimization models for the PMU placement problem that addresses more realistic assumptions than simple infinite-capacity placement models. Specifically, instead of assuming that a PMU can sense all lines incident to the bus at which it is placed, we impose the more realistic assumption that PMUs have restricted channel capacity, with per-unit cost given as a function of channel capacity. The optimization objective is then to minimize the total cost of placed PMUs, in contrast to their number. Further, we leverage the zero-injection bus properties to reduce the quantity and cost of placed PMUs. In formulating our optimization models, we identify a close relationship between the PMU placement problem (PPP) and a classic combinatorial problem, the set cover problem (SCP). If channel capacity limits are ignored, there is a close relationship between the PPP and the dominating set problem (DSP), a special case of the SCP. Similarly, when measurement redundancy is imposed as a design requirement, there is a close relationship between the PPP and the set multi-cover problem (SMCP), a generalized version of the SCP. These connections to well-studied combinational problems are not well-known in the power systems literature, and can be leveraged to improve solution algorithms. We demonstrate that more realistic, high-fidelity PPP optimization models can be solved to optimality using commercial integer programing solvers such as CPLEX. Specifically, run-times for all test cases, ranging from IEEE 14-bus to 300-bus test systems, are less than a second. This result indicates that the size of system that can be analyzed using state-of-the-art solvers is considerable. Further, our results call into question the need for problem-specific heuristic solution algorithms for the PPP, many of which have been proposed over the past decade. Finally, we analyze cost versus performance tradeoffs using our PPP optimization models on various IEEE test systems.

AB - Phasor Measurement Units (PMUs) are starting to see increased deployment, enabling accurate measurement of power grid electrical properties to determine system health. Due to the costs associated with PMU acquisition and maintenance, it is practically important to place the minimum number of PMUs in order to achieve system complete observability. In this paper, we consider a variety of optimization models for the PMU placement problem that addresses more realistic assumptions than simple infinite-capacity placement models. Specifically, instead of assuming that a PMU can sense all lines incident to the bus at which it is placed, we impose the more realistic assumption that PMUs have restricted channel capacity, with per-unit cost given as a function of channel capacity. The optimization objective is then to minimize the total cost of placed PMUs, in contrast to their number. Further, we leverage the zero-injection bus properties to reduce the quantity and cost of placed PMUs. In formulating our optimization models, we identify a close relationship between the PMU placement problem (PPP) and a classic combinatorial problem, the set cover problem (SCP). If channel capacity limits are ignored, there is a close relationship between the PPP and the dominating set problem (DSP), a special case of the SCP. Similarly, when measurement redundancy is imposed as a design requirement, there is a close relationship between the PPP and the set multi-cover problem (SMCP), a generalized version of the SCP. These connections to well-studied combinational problems are not well-known in the power systems literature, and can be leveraged to improve solution algorithms. We demonstrate that more realistic, high-fidelity PPP optimization models can be solved to optimality using commercial integer programing solvers such as CPLEX. Specifically, run-times for all test cases, ranging from IEEE 14-bus to 300-bus test systems, are less than a second. This result indicates that the size of system that can be analyzed using state-of-the-art solvers is considerable. Further, our results call into question the need for problem-specific heuristic solution algorithms for the PPP, many of which have been proposed over the past decade. Finally, we analyze cost versus performance tradeoffs using our PPP optimization models on various IEEE test systems.

KW - Dominating set problem

KW - Integer programming

KW - Multi-channel PMUs

KW - PMU placement

KW - Set cover problem

KW - Set multi-cover problem

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U2 - 10.1007/s12667-014-0132-6

DO - 10.1007/s12667-014-0132-6

M3 - Article

VL - 6

JO - Energy Systems

JF - Energy Systems

SN - 1868-3967

IS - 1

ER -