A Data-Driven Optimal Power Flow Model under Partial Observability

doi:10.11930/j.issn.1004-9649.202306041

Abstract

Abstract:

The linearized power flow (PF) model is mainly used to make the optimal power flow (OPF) problem convex. However, existing data-driven linear PF models are mostly based on complete system measurement data. Moreover, the systems are usually partially observable due to limited measuring devices for economical installation. This paper addresses the partial observability issue by proposing a data-driven linear PF model, which can be embedded in OPF. The model is robust against bad data in measurements, with its accuracy verified by numerical tests.

Key words: data-driven, linear optimal power flow (OPF) model, partial observability

Penghua LI, Zhuoran SONG, Wenchuan WU. A Data-Driven Optimal Power Flow Model under Partial Observability[J]. Electric Power, 2023, 56(12): 51-57.

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URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202306041

https://www.electricpower.com.cn/EN/Y2023/V56/I12/51

Figures/Tables 13

References 26

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场景	类型	可观测部分	不可观测部分
一	节点	1~15, 19, 20, 23, 26~31	16~18, 21, 22, 24, 25, 32, 33
一	支路	1—2, 2—3, 3—4, 4—5, 5—6, 6—7, 7—8, 8—9, 9—10, 10—11, 11—12, 12—13, 13—14, 14—15, 2—19, 19—20, 3—23, 6—26, 26—27, 27—28, 28—29, 29—30, 30—31	15—16, 16—17, 17—18, 20—21, 21—22, 23—24, 24—25, 31—32, 32—33
二	节点	1~8, 11~15, 19, 20, 23, 26~31	9, 10, 16~18, 21, 22, 24, 25, 32, 33
二	支路	1—2, 2—3, 3—4, 4—5, 5—6, 6—7, 7—8, 10—11, 11—12, 12—13, 13—14, 14—15, 2—19, 19—20, 3—23, 6—26, 26—27, 27—28, 28—29, 29—30, 30—31	15—16, 16—17, 17—18, 20—21, 21—22, 23—24, 24—25, 31—32, 32—33, 8—9, 9—10

场景	类型	可观测部分	不可观测部分
一	节点	1~15, 19, 20, 23, 26~31	16~18, 21, 22, 24, 25, 32, 33
一	支路	1—2, 2—3, 3—4, 4—5, 5—6, 6—7, 7—8, 8—9, 9—10, 10—11, 11—12, 12—13, 13—14, 14—15, 2—19, 19—20, 3—23, 6—26, 26—27, 27—28, 28—29, 29—30, 30—31	15—16, 16—17, 17—18, 20—21, 21—22, 23—24, 24—25, 31—32, 32—33
二	节点	1~8, 11~15, 19, 20, 23, 26~31	9, 10, 16~18, 21, 22, 24, 25, 32, 33
二	支路	1—2, 2—3, 3—4, 4—5, 5—6, 6—7, 7—8, 10—11, 11—12, 12—13, 13—14, 14—15, 2—19, 19—20, 3—23, 6—26, 26—27, 27—28, 28—29, 29—30, 30—31	15—16, 16—17, 17—18, 20—21, 21—22, 23—24, 24—25, 31—32, 32—33, 8—9, 9—10

相对误差	$ \varphi $	场景一		场景二
相对误差	$ \varphi $	平均误差	最大误差	平均误差	最大误差
P_ij	A	1.89×10^–3	6.59×10^–3	1.59×10^–3	7.07×10^–3
	B	1.18×10^–3	5.27×10^–3	2.27×10^–3	1.39×10^–2
	C	1.35×10^–3	7.22×10^–3	1.97×10^–3	8.34×10^–3
Q_ij	A	6.80×10^–3	1.43×10^–2	9.32×10^–3	1.84×10^–2
	B	4.65×10^–3	1.56×10^–2	8.09×10^–3	1.92×10^–2
	C	5.25×10^–3	1.49×10^–2	7.23×10^–3	1.72×10^–2
V	A	3.68×10^–4	8.06×10^–4	4.47×10^–4	9.30×10^–4
	B	3.90×10^–4	9.41×10^–4	5.29×10^–4	1.20×10^–3
	C	4.01×10^–4	8.93×10^–4	5.04×10^–4	1.14×10^–3

相对误差	$ \varphi $	场景一		场景二
相对误差	$ \varphi $	平均误差	最大误差	平均误差	最大误差
P_ij	A	1.89×10^–3	6.59×10^–3	1.59×10^–3	7.07×10^–3
	B	1.18×10^–3	5.27×10^–3	2.27×10^–3	1.39×10^–2
	C	1.35×10^–3	7.22×10^–3	1.97×10^–3	8.34×10^–3
Q_ij	A	6.80×10^–3	1.43×10^–2	9.32×10^–3	1.84×10^–2
	B	4.65×10^–3	1.56×10^–2	8.09×10^–3	1.92×10^–2
	C	5.25×10^–3	1.49×10^–2	7.23×10^–3	1.72×10^–2
V	A	3.68×10^–4	8.06×10^–4	4.47×10^–4	9.30×10^–4
	B	3.90×10^–4	9.41×10^–4	5.29×10^–4	1.20×10^–3
	C	4.01×10^–4	8.93×10^–4	5.04×10^–4	1.14×10^–3

相对误差	$ \varphi $	场景一		场景二
相对误差	$ \varphi $	平均误差	最大误差	平均误差	最大误差
P_ij	A	2.46×10^–3	9.86×10^–3	1.74×10^–3	8.21×10^–3
	B	1.99×10^–3	6.61×10^–3	2.78×10^–3	1.42×10^–2
	C	1.92×10^–3	6.02×10^–3	2.19×10^–3	1.67×10^–2
Q_ij	A	6.40×10^–3	3.28×10^–2	2.66×10^–3	8.94×10^–3
	B	5.54×10^–3	2.90×10^–2	4.28×10^–3	2.06×10^–2
	C	9.85×10^–3	2.41×10^–2	3.80×10^–3	1.82×10^–2
V	A	4.85×10^–4	1.76×10^–3	2.15×10^–4	6.81×10^–4
	B	2.16×10^–4	9.90×10^–4	1.15×10^–4	5.35×10^–4
	C	4.43×10^–4	1.14×10^–3	1.39×10^–4	7.31×10^–4