Citation: Liu, J.; Liu, Y.; Qiu, G.; Shao,
X. Learning-Aided Optimal Power
Flow Based Fast Total Transfer
Capability Calculation. Energies 2022,
15, 1320. https://doi.org/10.3390/
en15041320
Academic Editors: Luis
Hernández-Callejo, Sergio
Nesmachnow and Sara Gallardo
Saavedra
Received: 30 December 2021
Accepted: 7 February 2022
Published: 11 February 2022
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Article
Learning-Aided Optimal Power Flow Based Fast Total Transfer
Capability Calculation
Ji’ang Liu
1,
*, Youbo Liu
1
, Gao Qiu
1,
* and Xiao Shao
2
1
College of Electrical Engineering Technology, Sichuan University, Chengdu 610065, China;
liuyoubo@scu.edu.cn
2
State Grid Tianfu New Area Electric Power Supply Company, Chengdu 610041, China; shaoxiao@163.com
* Correspondence: ymm_liujiang@163.com (J.L.); qiugscu@scu.edu.cn (G.Q.)
Abstract:
Total transfer capability (TTC) is a vital security indicator for power exchange among areas.
It characterizes time-variants and transient stability dynamics, and thus is challenging to evaluate
efficiently, which can jeopardize operational safety. A leaning-aided optimal power flow method is
proposed to handle the above challenges. At the outset, deep learning (DL) is utilized to globally
establish real-time transient stability estimators in parametric space, such that the dimensionality of
dynamic simulators can be reduced. The computationally intensive transient stability constraints
in TTC calculation and their sensitivities are therewith converted into fast forward and backward
processes. The DL-aided constrained model is finally solved by nonlinear programming. The
numerical results on the modified IEEE 39-bus system demonstrate that the proposed method
outperforms several model-based methods in accuracy and efficiency.
Keywords:
total transfer capability; surrogate assisted method; transient stability; deep learning;
interior point method
1. Introduction
Power systems are currently operated near their stability boundary with the significant
proliferation of interconnected grids and renewable penetration [
1
]. Therefore, online
monitoring to transfer security margin of inter-area power transfer is in urgent demand. In
the electric industry, total transfer capability (TTC), defined as maximum power exchange
allowed to withstand multifarious security contingencies, is a widespread metric to quantify
such a security margin. Limited by this issue, dispatchers generally use a conservative
constant of offline TTC to decide online operations. Undoubtedly, such TTC values can
incur the unwanted waste of line capacity and incorrect estimation to security margin. To
untie these knots, the essence is to accelerate TTC calculation.
Thus far, several approaches have been proposed to model TTC calculation [
2
–
4
].
Among them, methods with only steady-state considered are inapplicable for TTC evalua-
tion involving transient stability (TS) [
5
]. To enable TS assessment (TSA), TTC is preferred
to be modeled as TS constrained (TSC) programming problem. As the models shown
in [
6
–
10
], differential-algebraic equations (DAEs) representing system dynamics and TS
constraints are discretized throughout the time domain simulation period. And the re-
sulting differential equations are incorporated into the optimal power flow (OPF) model.
Nevertheless, as mentioned before, solving such models is quite computationally expensive
due to the high-dimensional and nonlinear DAEs involved. In light of this, under current
time-varying power grids, inefficient physics-dominated methods can be problematic for
fast TTC monitors.
Data-driven approaches have become mainstream to increase calculation speed for
security assessment in large-scale power systems [
11
–
13
]. Reference [
11
] proposed an
online measurement-based TTC estimator using the nonparametric estimation. Sun et al.
developed an automatic learning technique based on the linear least-squares fitting method
Energies 2022, 15, 1320. https://doi.org/10.3390/en15041320 https://www.mdpi.com/journal/energies
