Voltage instability occurs when a power system is unable
to meet reactive power demand at one or more buses.
Voltage instability events have caused several major outages
and promise to become more frequent due to increasing
energy demand. The future smart grid may
help to ensure voltage stability by enabling rapid detection
of possible voltage instability and implementation
of corrective action. These corrective actions will only
be effective in restoring stability if they are chosen in a
timely, scalable manner. Current techniques for selecting
control actions, however, rely on exhaustive search,
and hence may choose an inefficient control strategy. In
this paper, we propose a submodular optimization approach
to designing a control strategy to prevent voltage
instability at one or more buses. Our key insight is
that the deviation from the desired voltage is a supermodular
function of the set of reactive power injections
that are employed, leading to computationally efficient
control algorithms with provable optimality guarantees.
Furthermore, we show that the optimality bound of our
approach can be improved from 1/3 to 1/2 when the
power system operates under heavy loading conditions.
We demonstrate our framework through extensive simulation
study on the IEEE 30 bus test case.
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This content will become publicly available on December 1, 2024
Using demand response to improve power system small-signal stability
With the increase of uncertain and intermittent renewable energy supply on the grid, the power system has become more vulnerable to instability. In this paper, we develop a demand response strategy to improve power system small-signal stability. We pose the problem as an optimization problem wherein the total demand-responsive load is held constant at each time instance but shifted between different buses to improve small-signal stability, which is measured by small-signal stability metrics that are functions of subsets of the system’s eigenvalues, such as the smallest damping ratio. To solve the problem, we use iterative linear programming and generalized eigenvalue sensitivities. We demonstrate the approach via a case study that uses the IEEE 14-bus system. Our results show that shifting the load between buses, can improve a small-signal stability margin. We explore the use of models of different fidelity and find that it is important to include models of the automatic voltage regulators and power system stabilizers. In addition, we show that load shifting can achieve similar improvements to generation shifting and better improvement than simply tuning power system stabilizers.
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- Award ID(s):
- 1845093
- NSF-PAR ID:
- 10486456
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Sustainable Energy, Grids and Networks
- Volume:
- 36
- Issue:
- C
- ISSN:
- 2352-4677
- Page Range / eLocation ID:
- 101214
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Summary This paper presents a method for determining the relevant buses for reduced models of power grid networks described by systems of differential‐algebraic equations and for constructing the coarse‐grain dynamical power grid systems. To determine these buses, time integration of differential equations is not needed, but rather, a stationary system is analyzed. However, unlike stationary‐system approaches that determine only coarse generator buses by approximating the coherency of the generators, the proposed method analyzes the graph Laplacian associated with the admittance matrix. The buses for the reduced model are chosen to ensure that the graph Laplacian of the reduced model is an accurate approximation to the graph Laplacian of the full system. Both load and generator buses can be selected by this procedure since the Laplacian is defined on all the buses. The basis of this proposed approach lies in the close relationship between the synchrony of the system and the spectral properties of this Laplacian, that is, conditions on the spectrum of this Laplacian that almost surely guarantee the synchrony of the system. Thus, assuming that the full system is in synchrony, our strategy is to coarsen the full‐system Laplacian such that the coarse Laplacian possesses good approximation to these spectral conditions. Accurate approximation to these conditions then can better lead to synchronous reduced models. The coarsened Laplacian is defined on coarse degrees of freedom (DOFs), which are associated with the relevant buses to include in the reduced model. To realize this coarse DOF selection, we use multigrid coarsening techniques based on compatible relaxation. Multigrid is the natural choice since it has been extensively used to coarsen Laplacians arising from discretizations of elliptic partial differential equations and is actively being extended to graph Laplacians. With the selection of the buses for the reduced model, the reduced model is completed by constructing the coarse admittance matrix values and other physical parameters using standard power grid techniques or by using the intergrid operators constructed in the coarse DOFs selection process. Unfortunately, the selection of the coarse buses and the coarsening of the admittance matrix and physical parameters are not sufficient by themselves to produce a stable reduced system. To achieve a stable system, system structures of the fine‐grain model must be preserved in the reduced model. We analyze this to develop a multigrid methodology for constructing stable reduced models of power grid systems. Numerical examples are presented to validate this methodology.
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