16 research outputs found
Nonlinear Analysis of an Improved Swing Equation
In this paper, we investigate the properties of an improved swing equation
model for synchronous generators. This model is derived by omitting the main
simplifying assumption of the conventional swing equation, and requires a novel
analysis for the stability and frequency regulation. We consider two scenarios.
First we study the case that a synchronous generator is connected to a constant
load. Second, we inspect the case of the single machine connected to an
infinite bus. Simulations verify the results
Permanent Magnet Synchronous Motors are Globally Asymptotically Stabilizable with PI Current Control
This note shows that the industry standard desired equilibrium for permanent
magnet synchronous motors (i.e., maximum torque per Ampere) can be globally
asymptotically stabilized with a PI control around the current errors, provided
some viscous friction (possibly small) is present in the rotor dynamics and the
proportional gain of the PI is suitably chosen. Instrumental to establish this
surprising result is the proof that the map from voltages to currents of the
incremental model of the motor satisfies some passivity properties. The
analysis relies on basic Lyapunov theory making the result available to a wide
audience
Energy-based Stabilization of Network Flows in Multi-machine Power Systems
This paper considers the network flow stabilization problem in power systems
and adopts an output regulation viewpoint. Building upon the structure of a
heterogeneous port-Hamiltonian model, we integrate network aspects and develop
a systematic control design procedure. First, the passive output is selected to
encode two objectives: consensus in angular velocity and constant excitation
current. Second, the non-Euclidean nature of the angle variable reveals the
geometry of a suitable target set, which is compact and attractive for the zero
dynamics. On this set, circuit-theoretic aspects come into play, giving rise to
a network potential function which relates the electrical circuit variables to
the machine rotor angles. As it turns out, this energy function is convex in
the edge variables, concave in the node variables and, most importantly, can be
optimized via an intrinsic gradient flow, with its global minimum corresponding
to angle synchronization. The third step consists of explicitly deriving the
steady-state-inducing control action by further refining this sequence of
control-invariant sets. Analogously to solving the so called regulator
equations, we obtain an impedance-based network flow map leading to novel error
coordinates and a shifted energy function. The final step amounts to decoupling
the rotor current dynamics via feedback-linearziation resulting in a cascade
which is used to construct an energy-based controller hierarchically.Comment: In preparation for MTNS 201
Inverse Stability Problem and Applications to Renewables Integration
In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range of operating points would be essential to assuring their reliable operation, and possibly allow higher integration of renewable resources. This letter introduces a non-traditional way to think about the stability assessment problem of power systems. Instead of estimating the set of initial states leading to a given operating condition, we characterize the set of operating conditions that a power grid converges to from a given initial state under changes in power injections and lines. We term this problem as "inverse stability," a problem which is rarely addressed in the control and systems literature, and hence, poorly understood. Exploiting quadratic approximations of the system's energy function, we introduce an estimate of the inverse stability region. Also, we briefly describe three important applications of the inverse stability notion: 1) robust stability assessment of power systems with respect to different renewable generation levels; 2) stability-constrained optimal power flow; and 3) stability-guaranteed corrective action design. ©2017 IEEE.MIT/Skoltech, Ministry of Education and Science of Russian Federation (Grant no.14.615.21.0001.)NSF (1508666)NSF (1550015
Mixed Voltage Angle and Frequency Droop Control for Transient Stability of Interconnected Microgrids with Loss of PMU Measurements
We consider the problem of guaranteeing transient stability of a network of
interconnected angle droop controlled microgrids, where voltage phase angle
measurements from phasor measurement units (PMUs) may be lost, leading to poor
performance and instability. In this paper, we propose a novel mixed voltage
angle and frequency droop control (MAFD) framework to improve the reliability
of such angle droop controlled microgrid interconnections. In this framework,
when the phase angle measurement is lost at a microgrid, conventional frequency
droop control is temporarily used for primary control in place of angle droop
control. We model the network of interconnected microgrids with the MAFD
architecture as a nonlinear switched system. We then propose a
dissipativity-based distributed secondary control design to guarantee transient
stability of this network under arbitrary switching between angle droop and
frequency droop controllers. We demonstrate the performance of this control
framework by simulation on a test 123-feeder distribution network.Comment: American Control Conference (ACC), 202
An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages
This paper studies the problem of frequency regulation in power grids under
unknown and possible time-varying load changes, while minimizing the generation
costs. We formulate this problem as an output agreement problem for
distribution networks and address it using incremental passivity and
distributed internal-model-based controllers. Incremental passivity enables a
systematic approach to study convergence to the steady state with zero
frequency deviation and to design the controller in the presence of
time-varying voltages, whereas the internal-model principle is applied to
tackle the uncertain nature of the loads.Comment: 16 pages. Abridged version appeared in the Proceedings of the 21st
International Symposium on Mathematical Theory of Networks and Systems, MTNS
2014, Groningen, the Netherlands. Submitted in December 201