Quantitative Control Approach for Wind Turbine Generators to Provide Fast Frequency Response with Guarantee of Rotor Security

Wind generation is expected to reach substantially higher levels of penetration in the near future. With the converter interface, the rotor inertia of doubly-fed induction generator (DFIG) based wind turbine generator is effectively decoupled from the system, causing a reduction in inertial response. This can be compensated by enabling the DFIG to provide fast frequency response. This paper proposes a quantitative control approach for DFIG to deliver fast frequency response in the inertial response time scale. A supplementary power surge function is added to the active power reference of DFIG. The exact amount of power surge that is available from DFIG-based wind turbine is quantified based on estimation of maximum extractable energy. Moreover, the operational constraints such as rotor limits and converter over-load limit are considered at the same time. Thus, the proposed approach not only provides adequate inertial response but also ensures the rotor speed is kept within a specified operating range. Rotor safety is guaranteed without the need for an additional rotor speed protection scheme.Comment: 5 page

Security Constrained Multi-Stage Transmission Expansion Planning Considering a Continuously Variable Series Reactor

This paper introduces a Continuously Variable Series Reactor (CVSR) to the transmission expansion planning (TEP) problem. The CVSR is a FACTS-like device which has the capability of controlling the overall impedance of the transmission line. However, the cost of the CVSR is about one tenth of a similar rated FACTS device which potentially allows large numbers of devices to be installed. The multi-stage TEP with the CVSR considering the $N-1$ security constraints is formulated as a mixed integer linear programming model. The nonlinear part of the power flow introduced by the variable reactance is linearized by a reformulation technique. To reduce the computational burden for a practical large scale system, a decomposition approach is proposed. The detailed simulation results on the IEEE 24-bus and a more practical Polish 2383-bus system demonstrate the effectiveness of the approach. Moreover, the appropriately allocated CVSRs add flexibility to the TEP problem and allow reduced planning costs. Although the proposed decomposition approach cannot guarantee global optimality, a high level picture of how the network can be planned reliably and economically considering CVSR is achieved.Comment: Accepted by IEEE Transactions on Power System

Generalized Gaussian wave packet dynamics: Integrable and Chaotic Systems

The ultimate semiclassical wave packet propagation technique is a complex, time-dependent WBK method known as generalized Gaussian wave packet dynamics (GGWPD). It requires overcoming many technical difficulties in order to be carried out fully in practice. In its place roughly twenty years ago, linearized wave packet dynamics was generalized to methods that include sets of off-center, real trajectories for both classically integrable and chaotic dynamical systems that completely capture the dynamical transport. The connections between those methods and GGWPD are developed in a way that enables a far more practical implementation of GGWPD. The generally complex saddle point trajectories at its foundation are found using a multi-dimensional, Newton-Raphson root search method that begins with the set of off-center, real trajectories. This is possible because there is a one-to-one correspondence. The neighboring trajectories associated with each off-center, real trajectory form a path that crosses a unique saddle; there are exceptions which are straightforward to identify. The method is applied to the kicked rotor to demonstrate the accuracy improvement as a function of $\hbar$ that comes with using the saddle point trajectories.Comment: 18 pages, 9 figures, corrected a typo in Eqs. 29,3

Partial local density of states from scanning gate microscopy

Scanning gate microscopy images from measurements made in the vicinity of quantum point contacts were originally interpreted in terms of current flow. Some recent work has analytically connected the local density of states to conductance changes in cases of perfect transmission, and at least qualitatively for a broader range of circumstances. In the present paper, we show analytically that in any time-reversal invariant system there are important deviations that are highly sensitive to imperfect transmission. Nevertheless, the unperturbed partial local density of states can be extracted from a weakly invasive scanning gate microscopy experiment, provided the quantum point contact is tuned anywhere on a conductance plateau. A perturbative treatment in the reflection coefficient shows just how sensitive this correspondence is to the departure from the quantized conductance value and reveals the necessity of local averaging over the tip position. It is also shown that the quality of the extracted partial local density of states decreases with increasing tip radius.Comment: 16 pages, 9 figure