Learning power and language expressiveness

The topic of the present work is to study the relationship between the power of the learning algorithms on the one hand, and the expressive power of the logical language which is used to represent the problems to be learned on the other hand. The central question is whether enriching the language results in more learning power. In order to make the question relevant and nontrivial, it is required that both texts (sequences of data) and hypotheses (guesses) be translatable from the “rich” language into the “poor” one. The issue is considered for several logical languages suitable to describe structures whose domain is the set of natural numbers. It is shown that enriching the language does not give any advantage for those languages which define a monadic second-order language being decidable in the following sense: there is a fixed interpretation in the structure of natural numbers such that the set of sentences of this extended language true in that structure is decidable. But enriching the original language even by only one constant gives an advantage if this language contains a binary function symbol (which will be interpreted as addition). Furthermore, it is shown that behaviourally correct learning has exactly the same power as learning in the limit for those languages which define a monadic second-order language with the property given above, but has more power in case of languages containing a binary function symbol. Adding the natural requirement that the set of all structures to be learned is recursively enumerable, it is shown that it pays o6 to enrich the language of arithmetics for both finite learning and learning in the limit, but it does not pay off to enrich the language for behaviourally correct learning.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

Torsional Interaction Studies on a Power System Compensated by SSSC and Fixed Capacitor

In this paper, a static synchronous series compensator (SSSC), along with a fixed capacitor, is used to avoid torsional mode instability in a series compensated transmission system. A 48-step harmonic neutralized inverter is used for the realization of the SSSC. The system under consideration is the IEEE first benchmark model on SSR analysis. The system stability is studied both through eigenvalue analysis and EMTDC/PSCAD simulation studies. It is shown that the combination of the SSSC and the fixed capacitor improves the synchronizing power coefficient. The presence of the fixed capacitor ensures increased damping of small signal oscillations. At higher levels of fixed capacitor compensation, a damping controller is required to stabilize the torsional modes of SSR.

TCSC control design for transient stability improvement of a multi-machine power system using trajectory sensitivity

This paper discusses the effects of thyristor controlled series compensator (TCSC), a series FACTS controller, on the transient stability of a power system. Trajectory sensitivity analysis (TSA) has been used to measure the transient stability condition of the system. The TCSC is modeled by a variable capacitor, the value of which changes with the firing angle. It is shown that TSA can be used in the design of the controller. The optimal locations of the TCSC-controller for different fault conditions can also be identified with the help of TSA. The paper depicts the advantage of the use of TCSC with a suitable controller over fixed capacitor operation.

Performance study of two different compensating devices in a custom power park

Simulation study of a custom power park (CPP) is presented. It is assumed that the park contains unbalanced and nonlinear loads in addition to a sensitive load. Two different types of compensators are used separately to protect the sensitive load against unbalance and distortion caused by the other loads. It has been shown that a shunt compensator can regulate the voltage of the CPP bus, whereas the series compensator can only regulate the sensitive load terminal voltage. Additional issues such as the load transfer through a static transfer switch, detection of sag/fault etc. are also discussed. The concepts are validated through PSCAD/EMTDC simulation studies on a sample distribution system.