An accurate technique for supervising distance relays during power swing

Power swing is a power system transient phenomenon that arises due to several reasons including line switching, line outage, sudden increment or decrement in load, faults, etc. Unnecessary tripping during power swing and unnecessary blocking for faults occur during power swing result in distance relay maloperation. Several cascaded outages and major worldwide blackouts have occurred due to maloperation of distance relays. This paper proposes a technique for supervising distance relays during power swing. The proposed online technique discriminates real faults and power swing accurately. It relies on constructing a locus diagram for the current and voltage differences (∆I-∆V) between the two ends of the protected line. The locus is estimated at every power frequency cycle to continuously monitor the state of the line by utilizing the synchrophasor measurements at the sending and receiving ends of the line. The proposed technique is tested for two-area, four-machine power system under faults at different locations of zone-1 and zone-2 regions of distance relays, fault resistances, fault inception angles and slip frequencies using MATLAB software. The simulation results proved the superior improvement of distance relay performance for handling power swing blocking and unblocking actions.

Limit Cycles in the Equation of Whirling Pendulum With Piecewise Smooth Perturbations

This paper deals with the problem of limit cycles for the whirling pendulum equation ẋ = y, ẏ = sin x(cos x-r) under piecewise smooth perturbations of polynomials of cos x, sin x and y of degree n with the switching line x = 0. The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained by using the Picard-Fuchs equations which the generating functions of the associated first order Melnikov functions satisfy. Further, the exact bound of a special case is given by using the Chebyshev system.

The existence and properties of the solution of a class of nonlinear differential equations with switching at variable times

<p style='text-indent:20px;'>In this paper, we deal with the qualitative theory for a class of nonlinear differential equations with switching at variable times (SSVT), such as the existence and uniqueness of the solution, the continuous dependence and differentiability of the solution with respect to parameters and the stability. Firstly, we obtain the existence and uniqueness of a global solution by defining a reasonable solution (see Definition 2.1). Secondly, the continuous dependence and differentiability of the solution with respect to the initial state and the switching line are investigated. Finally, the global exponential stability of the system is discussed. Moreover, we give the necessary and sufficient conditions of SSVT just switching <inline-formula><tex-math id="M1">\begin{document}$ k\in \mathbb{N} $\end{document}</tex-math></inline-formula> times on bounded time intervals.</p>

Synthesis of a Quasi-Optimal Multi-Mode Control Law Based on the Condition of the Maximum of the Function of the Generalized Power and the Principle of Release

A quasi-optimal multimode control law is developed on the basis of the condition for the maximum of the function of generalized power, taking into account the principle of exemption for control objects that can be represented by Lagrange equations of the second kind. A comparative analysis of the obtained solution was carried out on the basis of mathematical modeling. It is found that the modes of the proposed control law provide a high accuracy of approximation to the optimal speed laws and Fuller&#x27;s laws with the possibility of eliminating more frequent switching. The developed control law by changing the switching line makes it possible to implement a wide range of linear and nonlinear operating modes, which allows the resulting control law to be classified as multimode.

Optimal Control of a Multilayer Electroelastic Engine with a Longitudinal Piezoeffect for Nanomechatronics Systems

A electroelastic engine with a longitudinal piezoeffect is widely used in nanotechnology for nanomanipulators, laser systems, nanopumps, and scanning microscopy. For these nanomechatronics systems, the transition between individual positions of the systems in the shortest possible time is relevant. It is relevant to solve the problem of optimizing the nanopositioning control system with a minimum control time. This work determines the optimal control of a multilayer electroelastic engine with a longitudinal piezoeffect and minimal control time for an optimal nanomechatronics system. The expressions of the control function and switching line are obtained with using the Pontryagin maximum principle for the optimal control system of the multilayer electroelastic engine at a longitudinal piezoeffect with an ordinary second-order differential equation of system. In this optimal nanomechatronics system, the control function takes only two values and changes once.

Discrete Sliding Mode Speed Control of Induction Motor Using Time-Varying Switching Line

Sliding mode control (SMC) of electric drives constitutes a very popular control method for nonlinear multivariable and time-varying systems, e.g., induction motor (IM) drives. Nowadays, IM are the most popular electrical machines (EM) applied in many industrial applications as motion control devices, including electrical and hybrid vehicles. Nowadays, the control systems of EM are mostly realized using digital techniques (microprocessors and microcontrollers). Therefore, all control algorithms should be discretized or the whole control system should be designed in the discrete-time domain. This paper deals with a discrete-time sliding mode control (DSMC) for IM drives. The discrete algorithms for sliding mode control of the motor speed and rotor flux are derived in detail and next tested in simulation research. The simulation tests include the discrete nature of the power converter supplying the IM and present excellent performance of the developed control structure. To obtain the rotor speed regulation invariant to external disturbances, like load torque or inertia, especially during the reaching phase of the switching line, the discrete version of a time-varying switching line was introduced. It is shown that the assumed dynamics of the IM flux and speed is achieved and the proposed control algorithm can be realized using commonly available microcontrollers. The paper is illustrated with comprehensive simulation results for 1.5 kW IM drive, which are verified by experimental tests.

The condition for the maximum of the generalized power function in the problem of forming a multi-mode control law with limitation

A quasi-optimal control law is developed based on the condition for the maxi-mum of the generalized power function taking into account the stationarity of the Hamiltonian on the switching line for control objects that can be represented by the Lagrange equations of the second kind. The comparative analysis is carried out based on the mathematical simulation using the optimal nonlinear control laws with respect to several criteria. We found that the modes of the proposed control law provide high accuracy of approximation to the optimal performance laws and the Fuller laws, reducing energy costs for control by eliminating more frequent switching. The choice of the parameters of the developed control law makes it possible to implement a wide range of both nonlinear and linear operating modes, which allows to classify the obtained control law as multimode law.

Control of Dynamic Objects in the Conditions of Uncertainty in the Point Sliding Mode

There is development of the well-known sliding mode, which in the classical formulation didn’t find the development to be applied to control systems discussed. Alternatively, there is method of organizing one of the uniformity of the sliding mode called the "point sliding mode" proposed. The distinctive feature of this mode is that here the control gaps occur at time-equal points of the switching line (hyperplane) which allows the origin of coordinates for a finite number of switches. The possibility of changing the time interval between these points makes it possible to obtain various modes: a finite mode, in which a given point is reached from any initial state in one switch, and in this mode the switch line is "isochronous"; point sliding mode in which a given point is reached in a finite number of switchings; limit mode, when the length of time intervals tend to zero, and the switching frequency to infinity. Considering this feature the concept of "degree of slip" is introduced. It is shown that in the case of forced movement in the SPS, a sliding motion is observed, which does not allow for ensuring invariance with respect to external disturbances. There are two ways to eliminate the forced component of the movement offered. One of the advantages of using a point sliding mode is that, in order to improve performance, it is not necessary to use a boundary layer, which is realized by entering various logical conditions into the control algorithm. The practical significance of a point sliding mode lies in the fact that, with a small switching frequency, it is possible to maintain the quality indices of an undefined object within an acceptable interval. The studies were conducted for onedimensional second-order linear systems (SISO). Results can be generalized for higher order multidimensional systems. Solution of model problems on MATLAB / Simulink allows us to make a number of positive conclusions that are of great practical importance in terms of expanding the area of use of skipping modes, especially in relation to the management of undefined objects.