Initial State Point Research Articles

High-precision tracking differentiator via generalized discrete-time optimal control

An enhanced discrete-time tracking differentiator (TD) with high precision based on discrete-time optimal control (DTOC) law is proposed. This law takes the form of state feedback for a double-integral system that adopts the Isochronic Region approach. There, the control signal sequence is determined by a linearized criterion based on the position of the initial state point on the phase plane. The proposed control law can be easily extended to the TD design problem by combining the first-state variable of the double-integral system with the desired trajectory. To improve the precision of the discretization model, we introduced a zero-order hold on the control signal. We also discuss the general form of DTOC law by analysing the relationship between boundary transformations and boundary characteristic points. After comparing the simulation results from three different TDs, we determined that this new TD achieves better performance and higher precision in signal-tracking filtering and differentiation acquisition than do existing TDs. Also the comparisons of the computational complexities between the proposed DTOC law and normal one are demonstrated. For confirmation of its utility, we processed raw phasor measurement units data via the proposed TD. In the absence of complex power system modelling and historical data, it was verified that the proposed TD is suitable for applications of real-time synchrophasor estimations, especially when the states are corrupted by noise.

Closed‐form solution of discrete‐time optimal control and its convergence

The convergence of a new closed-form solution for the discrete-time optimal control is presented. First, a new time optimal control law with simple structure is constructed in the form of the state feedback for a discrete-time double-integral system by using the state backstepping approach. The control signal sequence in this approach is determined by the linearised criterion according to the position of the initial state point on the phase plane. This closed-form non-linear state feedback control law clearly shows that time optimal control in discrete time is not necessarily the bang-bang control. Second, the convergence of the time optimal control law is proved by demonstrating the convergence path of the state point sequence driven by the corresponding control signal sequence. Finally, numerical simulation results demonstrate the effectiveness of this new discrete-time optimal control law.

Multistage hybrid evolutionary computing-based optimal PMU placement for large scale power grid network

Phasor measurement unit (PMU) is one of the most significant grid components that plays vital role in ensuring reliable power transmission and distribution. The optimal PMU placement (OPP) in power system can not only ensure grid cost reduction, real-time monitoring and control, but can reduce the operational complexities and overheads significantly. This paper proposes a novel multistage hybrid evolutionary computing scheme for OPP solution. Our proposed model applied adaptive genetic algorithm (AGA) for initial state point retrieval for OPP, which was then fed as input to the pattern search (PS)-based PMU placement optimisation. Our proposed AGA-PS scheme ensures OPP solution by retrieving minimum number of PMUs and its optimal location across grid network to make power system completely observable under varied cases. The simulation results with IEEE 14, IEEE 39, IEEE 118 and KPTCL 155 bus networks has exhibited that the proposed AGA-PS outperforms major existing approaches in terms of optimal OPP solutions.

Multistage hybrid evolutionary computing-based optimal PMU placement for large scale power grid network

Phasor measurement unit (PMU) is one of the most significant grid components that plays vital role in ensuring reliable power transmission and distribution. The optimal PMU placement (OPP) in power system can not only ensure grid cost reduction, real-time monitoring and control, but can reduce the operational complexities and overheads significantly. This paper proposes a novel multistage hybrid evolutionary computing scheme for OPP solution. Our proposed model applied adaptive genetic algorithm (AGA) for initial state point retrieval for OPP, which was then fed as input to the pattern search (PS)-based PMU placement optimisation. Our proposed AGA-PS scheme ensures OPP solution by retrieving minimum number of PMUs and its optimal location across grid network to make power system completely observable under varied cases. The simulation results with IEEE 14, IEEE 39, IEEE 118 and KPTCL 155 bus networks has exhibited that the proposed AGA-PS outperforms major existing approaches in terms of optimal OPP solutions.

Volume change behaviour of unsaturated compacted weakly expansive soils

In order to investigate volume change behaviour of unsaturated weakly expansive soils with different initial densities and water contents, a series of wetting tests were performed on compacted specimens at different vertical pressures. The unsaturated compression line, consisting of the compression equilibrium points in an unsaturated state under different vertical pressures, and the swell-under-load line, consisting of the swelling or compression equilibrium points after saturation under different vertical pressures, can all be obtained from the wetting tests at different vertical pressures. From intersections of the unsaturated compression lines and the swell-under-load lines with different initial dry densities, a unique line called the demarcation line (DL) is obtained. The physical meaning of DL is that the specimen volume remains unchanged during wetting. Therefore, the volume change behaviour of expansive soils in the plane of void ratio versus logarithm of net vertical pressure can be divided in two regions: the swelling region and the compression region. In the swelling region, if the initial state point is below the DL, the specimen will swell during wetting. In the compression region, if the initial state point is above the DL, the specimen will compress during wetting. Finally, the swelling and compression mechanisms of weakly expansive soils are discussed based on the pore-size distribution from the results of the Mercury Intrusion Porosimetry (MIP) tests on weakly expansive soil.

Molecular dynamics simulation of fluid sodium

Liquid metals are known to interact via many-body (density-dependent) potential energy functions. While the form of such potentials is complicated, they consist of a large number of adjustable parameters, making their implementation in molecular simulation packages difficult. In this work we developed two methods to predict the microscopic structure and dynamics in liquid sodium. One of the methods involves calculation of the potential of mean force, in an iterative cycle, in such a way to be able to reproduce the experimental radial distribution function of liquid sodium at 378 K (close to the freezing point). This potential of mean force is shown to be able to well reproduce the structure and dynamics in liquid sodium in the vicinity (up to a temperature ≈ 600 K) of the initial state point at which it is derived. However at higher temperatures it fails to reproduce the experimental densities and diffusion coefficients accurately. The other method consists of employing a simplified two-parameter potential energy function, namely the Lennard-Jones potential in which the exponents are adjusted, for simulation of fluid sodium along the liquid-vapor coexistence curve. It is shown that this potential energy is able to predict the densities of liquid and vapor sodium over a wide range of temperatures, ranging from 378 K to 2300 K, in close agreement with experiment. In this case, the calculated diffusion coefficients of liquid sodium are: underestimated at low temperatures, in good agreement with experiment at moderate temperatures, and overestimated at very high temperatures.

Large amplitude water level oscillations in throttled surge tanks

After a theoretical analysis of system singularities, and normalized equations describing the water-level motion in the throttled surge tank of a hydropower plant are solved on a digital computer. The critical stability conditions for large amplitude oscillations are obtained by finding the conditions under which the initial state point of the system is, in the terminology of the phase plane method, on the limit cycle. The paper demonstrates the possibility of the existence of 2 limit cycles around the singularity representing the steady operating point and the feasibility of the adoption of surge tanks with a section smaller than Thoma critical value.