Two-region System Research Articles

Mechanism Analysis of the Effect of the Equivalent Proportional Coefficient of Inertia Control for a Doubly Fed Wind Generator on Frequency Stability in Extreme Environments

With the large-scale access of a doubly fed wind generator (DFWG) with inertia adjustment capability to the polar microgrid, the frequency stability characteristics of the polar microgrid become more complicated. To enhance DWFG frequency stability and ensure the safe and reliable operation of polar microgrids, a DFWG connected to a two-region interconnected polar microgrid is used as the research background for this paper. Firstly, the equivalent model of two regional inertia centers is derived, and the effect of DFWG virtual inertia on the rotor motion equation of the regional inertia center is analyzed when a DFWG is directly connected to the polar microgrid. Then, from the point of view of the transient energy of the system, the influence of the equivalent proportional coefficient of virtual inertia control of the DFWG in two regions on the transient energy during the acceleration and deceleration of the system is studied when the swing direction of the system power angle is different, and the influence mechanism of the swing direction on the frequency stability is further investigated. Finally, the maximum frequency offset is proposed to evaluate the frequency stability of the system, and the two-region system simulation model is built into the PSASP 7.4.1 simulation software to verify the correctness of the proposed theory.

Distributed Optimal Dispatching of Interconnected Electricity-Gas-Heating System

In the researching background of integrated energy system, a single electricity-gas-heating system (EGHS) can be regarded as an active producer. In order to solve the joint optimization of integrated energy systems under the condition of incomplete information, this paper proposes a distributed optimal scheduling framework of EGHS. First, establish a coupling model of the interconnected EGHS, and perform strict second-order cone convexity of the complex natural gas flow model. Next, use the bus splitting method to realize the decoupling between different regions of the interconnected system, and employ the alternating direction multiplier method (ADMM) to solve the model. Then, construct two-region energy system (78-node grid +40-node gas grid +40-node heat grid) and three-region energy system (117-node grid +60 node gas grid +60-node heat grid) as simulation examples to verify the effectiveness of the distributed optimization framework. In the end, the algorithm solution process, the effectiveness of scheduling results, and the comparison of optimization results under different interconnection methods are analyzed in detail.

Hierarchical perimeter control with guaranteed stability for dynamically coupled heterogeneous urban traffic

Perimeter control based on the Macroscopic Fundamental Diagram (MFD) is widely developed for alleviating or postponing congestion in a protected region. Recent studies reveal that traffic conditions might not be improved if the perimeter control strategies are applied to unstable systems where high demand generates heavy and heterogeneously distributed traffic congestion. Therefore, considering stability of the targeted traffic system is essential, for the sake of developing a feasible and then optimal control strategy. This paper sheds light on this direction. It integrates a stability characterization algorithm of MFD system equations into the Model Predictive Control (MPC) scheme, and features respectively an upper and a lower bound of the feasible control inputs, to guarantee system stability. Firstly, the dynamics of traffic heterogeneity and its effect on the MFD are analyzed, using real data from Guangzhou in China. Piecewise affine functions of average flow are proposed to capture traffic heterogeneity in both regional and subregional MFDs. Secondly, stability of a three-state two-region system is investigated via stable equilibrium and surface boundaries analysis. Finally, a three-layer hierarchical control strategy is introduced for the studied two-region heterogeneous urban networks. The first layer of the controller calculates the stable surface boundaries for the given traffic demands and then determines the bounds of control input (split rate). An MPC approach in the second layer is used to solve an optimization problem with two objectives of minimizing total network delay and maximizing network throughput. Heterogeneity among the subregions is minimized in the last layer by implementing simultaneously a subregional perimeter flow control and an internal flow control. The effectiveness and stability of the proposed control approach are verified by comparison with four existing perimeter control strategies.

Nonlinear Robust Traffic Flow Control in Urban Networks

Perimeter traffic flow control, based on Macroscopic Fundamental Diagram (MFD) has been developed for traffic congestion control in heterogeneously congested cities. The perimeter control can be realized based on a set of traffic signals on the border between the urban regions that manipulates transferring flows between the regions to regulate the overall urban traffic system states towards a desirable condition considering disturbances and uncertainties in the modeling and state observability. This paper presents robust control of the two-region MFD system with perimeter control addressing different sources of uncertainties. In this paper two types of controller, sliding mode control (SMC) and linear quadratic regulator (LQR) control, are designed based on nonlinear and linearized system dynamics, respectively. The SMC is designed to assure robustness against all type of uncertainty. A simulation study is performed to evaluate the effectiveness of the proposed control approaches.

Robust Repositioning for Vehicle Sharing

Problem definition: In this paper, we study the fleet repositioning problem for a free-float vehicle sharing system, aiming to dynamically match the vehicle supply and travel demand at the lowest total cost of repositioning and lost sales. Academic/practical relevance: Besides the analytical results on the optimal repositioning policy, the proposed optimization framework is applicable to practical problems by its computational efficiency as well as the capability to handle temporally dependent demands. Methodology: We first formulate the problem as a stochastic dynamic program. To solve for a multiregion system, we deploy the distributionally robust optimization (DRO) approach that can incorporate demand temporal dependence, motivated by real data. We first propose a “myopic” two-stage DRO model that serves as both an illustration of the DRO framework and a benchmark for the later multistage model. We then develop a computationally efficient multistage DRO model with an enhanced linear decision rule (ELDR). Results: Under a two-region system, we find a simple reposition up-to and down-to policy to be optimal, when the demands are temporally independent. Such a structure is also preserved by our ELDR solution. We also provide new analytical insights by proving the optimality of ELDR in solving the single-period DRO problem. We then show that the numerical performance of the ELDR solution is close to the exact optimal solution from the dynamic program. Managerial implications: In a real-world case study of car2go, we quantify the “value of repositioning” and compare with several benchmarks to demonstrate that the ELDR solutions are computationally scalable and in general result in lower cost with less frequent repositioning. We also explore several managerial implications and extensions from the experiments.

Robust constrained control of uncertain macroscopic fundamental diagram networks

This paper considers modeling and control of uncertain Macroscopic Fundamental Diagram (MFD) systems for multiple-region networks. First, the nonlinear vehicle conservation equations based on MFD dynamics, presented in earlier publications, are transformed to linear equations with parameter uncertainties. The parameter uncertainties include the destination decomposition fractions, that are difficult to estimate in reality. Then, the uncertain linear model is utilized to design a robust feedback controller by an interpolation-based approach. This approach (i) guarantees robustness against all parameter uncertainties, (ii) handle control and state constraints, and (iii) present a computationally cheap solution. The main idea is to interpolate between (i) a stabilizing outer controller that respects the control and state constraints and (ii) an inner robustly stable controller designed by any method. The robust control is further challenged to deal with different relative locations of reference accumulation points on the MFD diagrams. Numerical results for a two-region system show that the uncertain linear model can replace the nonlinear model for modeling and control. Moreover, the robust control law is presented as implicit and explicit solutions, where in the implicit case one linear programming (LP) problem is solved at each time instant, while in the explicit case, the control law is shown as a piecewise affine function of state. Finally, a comparison between the interpolating controller and other controllers in the literature is carried out. The results demonstrate the performance advantages from applying the robust interpolating controller.

Regulation capabilities of basic configurations of switch resistance motors for traction electric drives

In addition to a high power to weight ratio, traction electric drives require a rather large range of speed regulation at constant output power. In the case of conventional electric motors, this is achieved by application of two-region regulation systems with magnetic flux weakening. A switched reluctance motor (SRM) with an extremely simple, manufacturable, and reliable design has a higher power to weight ratio within a range of moderate and high power values than do to conventional electric motors, while the regulation properties and limit characteristics in the zone above the rated speed have not been sufficiently investigated. The number of phases and magnetic-system configuration varying within a wide range and set by the ratio of the number of stator teeth to the number of rotor teeth significantly affect electromechanical characteristics in an SRM. In this paper, maximum values of speeds have been determined for basic configurations of SRM6/4 and 8/6 at similar rated speed, output power, and main magnetic-system dimensions. A simulation model of an SRM produced in the Matlab/Simulink environment shows that, when the speed of an SRM is increased, the output power is maintained by shifting the turn on and turn off phases in the forward direction. For selected conditions of comparison, it was found that, at preset parameters providing equal torques at low speed, the output power of SRM 8/6 at the rated speed is 20% higher than the power of SRM 6/4. At these parameters, the attainable range of speed variation at constant output power for SRM 6/4 is equal to 4.5 : 1, while it is 10% higher for SRM 8/6. If powers are balanced at the rated speed by means of reduced turning on of the interval of SRM 8/6 phases, then its range is increased to 7.9: 1, which is a significant advantage for some applications in transportation.

Robust Constrained Control of Uncertain Macroscopic Fundamental Diagram Networks

This paper considers modeling and control of uncertain Macroscopic Fundamental Diagram (MFD) systems for multiple-region networks. First, the nonlinear vehicle conservation equations based on MFD dynamics, presented in earlier publications, are transformed to linear equations with parameter uncertainties. The parameter uncertainties include the destination decomposition fractions, that are difficult to estimate in reality. Then, the uncertain linear model is utilized to design a robust feedback controller by an interpolation-based approach. This approach (i) guarantees robustness against all parameter uncertainties, (ii) handle control and state constraints, and (iii) present a computationally cheap solution. The main idea is to interpolate between (i) a stabilizing outer controller that respects the control and state constraints, and (ii) an inner robustly stable controller designed by any method. The robust control is further challenged to deal with different relative locations of reference accumulation points on the MFD diagrams. Numerical results for a two-region system show that the uncertain linear model can replace the nonlinear model for modeling and control. Moreover, the robust control law is presented as implicit and explicit solutions, where in the implicit case one linear programming (LP) problem is solved at each time instant, while in the explicit case, the control law is shown as a piecewise affine function of state. Finally, a comparison between the interpolating controller and other controllers in the literature is carried out. The results demonstrate the performance advantages from applying the robust interpolating controller.

On the stability of traffic perimeter control in two-region urban cities

In this paper, stability analysis of traffic control for two-region urban cities is treated. It is known in control theory that optimality does not imply stability. If the optimal control is applied in a heavily congested system with high demand, traffic conditions might not change or the network might still lead to gridlock. A city partitioned in two regions with a Macroscopic Fundamental Diagram (MFD) for each of the regions is considered. Under the assumption of triangular MFDs, the two-region MFDs system is modeled as a piecewise second-order system. Necessary and sufficient conditions are derived for stable equilibrium accumulations in the undersaturated regimes for both MFDs. Moreover, the traffic perimeter control problem for the two-region MFDs system is formulated. Phase portraits and stability analysis are conducted, and a new algorithm is proposed to derive the boundaries of the stable and unstable regions. Based on these regions, a state-feedback control strategy is derived. Trapezoidal shape of MFDs are also addressed with numerical solutions.

Power System Osciliation Modes Identification Based on Eigen system Realization Algorithm via Empirical Mode Decomposition

With the application of wide-area measurement system (WAMS), the analysis of dynamic behavior of power system based on swing tracks acts as an important research field and is different from the past methods based on a given mathematical models. In this paper,EMD-based eigensystem realization algorithm is proposed for identifying frequency, damping and vibration in the low frequency oscillationidentify for low frequency oscillation frequency, damping and vibration. Through a example of a four-machine two-region system, it is proved that this method on distinguishing the oscillation frequency, damping ratio and mode shapes is validity. This method can be minimal realization of the system, damping controller for the design conditions.this method can achieve the simplest state space modal of system. It is important for designer to invent advanced damping controller.

A horizontal well in a composite system with planar interfaces

The goal of this work is to consider the situation where the well intersects a partial hydrologic barrier. A two-region composite system where a horizontal well taps both regions is considered. The method of sources and sinks is used to build the well model to determine the drawdown in the aquifer. A model to examine a system with several contiguous regions is presented. The viability of the mathematical model where a horizontal well traverses two regions with distinct properties is demonstrated through illustrative examples of the characteristics of the drawdown response and its logarithmic derivative. Further it is shown that the numerical computations match asymptotic limits and that solutions may be correlated with homogeneous-aquifer solutions under appropriate circumstances. If the well were to tap both regions, it behaves as if its effective length is the ratio of the sum of the conductivity weighted well lengths and the average conductivity of the system. Three flow regimes with characteristic signatures over specific time intervals may be evident. Equivalent system parameters that are useful as a starting point to analyze data are provided. The influence of the trajectory of the well in a composite system is documented. In addition to quantitative results, it is shown that the long-term drawdown response in terms of the logarithmic derivative is independent of the trajectory of the well and no particular signatures are evident to suggest that the well traverses regions with distinct properties. Thus, production logs may be particularly useful.

Development of appropriate equations for physiologically based pharmacokinetic modeling of permeability-limited and flow-limited transport

Although the implementation of a flow-limited, well-stirred tank (WST) single-compartment tissue model in pharmacokinetics and toxicokinetics is widespread, its use is not always justified biophysically or physiologically. The WST model introduces a loss of biophysical detail, specifically the vascular space, which is present in the standard permeability-limited two-subcompartment (PLT) tissue model. To address this loss of detail when evaluating the in vivo kinetics of drugs, toxins, nutrients, and endogenous metabolites, a novel set of physiologically based pharmacokinetic tissue compartment equations is developed through application of an asymptotic approximation to a two-region vascular-extravascular system to arrive at a permeability-limited two-region asymptotically reduced (P-TAR) model and a flow-limited (F-TAR) model. Development of the TAR modeling approach illustrates the importance of relative timescales in PBPK tissue compartment model selection and the conditions under which improved biophysical realism is advantageous. In the permeability-limited regime, the TAR model formulations enable drug or toxicant concentration to be modeled in the vascular and extravascular spaces equivalent to the PLT tissue model while invoking only one state variable to represent the vascular and extravascular spaces. In the flow-limited regime, the F-TAR model is more biophysically realistic than the WST model because it maintains the anatomical distinction between the vascular and extravascular spaces, and hence offers greater pharmacological and physiological insight than the WST model, without introducing additional computational complexity.

Two-Region Average Model for Cuttings Transport in Horizontal Wellbores II: Interregion Conditions

The theoretical derivation of the cuttings transport problem for a two-region system composed of a fluid bed and a stationary bed of drill cuttings, which was considered as a porous medium, was presented in part 1 of this article. The aim of this article is to derive the momentum and mass flux interregion conditions (jump conditions) that contain terms representing the excess surface due to accumulation, convection, stress, and bulk in addition to a term representing the exchange with the surrounding regions. The averaged equations obtained in part 1 of this article and the interregion conditions obtained in this work allow modeling the two-region system described above.

Two-Region Average Model for Cuttings Transport in Horizontal Wellbores I: Transport Equations

The aim of this article is to derive a mathematical model without length-scale restrictions for cuttings transport in horizontal wellbores using the non-local forms of the volume averaging method, which is a technique used to derive transport equations for multiphase systems and one of the main approaches in two-phase flow modeling. The theoretical derivation of the cuttings transport problem is for a two-region system composed of a fluid bed (ω region) and a stationary bed (η region) of drill cuttings that it is considered as a porous medium. The volume-averaged mathematical model obtained in this work consists of the mass and momentum equations for the ω and η regions. The model was the starting point to obtain one-equation models for both regions. The one-equation models together with adequate jump conditions can be used to predict the hydrodynamics of the ω and η regions. The mathematical derivations of the momentum and mass flux transfer jump conditions are presented in Part II of this article.

A Derivation of the Averaging Model for Cuttings Transport: Multi-Region Model

The aim of this paper is to derive a mathematical model for cuttings transport in horizontal wellbores using the volume averaging method, which is a technique used to derive transport equations for multiphase systems and one of the main approaches in two-phase flow modeling. The theoretical derivation of the cuttings transport problem is for a two-region system composed of a fluid bed and a stationary bed of drill cuttings, which is considered as a porous medium. A one-equation model for fluid bed was derived and was used to obtain the multi-region model. This model can be used to study the hydraulic transport of solid particles in horizontal wellbores.

Averaging model for cuttings transport in horizontal wellbores

This paper presents a theoretical analysis of the problem of cuttings transport for a two-region system composed of a fluid bed ( ω-region) and a stationary bed of drill cuttings, which is considered as a porous medium ( η-region) in the two-phase system. The ω-region is made up of a solid phase ( σ-phase) dispersed in a continuos fluid phase ( β-phase), while the η-region consists of a stationary solid phase ( σ-phase) and a fluid phase ( β-phase). The volume averaging method was applied in this study. Volume-averaged transport equations were derived for both the fluid bed and the porous medium regions. These equations are based on the non-local form of the volume-averaged momentum transport equation that is valid within the bounded region. Outside this region, the non-local form reduces to the classic volume-averaged transport equation. From these equations, a one-equation model was obtained, and the constraints that the one-equation model must satisfy were applied. For estimating the averaged pressure drop and the averaged velocity, the one-equation model was solved numerically by using the finite-difference technique in the implicit scheme. Numerical results are in agreement with experimental data and theoretical results reported in the literature.

Thermal neutron diffusion cooling in two-region small systems

The thermal neutron diffusion cooling effect is a result of the perturbation of the thermal neutron energy distribution owing to the leakage of neutrons outside a finite volume of the medium. In multi-zone systems an additional perturbation appears because of diffusion of neutrons between regions which have different diffusion cooling properties. A study of the thermal neutron diffusion cooling in two-region small cylindrical systems is presented in this paper. A Plexiglas shell (hydrogenous medium) completely surrounds the inner cylinder filled with an absorbing aqueous solution (hydrogenous medium) or with a mixture of hydrogenous and non-hydrogenous substances. The pulsed neutron technique has been used for the experimental investigation of the problem. The time decay constant of the thermal neutron flux in the two-zone systems has been measured. It has also been calculated as a function of the system geometry and neutron dynamic parameters, one of these being the diffusion cooling coefficient of the outer Plexiglas shell. From a combination of results of the calculation and the experiments, it has been found that the obtained function for the particular diffusion cooling coefficient of the Plexiglas shell is controlled by the scattering properties of the inner zone of the system.

Effective sensitivity and heat capacity in the response of climate models to greenhouse gas and aerosol forcings

Simulations of greenhouse-gas-induced climate change from the pre-industrial period to 2100 by the CSIRO (Mark 2, Mark 3), Hadley Centre (HadCM2) and Canadian (CGCM1) coupled atmosphere–ocean general-circulation models are compared with those from mixed-layer ocean (MLO) versions of the models. The effect of additional transient aerosol and ozone forcings in Mark 2 is examined. Some of the variation in the global-mean surface warming of the coupled models can be attributed to the rate of heat uptake by the subsurface ocean. Based on the effective heat-capacity diagnostic, the HadCM2 ocean retards the warming more effectively than the ocean in the other models. Much of the variation between both the coupled and MLO models is due to the differing effective sensitivity (to doubled CO2) of the models. In particular, the rapid warming after 2000 from CGCM1 relates to increasing sensitivity that is largely associated with rising feedback from the snow-free or low latitudes, according to a regional feedback analysis. The Hadley Centre model has a lower global sensitivity than Mark 2, related to the high-latitude feedback. The lowest warming, in both model versions, is from Mark 3, which has relatively low feedbacks. The addition of aerosol forcing is shown to raise the net effective sensitivity in Mark 2. A simple two-region system including horizontal heat transport based on Mark 2 is used to explore the effect of variations in forcings and feedbacks on surface warming at equilibrium. Effective sensitivity can vary by −20% to +70% compared with the standard doubled CO2 case as forcing is confined to either the low- or high-latitude regions. Choosing extreme feedbacks from the other models leads to variation from 2.7 K to 7.2 K. A two-parameter transport model, which allows poleward net flux changes consistent with HadCM2 and Mark 3, demonstrates additional variation in the global sensitivity depending on transport characteristics. Copyright © 2005 Royal Meteorological Society

Wage payoffs and distance deterrence in the journey to work

In this paper we suggest a microeconomic model for how commuting flows relate to traveling distance in a two-region system. Commuting is the preferred choice of a worker whenever he can obtain an increase in wages greater than the cost of commuting. Our framework is based on an approach where workers apply for jobs according to a strategy that maximizes their expected payoffs (wages minus commuting costs). We also discuss the possibility of a systematic bias when actual traveling distances are represented by distances between city centers, ignoring intrazonal distances.

Performance of Reuse Partitioning in Cellular Systems with Mobile Users

Reuse partitioning (RP) is a simple technique that can be used to increase the traffic capacity in a cellular system. With RP, a cell is divided into several concentric regions, each associated with a different cluster size. In this article, a traffic model is developed to analyze the impact of mobile users on a two-region RP system using fixed channel assignment. The influence of user speed and cell size on the new call blocking probability, Pb, and the call dropping probability, Pd, is investigated. A simpler model that can be used to estimate Pb and Pd in some cases is described. The effect on system capacity of reserving some channels for handoff calls is also studied. It is found that even though prioritized handoff can reduce Pd, it may also degrade the capacity. The accuracy of the analysis is verified using simulation for three mobility models.