Power sharing and stability enhancement of an autonomous microgrid with inertial and non-inertial DGs with DSTATCOM

This paper proposes a method of enhancing system stability with a distribution static compensator (DSTATCOM) in an autonomous microgrid with multiple distributed generators (DG). It is assumed that there are both inertial and non-inertial DGs connected to the microgrid. The inertial DG can be a synchronous machine of smaller rating while inertia less DGs (solar) are assumed as DC sources. The inertia less DGs are connected through Voltage Source Converter (VSC) to the microgrid. The VSCs are controlled by either state feedback or current feedback mode to achieve desired voltage-current or power outputs respectively. The power sharing among the DGs is achieved by drooping voltage angle. Once the reference for the output voltage magnitude and angle is calculated from the droop, state feedback controllers are used to track the reference. The angle reference for the synchronous machine is compared with the output voltage angle of the machine and the error is fed to a PI controller. The controller output is used to set the power reference of the synchronous machine. The rate of change in the angle in a synchronous machine is restricted by the machine inertia and to mimic this nature, the rate of change in the VSCs angles are restricted by a derivative feedback in the droop control. The connected distribution static compensator (DSTATCOM) provides ride through capability during power imbalance in the microgrid, especially when the stored energy of the inertial DG is not sufficient to maintain stability. The inclusion of the DSATCOM in such cases ensures the system stability. The efficacies of the controllers are established through extensive simulation studies using PSCAD.

Primary control level of parallel distributed energy resources converters in system of multiple interconnected autonomous microgrids within self-healing networks

To minimise the number of load sheddings in a microgrid (MG) during autonomous operation, islanded neighbour MGs can be interconnected if they are on a self-healing network and an extra generation capacity is available in the distributed energy resources (DER) of one of the MGs. In this way, the total load in the system of interconnected MGs can be shared by all the DERs within those MGs. However, for this purpose, carefully designed self-healing and supply restoration control algorithm, protection systems and communication infrastructure are required at the network and MG levels. In this study, first, a hierarchical control structure is discussed for interconnecting the neighbour autonomous MGs where the introduced primary control level is the main focus of this study. Through the developed primary control level, this study demonstrates how the parallel DERs in the system of multiple interconnected autonomous MGs can properly share the load of the system. This controller is designed such that the converter-interfaced DERs operate in a voltage-controlled mode following a decentralised power sharing algorithm based on droop control. DER converters are controlled based on a per-phase technique instead of a conventional direct-quadratic transformation technique. In addition, linear quadratic regulator-based state feedback controllers, which are more stable than conventional proportional integrator controllers, are utilised to prevent instability and weak dynamic performances of the DERs when autonomous MGs are interconnected. The efficacy of the primary control level of the DERs in the system of multiple interconnected autonomous MGs is validated through the PSCAD/EMTDC simulations considering detailed dynamic models of DERs and converters.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Decentralized linear quadratic power system stabilizers for multi-machine power systems

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead-lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not available in most of the power plants. Full state feedback controllers require feedback of other machine states in a multi-machine power system and necessitate block diagonal structure constraints for decentralized implementation. This paper investigates the design of Linear Quadratic Power System Stabilizers using a recently proposed modified Heffron-Phillip's model. This model is derived by taking the secondary bus voltage of the step-up transformer as reference instead of the infinite bus. The state variables of this model can be obtained by local measurements. This model allows a coordinated linear quadratic control design in multi machine systems. The performance of the proposed controller has been evaluated on two widely used multi-machine power systems, 4 generator 10 bus and 10 generator 39 bus systems. It has been observed that the performance of the proposed controller is superior to that of the conventional Power System Stabilizers (PSS) over a wide range of operating and system conditions.

Determination of structurally constrained controllors

This paper reports on determination of structurally constrained controllers for linear uncertain time-invariant systems from state controllers. It is shown that practical structures such as output and decentralized controllers may be derived from state feedback controllers. A previously studied load frequency control of a two-area interconnected power system is considered to illustrate the proposed approach.

Stabilizing controller design for uncertain nonlinear systems using fuzzy models

A Lyapunov-based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed. The controller is constructed using a design model of the dynamical process to be controlled. The design model is obtained from the truth model using a fuzzy modeling approach. The truth model represents a detailed description of the process dynamics. The truth model is used in a simulation experiment to evaluate the performance of the controller design. A method for generating local models that constitute the design model is proposed. Sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state-feedback controllers are given. The results obtained are illustrated with a numerical example involving a four-dimensional nonlinear model of a stick balancer.

Alocação de zeros aplicada a sistemas de controle via LMI

A systematic procedure of zero placement to design control systems is proposed. A state feedback controller with vector gain K is used to perform the pole placement. An estimator with vector gain L is also designed for output feedback control. A new systematic method of zero assignment to reduce the effect of the undesirable poles of the plant and also to increase the velocity error constant is presented. The methodology places the zeros in a specific region and it is based on Linear Matrix Inequalities (LMIs) framework, which is a new approach to solve this problem. Three examples illustrate the effectiveness of the proposed method.

Exponential stabilization for state and input delay systems via output feedback

This paper considers the exponential stabilization problem via static and dynamic output feedback controllers of linear systems with a time delay in both the state and input. By using a change of the state variable and combining with the Lyapunov-Krasovskii method, new sufficient conditions for exponential stabilization via static and dynamic output feedback controllers are proposed. The conditions are expressed in terms of matrix inequalities but with only one parameter needs to be tuned and therefore can be efficiently solved by incorporating an one-dimensional search method into the Matlab’s LMI toolbox. Two numerical examples are provided to illustrate the obtained results.

Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

Robust Controller Design of Networked Control Systems with Nonlinear Uncertainties

We address robust stabilization problem for networked control systems with nonlinear uncertainties and packet losses by modelling such systems as a class of uncertain switched systems. Based on theories on switched Lyapunov functions, we derive the robustly stabilizing conditions for state feedback stabilization and design packet-loss dependent controllers by solving some matrix inequalities. A numerical example and some simulations are worked out to demonstrate the effectiveness of the proposed design method.

A Flight control scheme to improve position tracking performance of rotary-wing UASs

This paper outlines an innovative and feasible flight control scheme for a rotary-wing unmanned aerial system (RUAS) with guaranteed safety and reliable flight quality in a gusty environment. The proposed control methodology aims to increase gust-attenuation capability of a RUAS to ensure improved flight performance when strong gusts occur. Based on the design of an effective estimator, an altitude controller is firstly constructed to synchronously compensate for fluctuations of the main rotor thrust which might lead to crashes in a gusty environment. Afterwards, a nonlinear state feedback controller is proposed to stabilize horizontal positions of the RUAS with gust-attenuation property. Performance of the proposed control framework is evaluated using parameters of a Vario XLC helicopter and high-fidelity simulations show that the proposed controllers can effectively reduce side-effect of gusts and demonstrate performance improvement when compared with the proportional-integral-derivative (PID) controllers.

Interconnected autonomous microgrids in smart grids with self-healing

In order to minimize the number of load shedding in a Microgrid during autonomous operation, islanded neighbour microgrids can be interconnected if they are on a self-healing network and an extra generation capacity is available in Distributed Energy Resources (DER) in one of the microgrids. In this way, the total load in the system of interconnected microgrids can be shared by all the DERs within these microgrids. However, for this purpose, carefully designed self-healing and supply restoration control algorithm, protection systems and communication infrastructure are required at the network and microgrid levels. In this chapter, first a hierarchical control structure is discussed for interconnecting the neighbour autonomous microgrids where the introduced primary control level is the main focus. Through the developed primary control level, it demonstrates how the parallel DERs in the system of multiple interconnected autonomous microgrids can properly share the load in the system. This controller is designed such that the converter-interfaced DERs operate in a voltage-controlled mode following a decentralized power sharing algorithm based on droop control. The switching in the converters is controlled using a linear quadratic regulator based state feedback which is more stable than conventional proportional integrator controllers and this prevents instability among parallel DERs when two microgrids are interconnected. The efficacy of the primary control level of DERs in the system of multiple interconnected autonomous microgrids is validated through simulations considering detailed dynamic models of DERs and converters.

Joint Performance Analysis of Channel Quality Indicator Feedback Schemes and Frequency-Domain Scheduling for LTE

Frequency-domain scheduling and rate adaptation enable next-generation orthogonal frequency-division multiple access (OFDMA) cellular systems such as Long-Term Evolution (LTE) to achieve significantly higher spectral efficiencies. LTE uses a pragmatic combination of several techniques to reduce the channel-state feedback that is required by a frequency-domain scheduler. In the subband-level feedback and user-selected subband feedback schemes specified in LTE, the user reduces feedback by reporting only the channel quality that is averaged over groups of resource blocks called subbands. This approach leads to an occasional incorrect determination of rate by the scheduler for some resource blocks. In this paper, we develop closed-form expressions for the throughput achieved by the feedback schemes of LTE. The analysis quantifies the joint effects of three critical components on the overall system throughput-scheduler, multiple-antenna mode, and the feedback scheme-and brings out its dependence on system parameters such as the number of resource blocks per subband and the rate adaptation thresholds. The effect of the coarse subband-level frequency granularity of feedback is captured. The analysis provides an independent theoretical reference and a quick system parameter optimization tool to an LTE system designer and theoretically helps in understanding the behavior of OFDMA feedback reduction techniques when operated under practical system constraints.

Joint evaluation of channel feedback schemes, rate adaptation, and scheduling in OFDMA downlinks with feedback delays

Orthogonal frequency-division multiple access (OFDMA) systems divide the available bandwidth into orthogonal subchannels and exploit multiuser diversity and frequency selectivity to achieve high spectral efficiencies. However, they require a significant amount of channel state feedback for scheduling and rate adaptation and are sensitive to feedback delays. We develop a comprehensive analysis for OFDMA system throughput in the presence of feedback delays as a function of the feedback scheme, frequency-domain scheduler, and rate adaptation rule. Also derived are expressions for the outage probability, which captures the inability of a subchannel to successfully carry data due to the feedback scheme or feedback delays. Our model encompasses the popular best-n and threshold-based feedback schemes and the greedy, proportional fair, and round-robin schedulers that cover a wide range of throughput versus fairness tradeoff. It helps quantify the different robustness of the schedulers to feedback overhead and delays. Even at low vehicular speeds, it shows that small feedback delays markedly degrade the throughput and increase the outage probability. Further, given the feedback delay, the throughput degradation depends primarily on the feedback overhead and not on the feedback scheme itself. We also show how to optimize the rate adaptation thresholds as a function of feedback delay.