The problem of **time** **delay** **compensation** in **deadbeat** **control** for **power** **converters** are considered but not solved systematically, by far. A linear phase-lead **compensation** solution is successfully employed in repetitive **control** systems to compensate the **time** **delay** [14]-[16]. However, it is impractical to be adopted in the conventional **deadbeat** **control** frame due to its incausal lead-**time** item. A state estimator is adopted for **compensation** of computational **delay** [3]. Also focused on this problem, another simple design method of two steps forward prediction approach is proposed in the frame of model predictive **control** [10], [17], [18]. In these solutions, computational **delay** effects are effectively removed and **control** accuracy is prominently improved. However, as mentioned above, apart from computational **delay**, many other factors lead to the **delay** problem in practical systems. In these cases, the above mentioned approaches are not suitable and fail to achieve satisfying **control** performance. Therefore, a universal **delay** **compensation** approach for the **deadbeat** **control** schemes should be investigated in practical applications.

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Sahu et al. [32] have outlined around the design and style as well as effectiveness evaluation regarding Differential Evolution (DE) algorithm based parallel 2-Degree Freedom of Proportional-Integral-Derivative (2-DOF PID) controller for Load Frequency **Control** (LFC) of interconnected **power** system process. The planning issue has been formulated as an optimization issue and DE has been currently employed to look for optimal controller parameters. Standard as well as improved aim features have been used for the planning goal. Standard aim features currently employed, which were Integral of **Time** multiplied by Squared Error (ITSE) and Integral of Squared Error (ISE). To be able to additionally raise the effec- tiveness in the controller, some sort of improved aim operate is derived making use of Integral **Time** multiply Absolute Error (ITAE), damping ratio of dominant eigenvalues, settling times of frequency and peak overshoots with appropriate weight coefﬁcients. The particular ﬁneness in the recommended tech- nique has become conﬁrmed by simply contrasting the results with a lately published strategy, i.e. Craziness based Particle Swarm Optimization (CPSO) for the similar interconnected electric **power** process. Further, level of sensitivity evaluation has been executed by simply varying the machine details as well as managing load conditions off their nominal valuations. It is really observed which the recommended controllers are quite powerful for many the system parameters as well as man- aging load conditions off their nominal valuations.

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which have **time** delays in sensor to controller and controller to actuator paths. Using the linear model of the plant, they obtained a sequence of **control** predictions, and then it was transmitted to the actuator, and the actuator chose the most appropriate data to compensate for the **time** **delay**. Hu et al. [12] used a fuzzy **control** algorithm and Smith method to compensate for the **time** **delay** in networked **control** systems. They provided a fuzzy adaptive PID controller with Smith’s prediction. Using a discrete nonlinear model of the plant and taking advantage of Lyapunov-Krasovskii stability theorem, Peng et al. in [13] derived the maximum allowable **delay** bound and the feedback gain of a controller by solving a set of linear matrix inequalities. In [16], the prediction method based on MPC model for linear systems to compensate for the effect of **time** **delay** and data dropout was studied. The authors of [17] dealt with the **compensation** for data dropout in the linear networked **control** system using the **fractional**-**order** Kalman filter method. Fulto et al. [18] utilized two methods of neutral and extended Kalman filters to compensate for the data dropout in nonlinear systems and compared their performance with each other. Khan et al. [19] investigated the positioning and tracking performance of extended Kalman filter in wireless sensors network. Further, localization performance under varying number of sensors was also evaluated.

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he first step towards the development of new testing procedures for **power** components was demonstrated with the development of hardware-in-the-loop simulation (HIL), which is able to merge the two traditional testing procedures (computer simulation and hardware testing) by interfacing the software simulation with the real hardware under test. Mainly controller devices are used as testing devices for HIL simulation due to the fact that they only need low **power** and voltage signals to be exchanged and consequently this procedure is also called controller-hardware- in-the-loop (C-HIL) simulation. Since just low level signals are exchanged between the software simulation and the hardware under test, this procedure is not valid for **power** components such as motors, generators or **power** **converters** that require higher levels of **power** to be exchanged. Hence, in **order** to achieve an improvement in cost, **time**, flexibility, risk, and accuracy of the testing methodology for these **power** components further development was required. The solution for HIL simulation with **power** components was achieved by the addition of a **power** interface between the software simulation and the hardware under test, as shown in Fig.1. The

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Due to its complexity and diversity, many systems, such as communication systems, **power** systems, biological systems, network transmission systems, always inevitably show hysteresis: the rate of change of the current state is not only related to the state of the cur- rent moment, but it also depends on the state of a certain moment or a certain period of **time** in the past. This property of the systems is called **time** **delay**, and researchers have introduced diﬀerential equations with **time** **delay** to describe and study the **time**-**delay** system. Especially, the dynamics of predator–prey (PP) systems with **delay** have been pro- posed and studied extensively. Many researchers have considered the impact of the past states of biological systems on the present and the future, i.e. incorporating **time** **delay** into biological models to describe resource regeneration **time**, maturation **time**, reaction **time**, capturing **time**, feeding **time**, gestation period [27, 28]. On the other hand, **time**-**delay** bi- ological systems have more complex and richer dynamic behaviors: delays can cause the loss of stability and can induce periodic solutions (Hopf bifurcation), chaos and various oscillations [29–34].

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function expansion in series of exponentials and definition of n th **order** derivative by operating term-by-term, while Riemann introduced the definite integral applicable to **power** series with non-integer exponents. Later, Grunwald and Krug unified the results of Liouville and Riemann, with the first application of **fractional** calculus dating from 1823. Heav- iside developed symbolic methods for solving linear dif- ferential equations of constant coefficients, while Weil and Hardy defined the differ-integral operator properties and Riesz extended the result to multivariable functions, etc. [20]. In the last decades, the number of applications for **fractional**- **order** calculus has been growing exponentially, mainly in the fields of **control** engineering, signal processing and system theory. The main advances were made by Bode’s ideal loop transfer function, followed by Manabe’s results on frequency and transient response of the non-integer integral and its application in **control**. The first occurrence of **fractional** **order** controller may be attributed to Oustaloup, who introduced and demonstrated the superiority of the Commande Robuste dOrdre Non Entier (CRONE) controller. The generalization of the integer **order** proportional-integrative-derivative (PID) controller to **fractional** **order** has been proposed by Podlubny [21]. The **fractional** **order** basic **control** actions, proportional, integral and derivative, add more flexibility to the set of performance specifications the closed loop system is able to fulfill. This is mainly due to the extra tuning parameters of the **fractional** **order** PID (FOPID): the **fractional** **order** of integra- tion and the **fractional** **order** of differentiation. Even though the FOPID represents the most common **fractional** **order** **control** algorithm, other types of **fractional** **order** controllers have been designed, as it will be indicated later in this paper. Review papers focusing on the use of **fractional** calculus in **control** engineering have been published recently such as [22]–[25] and provide an insight into **fractional** **order** **control** of different types. Analytic, numerical and rule-based tuning methods for **fractional** **order** PID controllers only has also been published [26]. Some of these methods can also be used to **control** **time** **delay** systems.

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This paper studies the ﬁnite-**time** stability of **fractional** singular **time**-**delay** systems. First, by the method of the steps, we discuss the existence and uniqueness of the solutions for the equivalent systems to the **fractional** singular **time**-**delay** systems. Furthermore, we give the Mittag-Leﬄer estimation of the solutions for the equivalent systems and obtain the suﬃcient conditions of the ﬁnite-**time** stability for the original systems.

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using a fixed FROH in the closed loop behavior and, it investigates the performance of two different multi-model schemes. It is supported by the idea that FROH with intermediate adaptation rate modifies the location of the zeros of the discrete transfer function with respect to those obtained from the use of a zero-**order**-hold (ZOH) or a first-**order**-hold (FOH). Two possible advantages are: a) the stability degree of stable zeros can be improved so that some of them can be better cancelled when implementing a model-following **control** design while improving the transient closed- loop behavior; b) the discrete **control** can better accommodate the rippling effect in-between any two consecutive sampling instants when applying a discrete-**time** **control** to a continuous-**time** plant. The reason is that there is there is a kind of practical interpolation in continuous **time** from measured data in-between two consecutive such samples due to the structure of the FROH what allows to accommodate the **control** law in continuous **time** while just using discrete-**time** data. 18,19,20 As a result, the controller can lead, for example, to produce better surface finish and maintenance of the tool and machine tool components and to minimize wear of the tool while avoiding or minimizing electrical ripple. Multi-model schemes are also useful, for instance, when the system works in different states governed by different equations from the milling case or, to modify the closed-loop structure in one working point achieving best tracking performance. So, the algorithm methodologies can be useful when the holistic **control** of the milling process is taking into account in **order** to achieve better surface finish or to deal with some kind of intrinsic non-linearity. Also, FROH has potential benefits when dealing with ramp form milled parts or to improve transient responses leading to further potential benefits.

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In distribution systems, there will be sudden increase or decreases in the load similar to nonlinear load .The load draws non-sinusoidal currents from the AC mains and these causes the load harmonics and reactive **power**, and excessive neutral currents that pollute **power** systems. Most of the **power** quality issues are created by nonlinear characteristics and fast switching of **power** electronic devices. A single distribution generation interfacing **converters** are generally used for harmonic **compensation** in DG but this may cause amplification of supply voltage harmonics when the system is connected to a sensitive load. In this paper we proposed a **compensation** strategy in which to shunt interfacing **converters** are used, first one for voltage harmonic suppression and the second one for current harmonic suppression that resulted due to the interaction between the first interfacing converter and the local nonlinear load

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III. P ROTECTION OF D ISTRIBUTED G ENERATION We use the impedance measurement to identify the proximity of a grid fault to PEE. This measurement is used to decide whether PEE should ride through certain remote faults to avoid nuisance trips. Islanding may also be detected. Consider the system in Fig. 6 in which a small **power** system is defined to be a “protected zone” in a larger **power** system. Details of the system parameters, which are based on a medium voltage distribution system, are given in the Appendix. Within the zone there are distributed generation and **power** electronic equipment – for example an active filter, a grid interface for a wind turbine, or photovoltaic system – which are connected at the point of measurement (POM).

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Stability analysis of nonlinear systems is necessary to design a controller. Several works have investigated stability analysis of nonlinear systems by means of **fractional** calculus [26-30]. In [26], **fractional** generalization of concept of stability was considered. In [27], a definition for Mittag-Leffler stability and **fractional** Lyapunov direct method were presented. In [28], stability analysis of FO nonlinear systems was derived using the Lyapunov direct method with Mittag-Leffler stability. In [29], stability of **fractional** differential systems based on the conformable **fractional** derivatives was studied. However, there are very few papers considering modelling of the nonlinear systems with conformal FO definition [29,30]. Therefore, application of the conformable FO operators in the design of FO controller is an open area. Accordingly, for the first **time**, in this paper, a FO sliding mode **control** is designed for a class of conformable **fractional** **order** chaotic system using the conformable **fractional** derivative and the superiority of the proposed controller is shown. Having these facts in mind, the main contributions of this paper in comparison with previous researches are as follows. A novel FO manifold using conformable FO operators is proposed to **control** chaotic systems in the presence of uncertainties and disturbances. The conformable FO operator as an interesting definition is applied in designing of the FO sliding mode controller. Based on conformable FO operators, the stability of the controller is derived using the Lyapunov direct method. The main advantage of the proposed **control** method is fast convergence speed with together less chattering and complexity in calculations.

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ower hardware-in-the-loop (PHIL) simulation is an ex- tension of the widely known hardware-in-the-loop (HIL) simulation concept. However, in contrast with the most common procedure of HIL called controller hardware-in-the- loop (CHIL), where the hardware under test (HUT) is a con- troller that only exchanges **control** signals with the simulated system, PHIL allows the testing of **power** components by exchanging **power** with the simulated system through the **power** interface. The **power** interface electrically couples and converts the low voltage/**power** signals of the real **time** simu- lator (RTS) into high voltage/**power** signals going into the HUT. The HUT responds to the applied signal (current or voltage), and the measurement of this response is fed back (by the **power** interface or an external measurement unit) to the RTS closing the loop, and therefore creating a simulation system that ideally would match with the real one. This struc- ture of a PHIL simulation is shown in Fig. 1. However, stabil- ity and accuracy issues exist when an interface is used, this is due to the introduced error during the simulation and amplifi- cation stages, and also to additional components introduced to compensate for the **time**-**delay** or for a stability improvement [1-4].

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This article discusses the **control** system of **fractional** endpoint variable variational problems. For this problem, we prove the Euler-Lagrange type necessary conditions which must be satisﬁed for the given functional to be extremum. Finally, one example is provided to show the application of our results.

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Grünwald–Letnikov sense. Stability analysis of ﬁxed points is studied. Corresponding **fractional** optimal **control** problem, with **time** delays in both state and **control** variables, is formulated and studied. Two simple numerical methods are used to study the nonlinear **fractional** **delay** optimal **control** problem. The methods are standard ﬁnite diﬀerence method and nonstandard ﬁnite diﬀerence method. Comparative studies are implemented, it is found that the nonstandard ﬁnite diﬀerence method is better than the standard ﬁnite diﬀerence method.

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Abstract - The **power** electronic **converters** plays crucial role in conversion and **control** of the electrical **power**. The production of solar energy is based on the idea of converting a type of energy mostly solar energy into electrical energy. The most appealing renewable energy source is photovoltaic which transform the solar energy into DC electrical energy. **Power** electronics **converters** are used to **control** frequency and magnitude of the current resultant from the conversion between energies. The objective of this paper is to model and **control** of transformer-less grid connected PV system with Hysteresis controller which can be used to supply the electric **power** to utility grid. This system uses two stage conversion process. DC to DC stage which utilizes MPPT technique to extract the maximum **power**. DC to AC which used to **control** inverter output by using hysteresis Current controller. The problem of maximum **power** transferring is enhanced by using Incremental conductance algorithm and phase locked loops are utilized in conjunction to make supply in synchronization with the grid which reduces the two problems described. The studied system is modeled and simulated in the MATLAB/SIMULINK environment.

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However, to the best of the authors’ knowledge, to this day, still less scholars consider the adaptive impulsive synchronization of **delay** **fractional**-**order** chaotic systems. Motivated by the above works, the adaptive impulsive synchronization for a class of **fractional**-**order** chaotic systems with an unknown Lipschitz constant and **time** **delay** is discussed. The rest of this paper is organized as follows: In Section 2, some preliminaries of **fractional** derivative are briefly introduced. A new adaptive impulsive synchronization method of **delay** **fractional**-**order** chaotic systems is proposed in Section 3, based on the theory of Lyapunov stability and impulsive differential equations. Finally, conclusions are addressed in Section 4.

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share is expected to double in the next 15 years, partly due to the rapid growth of variable renewable energy from solar photo voltaics and wind. This IRENA/IEA-ETSAP Technology Brief provides an overview of the main performance and costs of technologies that are used to support renewable energy grid integration, an overview of the shares of variable renewable energy across the world, and existing operational experiences in continental and island systems. There are several technology options available that can help integrate variable renewable energy into **power** systems. Furthermore, new advances in wind and solar technologies allow them to be used over a wider range of conditions. In the longer run, however, **power** systems with high shares of variable renewable **power** generation will require a re-thinking the traditional designs, operations, and planning practices from a technical and an economical point of view.Two immediate applications for innovative technologies and operation modes for the integration of high shares of solar photovoltaics and wind are in mini-grids and islands. Furthermore, any economic analysis of the transition towards a renewables -based system should always consider the total system costs, including social and environmental benefits

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The **fractional** calculus is the area of mathematics that handles derivatives and integrals of any arbitrary **order** (**fractional** or integer, real or complex **order**).Although the concept of the **fractional** calculus was discussed in the same **time** interval of integer **order** calculus, the complexity and the lack of applications postponed its progress till a few decades ago. During the last few decades, most of the dynamical systems based on the integer-**order** calculus have been modified into the **fractional** **order** domain due to the extra degrees of freedom and the flexibility which can be used to precisely fit the experimental data much better than the integer- **order** modeling and **fractional** calculus has become a powerful tool in describing the dynamics of complex systems which appear frequently in several branches of science and engineering. Therefore **fractional** differential

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For analogy, the performance of controller tuning methods is compared for variations in load and set point when they undergo a step change of unit magnitude. L/T ratio is a signifi- cant factor which affects the controller performance and sensi- tivity of the feedback **control** system. The effect of L/T ratio on different tuning methods was studied by varying **time** **delay** L so that the ratio L/T varies from 0.1 to 2 covering lag dominant, balanced and **delay** significant processes. The simulations were carried out on different FOPTD processes. The main reason for varying the L/T ratio is that it affects the robustness of **control**- ler and performance of the closed loop system. For each varia- tion of L/T, new controller settings are calculated and closed loop response (both servo and regulatory) is observed, thus recording IAE, TV and M s . The trends of the performance

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