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Networked distributed automatic generation control of power system with dynamic participation of wind turbines through uncertain delayed communication network

2017; Institution of Engineering and Technology; Volume: 11; Issue: 8 Linguagem: Inglês

10.1049/iet-rpg.2016.0508

1752-1424

Ehsan Bijami, Malihe M. Farsangi,

Wind Turbine Control Systems

IET Renewable Power GenerationVolume 11, Issue 8 p. 1254-1269 Special Issue: Active Power Control of Renewable Energy Generation SystemsFree Access Networked distributed automatic generation control of power system with dynamic participation of wind turbines through uncertain delayed communication network Ehsan Bijami, Corresponding Author Ehsan Bijami e.bijami@eng.uk.ac.ir Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, IranSearch for more papers by this authorMalihe M. Farsangi, Malihe M. Farsangi Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, IranSearch for more papers by this author Ehsan Bijami, Corresponding Author Ehsan Bijami e.bijami@eng.uk.ac.ir Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, IranSearch for more papers by this authorMalihe M. Farsangi, Malihe M. Farsangi Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, IranSearch for more papers by this author First published: 16 June 2017 https://doi.org/10.1049/iet-rpg.2016.0508Citations: 8AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study proposes a new distributed networked control (DNC) scheme and its stability analysis framework for automatic generation control in networked interconnected power systems with participation of wind turbine. It is assumed that the remote control signals are measured at locations away from the control site and exchanged among a non-ideal communication network with both time-varying delays and random packet dropouts. First, a model is proposed for large-scale DNC system consisting of subsystems, in which the states of each subsystem have their own time-varying delay and there are also delay and packet dropouts in their interconnection links. Then, a linear matrix inequality (LMI)-based method is proposed to design the distributed controller for better system performance. For this, a new Lyapunov–Krasovskii function is developed to conclude some LMI-based delay-independent theorem for designing control law. To evaluate the proposed method, a multi-area power system with participation of wind turbine is considered. Simulation results show the capability of the proposed approach to enhance the performance of networked power system in the presence of load perturbation among a non-ideal communication network with both time-varying delays and random packet dropouts. 1 Introduction Owing to a steady increase in energy demand and environmental, the concerns focus has changed to generating power from renewable energy sources [1]. Wind energy is one of the most rapidly growing promising renewable energy sources due to the environmental and economical benefits. In the modern electric grids especially when penetrated with wind power, due to variable characteristic of wind power, a serious degree of disturbance in the power system has happened that leading to the changes in tie-line power and system frequency. To eliminate the frequency deviation quickly and to keep the tie-line power at its nominal value, the automatic generation control (AGC) concept is employed. AGC performs an important role in the large-scale multi-area interconnected power systems to balance demand and supply; and maintains system frequency and tie-line power at their scheduled values [2, 3]. In the last four decades, the AGC problem has been extensively studied by researchers around the world and many control strategies have been applied to solve the problem [3]. Typically, design of AGC has been proposed based on centralised control frameworks [3-7]. Although, centralised control is known to provide the best performance due to imposing the least constraints on the control signals, but the computational burden and organisational complexity relevant to centralised controllers often makes their implementation impractical, especially for large-scale power systems with highly interconnected subsystems and complex dynamics. Furthermore, the consequences of failures in a centralised control scheme can influence on the overall system [8]. Moreover, one of the major attributes of modern smart grid is integration of geographically distributed renewable power resources into the traditional power grid [9]. As a result, traditional centralised control is not always suitable in smart grids, and distributed control is essential for flexible energy management [10] due to providing appropriate structure which reduces the computations through the coordination and parallel processing. Therefore, different distributed control methods are proposed by researchers to solve the AGC problem in large-scale power systems [8, 11-14]. In addition, with the integration of communication technologies into the power system and the advancements of the wide-area measurement system technology, remote signals have become available as the feedback signals to design controller for geographically distributed large-scale power systems [15]. The availability of remote signals provides an additional prospect of controlling power systems and enhancing the dynamic performance. However, the usage of remote signals through the communication networks introduces new serious challenges into the design of wide-area AGC system such as time-delay and packet dropouts which will inevitably degrade the performance or may even destabilise entire system [16]. The control systems (CSs) over communication networks are typically referred to as networked CSs (NCSs). The NCS poses many outstanding advantages over the traditional control architectures including low cost of installation, ease of maintenance and greater flexibility. In the literature, substantial works have been reported for modelling of NCS such as using discrete Markov switching systems [17], stochastic hybrid systems [18] and delay impulsive systems [19], in which the effect of packet dropouts and time delays on the control design and the stability of the NCS are not studied simultaneously in them. Besides, in recent years NCS is extended to geographically distributed system. However, in most of the existing literatures relating to distributed NCSs (DNCSs), it is premised that the controllers and plants exchange information through an ideal communication network with no time delays or packet dropouts. A few exceptions to this are the works carried out in [20-23]. Moreover, an important aspect of DNCS is how to take care of the communication latency affecting the communication links between the subsystems which is not considered in the literature. In view of these points, this paper aims at proposing a new DN approach in order to take the above-mentioned issues into account in modelling and control of DN systems. Then, reflecting the proposed approach to distributed power system AGC problem in networked interconnected power systems concerning the integration of wind power units. To the best knowledge of the authors, there are few papers on the networked controller design of power system by considering network packet dropouts and time delays [24-28]. These papers do not consider the aforementioned network-induced problems in the communication links between the subsystems, which motivates the research in this paper. Thus in this paper, first, within the generic framework of NCS, a new model is developed for DNCS, consisting of subsystems interconnected through their states, in which the states of each subsystem have their own time-varying delay and there are also delays and packet dropouts in their interconnection links. Then, to compensate the influence of subsystems on each other and enhance performance and stability margin of the closed-loop system, a most general possible feedback control law is proposed. The stability criteria are provided based on Lyapunov–Krasovskii and LMI techniques. For this, a new LMI-based delay-independent theorem is developed for designing control law under network-induced packet dropouts and time delays. To show the capability and effectiveness of the proposed approach, a representative power system with several interconnected areas and with different cases of perturbations is considered for simulation studies. The main contributions of this paper can be summarised as follows: (i) Presenting a new model for DNCS with interconnected subsystems, which is independent from subsystem's interconnection topology and both network packet dropouts and time delays are considered in communication links between its coupling subsystems. (ii) Developing a new DNC scheme for DNCS with interconnected subsystems featuring non-ideal communication network with both time-varying delays and random packet dropouts. (iii) Providing delay-independent stability criteria and extracting a sufficient condition for asymptotic stability of closed-loop DNCS system in terms of LMI theorems. (iv) Reflecting the proposed modelling and control of DNCS to AGC of networked multi-area power system with considering wind turbine. The rest of this paper is organised as follows. A distributed model for DNCS is described in Section 2. Section 3 presents the proposed control strategy and its LMI-based stability analysis. Simulation studies on a representative multi-area interconnected power system are presented in Section 4. In the case study, the frequency deviations in the networked power system are controlled using feedback signals which are transmitted over a non-ideal communication network. Finally, Section 5 concludes this paper. The nomenclatures of the parameters which are used in this paper are listed in Table 1. Table 1. Nomenclatures Parameter/variable Description ni-dimensional Euclidean space the set of all matrices Ts sampling period, s τij interconnection delay, s τi state delay, s τijm lower bound of interconnection delay, s τijM upper bound of interconnection delay, s τim lower bound of state delay, s τiM upper bound of state delay, s xi state vector ui control input Ai state matrix Bi input matrix Adi state delay matrix Aij interconnection matrix N number of subsystems Ki feedback gains of local feedbacks Kdj feedback gains of delayed state feedbacks Kij feedback gains of supplemental feedbacks * stands for a term that is induced by symmetry in the symmetric block matrices T denotes the transpose of a matrix or a vector Row{Ai} for i = 1, 2, …, N shows the matrix max[A1, A2, …, AN] 2 Modelling of large-scale DNCS DNCS consists of numerous coupled subsystems interact through a communication network. However, because of finite bandwidth and possible data concussions in communication networks, transmission/propagation delays and packet dropouts are inescapable in an NCS [29]. 2.1 Modelling of network-induced delay and packet dropouts in DNCS To develop a new DNCS model with network-induced delay and packet dropouts, without loss of generality, two discrete-time subsystems are considered as illustrated in Fig. 1, in which the controllers exchange information within a non-ideal communication channel, where denotes the network-induced delay. Before presenting the DNCS model, it is necessary to provide some explanations as below. Fig. 1Open in figure viewerPowerPoint Non-ideal communication link model of a DNCS The jth local controller sends the states of its relative subsystem, i.e. , at each k time-step with a period of seconds, and the ith subsystem receives data at moments. The data packet disorder phenomenon often occurs in many communication networks [22]. If the data packet disorder phenomenon has occurred, then wrong data may be used in producing of control commands which leads to a bad performance [30]. Therefore, the right data and the most recent data must be selected to compute the control signal. As a result, to compensate the wrong packet sequences, each packet of data is labelled with a 'time stamp' that contains the information of the corresponding sampling time. Also, each local controller consists of a buffer that saves the last arrived data packet until the entrance of the next packet; as soon as a new packet is received, its time stamp is compared with the time stamp of the present packet in the ith buffer. If the recently received packet data is newer than the present packet, then the ith buffer updates; otherwise, the newly arrived packet will be passed up. This procedure provides an assurance that the most newly possible data is employed in producing of control commands. Thus, by using this strategy, the performance depreciation will be decreased. To the time-stamped data to be precise, the clocks of the sensors and all subsystems' controller should be synchronised. In this regard, some real-time clocks and well-established synchronisation methods are carried out in the literature [31]. Suppose at moment , the ith subsystem receives a more new packet, consisting of the data states from the jth subsystem with a delay of . Therefore, the buffer of the ith subsystem will be updated. Now, suppose that the next newer packet receives at instant and within the time to , the packet dropouts are occurred in the network for times sequentially, which means that the switch w in Fig. 1 will remain open for time steps. Thus, within the time –, the ith controller uses the information stored in the buffer that has been received at moment which is shown by . As a result, the model of a DNCS with time delays and packet loss can be presented as follows: (1) According to (1), the DNCS with time-varying delay and accumulated sequentially dropped data packets is shown by , in which is an uncertain time-varying interconnection delay that stands for both network-induced delays and packet dropouts. This interconnection delay satisfies and is so-called as interval-like delay [32] which means that the lower bound (minimum size of delay) and the upper bound (maximum size of delay) are known. Remark 1.It should be noted that the delays induced by the network may not certainly be an integer multiples of the sampling periods. This means that data packets may arrive between sampling moments. Nevertheless, the ith buffer will be updated at instants , where . Therefore, the transmission delay is equal to , in which stands for ceiling operator. As a result, is integer valued. Remark 2.Considering interconnection delay as interval-like delay is more comprehensive due to the lower bound. Since, if , the interval-like delay reduces to a usual limited delay, and if the time-varying delay becomes a constant delay. 2.2 Plant description Consider a DN plant S containing N subsystems . These N subsystems are interconnected together and each subsystem receives information from neighbouring subsystems. If subsystem is coupled with subsystem , then the jth controller sends data about the states of subsystem to the ith controller. In this case, is so-called a neighbouring subsystem of . The set of all neighbouring subsystems of is described by As mentioned before, the interconnection delay consists of both delays and packet dropouts induced by non-ideal communication links. Also, it should be noted that each controller only has access to the variables of those neighbouring subsystems that interact with its corresponding subsystem's dynamic through the communication channels. The general model of the ith subsystem of a large-scale distributed system with interconnection is as follows [33]: (2) Thus, the dynamic model of the ith subsystem with time-varying delays in its states and interconnections can be described as below (3) with the initial condition for where . Also, and , show state vector and control input, respectively. Furthermore, , , and are real and constant matrices, in which and are the system's matrices and and show the state delay matrix and interconnection matrix, respectively. Moreover, and for , , are uncertain time-varying state and interconnection delays, respectively, meet the following conditions: Remark 3.On the basis of [34-36], if the properties of the network are known, then the upper bound of delays can be estimated. Therefore, in this paper, all considered lower and upper bounds of delays are assumed to be known and constant integers. Although in designing of controller, we do not need to use the lower bounds of delay. Assumption 1.It is assumed that we have connection oriented and active queue management protocol as congestion avoidance algorithm. Moreover, the interconnection term , where , represents the impact of the jth subsystem on the ith subsystem. If the states of the jth subsystem are not coupled with the ith subsystem, matrix will be zero. The proposed model in (1) is a general description of the subsystems which are connected together and is independent from subsystem's interconnection topology. 3 Proposed control strategy and its stability analysis 3.1 Control strategy In this section, a new state feedback control law is proposed for a DNCS, in which the subsystems of network are modelled with (3) and are interconnected to each other through a non-ideal communication link. For each subsystem, the control law is proposed as follows: (4) where and are the feedback gains of local feedbacks, delayed state feedbacks and supplemental feedbacks, respectively. In this control strategy, in addition to local feedbacks , other two types of feedbacks are also considered. The delayed state feedbacks are useful for improvement of performance and stability margin. Furthermore, the term is supplemental feedbacks which are designed to enhance both stability and performance by compensating the influence of the jth neighbouring subsystem on the dynamics of the ith subsystem. Remark 4.In (4), though time-varying delays are used in control signal, but, if they are unknown, we can use the upper bounds of delays ( and ) instead of and where according to Remark 3, the upper bounds of delays can be estimated. It is worthwhile to express that the proposed control strategy is the most general possible form for control law, where other control structures can be taken straight from it. For instance, by selecting a fully decentralised control structure is deduced from (4) and with it becomes a distributed control strategy with no memory. The main objective of this paper is considering of all three feedback terms simultaneously, ensuring stability and improving the performance for greater category of large-scale DNCSs, with interconnected subsystems. In this regard, in the next section a sufficient condition is provided for the asymptotic stability of the closed-loop DNCSs. 3.2 Closed-loop system formulation and stability analysis In this section, a sufficient condition is provided to investigate the stability of the overall closed-loop DNCS with the control law proposed in (4). In general, the stability analysis of an NCS with network-induced delays can be categorised into two major classes [21]: the delay-independent case and the delay-dependent case. In the time-delay-independent stability analysis there is no need to know the values of delays or even the upper and lower bounds of them. Therefore, the stability criteria are obtained independent from the size of the delays. In this paper, the delay-independent stability analysis is considered and an LMI-based delay-independent theorem is proposed to obtain the sufficient condition for asymptotic stability of the closed-loop system. By applying the proposed control law in (4) to the open-loop subsystem (3), the closed-loop dynamical system is given as follows: (5) where , and for , . The above closed-loop dynamical system is shown in Fig. 2. Fig. 2Open in figure viewerPowerPoint Closed-loop of dynamical system Assuming and are known, an LMI-based delay-independent sufficient condition can be derived for asymptotic stability of closed-loop DNCS presented in (5) through Theorem 1. Theorem 1.The closed-loop DNCS S, consists of N subsystems and described by (5), is delay-independent asymptotically stable if there exist matrices , , and of appropriate dimensions, such that satisfy LMI (6) as (6) where , , and are symmetric positive definite matrices of appropriate dimensions and must be chosen such that satisfy LMI (6), where Proof.Consider a Lyapunov–Krasovskii function (V) for the entire system S as (7) where k is the discrete-time index. Furthermore, i is the index of the ith subsystem where and N is the number of subsystems. Also, we have With taking the forward difference along (7) and using (5), we have thus Also, we have To reduce conservatism of stability condition, an efficient method is to introduce slack variables to provide more freedom to optimise the LMI solution [37, 38]. Therefore, to derive Theorem 1, the slack variable Hi is introduced through (8), where the purpose is to reduce conservatism and more flexibility in the existing delay-independent stability conditions [LMI condition (6)] (8) thus we obtain (9) With some mathematical manipulation, it leads to (10) where is shown in (6) and we have where index nei stands for the states of neighbouring subsystem . Also, for an arbitrary matrix such as , for shows the matrix .Now, if inequality (6) is satisfied, i.e. , the ith subsystem is asymptotically stable. Besides, since results in , the global system S becomes asymptotically stable.□ 3.3 Design of DNCS controller This section proposes an LMI-based method to design the DN controller suggested in (4). As can be seen from (6), when feedback's gains in (4), i.e. , and for are unknown, (6) will become non-linear and LMI approaches would not be enforceable in the controller design. As a result, some modifications are necessary to change non-LMI (6) into a linear one. As soon as this conversion is done, the designer becomes able to use existing LMI solvers and compute the stabilising feedback gains , and , easily. For this, first, the Schur complement lemma is given followed by Theorem 2 which converts non-LMI (6) to an LMI to enable the designer to design the independent-delay stabilising feedback's gains for all subsystems. Lemma 1.: (Schur complement [39]): Consider constant matrices Q, L,and with appropriate dimensions, where and are symmetric matrices, then and if and only if or equivalently Theorem 2.Given subsystem described in (3), for any delay in states and delay in interconnections , there is the state feedback controller (4) in such a way that the closed-loop system (5) is asymptotically stable, if there exist matrices , , , , , and for of appropriate dimensions, such that satisfy (11) where Moreover, controller's gains are calculated as and . Also, for are obtained directly. Proof.By applying Lemma 1 to inequality (6), it can be seen that if the following inequality is satisfied: (12) where .By defining and multiplying to both sides of (12) and using and the LMI (12) is obtained. □ Therefore, by solving LMI (6) using one of the existing convex programming tools such as LMI toolbox MATLAB, the asymptotically stable feedback controller will be straightforwardly designed for each subsystem. 4 AGC system design In this section, an interconnected power system with participation of wind turbine, adopted from [13], is provided to show the capability of the proposed DN AGC system. 4.1 Distributed model of large-scale interconnected power system with wind turbine A four-area interconnected power system model which consists of thermal power plant, variable speed wind turbine (VSWT) and hydro power plant, as shown in Fig. 3, is considered for design of DN AGC system. As illustrated in Fig. 3, wind turbine is installed in area 1. Also, area 4 includes the thermal power plant, while area 2 and area 3 are hydro power plants. Details of the compositions of each area and the mathematical presentation of wind turbine, thermal power plant and hydro power plants are the same as those are given in [13]. Moreover, area 1 consists of an aggregated wind turbine model which comprises of 40 VSWT units and the capacity of thermal plant is 600 MW. Fig. 3Open in figure viewerPowerPoint Four-area interconnected power system Suppose that the ith control area (i = 1, 2, 3, 4) is to be interconnected with the jth control area, through a tie-line. Subsequently, the state space equation of each control areas can be presented with the following equations [13]: (13) where , and are the state vector, the control signal vector and the vector of output of the ith control area, respectively. Also, is the state vector of neighbour control area. The state and output vectors for the ith area are defined as follows [13]: (14) where , , and show the frequency deviation, tie-line active power deviation, generator output power deviation and the governor valve position deviation of the ith area, respectively. Also, and stand for the deviation of drivetrain torsion, angular velocity of rotor deviation, angular velocity of high-speed shaft and generator deviation and pitch angle deviation, respectively. Moreover, is the area control error of the ith area. Furthermore, , and are real and constant matrices, in which and are the system's matrices of control area i and represents the interconnection matrix, which are described in the Appendix. 4.2 DN AG controller design The general structure of the AGC system with the proposed DN controller of the study system is shown in Fig. 4. Fig. 4Open in figure viewerPowerPoint Structure of DN AG controller As mentioned before, the mathematical presentation of wind turbine, thermal power plant and hydro power plant are considered as the same as [13]. Thus, according to Zhang et al. [13] and as illustrated in Fig. 4, the control vector for the first area is considered as , where and are deviations in speed changer setting, pitch demand and generator reaction torque, respectively. Also, for other three areas the control vector is . As shown in Fig. 4, the control signals should be obtained using (4) and applied to each area. To obtain the control law (4), the local feedback gains , delayed state feedback gains and the supplemental feedback gains should be computed. For this, at first the interconnected system (13) should be discretised with an appropriate sampling period. According to Wang et al. [40], the sampling time could be chosen, such that , where is the maximum eigenvalue of state matrix (A). According to this, the highest possible value of the sampling time for such power system is obtained ∼50 ms. Moreover, the sampling time must be chosen as small as possible, but then the identified matrix (A) will be close to the identity matrix and so gives no information about the original continuous system [41]. As a result, a sampling time of 25 ms is chosen in this paper. Thus, with a sampling time of Ts = 0.025 s, the interconnected system (13) is discretised and matrices , and are used in simulation. Afterwards, by choosing the state vector of the ith area as the same as presented in (14) and employing the LMI-solver yet another LMI parser (YALMIP) [42], based on Theorem 1; the AGC feedback gains as well as the control signal (4) are obtained. To show the ability and effectiveness of the proposed method, a distributed model predictive controller (DMPC) approach, which is presented in [13], is applied for comparison. In the applied DMPC approach, as discussed in [13], the power system is decomposed into four areas and each area has its own local MPC, in which the local controllers coordinated with each other by transferring their information through an ideal communication links. These areas based MPCs transfer their local measurements and predictions by communication link and combine the data from other MPC controllers into their local objective to coordinate with each other. In the implemented DMPC, all controller parameters are considered the same as those given in [13]. To indicate the effectiveness of the proposed approach, three cases are considered as follows: Case 1: The information is exchanged through an ideal communication network, i.e. there are no delays or packet dropouts (as considered in [13]) and a step load change of 0.01 pu is applied as load disturbance. Case 2: The information is exchanged among a non-ideal communication network with both time-varying delays and random packet dropouts and a step load change of 0.01 pu is applied as load disturbance. Case 3: The information is exchanged among a non-ideal communication network with both time-varying delays and random packet dropouts and a step load change of 0.1 pu is applied as load disturbance. To have a better perceptiveness about the improvement of the system by the proposed approach comparing with DMPC, the settling time and two performance indices, and [(15) and (16)] are calculated for the obtained results (15) (16) where