Quasi‐oppositional harmony search algorithm based optimal dynamic load frequency control of a hybrid tidal–diesel power generation system
2017; Institution of Engineering and Technology; Volume: 12; Issue: 5 Linguagem: Inglês
10.1049/iet-gtd.2017.1115
ISSN1751-8695
Autores Tópico(s)Wind Turbine Control Systems
ResumoIET Generation, Transmission & DistributionVolume 12, Issue 5 p. 1099-1108 Research ArticleFree Access Quasi-oppositional harmony search algorithm based optimal dynamic load frequency control of a hybrid tidal–diesel power generation system Akshay Kumar, Akshay Kumar Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, IndiaSearch for more papers by this authorGauri Shankar, Corresponding Author Gauri Shankar gauri1983@gmail.com Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, IndiaSearch for more papers by this author Akshay Kumar, Akshay Kumar Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, IndiaSearch for more papers by this authorGauri Shankar, Corresponding Author Gauri Shankar gauri1983@gmail.com Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, IndiaSearch for more papers by this author First published: 29 January 2018 https://doi.org/10.1049/iet-gtd.2017.1115Citations: 21AboutSectionsPDF 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 In recent years, high penetration of distributed generations based on wind energy, solar energy and so on in the existing power system network has been noticed. However, due to their stochastic behaviour, operations under autonomous mode as well as in grid-connected mode are not an easy task. This has forced the power utilities to re-define frequency regulation criteria to enhance the overall system stability and reliability. In line with the same, dynamic performance analysis of load frequency control (LFC) of an autonomous hybrid power system model (HPSM) consisting of tidal power plant (TPP) and diesel power plant is explored in this study. A concept of deloaded TPP is adopted in the studied HPSM to utilise the available reserve power for the frequency support. Apart from this, the studied model also incorporates frequency regulation through inertia and damping control and supplementary control strategies. These control strategies are realised through conventional controllers whose gain values are optimised using quasi-oppositional harmony search algorithm (QOHSA) for the optimal dynamic performance of LFC. The efficacy of the proposed QOHSA is corroborated by comparing the results with those yielded by few other existing state-of-the-art algorithms. 1 Introduction The deregulation of electricity markets has attracted many new renewable forms of modular power generation system, known as distributed generations (DGs). Renewable energy sources (RESs) based power generating units are stochastic regarding power output. Therefore, use of DGs along with the fossil fuel-fired based power generating units has given birth to a new concept of hybrid power system model (HPSM). DGs are economical and environmentally suitable. However, the high penetration of RESs may affect the power quality, stability and reliability of the existing electrical power system (having conventional generating units) [1]. In modern power system dynamics, the control of generation and frequency is the most important issues for its reliable operation. Among these two, load frequency control (LFC) plays an important role to keep diversified multi-source power generation systems in synchronism by regulating the real power outputs [2]. In the recent years, tidal energy is emerging as a leading renewable source of electrical power in the form of a tidal power plant (TPP). A review on the feasibility of tidal energy technology and its associated challenges along with the future development of current devices are discussed in [3]. It may be seen either as an alternative or as an addition to the wind power plant (WPP) based HPSM located near sea-shore, in particular. Integration of TPP with the grid system has gained wide popularity in the past few decades [4]. Addition of generating units like TPP or WPP with the existing power system network is always welcomed. However, frequency regulation in their presence is a big challenge. As a result, in the past, problems associated with the LFC in WPP-based HPSM are widely investigated by the researchers (see [5]). It may be observed from the previous studies that, owing to varying nature of power generation (such as from WPP), use of conventional fossil fuel based generating unit like diesel power plant (DPP), as a standby source to meet the deficit power generation for balancing supply–load demand, is inevitable [6]. Active participation of DPP in frequency regulation is quite instant, natural and automatic. However, in comparison to conventional generating units, RESs-based generating units do not automatically participate in frequency regulation. In other words, it may be inferred that these units do not offer any contribution to the system inertia [7]. Therefore, operation of these RESs-based power generating units needs to be modified so as these may participate in the process of frequency regulation. Hence, the concept of deloading in dynamic performance analysis of LFC in WPP-based HPSM is used in [7] to create reserve margin to allow active participation of WPP in primary frequency regulation process. The deloading operation is achieved by shifting the operating point to a reduced power level away from the maximum power point (MPP). It is found that only deloading scheme is not capable of decreasing the slope of frequency deviation and, hence, frequency sensitive controls such as inertia and damping control are also implemented [8]. As discussed earlier, TPP is seen as a viable option to WPP. To further establish this technology, an exhaustive study on the performance of TPP in delivering quality power supply to the consumers' need is to be carefully explored. In this regard, Whitby and Ugalde [9] have examined the dynamic behaviour of a pitch and stall regulated tidal stream turbine (TST). Impact of TPP on Ireland power system network is analysed in [4]. A novel control strategy for MPP tracking in a TPP under varying tidal current speed is presented in [10]. Dynamic performance study of hybrid off-shore wind and turbine energy conversion system is carried out in [11, 12]. As surfaced in the literature, it may be observed that hardly any work is reported on performance analysis of LFC pertaining to TPP-based HPSM. Therefore, in the present work, investigation on the performance of LFC is carried out in TPP- and DPP-based HPSM. It may be observed that operation of TPP is same as that of WPP. Hence, in the present work, effects of deloading of TPP and control strategies such as inertia, damping and supplementary controls [realised using conventional proportional–integral–derivative (PID) controller] on the overall dynamic performance of LFC are investigated. Control and operation of the modern power system are getting intricated day by day. Therefore, to tackle this situation, application of intelligent optimisation techniques has become inevitable. Therefore, from past few decades, optimisation algorithms such as particle swarm optimisation (PSO) [13], genetic algorithm (GA) [14], teaching learning based optimisation (TLBO) [15] and so on have been widely used by the researchers for solving different problems associated with the LFC of the power system network. Application of these optimisation techniques has become more substantial owing to uncertainties involved with the generating units like WPP and TPP. In view of the above, harmony search algorithm (HSA), one of the powerful and state-of-the-art metaheuristic optimisation technique introduced by Geem et al. in [16], has been used by the researchers in the past for solving many complex engineering/non-engineering problems. HSA is based on the musical improvisation process of probing a seamless state of harmony. In comparison to other optimisation algorithms, HSA is a derivative-free algorithm and it requires little mathematics to solve any optimisation problem. In the recent years, a few new variants of HSA have been evolved. A self-adaptive global best HSA for solving continuous optimisation problems has been proposed in [17]. An idea of dynamically obtaining the optimal value of its key parameters has been presented in [18]. To enhance convergence rate of the basic HSA, an idea of opposition-based learning (OBL) is utilised for solving combined economic and emission dispatch problems of the power system by Chatterjee et al. in [19]. Further to HSA with OBL, a new version of HSA with quasi-oppositional based learning (QOBL), termed as QOHSA, is studied by Shankar and Mukherjee in [20]. It is observed that with QOBL-based population initialisation and with the concept of generation jumping, the exploring capability of the basic HSA has been further enhanced [20, 21]. Owing to the above advantages of QOHSA, the authors have utilised its potential in the present work to solve the LFC problem associated with the studied HPSM optimally. The results yield by employing QOHSA is compared with that of the other optimisation algorithms. The main contributions of the present work are given below: (a) An attempt on the LFC study of an autonomous HPSM consisting of TPP and DPP is carried out in the present work. (b) Effect of deloading in TPP, using blade pitch control, on LFC is investigated. (c) Effect of inertia and damping controls in the presence of supplementary control on the dynamic performance of LFC is examined. (d) The effectiveness of QOHSA in tuning the gains of the classical controller for LFC study is analysed concerning different load perturbation and the results yielded using QOHSA are compared with other existing algorithms. The rest of the paper is organised as follows. In Section 2, HPSM and its components are presented. Adopted control strategies are briefed in Section 3. In Section 4, mathematical problem formulation is discussed. QOHSA is outlined in Section 5. In Section 6, time-domain-based simulation results are presented, followed by conclusion in Section 7. 2 Studied HPSM and its components The studied HPSM consists of TPP and DPP (as shown in Fig. 1a) and their corresponding mathematical descriptions are presented in the following subsections. Fig. 1Open in figure viewerPowerPoint Studied TPP based (a) HPSM, (b) Power curve 2.1 Modelling of TPP As discussed earlier, the principle of operation and control scheme associated with the TPP is similar to that of the WPP [22]. However, operating speed of TST in the TPP is observed to be much lower in comparison to that of the wind turbine. In general, rated wind speed lies in the range of 12–15 m/s [23]. While, tidal speed lies in the range of 2–3 m/s [24]. Also, the size of TPP is less as compared to the WPP of the same rating. 2.1.1 TST aerodynamics The expression of the mechanical power output () from the TST is given by the following equation[9]: (1) where is the water density (in ), A is the swept area of the turbine blades (in ), V is the tidal speed flow (in ) and is the power coefficient which is a function of tip speed ratio () and blade pitch angle (). and are expressed by the following equations [25], respectively (2) (3) where R is the radius of the blades (in m) and is the rotational speed of the blades (in ). 2.1.2 Pitch angle controller TPP offers four modes of operation under different ranges of tidal speed, marked as cut-in speed (), rated speed () and cut-out speed () as shown in Fig. 1b [26]. (a) Mode 1 (): There is no power generation by TPP in this mode due to its uneconomical operation in terms of more losses and high operating cost. Hence, the pitch angle is set to . (b) Mode 2 (): In this mode, TPP operates at an optimum efficiency to extract optimum power from TST and so, in the present study, the value of pitch angle is set to . (c) Mode 3 (): TPP operates at constant power mode of operation. In this mode of operation, the pitch angle is variably adjusted within the range from to to avoid overloading. (d) Mode 4 (): The operation is uneconomical here due to over speeding of TST. The output from TPP is zero and the pitch angle is set to . Power variation in the TPP is regulated by pitch system which consists of a controller that generates the pitch angle command signal () from control system block (see Fig. 1a). Pitch controller dynamics is realised using conventional PID controller and the input to it is the error between change in measured turbine rotor speed () and change in reference speed (). TST gives power output according to the rotor speed of turbine at different blade pitch angle values, as depicted in Fig. 2a. Fig. 2Open in figure viewerPowerPoint TPP characteristics and deloading operation (a) Tidal turbine output power variation at different blade pitch angles, (b) MPP and deloading power curve of TPP, (c) Pitch angle control characteristics, (d) Calculation of power reference for deloading operation 2.1.3 Deloading operation of TPP To take part in the frequency regulation, TPP may be operated at sufficient generation margin instead of being operated at MPP. It is referred as the deloading operation of TPP, as illustrated in Fig. 2b. Deloading operation may be realised either from the left (under speeding) or from the right side (over speeding) of the MPP. As seen from Fig. 2b, the power output of the TPP may be varied between the operating point at deloading () and the rated maximum power (). This is achieved by varying its rotor speed from the speed at deloading operation to the rated speed () at . The maximum deloading percentage is to be calculated using the maximum limit of rotor speed of the tidal generator. In this paper, over-speeding-based deloading operation is considered for the analysis. Power–speed characteristics of TPP at the tidal speed of 2.4 m/s are shown in Fig. 2c. In this figure, point ‘A’ is the MPP at which the TPP delivers Pmax = 1 p.u. at a speed of wr = 0.9 p.u. (considering pitch angle, ) and after considering 15% deloading (x), the operating point comes to point ‘B’ on the curve. The deloading power (i.e. Pdel = 0.85 p.u.) is delivered with rotor speed rising to wdel = 1.29 p.u. With the increase in per cent deloading, the power reserve margin offered by the TPP increases. However, this may increase the rotor speed (refer Fig. 2c) and, therefore, the pitch angle controller comes into action to control the speed by adjusting the blade pitch angle. After the action of pitch angle controller, the TPP operates at point ‘C’ on the curve and delivers the power () with reduced speed () of 0.85 p.u. at a new pitch angle of . The dynamic operating power reference () of the TPP at a specific rotor speed and reference speed () are shown in Fig. 2d and these are, in order, expressed in the following equations [5]: (4) (5) where is the measured mechanical torque (in p.u.). 2.1.4 Inertia, damping and supplementary control In Fig. 3, a combined inertia and damping control strategy is shown which adds a signal ( in p.u.) to the power reference output to be tracked by the non-conventional machine equivalent controller. This control strategy improves the transient frequency response of the system which is represented as the function of two signals, i.e. frequency deviation () and rate of change of frequency deviation () and it is described in the following equation [8]: (6) where determines the additional inertia, and determines the additional damping. A washout filter (high-pass filter) is used so that permanent frequency deviation has no effect on the control strategy. Fig. 3Open in figure viewerPowerPoint Inertia and damping control TST must recover the optimal speed after the transient condition gets over. However, as shown in Fig. 3, for this, a power reference ( in p.u.) is used for forcing the speed to track the desired speed reference. The same is computed using the following equation [8]: (7) where and are the optimised controller gains of the speed regulator. From (6) and (7), the total active power reference ( in p.u.) for TPP may be given as (8) In case of TPP, high-speed switching power converter comes into the picture in regulating electrical power output. Hence, it may be assumed that there is no dynamics between the power reference and the non-conventional total power injection. Therefore, power output from TST is considered to lie same as the power input to TST (i.e. ). The relationship between sum of power output from conventional generating unit and power generated by TPP (), load demand () and may be expressed by the following equation [8]: (9) where is the power generated by conventional unit, M is the equivalent inertia constant and D is the load damping characteristics. From (6), the following equation follows: (10) Equation (10) shows that additional inertia (due to ) and additional damping control (due to ) help to improve the transient condition. For enhancing the steady-state output variation, a supplementary control is added to the TPP and it is represented as supplementary control integral constant (). The value determines permanent TPP partnership in frequency regulation. In the studied model, additional inertia, damping and supplementary control strategies are realised using a conventional PID controller for the purpose of frequency regulation. The proportional, integral and differential gains of the PID controller are referred as , and , respectively. These coefficients are optimised by using studied QOHSA. 2.1.5 Dynamic model of TPP Dynamic model of the studied TPP is shown in Fig. 1a. The power output variation is expressed as follows [27]: (11) where is the tidal power output variation for a specific variation in tidal speed, is the tidal power output variation for a specific variation in turbine rotor speed and is the tidal power output variation for a specific variation in blade pitch angle. The values of , and may be calculated by the following equations [27]: (12) (13) (14) (15) (16) The TST power output variation depends on three factors such as (i) change in tidal speed change (), (ii) turbine rotor speed variation () and (iii) change in blade angle (). This power variation is injected into the system using available additional inertia, additional damping and supplementary control with speed regulator. As shown in Fig. 1a, the change in speed (), acting as input, determines using pitch angle control and also power reference value using speed regulator. The values of the parameters of the studied TPP model are presented in Appendix. 2.2 Modelling of DPP In HPSM, electrical power supplied from TPP is not constant. Therefore, it may be integrated with some conventional power sources such as DPP to supply a steady power output to the consumer. DPP involves speed governor, turbine and the associated controller as shown in Fig. 1a [5]. Speed governor is used to control the speed by regulating the fuel injection. Droop control is used as a primary control (which is responsible for the maximum change in the system output) while a conventional controller is used as a secondary control to offset the steady-state error to zero (which is not achieved by the primary control alone). Power output from DPP is expressed in the following equation: (17) where and are the time constants (in seconds) of speed governor and turbine, respectively, is the change in the control signal (in p.u.) and it may be given as (18) where R is the speed regulation parameter (in Hz/p.u. MW) and is the change in the control signal (in p.u.). The values of parameters associated with the DPP are presented in Appendix. 2.3 Studied HPSM TPP and DPP are used together to form the proposed HPSM as shown in Fig. 1a. From Fig. 1a, the change in total power output generation from HPSM () is expressed as (19) The difference () between and the deviation in load demand (), i.e. power balance equation is given as (20) The transfer function of the power system () in terms of and is formulated in the following equation: (21) 3 Adopted control strategy PID controller is the most effective controller to minimise error signal [20]. The input to the PID controller may be an error between the reference value and the measured value. By controlling the error signal using PID controller, a good quality of power may be supplied to the load. In the studied model, PID controllers are used with the TPP and the DPP. The transfer function of a PID controller is stated in the following equation: (22) where is the proportional gain, is the integral gain and is the derivative gain. 4 Mathematical problem formulation To get the optimal performance from the system, selection of proper objective function is the most crucial aspect of any optimisation algorithm in tuning the controller gains. Different types of performance indices are integral absolute error (IAE), integral time absolute error (ITAE), integral square error (ISE) and integral time square error (ITSE). In the present work, ISE is chosen as the objective function for tuning the controller's parameters installed within the studied HPSM [27]. The aim of the objective function is to minimise the present in the studied system. The objective function [termed as figure of demerit (FOD)] formulated for optimal performance analysis of LFC of the studied power system model is defined by the following equation: (23) where t is the time duration of simulation (in seconds). 4.1 Mathematical optimisation problem and constraints In the present study, the adopted optimisation problem for the studied HPSM is expressed as (24) subject to the constraints given in the following equation: (25) where and are the minimum and the maximum values of gains of the adopted controller. 4.2 Measure of performance As a measure of performance, indices like IAE, ITAE and ITSE are also calculated at the end of the developed program to further corroborate the efficacy of QOHSA. These indices are, sequentially, expressed as (26) (27) (28) 5 Proposed QOHSA In this paper, QOHSA is employed in which the concept of QOBL is embedded within the framework of HSA. The pseudo-code of the proposed QOHSA is presented in [20, 21]. 6 Simulation results and discussions In this section, dynamic performance of the LFC for the studied HPSM (shown in Fig. 1a) is analysed under different operating conditions. TPP is operating at a tidal speed of 2.4 m/s having deloading effect with blade pitch angle of . The parameters of PID controllers are optimised using studied QOHSA. Modelling of the present work is done using MATLAB/SIMULINK® and the code for the proposed QOHSA is realised using MATLAB® software. The best chosen values of the parameters used for QOHSA are: HMS = 60, HMCR = 0.4, PARmin = 0.45, PARmax = 0.98, BWmin = 0.00005, BWmax = 50, number of iterations = 100 and jumping rate (Jr) = 0.4. The dynamic performance analysis of LFC on the above proposed models are carried out, under the action of QOHSA tuned PID controller (installed in these systems), subjected to the following operating conditions (referred as scenarios): Scenario 1 : A step increase in load demand. Scenario 2 : Random change in load demand. Scenario 3 : Sinusoidal load change. 6.1 Performance analysis under scenario 1 In this scenario, the proposed HPSM is subjected to 5% step load perturbation (SLP) () applied at t = 2 s. Three cases of simulation using different control strategies (in relation to the operation of TPP) have been carried out. Also, the comparative performance of these control strategies is presented. These studied cases are as follows: Case a: The system is simulated without control. Case b: The system is simulated with additional inertia and additional damping control. Case c: The system is simulated with the additional inertia, additional damping and supplementary control (proposed control). The comparative response profiles of frequency deviation, power output deviation observed in TPP and DPP, employing different control strategy are plotted in Figs. 4a–c, respectively. The various responses, shown in Fig. 4, are obtained utilising QOHSA only. As because, in case (b) and case (c), it is proved that QOHSA outperforms other studied optimisation algorithms. It may be observed from Fig. 4a that in case of without any control [case (a)] in TPP [means that TPP offers no participation in frequency support in the absence of control strategies mentioned in case (b) and case (c)], frequency response profile has the maximum variation of −0.00165 p.u. value and also it has large settling time. Using the inertia and damping control [case (b)], the TPP injects additional inertia and damping into the system and, hence, frequency deviation is improved with the maximum value being reduced to −0.00085 p.u. To further improve frequency regulation, the proposed scheme [case (c)] is simulated. As observed from Figs. 4a–c, the proposed control provides enough power injection into the system for improving the transient and steady-state condition. The maximum frequency deviation is observed to be −0.0007 p.u. which is minimum in comparison to the other cases. From the simulated results, it may be inferred that the frequency variation is less for the proposed control and also fast settling time improves the power quality of the system. The responses are in consonance with the results shown in Figs. 4b and c. It may be observed from these figures that, in the absence of studied control strategies, participation from TPP is zero and the load (i.e. 0.05 p.u) is shared by DPP only. While, in the presence of inertial and damping control, the TPP injects inertia to support frequency regulation at the beginning (following load disturbance). However, TPP cannot vary its power output during steady-state condition. This control method brings the power change at a slow rate and yet the transient response (see Fig. 4a) is observed to be better in terms of overshoot, undershoot and settling time (calculated based on 2% criteria). From Fig. 4b, it is observed that TPP transiently participates (with the maximum power injection of 0.005 p.u.) for a short period and attains zero value after a time lapse of 16.76 s. Under the effect of proposed control, the power output through TPP changes smoothly and increases continuously up to steady-state value of 0.039 p.u. The smooth slope of power output variation in TPP is noticed because of the reserved power margin available within the TPP. While DPP, initially, increases its power output to compensate the load demand quickly and reached the peak power deviation output up to 0.035 p.u. After the transient is over, its steady-state value comes to 0.011 p.u., as shown in Fig. 4c. It may be observed that with the proposed method of control, the participation of TPP decreases the burden on DPP and improves frequency profile, as seen in Fig. 4a. Fig. 4Open in figure viewerPowerPoint Comparative response profiles obtained under different studied control methods pertaining to scenario 1 (a) Frequency deviation, (b) Deviation in power output from TPP, (c) Deviation in power output from DPP, (d) Pitch angle variation of the TPP Referring Fig. 2c, it is already stated earlier that initially the TPP is operating with 15% deloading state (for generating additional power reserve margin) which is achieved by keeping the blade pitch angle . As shown in Fig. 4d, in case of without control, no change in is observed. In case of presence of inertia and damping control, a transient behaviour is observed in the profile of (see Fig. 4d) following load change in the beginning (to inject inertial power to the system for frequency regulation) and attains the initial value after some time. However, with the proposed control, it may be observed that there is permanent participation from TPP in frequency stabilisation and, hence, the value of gets adjusted from initial value to a new value of . Moreover, proper selections of these gains/coefficients would result in optimal frequency response in the studied HPSM. Keeping in view of the above, in the present work, the value of these gains/coefficients are optimised incorporating QOHSA. In order to establish the supremacy of QOHSA for the present application, the results yielded are compared with those obtained by using other state-of-the-art algorithms (such as GA, PSO and TLBO). Therefore, it would be fascinating to note that the profile of frequency deviations and different power deviations, shown in Figs. 5a–d [particularly, related to that of case (b) and case (c)], are obtained under QOHSA tuned conventional controllers (refer Tables 1 and 2). However, to corroborate the efficacy of the studied QOHSA for its application in rest of the studied scenarios, its results are compared with the results obtained by using other adopted algorithms. The comparative profile of frequency responses (for SLP of 5%) using the optimised gain values
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