# Centralized Airflow Control to Reduce Output Power Variation in a Complex OWC Ocean Energy Network

Authors: Sunil Kumar Mishra; Bhargav Appasani; Amitkumar Vidyakant Jha; Izaskun Garrido; Aitor J. Garrido
Journal: Complexity
 (2020)

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## Abstract

A centralized airflow control scheme for a complex ocean energy network (OEN) is proposed in this paper to reduce the output power variation (OPV). The OEN is an integrated network of multiple oscillating water columns (OWCs) that are located at different geographical sites connected to a common electrical grid. The complexity of the OWC-OEN increases manifolds due to the integration of several OWCs and design of controllers become very challenging task. So, the centralized airflow control scheme is designed in two stages. In control stage-1, a proportional-integral- (PI-) type controller is designed to provide a common reference command to control stage-2. In control stage-2, the antiwindup PID controllers are implemented for the airflow control of all the OWCs simultaneously. In order to tune the large number of control parameters of this complex system, a fitness function based on integral squared error (ISE) is minimized using the widely adopted particle swarm optimization (PSO) technique. Next, the simulation results were obtained with random wave profiles created using the Joint North Sea Wave Project (JONSWAP) irregular wave model. The OPV of the proposed OWC-OEN was reduced significantly as compared to the individual OWC. It was further observed that the OPV of the proposed scheme was lower than that achieved with uncontrolled and MPPT controlled OWC-OEN. The effect of communication delay on the OPV of the proposed OWC-OEN scheme was also investigated with the proposed controller, which was found to be robust for a delay up to 100 ms.


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## Body

## 1. Introduction

Many countries around the world with a long coastal zone have been actively exploring ocean waves as an alternate energy source over the past five decades [1–9]. European countries have taken a leading role in the research and development of this sector [1–3]. Research in ocean wave energy also started later in countries such as Australia, Brazil, China, India, Indonesia, Japan, Korea, Maldives, Taiwan, and the United States [4–9]. The majority of the ocean wave power plants across the globe use oscillating water column technology (OWC) [10–12]. With a lot of consistent efforts by the research community, this technology has matured enough in recent years. However, due to high output power variation (OPV), hurdles remain in its grid integration. The OPV is defined as the difference between the maximum and minimum power generated from the OWC plant. Reducing OPV is one of the major challenges of OWC. It requires advanced control systems to minimize OPV as much as possible.


### 1.1. Literature Review of OWC Control

Over the years, the OWC has been tried and tested by several control schemes [13–41]. The initial stage of the controller design for OWC was primarily on phase control [13] and latching control [14]. Subsequently, in [15], a controller by swinging rotor-blades of the wells turbine was proposed to optimize OWC performance. A reactive controller for a fixed two-dimensional OWC was developed in [16]. In [17], an airflow control scheme for OWC-Wells turbine using throttle and bypass valves was discussed. Justino and Falcao [18] presented the rotational speed controller for OWC-Wells turbine and electrical generator. An approach for obtaining the maximum output power from the OWC plant was described in [19]. In [20], a power electronic controller was designed for an OWC system with an induction generator-Wells turbine. In [21], the rotor side controller with constant frequency and variable speed operation of OWC was presented.After the establishment of the OWC plant at the Mutriku harbor in Spain, a neural network network-based controller for OWC module was proposed in [22], which was supposed to change the external rotor resistance values to vary the induction generator slip. The PID-based control approaches for OWC plants were developed in [23] for airflow and rotor speed control. In [24], the control schemes proposed in [23] were validated on the experimental module. Neural network-based optimum speed reference for PI-based rotational speed control of the OWC system was proposed in [25]. In [26], an analysis was executed on fault-ride-through capability of OWC stations. It was equipped with doubly fed induction generator (DFIG) and an airflow-based controller. In [27], a sliding-mode control of OWC plants for maximizing output power of DFIG was designed.In recent years, many advanced control techniques for OWC airflow as well as turbine rotor speed control techniques have been developed. In [28], a control technique was developed for efficiency enhancement of Wells turbine-OWC devices. A comprehensive survey of electrical controllers for ocean energy devices including OWC was discussed in [29]. In [30], the controller for merging local energy storage with OWC was proposed. A rotational speed optimization approach was applied in [31] to attain maximum power point tracking (MPPT) of OWC. In [32] as well, a latching control scheme was developed for MMPT of a floating OWC wave energy converter. An optimal speed controller based on the fuzzy-backstepping method was designed in [33]. Three Lyapunov-based nonlinear controllers were proposed in [34] for OWC plant emulation, rotational speed control, and DC link voltage control of DFIG’s grid side converter (GSC), respectively. The flow controller was designed in [35] for Wells turbines for harnessing maximum wave power using OWC. An event-triggered controller for the OWC energy plant was presented in [36] wherein the main objective was to minimize control updates when the controller and plant interact with the other via communication channel. In [37], a fuzzy gain scheduled and PI-type airflow controller for an OWC, which was an advanced version of the airflow controller, were presented earlier in [23, 24]. Recently, some artificial intelligence-based airflow controller techniques have been proposed [38–40]. A self-adaptive global best harmony search algorithm-based airflow control of OWC was proposed by [38] wherein four variants of the harmony search algorithm were implemented and tested to optimize the control design of the PID controller in the airflow control scheme. In [39], another approach for airflow control was proposed which utilized symmetry-breaking concept to design the controller. Furthermore, an artificial neural network-based airflow controller was designed using surface elevation measurements [40]. This study considered real measured wave input data and generated power of the NEREIDA wave power plant. For more details on the control of OWC plants, please refer [41].


### 1.2. Main Contributions

In the above-discussed control schemes, the output power of OWC can be maximized successfully using rotor speed regulation wherein actual rotor speed follows optimum reference speed. Also, output power can be controlled to some extent by using an air flow controller but the high OPV is still a huge challenge in OWC. To the best of the authors’ knowledge this issue has not been addressed so far by forming a large network of OWC. The randomness in ocean wave input at the OWC plant is a serious concern. If the multiple OWCs operating at different geographical locations are integrated, then the same randomness of ocean waves might be helpful in reducing OPV as compared to that of an isolated OWC. The OPV can also be reduced further by suitably designing a centralized airflow controller for regulating the airflow of OWC chambers situated at different geographical sites. However, the design complexity of the controller for this system is increased.Hence, in this paper, the issue of high OPV has been addressed by integrating multiple OWC sites located at different geographical locations. Hereafter, the integrated OWC sites would be referred to as OWC ocean energy network (OEN). Now, two control schemes would be designed for OWC-OEN: (i) localized MPPT control and (ii) centralized airflow control for reducing OPV. The localized MPPT control law would again be consisting of two sections: (i) an algorithm for optimum reference speed calculation and (ii) backstepping controller for rotor speed regulation. The centralized airflow controller would provide common commands to all individual OWC sites. The centralized airflow controller is a two stage control scheme. In control stage-1, a proportional-integral- (PI-) type controller is designed to provide a common reference command to control stage-2. In control stage-2, the antiwind PID controllers are implemented for the airflow control of all OWC sites. Suppose, there areN number of OWC sites included in OWC-OEN, two unknown parameters of the PI controller in control stage-1, and three unknown PID parameters of each OWC site in control stage-2. Then, the 3N + 2 number of controller design parameters would be required to be properly selected so that OPV of OWC-OEN can be reduced considerably. In order to tune the 3N + 2 parameters, an integral squared error- (ISE-) type fitness function is defined. The fitness function is minimized with the help of particle swarm optimization (PSO) algorithm [42–45]. The PSO method is very instrumental in optimizing the parameters of complex systems.The numerical simulations were performed on MATLAB® platform using Joint North Sea Wave Project (JONSWAP) irregular wave model [46]. Several JONSWAP wave profiles are generated randomly using Wave Analysis for Fatigue and Oceanography (WAFO) MATLAB® toolbox [47]. The performance of an arbitrarily selected OWC site has been analyzed for relevant OWC parameters such as rotor speed, control signal, Wells turbine flow coefficient, and DFIG output power of controlled/uncontrolled OWC. The performance of the proposed control system of OWC-OEN has been validated using a newly introduced performance index referred to as OPV index. The OPV index of all OWC sites, uncontrolled OWC-OEN, localized MPPT control of OWC-OEN, and centralized airflow control of OWC-OEN are compared. Also, the effect of transmission delay has been studied by introducing the delay in the OWC-OEN.The rest of the paper would be discussed with following sections. Wave-to-wire modelling and control of an individual OWC site in Section2; design of OWC-OEN and centralized airflow controller in Section 3; discussion on simulation results in Section 4 ,and concluding remarks and future scopes in Section 5.


## 1.1. Literature Review of OWC Control

Over the years, the OWC has been tried and tested by several control schemes [13–41]. The initial stage of the controller design for OWC was primarily on phase control [13] and latching control [14]. Subsequently, in [15], a controller by swinging rotor-blades of the wells turbine was proposed to optimize OWC performance. A reactive controller for a fixed two-dimensional OWC was developed in [16]. In [17], an airflow control scheme for OWC-Wells turbine using throttle and bypass valves was discussed. Justino and Falcao [18] presented the rotational speed controller for OWC-Wells turbine and electrical generator. An approach for obtaining the maximum output power from the OWC plant was described in [19]. In [20], a power electronic controller was designed for an OWC system with an induction generator-Wells turbine. In [21], the rotor side controller with constant frequency and variable speed operation of OWC was presented.After the establishment of the OWC plant at the Mutriku harbor in Spain, a neural network network-based controller for OWC module was proposed in [22], which was supposed to change the external rotor resistance values to vary the induction generator slip. The PID-based control approaches for OWC plants were developed in [23] for airflow and rotor speed control. In [24], the control schemes proposed in [23] were validated on the experimental module. Neural network-based optimum speed reference for PI-based rotational speed control of the OWC system was proposed in [25]. In [26], an analysis was executed on fault-ride-through capability of OWC stations. It was equipped with doubly fed induction generator (DFIG) and an airflow-based controller. In [27], a sliding-mode control of OWC plants for maximizing output power of DFIG was designed.In recent years, many advanced control techniques for OWC airflow as well as turbine rotor speed control techniques have been developed. In [28], a control technique was developed for efficiency enhancement of Wells turbine-OWC devices. A comprehensive survey of electrical controllers for ocean energy devices including OWC was discussed in [29]. In [30], the controller for merging local energy storage with OWC was proposed. A rotational speed optimization approach was applied in [31] to attain maximum power point tracking (MPPT) of OWC. In [32] as well, a latching control scheme was developed for MMPT of a floating OWC wave energy converter. An optimal speed controller based on the fuzzy-backstepping method was designed in [33]. Three Lyapunov-based nonlinear controllers were proposed in [34] for OWC plant emulation, rotational speed control, and DC link voltage control of DFIG’s grid side converter (GSC), respectively. The flow controller was designed in [35] for Wells turbines for harnessing maximum wave power using OWC. An event-triggered controller for the OWC energy plant was presented in [36] wherein the main objective was to minimize control updates when the controller and plant interact with the other via communication channel. In [37], a fuzzy gain scheduled and PI-type airflow controller for an OWC, which was an advanced version of the airflow controller, were presented earlier in [23, 24]. Recently, some artificial intelligence-based airflow controller techniques have been proposed [38–40]. A self-adaptive global best harmony search algorithm-based airflow control of OWC was proposed by [38] wherein four variants of the harmony search algorithm were implemented and tested to optimize the control design of the PID controller in the airflow control scheme. In [39], another approach for airflow control was proposed which utilized symmetry-breaking concept to design the controller. Furthermore, an artificial neural network-based airflow controller was designed using surface elevation measurements [40]. This study considered real measured wave input data and generated power of the NEREIDA wave power plant. For more details on the control of OWC plants, please refer [41].


## 1.2. Main Contributions

In the above-discussed control schemes, the output power of OWC can be maximized successfully using rotor speed regulation wherein actual rotor speed follows optimum reference speed. Also, output power can be controlled to some extent by using an air flow controller but the high OPV is still a huge challenge in OWC. To the best of the authors’ knowledge this issue has not been addressed so far by forming a large network of OWC. The randomness in ocean wave input at the OWC plant is a serious concern. If the multiple OWCs operating at different geographical locations are integrated, then the same randomness of ocean waves might be helpful in reducing OPV as compared to that of an isolated OWC. The OPV can also be reduced further by suitably designing a centralized airflow controller for regulating the airflow of OWC chambers situated at different geographical sites. However, the design complexity of the controller for this system is increased.Hence, in this paper, the issue of high OPV has been addressed by integrating multiple OWC sites located at different geographical locations. Hereafter, the integrated OWC sites would be referred to as OWC ocean energy network (OEN). Now, two control schemes would be designed for OWC-OEN: (i) localized MPPT control and (ii) centralized airflow control for reducing OPV. The localized MPPT control law would again be consisting of two sections: (i) an algorithm for optimum reference speed calculation and (ii) backstepping controller for rotor speed regulation. The centralized airflow controller would provide common commands to all individual OWC sites. The centralized airflow controller is a two stage control scheme. In control stage-1, a proportional-integral- (PI-) type controller is designed to provide a common reference command to control stage-2. In control stage-2, the antiwind PID controllers are implemented for the airflow control of all OWC sites. Suppose, there areN number of OWC sites included in OWC-OEN, two unknown parameters of the PI controller in control stage-1, and three unknown PID parameters of each OWC site in control stage-2. Then, the 3N + 2 number of controller design parameters would be required to be properly selected so that OPV of OWC-OEN can be reduced considerably. In order to tune the 3N + 2 parameters, an integral squared error- (ISE-) type fitness function is defined. The fitness function is minimized with the help of particle swarm optimization (PSO) algorithm [42–45]. The PSO method is very instrumental in optimizing the parameters of complex systems.The numerical simulations were performed on MATLAB® platform using Joint North Sea Wave Project (JONSWAP) irregular wave model [46]. Several JONSWAP wave profiles are generated randomly using Wave Analysis for Fatigue and Oceanography (WAFO) MATLAB® toolbox [47]. The performance of an arbitrarily selected OWC site has been analyzed for relevant OWC parameters such as rotor speed, control signal, Wells turbine flow coefficient, and DFIG output power of controlled/uncontrolled OWC. The performance of the proposed control system of OWC-OEN has been validated using a newly introduced performance index referred to as OPV index. The OPV index of all OWC sites, uncontrolled OWC-OEN, localized MPPT control of OWC-OEN, and centralized airflow control of OWC-OEN are compared. Also, the effect of transmission delay has been studied by introducing the delay in the OWC-OEN.The rest of the paper would be discussed with following sections. Wave-to-wire modelling and control of an individual OWC site in Section2; design of OWC-OEN and centralized airflow controller in Section 3; discussion on simulation results in Section 4 ,and concluding remarks and future scopes in Section 5.


## 2. Wave-to-Wire Modelling and Control of an Individual OWC Plant

Figure1 displays the schematic representation of OWC plant configuration and its control schemes. As shown in Figure 1, the OWC consists of a chamber, turbine, electrical generator, and controller [34]. The waves of the sea hit the front of the chamber, causing an increase and fall in the water. In the chamber, the air moves back and forth to a circular cavity above the chamber. Thus, the Wells turbine generator machine, which is mounted in the cavity, is operated by two-way air flow [16].Figure 1
Different configurations of an individual OWC plant and its control schemes.The controllers are certainly an essential component of OWC systems. There are mainly three control configurations of OWC plants as uncontrolled, MPPT control, and airflow control. In uncontrolled OWC plant configuration, OWC operates without any control action. The output power generated in uncontrolled condition directly depends upon the sea wave input and the characteristics of turbine generator. In case of MPPT control, the rotor speed is regulated as per the reference rotor speed wherein the reference speed depends upon the sea wave input to the plant. This mechanism helps in extracting maximum output power from the OWC plant. Finally, in airflow control of the OWC plant, the control valve is used to restrict the airflow inside the OWC chamber in such a manner that desired electrical power is generated. Next, we will discuss OWC device modelling and its MPPT control.


### 2.1. Ocean Waves

Most OWC experiments have chosen regular types of ocean waves for OWC output evaluation, but real sea wave actions and irregularities are highly unpredictable. In order to deal with this problem, researchers have therefore developed a number of practical sea wave models [46, 47]. In this analysis, the irregular JONSWAP wave pattern is used to test the efficiency of the proposed controls. It is one of the commonly used models for marine technical research.The characterization parameters for JONSWAP are significant wave height (Hm0), peak wave period (Tp), and peakedness parameter (γ). The JONSWAP model gives best characterization in the range 3.6Hmo<Tp<5Hmo and 1 < γ < 7 [34]. The JONSWAP wave spectrum for the values of Hm0, Tp, and γ given in Table 1 is shown in Figure 2 wherein the highest frequency component is around 0.5 rad/s.Table 1
JONSWAP wave model, OWC chamber, Wells turbine, and DFIG parameters.
JONSWAP wave model:Hm0 = 7 m; Tp = 11 s; γ = 2.3853DFIG:p = 4; Rs = 0.0181; Rr = 0.0334; Ls = 7.543; Lr = 7.573; Lm = 7.413; Vs=390/3V; ωe = 100π rad/s; F = 0.02; J = 50; Pg−rated=100.0kW (individual OWC site); Pgtotal−rated=2.0MW (OWC-OEN)Chamber:AOWC = 7.5 m2; Aduct = 1.18 m2; Avalve = 1 m2Wells turbine:n = 8; kt = 0.7079; b = 0.4 m; r = 0.3643 m; l = 0.38 mInitial conditions:ωr0 = 100 rad/s; ψds0=ψs=Vs/ωe=0.7167Wb; ψqs0 = ψdr0 = ψqr0 = 0 WbFigure 2
JONSWAP wave spectrum.


### 2.2. OWC Chamber Model

The OWC consists of a closed room with four side walls with openings at top and bottom (Figure1). It is partly immersed in water and waves hit the lower section of the chamber. As the water level rises and falls, a two-way air flow is produced. The water level change is also referred to as the wave height. The air velocity mathematical definition is provided by [36](1)Vx=AOWCAduct+Avalve.∂ht∂t.The air velocity definition established by (1) is the input for the Wells turbine. Here, it has been assumed that Avalve=uv. It means that the control valve has unity transfer function for a simplified case or does not have any actuator delay.


### 2.3. Wells Turbine Model

The Wells turbine [24, 48] is a turbine of unique features and can be seen in Figure 3. This rotates in the same direction by input of two-way air flow, but has a restriction of stalling. The power output falls considerably because of the stalling. A control unit is therefore necessary to prevent the stall.Figure 3
Wells turbine schematic diagram.Turbine torque description is given as follows [24]:(2)Tt=ftφ⋅Vx2,where ft (ϕ) is stated as follows:(3)ftφ=Ct⋅kt⋅r⋅1+φ−2,where Ct is the Wells turbine torque coefficient and depends on ϕ as displayed in Figure 3. The ϕ is given by(4)φ=Vx⋅rωr−1.As shown in Figure4, ϕ ≤ ϕth = 0.3 provides the highest torque coefficient to deliver the maximum torque and therefore the maximum output power.Figure 4
Turbine characteristics.The turbine is attached to a DFIG. The coupling function of the turbine generator can thus be expressed as follows:(5)dωrdt=1JTt−F⋅ωr−Te,where ωr has initial condition ωr0.


### 2.4. DFIG Dynamics

This analysis considered a direct-quadrature (dq) dynamic DFIG model. The dq dynamic model’s benefit is that every three-phase voltage or current in the stationary frame can be interpreted as DC voltage or current in a synchronous revolving frame [15, 16]. The state equations of dq-axis stator and rotor flux states of DFIG are given as follows [20]:(6)dψdsdt=−RsLrKψds+ωeψqs+RsLmKψdr+vds,dψqsdt=−ωeψds−RsLrKψqs++RsLmKψqr+vqs,dψdrdt=RrLmKψds−RrLsKψdr−ωr−ωeψqr+vdr,dψqrdt=RrLmKψqs+ωr−ωeψdr+vqr,where K=LsLr−Lm2. ψds, ψqs, ψdr, and ψqr are stator and rotor dq flux quantities. Rs and Rr are stator and rotor resistances, whereas Ls, Lr, and Lm are the stator, rotor, and mutual inductances. ωe is the stator supply frequency, vds, vqs, vdr, and vqr are stator and rotor dq voltages. The flux states ψds, ψqs, ψdr, and ψqr are subjected to initial conditions ψds0, ψqs0, ψdr0, and ψqr0, respectively. The electromagnetic torque and output power expressions are(7)Te=−Mψqsψdr−ψdsψqr,Pg=Teωr,where M=−3/2p/2Lm/K and p is number of poles of DFIG.Thedq-axis voltages of the rotor are converted into abc-axis voltages of the rotor. Furthermore, the abc-axis voltage signals will be sent to pulse width modulation (PWM), the gate pulses of which will be sent to DFIG’s DC/AC rotor side converter (RSC) [11, 12, 23].


### 2.5. Localized MPPT Control of an Individual OWC Plant

The airflow control and rotor speed regulation blocks, as shown in Figure1, are the two most important controllers for OWC control. As mentioned earlier, the rotor speed regulator is considered for localized MPPT control of the OWC plant. The MPPT control can be achieved using linear or nonlinear controller in which the actual rotor speed is forced to track an optimum speed reference [24, 25, 27, 31, 33, 34, 36]. The optimum reference speed calculation algorithm is designed in such a manner that it would always lead to maximum output power. In this work, a backstepping-type rotor speed controller and optimum reference speed calculation algorithm have been designed using the approach described in [36].The optimum reference speed calculation algorithm [36] is presented next. It is calculated using air velocity information in the following steps:(i)
Step 1: calculate the value ofVx using (1).(ii)
Step 2: calculate peak values ofVx as follows:(8)ifVx≠0,V˙x=0,Vxp=Vx,elseVxp=0.end(iii)
Step 3: passVxp through zero-order-hold (ZOH) as follows:(9)V¯xp=ZOHVxp.(iv)
Step 4: for threshold value of the flow coefficient,φth=0.3, calculate the reference speed using (4) as follows:(10)ωref=V¯xprφth−1.(v)
Step 5: calculateω1d by limiting the minimum and maximum values of ωref as follows:(11)ifωref≤ωe,ω1d=ωe,elseifωref≥ωe,ω1d=ωrp,elseω1d=ωref,endwhere ωe is the minimum value of ω1d and ωrp is the maximum value of ω1d.(vi)
Step 6: in order to avoid any sudden change in the reference value, passω1d through a low-pass filter. The new reference value is calculated as follows:(12)z1d=hf⊗ω1d.The frequency domain representation ofhf is given as follows:(13)Hfs=11+0.1s.As a result, thez1d is the optimum reference speed to be used for proposed controllers. Next, the backstepping-type rotor speed regulator would be designed to force the actual rotor speed to track the optimum reference speed z1d.The state space model from [36] is given below:(14)z˙1=k1z1+k2z2+D,z˙2=k3z1−ωe+k4z2+ur,where k1=−F/J; k2=−M/J; k3=Lr/LmψS; k4=−RrLs/K; ur=control signal=vqr; D=Tt/J; z1=ωr; and z2=ψqr.Furthermore, simplifying the above equation, we have(15)z˙1=f1z1,D+k2z2,(16)z˙2=f2z1,z2+ur,where f1z1,D=k1z1+D and f2z1,z2=k3z1−ωe+k4z2.A step by step design approach is applied for the backstepping controller. For a second-order system expressed by (15) and (16), the controller is designed in two stages. First, a virtual controller, z2d, is to be designed. Then, z2d would be used for designing final control law ur.For designing the virtual control law,z2d, let us choose the error component as follows:(17)z˜1=z1d−z1.Next, the first order derivative of (17) is written as follows:(18)z˜˙1=z˙1d−z˙1=z˙1d−f1z1,D−k2z2.Furthermore, by adding and subtractingk2z2d term, (18) becomes(19)z˜˙1=z˙1d−f1z1,D−k2z2+k2z2d−k2z2d.The virtual control lawz2d is chosen as follows:(20)z2d=k2−1z˙1d−f1z1,D+σ1z˜1,where σ1>0.Define(21)z˜2=z2d−z2.Substituting (20) and (21), (19) can be expressed as follows:(22)z˜˙1=−σ1z˜1+k2z˜2.Next, the derivative of (21) is given by(23)z˜˙2=z˙2d−z˙2=z˙2d−f2z1,z2−ur.For designing the control law which ensures the closed loop stability of systems (15) and (16), a Lyapunov function candidate, Vlpf, is chosen as follows:(24)Vlpf=12z˜12+z˜22.The first order time derivative of (23) is expressed as follows:(25)V˙lpf=z˜1z˜˙1+z˜2z˜˙2,⇒V˙lpf=z˜1−σ1z˜1+k2z˜2+z˜2z˙2d−f2z1,z2−ur,⇒V˙lpf=−σ1z˜12+z˜2z˙2d−f2z1,z2+k2z˜1−ur.The control lawur(26)ur=z˙2d−f2z1,z2+k2z˜1+σ2z˜2,gives(27)V˙lpf=−σ1z˜12−σ2z˜22≤0,where σ2>0.Here, (27) becomes negative semidefinite and V˙lpf does not contain any trajectories of error states z˜1 and z˜2 other than trivial trajectory z˜1=z˜2=0. Then, error states z˜1 and z˜2 converge asymptotically to zero. Hence, the system given by (15) and (16) with control law ur given in (26) is asymptotically stable.In Section3, the airflow control concept would be extended to the airflow control of OWC-OEN. As per the analysis of this work, the formation of OWC-OEN reduces the OPV as compared to the individual OWC plant. This could be further reduced by a centralized airflow controller to restrict the power generation as per the desired or reference power. The power output signal is sent by communication network to the controller. The controller output is again sent back to the OWC using the same channel. Needless to mention that the communication channel is a digital platform wherein the analog-to-digital (A/D) and digital-to-analog conversion (D/A) of plant and controller data also takes place simultaneously.


## 2.1. Ocean Waves

Most OWC experiments have chosen regular types of ocean waves for OWC output evaluation, but real sea wave actions and irregularities are highly unpredictable. In order to deal with this problem, researchers have therefore developed a number of practical sea wave models [46, 47]. In this analysis, the irregular JONSWAP wave pattern is used to test the efficiency of the proposed controls. It is one of the commonly used models for marine technical research.The characterization parameters for JONSWAP are significant wave height (Hm0), peak wave period (Tp), and peakedness parameter (γ). The JONSWAP model gives best characterization in the range 3.6Hmo<Tp<5Hmo and 1 < γ < 7 [34]. The JONSWAP wave spectrum for the values of Hm0, Tp, and γ given in Table 1 is shown in Figure 2 wherein the highest frequency component is around 0.5 rad/s.Table 1
JONSWAP wave model, OWC chamber, Wells turbine, and DFIG parameters.
JONSWAP wave model:Hm0 = 7 m; Tp = 11 s; γ = 2.3853DFIG:p = 4; Rs = 0.0181; Rr = 0.0334; Ls = 7.543; Lr = 7.573; Lm = 7.413; Vs=390/3V; ωe = 100π rad/s; F = 0.02; J = 50; Pg−rated=100.0kW (individual OWC site); Pgtotal−rated=2.0MW (OWC-OEN)Chamber:AOWC = 7.5 m2; Aduct = 1.18 m2; Avalve = 1 m2Wells turbine:n = 8; kt = 0.7079; b = 0.4 m; r = 0.3643 m; l = 0.38 mInitial conditions:ωr0 = 100 rad/s; ψds0=ψs=Vs/ωe=0.7167Wb; ψqs0 = ψdr0 = ψqr0 = 0 WbFigure 2
JONSWAP wave spectrum.


## 2.2. OWC Chamber Model

The OWC consists of a closed room with four side walls with openings at top and bottom (Figure1). It is partly immersed in water and waves hit the lower section of the chamber. As the water level rises and falls, a two-way air flow is produced. The water level change is also referred to as the wave height. The air velocity mathematical definition is provided by [36](1)Vx=AOWCAduct+Avalve.∂ht∂t.The air velocity definition established by (1) is the input for the Wells turbine. Here, it has been assumed that Avalve=uv. It means that the control valve has unity transfer function for a simplified case or does not have any actuator delay.


## 2.3. Wells Turbine Model

The Wells turbine [24, 48] is a turbine of unique features and can be seen in Figure 3. This rotates in the same direction by input of two-way air flow, but has a restriction of stalling. The power output falls considerably because of the stalling. A control unit is therefore necessary to prevent the stall.Figure 3
Wells turbine schematic diagram.Turbine torque description is given as follows [24]:(2)Tt=ftφ⋅Vx2,where ft (ϕ) is stated as follows:(3)ftφ=Ct⋅kt⋅r⋅1+φ−2,where Ct is the Wells turbine torque coefficient and depends on ϕ as displayed in Figure 3. The ϕ is given by(4)φ=Vx⋅rωr−1.As shown in Figure4, ϕ ≤ ϕth = 0.3 provides the highest torque coefficient to deliver the maximum torque and therefore the maximum output power.Figure 4
Turbine characteristics.The turbine is attached to a DFIG. The coupling function of the turbine generator can thus be expressed as follows:(5)dωrdt=1JTt−F⋅ωr−Te,where ωr has initial condition ωr0.


## 2.4. DFIG Dynamics

This analysis considered a direct-quadrature (dq) dynamic DFIG model. The dq dynamic model’s benefit is that every three-phase voltage or current in the stationary frame can be interpreted as DC voltage or current in a synchronous revolving frame [15, 16]. The state equations of dq-axis stator and rotor flux states of DFIG are given as follows [20]:(6)dψdsdt=−RsLrKψds+ωeψqs+RsLmKψdr+vds,dψqsdt=−ωeψds−RsLrKψqs++RsLmKψqr+vqs,dψdrdt=RrLmKψds−RrLsKψdr−ωr−ωeψqr+vdr,dψqrdt=RrLmKψqs+ωr−ωeψdr+vqr,where K=LsLr−Lm2. ψds, ψqs, ψdr, and ψqr are stator and rotor dq flux quantities. Rs and Rr are stator and rotor resistances, whereas Ls, Lr, and Lm are the stator, rotor, and mutual inductances. ωe is the stator supply frequency, vds, vqs, vdr, and vqr are stator and rotor dq voltages. The flux states ψds, ψqs, ψdr, and ψqr are subjected to initial conditions ψds0, ψqs0, ψdr0, and ψqr0, respectively. The electromagnetic torque and output power expressions are(7)Te=−Mψqsψdr−ψdsψqr,Pg=Teωr,where M=−3/2p/2Lm/K and p is number of poles of DFIG.Thedq-axis voltages of the rotor are converted into abc-axis voltages of the rotor. Furthermore, the abc-axis voltage signals will be sent to pulse width modulation (PWM), the gate pulses of which will be sent to DFIG’s DC/AC rotor side converter (RSC) [11, 12, 23].


## 2.5. Localized MPPT Control of an Individual OWC Plant

The airflow control and rotor speed regulation blocks, as shown in Figure1, are the two most important controllers for OWC control. As mentioned earlier, the rotor speed regulator is considered for localized MPPT control of the OWC plant. The MPPT control can be achieved using linear or nonlinear controller in which the actual rotor speed is forced to track an optimum speed reference [24, 25, 27, 31, 33, 34, 36]. The optimum reference speed calculation algorithm is designed in such a manner that it would always lead to maximum output power. In this work, a backstepping-type rotor speed controller and optimum reference speed calculation algorithm have been designed using the approach described in [36].The optimum reference speed calculation algorithm [36] is presented next. It is calculated using air velocity information in the following steps:(i)
Step 1: calculate the value ofVx using (1).(ii)
Step 2: calculate peak values ofVx as follows:(8)ifVx≠0,V˙x=0,Vxp=Vx,elseVxp=0.end(iii)
Step 3: passVxp through zero-order-hold (ZOH) as follows:(9)V¯xp=ZOHVxp.(iv)
Step 4: for threshold value of the flow coefficient,φth=0.3, calculate the reference speed using (4) as follows:(10)ωref=V¯xprφth−1.(v)
Step 5: calculateω1d by limiting the minimum and maximum values of ωref as follows:(11)ifωref≤ωe,ω1d=ωe,elseifωref≥ωe,ω1d=ωrp,elseω1d=ωref,endwhere ωe is the minimum value of ω1d and ωrp is the maximum value of ω1d.(vi)
Step 6: in order to avoid any sudden change in the reference value, passω1d through a low-pass filter. The new reference value is calculated as follows:(12)z1d=hf⊗ω1d.The frequency domain representation ofhf is given as follows:(13)Hfs=11+0.1s.As a result, thez1d is the optimum reference speed to be used for proposed controllers. Next, the backstepping-type rotor speed regulator would be designed to force the actual rotor speed to track the optimum reference speed z1d.The state space model from [36] is given below:(14)z˙1=k1z1+k2z2+D,z˙2=k3z1−ωe+k4z2+ur,where k1=−F/J; k2=−M/J; k3=Lr/LmψS; k4=−RrLs/K; ur=control signal=vqr; D=Tt/J; z1=ωr; and z2=ψqr.Furthermore, simplifying the above equation, we have(15)z˙1=f1z1,D+k2z2,(16)z˙2=f2z1,z2+ur,where f1z1,D=k1z1+D and f2z1,z2=k3z1−ωe+k4z2.A step by step design approach is applied for the backstepping controller. For a second-order system expressed by (15) and (16), the controller is designed in two stages. First, a virtual controller, z2d, is to be designed. Then, z2d would be used for designing final control law ur.For designing the virtual control law,z2d, let us choose the error component as follows:(17)z˜1=z1d−z1.Next, the first order derivative of (17) is written as follows:(18)z˜˙1=z˙1d−z˙1=z˙1d−f1z1,D−k2z2.Furthermore, by adding and subtractingk2z2d term, (18) becomes(19)z˜˙1=z˙1d−f1z1,D−k2z2+k2z2d−k2z2d.The virtual control lawz2d is chosen as follows:(20)z2d=k2−1z˙1d−f1z1,D+σ1z˜1,where σ1>0.Define(21)z˜2=z2d−z2.Substituting (20) and (21), (19) can be expressed as follows:(22)z˜˙1=−σ1z˜1+k2z˜2.Next, the derivative of (21) is given by(23)z˜˙2=z˙2d−z˙2=z˙2d−f2z1,z2−ur.For designing the control law which ensures the closed loop stability of systems (15) and (16), a Lyapunov function candidate, Vlpf, is chosen as follows:(24)Vlpf=12z˜12+z˜22.The first order time derivative of (23) is expressed as follows:(25)V˙lpf=z˜1z˜˙1+z˜2z˜˙2,⇒V˙lpf=z˜1−σ1z˜1+k2z˜2+z˜2z˙2d−f2z1,z2−ur,⇒V˙lpf=−σ1z˜12+z˜2z˙2d−f2z1,z2+k2z˜1−ur.The control lawur(26)ur=z˙2d−f2z1,z2+k2z˜1+σ2z˜2,gives(27)V˙lpf=−σ1z˜12−σ2z˜22≤0,where σ2>0.Here, (27) becomes negative semidefinite and V˙lpf does not contain any trajectories of error states z˜1 and z˜2 other than trivial trajectory z˜1=z˜2=0. Then, error states z˜1 and z˜2 converge asymptotically to zero. Hence, the system given by (15) and (16) with control law ur given in (26) is asymptotically stable.In Section3, the airflow control concept would be extended to the airflow control of OWC-OEN. As per the analysis of this work, the formation of OWC-OEN reduces the OPV as compared to the individual OWC plant. This could be further reduced by a centralized airflow controller to restrict the power generation as per the desired or reference power. The power output signal is sent by communication network to the controller. The controller output is again sent back to the OWC using the same channel. Needless to mention that the communication channel is a digital platform wherein the analog-to-digital (A/D) and digital-to-analog conversion (D/A) of plant and controller data also takes place simultaneously.


## 3. Formation of OWC-OEN and Centralized Airflow Controller Design

In this section, the concept depicted in Figure1 is extended to a network of multiple OWC sites at different geographical locations.


### 3.1. Formation of OWC-OEN

The OWC-OEN is proposed to be implemented in a smaller coastal region not greater than 50 km. OWC sites of OWC-OEN are independent from each other and are having at least 2 km distance between them. Typically, the distance covered by the wave front is a few hundred meters. As per the proposed configuration, two sites are separated by at least two kilometers and thus, the wave profiles at these two sites can be assumed to be uncorrelated. Next, each OWC site receives distinct sea wave input due to changed geographical location.It is also assumed that each OWC site of OWC-OEN supplies the current to a common electrical grid, as shown in Figure5, wherein the grid voltage and frequency are assumed to be constant. Hence, the total output power could be taken as a sum of output power of all individual OWC sites provided there is common grid voltage provided to each OWC. Suppose, there are N number of OWC sites connected to the grid network and are called as OWC-1, OWC-2, …, OWC-N. The output power from these OWC sites is denoted as Pg1,Pg2,…,PgN. The total output power, Pgtotal, is given as follows:(28)Pgtotal=∑k=1NPgk=∑k=1NTekωrk=∑k=1NVskIsk,where Tek is the electromagnetic torque of kth OWC site; ωrk is the rotor speed of kth OWC site; Vsk is the grid voltage of kth OWC site and Vs1=Vs2=⋯=VsN; and Isk is the current supplied by kth OWC site to grid and Is1≠Is2≠⋯≠IsN.Figure 5
Block diagram of OWC-OEN and its centralized control unit.The centralized airflow control unit, as displayed by Figure5, is located in the land area and is not very far (few tens of kilometers) from different OWC sites of OWC-OEN. Each OWC site is also equipped with MPPT control at a local level so as to extract maximized output power. We consider the use of high speed fiber-optic cables for communication between the central airflow control unit and the OWC-OEN. The output power data from OWC sites is transmitted to the controller and vice versa. The one-way delay time associated with fiber-optic cables for communication over large distances (several hundreds of kilometers) is typically around 100–150 ms [49]. As the distance between the central control unit and the OWC sites is only a few tens of kilometers, the communication delay would be much lower than 100 ms. In order to ensure a rigorous analysis of simulation results, three communication delays on higher side are considered as τ=100ms, 500ms, and 1000ms.Three types of configurations of OWC-OEN from the control point of view are considered in this study which are uncontrolled, localized MPPT control, and centralized airflow control. In uncontrolled configuration, the controllers are assumed to be absent at local (i.e., MPPT control) as well as central level (i.e., airflow control). Therefore, the output power of each OWC site is delivered to the grid without performing any control action. In localized MPPT control of OWC-OEN, each OWC site is coupled with MPPT control at the local level and the maximized power is extracted. Then, the maximized output power from each OWC site is delivered to the grid. In centralized airflow control of OWC-OEN, each OWC site is integrated with control valves. The control valves are operated at the central level using the airflow controller that controls the amount of total power delivered to the grid.


### 3.2. Centralized Airflow Controller Structure

The internal structure of central airflow control unit of OWC-OEN is shown in Figure6. It consists of two control stages as control stage-1 and control stage-2. Control stage-1 consists of a PI-type controller. The total output power, Pgtotal, is compared with the reference total output power, Pgtotal−ref, and error, egtotal, is fed to the PI controller. The PI controller provides a common control command Pg−ref to control stage-2. The internal structure of antiwindup PID-type controllers used for control stage-2 is shown in Figure 7.Figure 6
Block diagram of internal structure of central control unit.Figure 7
Antiwindup PID controller structure ofkth OWC site.The erroregkt in Figure 7 is given as follows:(29)egkt=Pg−ref−Pgk,where k=1,2,…,N. Pg−ref is the common reference command obtained from the central PI controller as depicted in Figure 6 and Pgk is the output power obtained from kth OWC site via communication network. The suffix k is used to denote the PIDk controller that belongs to kth OWC site. Similarly, Kpk, Tik, and Tdk are the proportional gain, integral time constant, and derivative time constant of the PIDk, respectively. Next, the output of PIDk controller, uvk, works as the input to the airflow control valve of kth OWC site. Antiwindup PID controller output characterises the effective valve area. Therefore, the effective turbine duct area fluctuates according to the deviations in the valve area, and the required output power is achieved by adjusting the air flow rate. For simplicity, the transfer ratio between the valve input (control signal) and the valve output was taken as unity. The saturation effect is due to the valve that works as the final control actuator. Therefore, the PID output is constrained to prevent the impact of valve saturation. The saturation range is taken between 0 and 1. The PID output has no effect on the valve reaction when the valve becomes saturated. The valve goes to a steady state, but the error between the actual and desired values causes the amplitude of the PID integrator to increase continuously. It enhances the control effort without affecting the valve response. To avoid this, the antiwindup PID control scheme has been implemented wherein the integral action of PID is reduced via algebraic feedback, as shown in Figure 7. The antiwindup PID controller scheme was also proposed earlier in [23, 24] for the OWC plant.


### 3.3. OPV Index of Individual OWC Sites and OWC-OEN

The OPV index is the difference between the maximum and minimum values of the actual output power of OWC divided by the total rated power of the OWC. The main objective of this paper is to reduce the deviations in the output power to make it suitable for electrical grid integration. In other words, the OPV index is the measurement of the suitability of the output power for the electrical grid, and it is desirable to keep this index as minimum as possible. Next, we define an OPV index as follows:(30)OPV=Pg−max−Pg−minPg−rated,where Pg−max and Pg−min are the maximum and minimum values of output power of an OWC, respectively.Now, for individual OWC sites, the OPV index is defined as follows:(31)OPV1=Pg1−max−Pg1−minPg1−ratedOPV2=Pg2−max−Pg2−minPg2−rated⋅⋅⋅OPVN=PgN−max−PgN−minPgN−rated.Next, the OPV for complete OWC-OEN is defined as follows:(32)OPVtotal=Pgtotal−max−Pgtotal−minPgtotal−rated,where Pgk−rated is the rated power of the kth OWC site and Pgtotal−rated is the rated power of OWC-OEN.The OPV index expressed in (10), (11), and (12) is very important for measuring the improvement in the power variation of OWC-OEN. The objective is to obtain the minimum possible value of OPV index by suitably designing the centralized airflow controller.


### 3.4. Centralized Airflow Controller Tuning Using PSO

The complex controller tuning involves 3N + 2 unknown parameters to be determined. Therefore, we choose PSO-based optimization approach for tuning controller parameters. Now, we define an ISE type fitness function as follows:(33)ISE=∫0Tsegtotal2dt,where egtotal is defined as follows:(34)egtotal=Pgtotal−ref−Pgtotal.Therefore, the ISE can be written as follows:(35)ISE=∫0TsPgtotal−ref−Pgtotal2dt,where Ts is simulation run time of the OWC-OEN model.Next, the objective is to minimize ISE in such a way that all 3N + 2 parameters of OWC-OEN controllers are properly selected. So, the PSO algorithm has been applied for optimum selection of control parameters of OWC-OEN.The population-based swarm intelligence method is widely adopted to find the optimal solution when solving complex optimization problems with a large search area. The PSO approach [39, 40] is a population-dependent search strategy that has a wide target field to address the problem of optimization. This approach represents the behavior of birds and fish schools. In a PSO system, an individual bird or fish is known as particles and each particle has its position and velocity. Now, particle travels in multidimensional search space depending on its own knowledge and the surrounding particle experience. The position and speed of the particles are changed during the search space movement. The velocity and position upgrading of particles depends on three factors which are inertia, cognitive, and social factors.The PSO is a very popular as well simple approach for tuning PID controllers. Several research studies have applied PSO in their works related to PID controller tuning [41, 42]. However, there are many optimization algorithms available in the literature and anyone of them could be utilized for tuning purpose. The comparison of optimization algorithms is not taken into account in this study because the proposed research work is mainly focused on reduction in OPV using centralized airflow controller.The velocity and position update of each particle can be calculated using the current velocity and position as follows:(36)Vjk+1=WVjk+cp1×rand×pbest,j−Xjk+cp2×rand×gbest,j−Xjk.Position update equation is given by(37)Xjk+1=Xjk+Vjk+1,where(38)Wp=Wp−max−Wp−max−Wp−min×kmaxk,and kp−max = maximum number of iterations, k = iteration number, j = particle number, Vjk = velocity of jth particle in kth iteration, Wp = inertia weight factor, Wp−max = Maximum inertia weight factor, Wp−min = Minimum inertia weight factor, cp1 = cognitive acceleration factor, cp2 = social acceleration factor, rand () = random numbers uniformly distributed in the range (0, 1), Xjk = position of jth particle in kth iteration, pbest = local best position, and gbest = global best position. The block diagram of PSO algorithm-based tuning of OWC-OEN controllers is given in Figure 8.Figure 8
PSO algorithm flowchart for tuning OWC-OEN controller parameters.


## 3.1. Formation of OWC-OEN

The OWC-OEN is proposed to be implemented in a smaller coastal region not greater than 50 km. OWC sites of OWC-OEN are independent from each other and are having at least 2 km distance between them. Typically, the distance covered by the wave front is a few hundred meters. As per the proposed configuration, two sites are separated by at least two kilometers and thus, the wave profiles at these two sites can be assumed to be uncorrelated. Next, each OWC site receives distinct sea wave input due to changed geographical location.It is also assumed that each OWC site of OWC-OEN supplies the current to a common electrical grid, as shown in Figure5, wherein the grid voltage and frequency are assumed to be constant. Hence, the total output power could be taken as a sum of output power of all individual OWC sites provided there is common grid voltage provided to each OWC. Suppose, there are N number of OWC sites connected to the grid network and are called as OWC-1, OWC-2, …, OWC-N. The output power from these OWC sites is denoted as Pg1,Pg2,…,PgN. The total output power, Pgtotal, is given as follows:(28)Pgtotal=∑k=1NPgk=∑k=1NTekωrk=∑k=1NVskIsk,where Tek is the electromagnetic torque of kth OWC site; ωrk is the rotor speed of kth OWC site; Vsk is the grid voltage of kth OWC site and Vs1=Vs2=⋯=VsN; and Isk is the current supplied by kth OWC site to grid and Is1≠Is2≠⋯≠IsN.Figure 5
Block diagram of OWC-OEN and its centralized control unit.The centralized airflow control unit, as displayed by Figure5, is located in the land area and is not very far (few tens of kilometers) from different OWC sites of OWC-OEN. Each OWC site is also equipped with MPPT control at a local level so as to extract maximized output power. We consider the use of high speed fiber-optic cables for communication between the central airflow control unit and the OWC-OEN. The output power data from OWC sites is transmitted to the controller and vice versa. The one-way delay time associated with fiber-optic cables for communication over large distances (several hundreds of kilometers) is typically around 100–150 ms [49]. As the distance between the central control unit and the OWC sites is only a few tens of kilometers, the communication delay would be much lower than 100 ms. In order to ensure a rigorous analysis of simulation results, three communication delays on higher side are considered as τ=100ms, 500ms, and 1000ms.Three types of configurations of OWC-OEN from the control point of view are considered in this study which are uncontrolled, localized MPPT control, and centralized airflow control. In uncontrolled configuration, the controllers are assumed to be absent at local (i.e., MPPT control) as well as central level (i.e., airflow control). Therefore, the output power of each OWC site is delivered to the grid without performing any control action. In localized MPPT control of OWC-OEN, each OWC site is coupled with MPPT control at the local level and the maximized power is extracted. Then, the maximized output power from each OWC site is delivered to the grid. In centralized airflow control of OWC-OEN, each OWC site is integrated with control valves. The control valves are operated at the central level using the airflow controller that controls the amount of total power delivered to the grid.


## 3.2. Centralized Airflow Controller Structure

The internal structure of central airflow control unit of OWC-OEN is shown in Figure6. It consists of two control stages as control stage-1 and control stage-2. Control stage-1 consists of a PI-type controller. The total output power, Pgtotal, is compared with the reference total output power, Pgtotal−ref, and error, egtotal, is fed to the PI controller. The PI controller provides a common control command Pg−ref to control stage-2. The internal structure of antiwindup PID-type controllers used for control stage-2 is shown in Figure 7.Figure 6
Block diagram of internal structure of central control unit.Figure 7
Antiwindup PID controller structure ofkth OWC site.The erroregkt in Figure 7 is given as follows:(29)egkt=Pg−ref−Pgk,where k=1,2,…,N. Pg−ref is the common reference command obtained from the central PI controller as depicted in Figure 6 and Pgk is the output power obtained from kth OWC site via communication network. The suffix k is used to denote the PIDk controller that belongs to kth OWC site. Similarly, Kpk, Tik, and Tdk are the proportional gain, integral time constant, and derivative time constant of the PIDk, respectively. Next, the output of PIDk controller, uvk, works as the input to the airflow control valve of kth OWC site. Antiwindup PID controller output characterises the effective valve area. Therefore, the effective turbine duct area fluctuates according to the deviations in the valve area, and the required output power is achieved by adjusting the air flow rate. For simplicity, the transfer ratio between the valve input (control signal) and the valve output was taken as unity. The saturation effect is due to the valve that works as the final control actuator. Therefore, the PID output is constrained to prevent the impact of valve saturation. The saturation range is taken between 0 and 1. The PID output has no effect on the valve reaction when the valve becomes saturated. The valve goes to a steady state, but the error between the actual and desired values causes the amplitude of the PID integrator to increase continuously. It enhances the control effort without affecting the valve response. To avoid this, the antiwindup PID control scheme has been implemented wherein the integral action of PID is reduced via algebraic feedback, as shown in Figure 7. The antiwindup PID controller scheme was also proposed earlier in [23, 24] for the OWC plant.


## 3.3. OPV Index of Individual OWC Sites and OWC-OEN

The OPV index is the difference between the maximum and minimum values of the actual output power of OWC divided by the total rated power of the OWC. The main objective of this paper is to reduce the deviations in the output power to make it suitable for electrical grid integration. In other words, the OPV index is the measurement of the suitability of the output power for the electrical grid, and it is desirable to keep this index as minimum as possible. Next, we define an OPV index as follows:(30)OPV=Pg−max−Pg−minPg−rated,where Pg−max and Pg−min are the maximum and minimum values of output power of an OWC, respectively.Now, for individual OWC sites, the OPV index is defined as follows:(31)OPV1=Pg1−max−Pg1−minPg1−ratedOPV2=Pg2−max−Pg2−minPg2−rated⋅⋅⋅OPVN=PgN−max−PgN−minPgN−rated.Next, the OPV for complete OWC-OEN is defined as follows:(32)OPVtotal=Pgtotal−max−Pgtotal−minPgtotal−rated,where Pgk−rated is the rated power of the kth OWC site and Pgtotal−rated is the rated power of OWC-OEN.The OPV index expressed in (10), (11), and (12) is very important for measuring the improvement in the power variation of OWC-OEN. The objective is to obtain the minimum possible value of OPV index by suitably designing the centralized airflow controller.


## 3.4. Centralized Airflow Controller Tuning Using PSO

The complex controller tuning involves 3N + 2 unknown parameters to be determined. Therefore, we choose PSO-based optimization approach for tuning controller parameters. Now, we define an ISE type fitness function as follows:(33)ISE=∫0Tsegtotal2dt,where egtotal is defined as follows:(34)egtotal=Pgtotal−ref−Pgtotal.Therefore, the ISE can be written as follows:(35)ISE=∫0TsPgtotal−ref−Pgtotal2dt,where Ts is simulation run time of the OWC-OEN model.Next, the objective is to minimize ISE in such a way that all 3N + 2 parameters of OWC-OEN controllers are properly selected. So, the PSO algorithm has been applied for optimum selection of control parameters of OWC-OEN.The population-based swarm intelligence method is widely adopted to find the optimal solution when solving complex optimization problems with a large search area. The PSO approach [39, 40] is a population-dependent search strategy that has a wide target field to address the problem of optimization. This approach represents the behavior of birds and fish schools. In a PSO system, an individual bird or fish is known as particles and each particle has its position and velocity. Now, particle travels in multidimensional search space depending on its own knowledge and the surrounding particle experience. The position and speed of the particles are changed during the search space movement. The velocity and position upgrading of particles depends on three factors which are inertia, cognitive, and social factors.The PSO is a very popular as well simple approach for tuning PID controllers. Several research studies have applied PSO in their works related to PID controller tuning [41, 42]. However, there are many optimization algorithms available in the literature and anyone of them could be utilized for tuning purpose. The comparison of optimization algorithms is not taken into account in this study because the proposed research work is mainly focused on reduction in OPV using centralized airflow controller.The velocity and position update of each particle can be calculated using the current velocity and position as follows:(36)Vjk+1=WVjk+cp1×rand×pbest,j−Xjk+cp2×rand×gbest,j−Xjk.Position update equation is given by(37)Xjk+1=Xjk+Vjk+1,where(38)Wp=Wp−max−Wp−max−Wp−min×kmaxk,and kp−max = maximum number of iterations, k = iteration number, j = particle number, Vjk = velocity of jth particle in kth iteration, Wp = inertia weight factor, Wp−max = Maximum inertia weight factor, Wp−min = Minimum inertia weight factor, cp1 = cognitive acceleration factor, cp2 = social acceleration factor, rand () = random numbers uniformly distributed in the range (0, 1), Xjk = position of jth particle in kth iteration, pbest = local best position, and gbest = global best position. The block diagram of PSO algorithm-based tuning of OWC-OEN controllers is given in Figure 8.Figure 8
PSO algorithm flowchart for tuning OWC-OEN controller parameters.


## 4. Discussion on Simulation Results

In this section, the centralized airflow controller has been validated through numerical simulations. The simulation parameters used for OWC-OEN airflow control and rotor speed regulation schemes are provided in Table1. The number of OWC sites are chosen to be N = 20. The WAFO toolbox in MATLAB® has been used for generating JONSWAP spectrum-based twenty distinct sea wave scenarios for twenty OWC sites located at different locations.The sea scenarioSW1 (Figure 9) is chosen for demonstrating the MPPT outcome of OWC-1, whereas all sea scenarios, i.e., SW1,SW2,…,SW20, are selected for evaluating the performance of OWC-OEN with MPPT, uncontrolled OWC-OEN, and OWC-OEN with centralized airflow control. The wave height and corresponding airflow velocity for sea scenario, SW1, is shown in Figure 9.Figure 9
Wave height and corresponding airflow velocity (absolute) for OWC-1 withSW1.


### 4.1. Performance Analysis of MPPT Control

The MPPT performance of OWC-1 at the local level has been evaluated in this section. The optimum reference speed,ωref−OWC1, is calculated first using the algorithm suggested in [36]. This reference is generated in a manner that the turbine flow coefficient always remains below the permissible threshold limit to escape the turbine stalling. If turbine stalling is avoided, then the output power can be maximized to its best possible level. Next, the backstepping-based nonlinear controller is implemented for rotor speed control that in turn provides the efficient tracking of reference speed by actual rotor speed. This is observed in Figure 10, wherein the actual rotor speed of OWC-1 very closely follows the optimum reference speed. The rotor speed for uncontrolled OWC-1 is clearly representing the turbine stalling case. The control effort needed to manipulate the rotor speed is also shown in Figure 10 which is having a range of ±150volts and is required only when the reference value is changing.Figure 10
Rotor speed and control signal for OWC-1 withSW1.Next, turbine flow coefficient and electrical power waveforms are shown by Figure11. The turbine flow coefficient for MPPT-controlled OWC-1 always remains below the threshold level, i.e., 0.3, whereas for uncontrolled OWC-1, it exceeds the threshold and causes the stalling in Wells turbine. Similarly, the output power gets maximized in case of MPPT control as compared to uncontrolled OWC-1. However, the OPV is very high as seen in power waveform for OWC-1. The OPV index of all OWC units is provided in Table 2 which would be compared with the OPV index of OWC-OEN later.Figure 11
Flow coefficient and output power for OWC-1 withSW1.Table 2
OPV index values of individual OWC sites.
OWC sitePg−min (kW)Pg−max (kW)OPV indexOWC-12.6−53.20.558OWC-22.5−54.50.570OWC-32.5−31.60.341OWC-42.6−55.20.578OWC-52.7−54.40.571OWC-62.6−54.10.567OWC-72.6−54.00.566OWC-82.7−48.60.513OWC-92.6−51.50.541OWC-102.7−54.60.573OWC-112.6−40.10.427OWC-122.6−53.50.561OWC-132.7−47.70.504OWC-142.7−54.50.572OWC-152.7−54.80.575OWC-162.7−54.30.570OWC-172.7−54.80.575OWC-182.7−48.60.513OWC-192.7−52.20.549OWC-202.7−54.60.573As shown in Figure12, the total output power has been analyzed with and without MPPT control after forming OWC-OEN. For uncontrolled case, the output power obtained has a peak value of Pgtotal−max=−373.3kW, whereas MPPT control provides the peak value of Pgtotal−max=−587.4kW. Again, the OPV index of OWC-OEN is not at an acceptable level. Therefore, the centralized airflow controller to be discussed next was required to deal with high OPV issue of OWC-OEN.Figure 12
Total output power for uncontrolled and MPPT-controlled OWC-OEN.The output power waveforms have negative amplitude which represents the generation mode of DFIG. In the generation mode, the negative peak of output power actually represents thePg−max. The value of output power that is close to time axis is treated as Pg−min. In the motor mode of DFIG, the power waveforms would have positive amplitude.


### 4.2. Performance Analysis of Centralized Airflow Control

The centralized airflow controller, as shown in Figure6, is designed using PSO. For N = 20, there are 62 control parameters which have been tuned with an objective to minimize the ISE as given in (35). The ISE was minimized by applying PSO algorithm as per the flowchart shown in Figure 8. The PSO parameters for running optimization are given in Table 3.Table 3
PSO parameters.
PSO parametersValuesNumber of particles50Particle dimension62Maximum number of iteration (kp−max)100Maximum inertia weight factor (Wp−max)0.9Minimum inertia weight factor (Wp−min)0.1Cognitive acceleration factor (cp1)2Social acceleration factor (cp2)2Next, the optimized control parameters were obtained by running the optimization algorithm for 100 iterations. The tuned parameters of centralized airflow controller are provided in Table4. The numerical simulations are obtained for OWC-OEN with a centralized airflow controller. Three cases of total output power reference (i) Pgtotal−ref=−50kW, (ii) Pgtotal−ref=−110kW, and (iii) Pgtotal−ref=−200kW have been considered for analyzing the controller performance. The Pgtotal−ref selection is based on observing the total output power waveforms. The total output power is more concentrated in the lower range (i.e., below −250 kW) and hence, the centralized airflow controller is found to be more effective in the lower range and the effectiveness gets reduced substantially at higher ranges.Table 4
Central airflow control unit parameters.
ControllersKpTiTdControl Stage-1PI0.1300.129—Control Stage-2PID18.5802.0781.131PID25.8500.6170.642PID39.7651.2781.989PID46.9052.1550.988PID511.5282.0921.734PID66.1210.8062.376PID75.2542.3291.096PID811.1912.0291.856PID97.2402.0252.764PID105.9152.4270.917PID113.3211.6391.970PID1211.8602.1970.804PID137.0702.4490.917PID1410.4581.8162.093PID155.0112.6421.617PID1610.4031.9451.140PID178.1312.4600.858PID1810.7510.7351.860PID1910.2932.4990.767PID206.3801.1500.912The total output power,Pgtotal, and corresponding error waveforms for different references are shown in Figure 13. The total output power of OWC-OEN successfully tracks the reference power. Although for lower as well as higher Pgtotal−ref, the OPV index is higher when compared with Pgtotal−ref=−110kW. The lowest OPV index of 0.0093 is achieved with Pgtotal−ref=−110kW. Overall, the airflow controller reduces the OPV significantly as compared to uncontrolled OWC-OEN and MPPT-controlled OWC-OEN. Next, a detailed comparison of OPV index values for uncontrolled OWC-OEN, MPPT-controlled OWC-OEN, and OWC-OEN with centralized airflow controller can be found in Table 5. It can be seen in the table that the centralized airflow controller leads to lowest OPV index among all configurations of OWC-OEN. The OPV index with MPPT controlled OWC-OEN is higher than that of uncontrolled OWC-OEN as provided in Table 5. The centralized airflow controller is also tested with different cases of communication delay in OWC-OEN in next section.Figure 13
OWC-OEN output power and error waveforms with centralized airflow controller. (a)Pgtotal−ref=−50kW, (b)Pgtotal−ref=−110kW, and (c)Pgtotal−ref=−200kW.
(a)(b)(c)Table 5
OPV index values of OWC-OEN.
OWC-OENPg−min (kW)Pg−max (kW)OPV indexUncontrolled−56.6−373.30.1583MPPT−56.2−587.40.2656Airflow controlPgtotal−ref=110kW−98.5−117.10.0093Pgtotal−ref=50kW−28.4−96.00.0338Pgtotal−ref=200kW−107.5−273.90.0832Airflow control with delayτ=100ms−98.1−118.70.0103τ=500ms−65.0−175.20.0551τ=1000ms−50.0−201.50.0757


### 4.3. Performance Analysis of Centralized Airflow Control with Communication Delay

The centralized airflow controller has been validated with different communication delays ofτ=100ms,500ms, and1000ms. The total output power and corresponding error waveforms are shown in Figure 14. The OPV index increases with increase in τ value as observed from the waveforms. So, it is required that the communication network should be able to transfer data with a very high speed in order to avoid any performance deterioration occurring due to delay. However, it is very much possible nowadays to transmit data with bandwidths in gigahertz range with advanced communication technology. It is also to be noted here that each OWC site may have different communication delays which needs further attention. It is observed that the total output power waveform in Figure 14(a) seems very similar to that of Figure 13(b) with Pgtotal−ref=−110kW. It is due to the time range of 40s in both Figures 14(a) and 13(b) which is very high as compared to the communication delay of 100ms. Therefore, the variation appears in the same Figures 14(a) and 13(b). However, there is clear difference in performance of both ceases in terms of the OPV index, as given in Table 5.Figure 14
OEN output power and error waveforms with communication delay. (a)τ=100ms. (b)τ=500ms. (c)τ=1000ms.
(a)(b)(c)


## 4.1. Performance Analysis of MPPT Control

The MPPT performance of OWC-1 at the local level has been evaluated in this section. The optimum reference speed,ωref−OWC1, is calculated first using the algorithm suggested in [36]. This reference is generated in a manner that the turbine flow coefficient always remains below the permissible threshold limit to escape the turbine stalling. If turbine stalling is avoided, then the output power can be maximized to its best possible level. Next, the backstepping-based nonlinear controller is implemented for rotor speed control that in turn provides the efficient tracking of reference speed by actual rotor speed. This is observed in Figure 10, wherein the actual rotor speed of OWC-1 very closely follows the optimum reference speed. The rotor speed for uncontrolled OWC-1 is clearly representing the turbine stalling case. The control effort needed to manipulate the rotor speed is also shown in Figure 10 which is having a range of ±150volts and is required only when the reference value is changing.Figure 10
Rotor speed and control signal for OWC-1 withSW1.Next, turbine flow coefficient and electrical power waveforms are shown by Figure11. The turbine flow coefficient for MPPT-controlled OWC-1 always remains below the threshold level, i.e., 0.3, whereas for uncontrolled OWC-1, it exceeds the threshold and causes the stalling in Wells turbine. Similarly, the output power gets maximized in case of MPPT control as compared to uncontrolled OWC-1. However, the OPV is very high as seen in power waveform for OWC-1. The OPV index of all OWC units is provided in Table 2 which would be compared with the OPV index of OWC-OEN later.Figure 11
Flow coefficient and output power for OWC-1 withSW1.Table 2
OPV index values of individual OWC sites.
OWC sitePg−min (kW)Pg−max (kW)OPV indexOWC-12.6−53.20.558OWC-22.5−54.50.570OWC-32.5−31.60.341OWC-42.6−55.20.578OWC-52.7−54.40.571OWC-62.6−54.10.567OWC-72.6−54.00.566OWC-82.7−48.60.513OWC-92.6−51.50.541OWC-102.7−54.60.573OWC-112.6−40.10.427OWC-122.6−53.50.561OWC-132.7−47.70.504OWC-142.7−54.50.572OWC-152.7−54.80.575OWC-162.7−54.30.570OWC-172.7−54.80.575OWC-182.7−48.60.513OWC-192.7−52.20.549OWC-202.7−54.60.573As shown in Figure12, the total output power has been analyzed with and without MPPT control after forming OWC-OEN. For uncontrolled case, the output power obtained has a peak value of Pgtotal−max=−373.3kW, whereas MPPT control provides the peak value of Pgtotal−max=−587.4kW. Again, the OPV index of OWC-OEN is not at an acceptable level. Therefore, the centralized airflow controller to be discussed next was required to deal with high OPV issue of OWC-OEN.Figure 12
Total output power for uncontrolled and MPPT-controlled OWC-OEN.The output power waveforms have negative amplitude which represents the generation mode of DFIG. In the generation mode, the negative peak of output power actually represents thePg−max. The value of output power that is close to time axis is treated as Pg−min. In the motor mode of DFIG, the power waveforms would have positive amplitude.


## 4.2. Performance Analysis of Centralized Airflow Control

The centralized airflow controller, as shown in Figure6, is designed using PSO. For N = 20, there are 62 control parameters which have been tuned with an objective to minimize the ISE as given in (35). The ISE was minimized by applying PSO algorithm as per the flowchart shown in Figure 8. The PSO parameters for running optimization are given in Table 3.Table 3
PSO parameters.
PSO parametersValuesNumber of particles50Particle dimension62Maximum number of iteration (kp−max)100Maximum inertia weight factor (Wp−max)0.9Minimum inertia weight factor (Wp−min)0.1Cognitive acceleration factor (cp1)2Social acceleration factor (cp2)2Next, the optimized control parameters were obtained by running the optimization algorithm for 100 iterations. The tuned parameters of centralized airflow controller are provided in Table4. The numerical simulations are obtained for OWC-OEN with a centralized airflow controller. Three cases of total output power reference (i) Pgtotal−ref=−50kW, (ii) Pgtotal−ref=−110kW, and (iii) Pgtotal−ref=−200kW have been considered for analyzing the controller performance. The Pgtotal−ref selection is based on observing the total output power waveforms. The total output power is more concentrated in the lower range (i.e., below −250 kW) and hence, the centralized airflow controller is found to be more effective in the lower range and the effectiveness gets reduced substantially at higher ranges.Table 4
Central airflow control unit parameters.
ControllersKpTiTdControl Stage-1PI0.1300.129—Control Stage-2PID18.5802.0781.131PID25.8500.6170.642PID39.7651.2781.989PID46.9052.1550.988PID511.5282.0921.734PID66.1210.8062.376PID75.2542.3291.096PID811.1912.0291.856PID97.2402.0252.764PID105.9152.4270.917PID113.3211.6391.970PID1211.8602.1970.804PID137.0702.4490.917PID1410.4581.8162.093PID155.0112.6421.617PID1610.4031.9451.140PID178.1312.4600.858PID1810.7510.7351.860PID1910.2932.4990.767PID206.3801.1500.912The total output power,Pgtotal, and corresponding error waveforms for different references are shown in Figure 13. The total output power of OWC-OEN successfully tracks the reference power. Although for lower as well as higher Pgtotal−ref, the OPV index is higher when compared with Pgtotal−ref=−110kW. The lowest OPV index of 0.0093 is achieved with Pgtotal−ref=−110kW. Overall, the airflow controller reduces the OPV significantly as compared to uncontrolled OWC-OEN and MPPT-controlled OWC-OEN. Next, a detailed comparison of OPV index values for uncontrolled OWC-OEN, MPPT-controlled OWC-OEN, and OWC-OEN with centralized airflow controller can be found in Table 5. It can be seen in the table that the centralized airflow controller leads to lowest OPV index among all configurations of OWC-OEN. The OPV index with MPPT controlled OWC-OEN is higher than that of uncontrolled OWC-OEN as provided in Table 5. The centralized airflow controller is also tested with different cases of communication delay in OWC-OEN in next section.Figure 13
OWC-OEN output power and error waveforms with centralized airflow controller. (a)Pgtotal−ref=−50kW, (b)Pgtotal−ref=−110kW, and (c)Pgtotal−ref=−200kW.
(a)(b)(c)Table 5
OPV index values of OWC-OEN.
OWC-OENPg−min (kW)Pg−max (kW)OPV indexUncontrolled−56.6−373.30.1583MPPT−56.2−587.40.2656Airflow controlPgtotal−ref=110kW−98.5−117.10.0093Pgtotal−ref=50kW−28.4−96.00.0338Pgtotal−ref=200kW−107.5−273.90.0832Airflow control with delayτ=100ms−98.1−118.70.0103τ=500ms−65.0−175.20.0551τ=1000ms−50.0−201.50.0757


## 4.3. Performance Analysis of Centralized Airflow Control with Communication Delay

The centralized airflow controller has been validated with different communication delays ofτ=100ms,500ms, and1000ms. The total output power and corresponding error waveforms are shown in Figure 14. The OPV index increases with increase in τ value as observed from the waveforms. So, it is required that the communication network should be able to transfer data with a very high speed in order to avoid any performance deterioration occurring due to delay. However, it is very much possible nowadays to transmit data with bandwidths in gigahertz range with advanced communication technology. It is also to be noted here that each OWC site may have different communication delays which needs further attention. It is observed that the total output power waveform in Figure 14(a) seems very similar to that of Figure 13(b) with Pgtotal−ref=−110kW. It is due to the time range of 40s in both Figures 14(a) and 13(b) which is very high as compared to the communication delay of 100ms. Therefore, the variation appears in the same Figures 14(a) and 13(b). However, there is clear difference in performance of both ceases in terms of the OPV index, as given in Table 5.Figure 14
OEN output power and error waveforms with communication delay. (a)τ=100ms. (b)τ=500ms. (c)τ=1000ms.
(a)(b)(c)


## 5. Concluding Remarks and Future Challenges

This paper presented a novel concept of OWC-OEN and its centralized airflow control to mitigate the OPV issue of ocean energy systems. The centralized airflow controller consisting of two control stages was designed using PSO due to complexity of tuning parameters. The PSO helped in choosing large number of control parameters of a very complex OWC-OEN by minimizing an ISE-type fitness function. A comprehensive simulation analysis was presented to validate the proposed airflow control scheme. The JOWNSWAP-based irregular wave patterns were randomly selected as the input to individual OWC sites. Also, an OPV index was defined to compare the output power waveforms of individual OWC sites and OWC-OEN. The OWC-OEN with centralized airflow control delivers the lowest OPV index as compared to uncontrolled OWC-OEN and MPPT controlled OWC-OEN. The centralized airflow controller works reasonably well when OWC-OEN is under the effect of communication delay. As with the case of any other spatially distributed control network, large communication delays degrade the performance of the OWC-OEN. The communication delays considered in this study are assumed to be uniform for all OWC sites. The unequal communication delays for OWC sites located at different geographical locations would further increase the complexity of OWC-OEN. It is an interesting subject, which needs thorough investigation in further studies on OWC-OEN.



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