Integrated Duty Cycle Control for Multiple Renewable Energy Sources in a Grid Connected System

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Item Type Article

Authors Pervez, Imran;Antoniadis, Charalampos;Ghazzai, Hakim;Massoud, Yehia Mahmoud

Citation Pervez, I., Antoniadis, C., Ghazzai, H., & Massoud, Y. (2023).

Integrated Duty Cycle Control for Multiple Renewable Energy Sources in a Grid Connected System. IEEE Open Journal of Power Electronics, 1–14. https://doi.org/10.1109/ojpel.2023.3270663 Eprint version Post-print

DOI 10.1109/ojpel.2023.3270663

Publisher Institute of Electrical and Electronics Engineers (IEEE) Journal IEEE Open Journal of Power Electronics

Rights Archived with thanks to IEEE Open Journal of Power Electronics under a Creative Commons license, details at: https://

creativecommons.org/licenses/by/4.0/legalcode Download date 2024-01-09 22:41:02

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Link to Item http://hdl.handle.net/10754/691375

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Received XX Month, XXXX; revised .

Integrated Duty Cycle Control for Multiple Renewable Energy Sources in

a Grid Connected System

Imran Pervez, Student Member, IEEE, Charalampos Antoniadis, Member, IEEE, Hakim Ghazzai, Senior Member, IEEE, and Yehia Massoud, Fellow, IEEE

1Innovative Technologies Laboratories (ITL), King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

ABSTRACT Due to their abundance, affordability, and clean energy production, Renewable Energy Sources (RESs) have emerged as crucial sources of electricity production. As a result, considerable effort has been made to integrate renewable energy sources into the grid to help it meet energy demands. One of the challenges is the Maximum Power Extraction (MPE), where the maximum power needs to be extracted from each RES. The cost of implementation rises linearly with the number of RESs if the MPE arrangements are being made for each RES individually. Additionally, the MPE through multiple RES systems gets more challenging, especially when several PhotoVoltaic (PV) strings are connected and each PV string receive non-uniform irradiance. This paper proposes an integrated MPE control system for a multi-RES grid-connected system. The proposed solution uses a single microcontroller to maximize power from all sources to overcome the linearly growing cost problem. Moreover, we propose an improved Multi-Dimensional Cuckoo (MDC) algorithm for MPE to tackle the non-uniform irradiation problem with multi-string PV, in contrast to prior works with grid-connected multiple sources. The proposed technique is first put up against the individual MPE control system, and then it is put up against the Jaya algorithm that is documented in the literature for a typical one-dimensional MPE.

INDEX TERMS Maximum power extraction (MPE), DC-DC converter, Metaheuristic algorithm, Multi- dimensional cuckoo algorithm, integrated grid power control

I. INTRODUCTION

I

N order to cope with the global energy demand, renewable energy is gaining more and more popularity due to its cleaner production and ample supply. By displacing fossil fuel energy production, renewable energy can help reduce harmful CO2 emissions. Using Renewable Energy Sources (RESs) for residential and commercial applications is possible as a standalone microgrid system and a system incorporated into the grid. However, due to the intermittent nature of RESs and the need to harvest clean power with the highest possible efficiency, integrating RESs with the grid presents a number of challenges. Maximum Power Extraction (MPE) has attracted much attention over the last decade [1]- [29], especially when considering a single standalone RES (e.g., a photovoltaic (PV) panel). With numerous RESs, the MPE task gets more complicated and expensive, especially when the PVs are coupled in a multi- string topology and receive irregular illumination. If not formulated correctly and solved through appropriate optimization algorithms, the MPE problem for multiple-RESs may not converge to a global optimum solution specifically

for non-uniform irradiance conditions, as explained in later sections.

Many studies have investigated the case of multiple RES grid-connected systems and aimed to address the MPE problem [30]- [38]. However, these studies have either applied MPE for each source separately using algorithms like Perturb

& Observe (P&O) or Incremental Conductance (InC), which are highly likely to converge to local solutions in MPE, mainly in the event of uneven irradiance on PV or when MPE is performed on a single RES (generally PV).

A hybrid PV and Fuel Cell (FC) system for grid connection with voltage-orientated inverter control was proposed in [30]. Using the Jaya algorithm, the MPE was only accomplished for the PV. The FC was exploited to reduce PV’s intermittency by giving it an additional supply when its power declines. In [31], a hybrid PV/wind energy system was investigated for grid integration. Considering the requirement for the chemical and semiconductor manufacturing industries to operate dependably, the hybrid system was designed to prevent intermittency in RESs. The dynamic voltage restorer (DVR) with Battery Energy Storage (BES) and Super Mag-

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netic Energy Storage (SMES) hybrid system was used to achieve smooth supply to the consumer side. In [32], a grid-connected PV-wind farm was investigated with a Fuzzy Logic Control (FLC)-based DVR to enhance the system’s power quality and voltage stability. The Incremental Con- ductance (InC) algorithm performed the MPE exclusively for the PV system. On the other hand, a hybrid PV and FC grid-connected system were suggested in [33] to reduce voltage fluctuations on the demand side. The FC was utilized to account for variations in PV power, and the perturb and observe (P&O) method was exclusively employed for MPE on the PV system. A grid-connected PV, wind, and FC system with a novel flywheel connection topology were proposed in [34]. Incorporating flywheel storage alongside PV, wind, and FC has simplified the management of load and source interruptions and disturbances on the grid. The MPE was only performed on the PV system using the perturb an observe (P&O) algorithm.

A grid-connected PV-wind hybrid system with Q-V inverter control was suggested in [35]. It was demonstrated that sliding mode control based on Lyapunov control was superior to straightforward Proportional Integral (PI) control.

While a separate voltage regulation was carried out for the wind system, a simple P&O technique was used for the PV MPE. A power management system for a PV-FC hybrid system connected to a standalone microgrid was proposed in [36]. The power management system helped control power under dynamic loading situations. The FC met the extra power demand, and the MPE was only carried out for the PV system. In [37], a PV-FC hybrid grid-connected system with model predictive control (MPC) for inverter control was suggested for coordinated power management in grid-connected and islanded modes. Similar to the previous system, only PV was considered for the MPE, and the FC was employed to sustain the fluctuation in PV power. It was suggested in [38] to use an energy management system based on an adaptive neuro-fuzzy inference system (ANFIS) to handle the intermittent behavior of RESs. Both the wind and the PV systems underwent individual MPEs.

As discussed previously, various hybrid RES grid- connected or microgrid systems have been discussed in the literature. In all the studies concerning PV-FC hybrid systems, the MPE is performed at the PV level only, while the FC is typically utilized to reduce PV power fluctuations.

Such a system cannot extract most of the power from different sources. It can only improve the reliability of the grid-connected RES system. Some works concerning wind and PV hybrid systems have performed MPE for all RESs, thereby utilizing the maximum power from each RES.

However, they have performed the MPE separately for each source using different microcontrollers, which raises the overall implementation cost. Moreover, they used straightforward algorithms for PV MPE, such as P&O, or InC, that are unsuitable for non-convex problems brought on by non- uniform irradiance on the PV system. Generally speaking,

PV systems are linked as multi-string PV systems, wherein various PV strings are parallelly connected, and they receive non-uniform irradiance on their surfaces, meaning that the irradiance received by the various modules in a PV string varies. Therefore, the non-convexity of the power concerning the voltage (P-V relation) of PVs is caused by the non- uniform irradiance, which makes the MPE problem more challenging, and needs to be considered by both of those mentioned above recent as well as old works.

Considering all the issues mentioned above, in this paper and to the best of our knowledge, we develop the first integrated control technique for MPE of hybrid RESs for a grid- linked system while considering the non-uniform irradiance on a PV string system. In contrast to prior studies that performed MPE for each RES separately and hence added a linear rise in cost, the proposed integrated control technique implements the MPE control mechanism such that a single microcontroller controls all RESs. Hence, the MPE control system transitions from linearly rising microcontrollers to a single microcontroller, which results in a multi-dimensional MPE problem. Furthermore, in contrast to previous work, this study considers the operational factors of connecting the PV system. Hence, the MPE is transformed into a non-convex multi-dimensional problem. To address this, we develop a multi-dimensional cuckoo (MDC) algorithm for integrated MPE control of the multi-RESs system, including multi-string PV and FC connected to the grid.

The proposed system is shown to be effective in achieving maximum power when compared to individual MPE systems. The proposed system, despite the significantly fewer microcontrollers, performs similarly. Our results demonstrate that the developed MDC algorithm can effectively solve the non-convex multi-dimensional problem with just one controller. Furthermore, we also compare the performance of the proposed method to that obtained using the Jaya algorithm, which was previously put forward for a one- dimensional MPE problem. The outcomes demonstrate that the MDC algorithm was superior to the Jaya algorithm in solving the multi-dimensional non-convex MPE problem.

In a nutshell, the contributions of this study can be summarized as follows:

• We propose an integrated MPE control technique to reduce the implementation cost for the hybrid FC and multi-string PV system.

• We optimize the extracted power from all the RESs instead of optimizing only through a PV.

• We define an initialization and solution updating strategy for MD-MPE.

• We design a modified cuckoo algorithm to solve the non-convex MD-MPE problem for RESs.

In addition to that, we perform extensive simulations to evaluate the hybrid system’s performance under a variety of non- uniform PS conditions. The proposed solution can be scaled to a large-scale RESs system where the number of RESs is

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I^beta

I^alpha I^d I^q

Ibeta

Ialpha

I^bI^c I^a

Microcontroller for converter

switching

DC-DC boost converter

switching

DC Bus

Load Rectifier

AC Bus

Clarke transformation

Park transformation

I^dref I^qref

+ - + - Inverse park transformation

SVPWM

FIGURE 1.A general grid connected RES system. Each RES/FC is connected to the inverter DC side which converts the DC RES output to AC in order to supply power to the AC load and the grid. The DC-AC conversion is carried out using clarke and park transformations for inverter switching.

greater than the number of I/O pins of one microcontroller.

Therefore, a similar architecture for integrated duty cycle control can be implemented by assigning multiple RES per microcontroller.

The rest of the paper is organized as follows. Section II describes the general grid control and conventional MPE systems. Section III explains the proposed integrated MPE system. Section IV describes the improved implementation method of the Multi-Dimensional Cuckoo (MDC) algorithm for the proposed system. Section V discusses the simulation results, and Section VI concludes the paper.

II. RES-Grid Control and Conventional RES-Grid Integration Systems

In this section, we start by providing a brief description of power control in a RES-grid integrated system. Afterward, we describe the generally available grid-connected MPE system.

A. RES-Grid Control

We illustrate in Fig. 1 the schematic of the grid-connected multiple RES system, which consists of parallel connections between PV, wind, and FC sources. Through DC link voltage regulation employing PI control, the DC bus (the common connection point between RESs and the inverter) is kept at a constant value of 1000 V. The reference direct-axis current

corresponding to which the actual direct-axis current is tuned is the output of the PI controller for DC link voltage management. In cooperation with the grid, the inverter converts the DC output from RESs to AC and supplies power to the load. Inverter switching with the d-q control implements the grid side control and meets the 2.1 MW load demand.

B. Conventional MPE for Multi-RESs

In conventional systems such as the ones investigated in [30]- [38], we have observed two possibilities for MPE with multi- RESs: individual MPE for each RES or MPE for the PV system only. Fig. 2 illustrates a single MPE grid-connected system consisting ofN PV strings connected in parallel with a FC. As it can be observed, each RES is coupled to a different MPE control system. In other words, each RES has its own microprocessor for MPE. Each RES’s microcontroller has an algorithm built into it, which receives an input of the voltage and current across each RES through voltage and current sensors, respectively. Consequently, the power (product of voltage and current) needs to be maximized as a function of the duty cycle. The microcontroller for each energy source updates the duty cycle value according to the voltage and current it receives from the RES at each iteration using the programmed algorithm to maximize the power. The updated duty cycle is used for DC-DC converter switching connected across each RES at each iteration. Each

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V^FC I^FC I^PVN V^PVN I^PV1 V^PV1

switching

DC Bus

Load AC Bus

switching

DC Bus

Load AC Bus

Photovoltaic (PV) String N

switching

DC-DC boost converter Photovoltaic

(PV) String N

switching

(PV) String 1

Fuel cell (FC)

FIGURE 2.Grid connected RES system with individual MPE. Each RES in this illustration is controlled through a single microcontroller.

I^PVN V^PVN

I^FC I^PV1

V^PV1 I^FC

VFC

I^PV1 V^PV1 Photovoltaic

(PV) String 1

Fuel cell (FC)

DC-DC boost converter Fuel cell (FC)

DC Bus

Load AC Bus

Microcontroller for converter switching V^FC Gate

driver To PV string 1

To FC Photovoltaic

DC-DC boost converter I^PVN

V^PVN

I^FC I^PV1

V^PV1 I^FC

VFC

I^PV1 V^PV1 Photovoltaic

(PV) String 1

Fuel cell (FC)

DC Bus

Load AC Bus

Microcontroller for converter switching V^FC Gate

driver To PV string 1

To FC Photovoltaic

V^PV2 I^PV2 V^PVN I^PVN To PV string 2

To PV string N

FIGURE 3.Grid connected RES system with proposed integrated MPE. Each RES is controlled by a single microcontroller that runs the proposed MDC algorithm for converter switching of each RES.

RES’s microprocessor updates the duty cycle continuously and simultaneously until each RES begins to operate at maximum power.

In the case of a PV-only MPE system, all the sources (FC for our case) are linked directly to the grid, and only a PV

system is subject to MPE. The MPE method for a PV-only system is similar to that of an individual MPE system, except that the maximum power is only retrieved through PV, while FC is used mainly for supplying power in a power deficiency situation.

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FIGURE 4.Multi-dimensional formulation for MPE. The objective function from each RES can be combined to form a single objective function which is the summation of each RESs objective functions. The resulting objective function is multi-dimensional as it includes all the variables each from an individual RES.

III. Proposed MPE for Multi-RESs

This section introduces the proposed system architecture process and how it resolves conventional system problems.

Then, it presents the MPE problem formulation for the proposed MD-MPE system.

A. Proposed Integrated MD-MPE System

Fig. 3 depicts the proposed MD-MPE system, including N PV strings and a FC. The two systems (individual MPE and PV-only MPE) stated earlier have problems related to cost and non-uniform irradiation circumstances that the suggested MD-MPE system is designed to mitigate. In the individual MPE system presented earlier, the number of microcontrollers increases linearly with the number of RESs, thereby linearly raising the controller cost. Moreover, as previously stated, individual MPE systems with several PV strings and FC are typically not examined in the literature under non-uniform irradiance conditions (non-convex P-V curve).

Finally, in the case of PV-only MPE systems, the power is maximized only through PV. The proposed system uses a single microcontroller for MPE, as shown in Fig. 3. A single microcontroller receives voltage and current values from all the sources simultaneously and, in turn, generates duty cycles for DC-DC boost converter switching of all the sources.

The duty cycle control provided by a single microcontroller eliminates the requirement for numerous microcontrollers, thereby reducing cost. The suggested system is also designed to address the non-convex MPE problem with numerous PV strings and a FC which is performed by programming the microcontroller with a Multi-Dimensional Cuckoo (MDC) algorithm, as it will be discussed in the following section.

Finally, the integrated system is designed to optimize power across RES with high efficiency, unlike the PV-only MPE system that optimizes only PV power.

B. MD-MPE Problem Formulation for the Proposed Integrated System

Although it offers several advantages compared to the conventional one, the integrated duty cycle management with the proposed system makes the optimization problem Multi- Dimensional (MD). Fig. 4 illustrates how integrated control leads to an MD problem using an example ofN multi-string PV systems connected with a FC. Each RES is represented as a function that takes duty cycle as input and produces power as an output, as seen in Fig. 4. Individual PV string 1,. . ., PV stringN, and FC powers are denoted asP₁^{P V},. . .,P_N^{P V}, and P^{F C}, respectively that can be written as a function of duty cycles asP₁^{P V} =f₁^{P V}(D₁),. . .,P_N^{P V} =f_N^{P V}(D_N), and P^{F C}=f_{F C}(D^{F C}), respectively as shown in Fig. 4. The sum of the output powers from all RESs, including f₁^{P V}(D₁), . . ., f_N^{P V}(D_N), and f^{F C}(D^{F C}), is known as the overall power output (P_total) as follows:

Ptotal=P₁^{P V} +· · ·+P_N^{P V} +P^{F C}

=f₁^{P V}(D1) +· · ·+f_N^{P V}(DN) +f^{F C}(D^{F C})

=f(D1, . . . , DN, D^{F C}),

(1) where the N + 1 variables D₁, . . ., D_N, and D^{F C} are the inputs to each RES and together determine the overall power P_total. Thus, a N-string PV with an FC in the illustrative example in Fig. 4 results in a N+1-dimensional MPE problem. The objective function (P_total) in (1) needs to be optimized to extract the maximum power through RESs as follows:

D^∗₁, ...D^∗_N, D^{F C∗}= argmax

D₁,...,D_N,D^{F C}

(Ptotal)

s.t. 0≤D₁, . . . , D_N, D^{F C}≤1,

(2) The overall objective function is the sum of individual RES objective functions. Each individual RES objective function is independent of each other. The complexity may arise in case the formulation of overall objective function exhibits exponential relationships between individual RES objective functions. In that case, the algorithm may require spreading more particles in the search space (the rows of matrix in (3) of the manuscript). Depending upon the type of non-convexity introduced through those complex dependencies between individual functions of the overall objective function the number of particle spreading might attain large values that may reserve more microcontroller memory.

Nevertheless, the MPE problem formulation does not have any such complex relationships and the overall objective function includes the summation of individual objective functions which will be sufficient even with fewer number of particles. The functions (f₁^{P V},. . .,f_N^{P V}) associated with the PV strings make the problem non-convex when PV strings receive non-uniform irradiance. Straightforward algorithms like P&O, InC, etc., fail to converge to the maximum power under non-uniform irradiance conditions. We thus propose to employ the cuckoo search algorithm, which provides a much higher probability of global power convergence owing to its search space exploration capability. In addition, we improved

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the initialization and updating methods for the MD-MPE problem for better power convergence accuracy.

IV. Cuckoo Search Algorithm for MD-MPE Problem for Multiple-RESs

As discussed earlier, the formulated optimization problem is non-convex. To solve it, we propose to employ the cuckoo search algorithm. In this section, we present the algorithm, its advantages, and how it is employed to solve the MD-MPE problem.

A. Cuckoo Search Algorithm,

The Cuckoo Search Algorithm (CSA), created by Xin- She Yang and Suash [39], is a metaheuristic algorithm for unconstrained multi-dimensional problems. CSA is based on numerous cuckoo species’ aggressive brood parasitism and egg-laying strategies [40]. The ability of CSA to achieve global convergence has been mathematically demonstrated in [41], giving it an edge over competing algorithms. To begin, CSA initializes many potential solutions (y_ij^t) to explore the optimization problem’s search space as in (3).

Y=







y^t₁₁ y₁₂^t y₁₃^t . . . y_1n^t y^t₂₁ y₂₂^t y₂₃^t . . . y_2n^t y^t₃₁ y₃₂^t y₃₃^t . . . y_3n^t

. . . . . . . . . . . . y_m1^t y^t_m2 y_m3^t . . . y_mn^t







, (3)

subject toLB≤Y ≤UB,

where the matrixYcontainsmparticles withndimensions, each randomly distributed within some problem-specific lower and upper bounds (LBandUB).

Then, as a Levy flight (LF) step, each candidate solution at iterationtis updated to identify the candidate solution for iterationt+ 1 as follows:

Y_i^t+1=Y^t_i+stepsize, (4) where

stepsize= 0.8×S×(Ybest−Y^t_i), (5) andS is defined as

S = a

|b|^1/bet, (6)

whereYbest represents the global best value and the value of the term betis kept as 1.5. To update (4), the algorithm selects a random number from a uniform distribution [0,1].

If the random number is greater than 0.25, the CSA updates thei^thsolution (Yi) using (4). Updating only a fractional part of the population maintains solution diversity in the search space thereby increasing the chances of global convergence.

The parametersa andb in (6) are drawn randomly from zero-mean normal distributions with standard deviationsϕa

andϕb, respectively, as follows:

a∼ N(0, ϕ²_a)andb∼ N(0, ϕ²_b), (7) The standard deviations ϕa andϕb are given as:

ϕa = Γ(1 +bet)×sin(π×bet/2) Γ(^1+bet₂ )×bet×2⁽^bet−1² ⁾

!

andϕb= 1, (8) The proposed integrated control for the Multiple-RESs system leads to the MD-MPE problem mentioned in the previous section. In contrast to the works with one-dimensional MPE in the literature, the cuckoo search method is then evolved as a Multi-Dimensional Cuckoo (MDC) algorithm.

This paper treats the MD-MPE cuckoo formulation dif- ferently from how the multi-dimensional problem is often solved. This is done by taking advantage of the independency between the power functions of each source. In the next section, both the traditional and modified approaches are explained.

B. Jaya Algorithm

The Jaya algorithm is another nature-inspired algorithm that takes inspiration from the word ”Jaya” which means victory in Sanskrit. The rule of thumb to attain victory is to avoid obstacles moving toward the path of success. Thus, the Jaya algorithm utilizes a similar strategy in its updating equations.

First, the algorithm initializes its solutions over the search space in the same way as in (3). Then, after the algorithm has explored the search space, the algorithm uses the following equations for the solution update:

Y^t+1_i =Y^t_i +r1× |Y_best^t −Y_i^t|+r2× |Y^t_worst−Y_i^t|, (9) whereY^t_bestandY_worst^t are the best and the worst solutions up to iterationt, respectively, andr1andr2are two random numbers between zero and one to adjust the search space exploration around Y_i^t. Finally, it compares the ”Fitness”

function value (Y^(t+1)_i ) of the candidate solution with the

”Fitness” function value (Y^t_i) of the prior solution (in our case, the ”Fitness” function is the Power) and replaces the current iteration’s solution (Y_i^(t+1)) with the one that has the highest ”Fitness” value, as illustrated below:

Y^t+1_i =

(Y_i^t+1, Fitness(Y^t+1_i ) better than Fitness(Y_i^t) Y_i^t, otherwise.

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C. Jaya vs. Cuckoo Search

This section describes the advantages of choosing the Cuckoo search algorithm over the Jaya algorithm. The main difference between both algorithms lies in their solution-updating methods. The Jaya algorithm updating equations consist of two components, |Y^t_best−Y_i^t| and |Y_worst^t −Y^t_i|, namely the best-enhancing component

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(BEC) and the worst-avoiding component (WAC), respectively. The BEC updates the current solution to bring it closer to the best solution by randomly updating the current solution value to the best solution. Similarly, the WAC component avoids the worst solutions by randomly updating the current solution value nearby to the worst solution. Adding the WAC and BEC components improves the algorithm’s exploration capability. However, it degrades the overall algorithm performance regarding convergence speed and power fluctuations while solving the MPE problem. This is due to a significant difference between the best and the worst solutions. The contribution of the WAC component takes the solution farther away from the best solution, slowing down the convergence speed and increasing power fluctuations by exploring very low-power regions. The Cuckoo Search Algorithm (CSA) avoids the problem of WAC update as it includes only the BEC component. Moreover, in contrast to the random update of BEC in the Jaya algorithm, the CSA updates the BEC term using the levy flight (LF) distribution.

The LF distribution solution update generates more informed solutions than updating through a random distribution. The LF distribution initially adds larger steps to the solution to maintain high initial diversification. The step size decreases as the solution approaches nearer to the optimum solution, achieving faster exploitation. The combination of LF distribution and BEC in CSA makes it faster in convergence with fewer power fluctuations while maintaining sufficient exploration to obtain global convergence, unlike the Jaya algorithm, which adds excessive random exploration, which reduces the convergence speed and increases power fluctuations. The exploration-exploitation capability of CSA thus makes it more suitable for MPE than the Jaya algorithm.

D. Solution to MD-MPE through Conventional Method The algorithm starts by detecting the number of active input pins by reading the values of external RESs connected to those pins. Upon detecting the number of active ports, the algorithm sets the problem dimension equal to the number of active ports. A vector (let’s say Di) made up of the duty cycles (D^t₁₁, D₁₂^t , ...D^t_ij ...) of the DC-DC converter connected across each RES is a potential solution vector for the MDC algorithm. As stated in IV.A, the algorithm randomly distributes several duty cycle vectors over the search space (using (3) by swapping outy^t_ij withD^t_ij). Each duty cycle vector (Di) is constrained by the vectorsLBand UB, which have values of 0.1 and 0.9, respectively. Next, the algorithm calculates the total power (Ptotal,i) as a function of Di (D₁₁^t , D^t₁₂, ... D^t_ij ...) as described in the preceding section by taking the voltage and current combinations from each RES and adding their products. Finally, the algorithm calculates Ptotal for each of the m duty cycle vectors dispersed over the search space, as shown below:

Ptotal=







Ptotal,1=f1(D₁₁^t , D^t₁₂, . . . , D_1n^t ) Ptotal,2=f2(D₂₁^t , D^t₂₂, . . . , D_2n^t ) Ptotal,3=f3(D₃₁^t , D^t₃₂, . . . , D_3n^t )

. . .

Ptotal,m=fm(D^t_m1, D_m2^t , . . . , D_mn^t )





 .

(11) The newly calculated P_total (across each dispersed duty cycle vector) is compared with the previously savedP_total. If the new powers and associated duty cycle vectors are better than the previous value, the best and worst duty cycle vectors are evaluated, and the new power values are recorded. The algorithm then uses (4) to update the duty cycle vector for each particle. Once the converter has switched to evaluate the new power, the duty cycles are resupplied. This process is repeated until the best duty cycle vector is determined to match the maximum power (max(P_total)).

E. Solution to MD-MPE through Modified Method

In the previous subsection, we explained the random initialization method for MPE, a general initialization method of metaheuristic algorithms for multi-dimensional problems.

However, the random initialization of duty cycle vectors in the search space is disadvantageous as it may lead to less accurate power convergence.

A limitation on the amount of duty cycle vectors that can be dispersed in the search space is the cause of the reduced convergence accuracy. In MPE, m=3 to m=5 duty cycle vectors are usually spread over the search space since a higher number of duty cycle vectors can lead to excessive power fluctuations and an increased computing strain on the microcontroller. The random initialization may locate the duty cycle vectors in a specific region far from the global best solution. The random initialization with less duty cycle vector spreading (small m) may add challenges related to several power fluctuations while searching for maximum power as the algorithm has to make extensive explorations in the search space in the search for optimum power, which can also lead to less accurate power convergence. This is specifically for the problems with higher dimensions (such as the proposed work with n=5 dimensions).

Spreading the duty cycle vectors’ elements using several non-random combinations (among the elements in each row of (3)) is another approach for initialization. The number of duty cycle vectors will rise exponentially with a higher dimension (n) if a particular combination of components ac- commodates each duty cycle vector. This solution, in contrast to the previous one, avoids the poor accuracy convergence problem, but the exponentially rising duty cycle vectors may burden the microcontroller with the problem dimension.

Thus, to solve the above-mentioned duty cycle vector initialization issues, we propose an initialization method involving equalizing all elements in a duty cycle vector

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(equating all elements in each row of (3)). LetD_i = {Dij|

⟨Dij⟩j=a = ⟨Dij⟩j=b},∋ a ̸= b, i.e, a duty cycle vector from a row of the matrix in (3), where a, b ϵ j= 1,2, ....n are indices of elements inD_i. Now, the initial best duty cycle vector is a vector among allmvectors in (3) corresponding to the highest power.

Db= argmax

{D1,D₂,....,D_n}

Ptotal(Di). (12) The proposed initialization method limits the solution diversification in the search space, which may result in the initial best-duty cycle vector being far from the optimum solution. Thus, the evaluation method of the initial best duty cycle vector is modified for the proposed initialization.

Unlike evaluating the initial best by comparing m powers corresponding to m duty vectors as in (12), the improved initial best evaluation method calculates the power across each duty vector element as in (13).

Ptotal=







P_total,11=f₁₁(D^t₁₁). . . P_total,1n=f_1n(D_1n^t ) Ptotal,21=f21(D^t₁₁). . . Ptotal,2n=f2n(D_2n^t ) P_total,31=f₃₁(D₃₁^t ). . . P_total,3n=f₁₁(D^t_3n)

. . .

P_total,m1=fm1(D^t_m1). . . P_total,mn=fmn(D_mn^t )





 ,

(13) The initial best vector is created by first grouping allnbest vector elements (i.e., the element with the highest power) into a single vector, as shown in (14). When the total power value for the enhanced best duty cycle vector was examined, it was discovered to be sufficiently high, indicating that the initial best solution to the global optimum was close. Let D^T represent the transpose of the matrix Y in (3) with the elements y_ij^t of Y being replaced byD^t_ij. Let nowDj

represent each column of the matrixD^T. The improvedD_b will then be represented as (3).

D_b=







argmax

{D11,D₁₂,....,D_1n}

⟨Ptotal(Dj)⟩j=1

argmax

{D21,D₂₂,....,D_2n}

⟨Ptotal(Dj)⟩j=2

argmax

{D31,D₃₂,....,D_3n}

⟨Ptotal(Dj)⟩j=3

. . . argmax

{Dm1,D_m2,....,D_mn}

⟨Ptotal(Dj)⟩j=m





 , (14)

The improved initial best strategy was made possible by taking advantage of the independency between the powers corresponding to each vector element. For instance, the power evaluated forD^t₁₁ is independent of the power evaluated for D^t₁₂ and thus can be evaluated individually. The proposed initialization and solution updating method thus significantly improve the power convergence accuracy as

Optimum value Initialized values

FIGURE 5. Random solution vector initialization on a two-dimensional non-convex space.

it will be confirmed by the simulations in the subsquent section.

V. Simulation Results

This section verifies the effectiveness of the suggested integrated duty cycle control system. Four PV strings comprise the entire grid system and, along with one FC, provide energy to the load. The PV module layout in two of the four strings consists of a collection of 282 PV arrays connected in parallel, each with seven modules in series. The PV module configuration for the latter two consists of 122 parallel connected arrays with 6 and 8 modules for each array, respectively. The developed FC stack has 900 cells with a notional stack efficiency of 42%. The maximum power the PV string and FC can produce is 2.1 MW.

The results are evaluated in two ways as follows:

• First, we compare the proposed integrated system with the non-integrated system. The cuckoo search algorithm is used in both systems, with the difference that the proposed system uses the improved Multi-Dimensional Cuckoo (MDC) while the non-integrated system em- ploys the conventional one-dimensional cuckoo.

• Second, we compare the proposed MDC and Multi- Dimensional Jaya (MDJaya) algorithms. The Jaya algorithm has been proposed in [33] for a one-dimensional MPE problem. The integrated system was used to evaluate and compare the performance of both the proposed MDC and MDJaya algorithms.

A. Comparison between Integrated System and Non-integrated Systems

This section compares the proposed integrated system’s MPE performance with the non-integrated system’s. The integrated and non-integrated systems are compared to demonstrate that, although having significantly fewer controllers, the performance of the proposed integrated system is comparable to that of the non-integrated system. The cuckoo search

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TABLE 1.Partial Shading Patterns on different modules of each string

Modules PS1 PS2 PS3

String 1 String 2 String 3 String 4 String 1 String 2 String 3 String 4 String 1 String 2 String 3 String 4

Module 1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

Module 2 920 900 900 920 690 670 660 620 940 600 600 930

Module 3 830 800 800 830 520 540 510 280 810 510 510 810

Module 4 710 700 700 400 400 220 710 370 210

Module 5 590 600 300 200 580 180

Module 6 470 180 420

FIGURE 6.Performance comparison between (a) individual MPE and (b) proposed integrated MPE systems. The figure shows both the systems have similar performances in terms of convergence speed and power convergence efficiency/accuracy. The different in convergence speed and power convergence in the figure is mainly due to random behavior of algorithms and not system specific differences.

algorithm is used in both systems. While the non-integrated system is built with a standard one-dimensional cuckoo, the integrated control system is built with the Multi-Dimensional Cuckoo (MDC).

We denote the different partial shading scenarios illustrated in Table 1 by partial shading (PS)1, PS2, and PS3. The performance of both systems for PS1 is shown in Fig. 10, which shows the power tracking performance with time for both systems. The proposed system initially produces a few large-size power fluctuations that reduce with time, while the non-integrated system has more power fluctuations of larger size. As a result, the convergence time of the proposed system is faster than the non-integrated system. Overall, both the systems perform similarly to the proposed but the proposed system does so more effectively for PS1. Thus, both systems will perform similarly despite the significantly fewer controllers in the proposed system. Table 2 summarizes the results in terms of achieved power and convergence time.

TABLE 2.Power and convergence time summary for comparison between proposed integrated and individual MPE systems

System type PS1

Power (MW)

Convergence time

(S)

True MPP (MW) Individual

MPE 1.47 3.28

1.515 Proposed integrated

MPE 1.49 2.6

B. Comparison between MDC and MDJaya for Integrated System

The effectiveness of the suggested MDC for the integrated system for various PS instances is demonstrated in this subsection. In order to compare with the proposed MDC method for the integrated system, the Jaya algorithm, which is already accessible in the literature for a one-dimensional MPE issue [30], is made multi-dimensional. Three different PS circumstances are used in this case’s comparison. The PS criteria for each string’s modules are listed in Table 1. and Figs 8, and 9.

The findings of the proposed MDC are compared to those of the MDJaya algorithm in Figs. 7-9.The comparison was made for three Partial Shading (PS) conditions, namely PS1, PS2, and PS3, as shown in Table 1. The comparison between MDC and MDJaya for PS1 is shown in Fig. 7, which shows the power tracking performance with the time of both algorithms for PS1. Ideally, during power tracking, the number and size of power fluctuations should be as least possible, and the convergence speed towards maximum power should be as fast as possible. As observed, when compared to the MDJaya method, the suggested MDC algorithm converges to the Maximum Power Point (MPP) more quickly.

Additionally, the suggested MDC effectively converged with fewer and smaller fluctuations than the MDJaya, which creates a substantial number and size of power fluctuations during tracking, as evident in Fig. 7. Similarly, Figs. 8 and 9 show the power tracking performance of both the algorithms for PS2 and PS3, respectively. In all instances, it is evident that the MDC significantly outperforms the MDJaya in terms of convergence speed, power fluctuation quantity, and size.

Table 3 illustrates both strategies’ convergence speed and converged power summary for all PS situations. The proposed algorithm for all PS scenarios is much faster compared to the Jaya algorithm with the percentage improvement

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TABLE 3.Power and convergence time summary for comparison between proposed MDC and Jaya algorithm

Algorithm PS1 PS2 PS3

Power (MW)

Convergence time

(S)

True MPP (MW)

Power (MW)

Convergence time

(S)

True MPP (MW)

Power (MW)

Convergence time

(S)

True MPP (MW)

MDJaya 1.42 5

1.515 0.9431 4.1

0.9761 1.074 4.328

1.1113

MDC 1.49 2.6 0.9272 3 1.07 2.78

FIGURE 7.Performance comparison between (a) Jaya and (b) proposed MDC algorithm for PS1. The proposed MDC algorithm exhibits significantly fewer power fluctuations compared to the Jaya algorithm with a much faster convergence speed under PS1 condition.

of upto nearly 200% in convergence speed. The power convergence efficiency/accuracy for proposed MDC and Jaya respectively are 98.3 and 93.7% for PS1, 95 and 96.6% for PS2, and 96.28 and 96.6% for PS3.

VI. Discussion on the Proposed System Complexity, Cost, and Scalability

Increasing the number of RESs/problem dimensions might result in exceeding/overflowing the microcontroller’s total memory, which can cause implementation issues. Microcon- troller total memory may be incapable of accommodating algorithms requiring the storage of hundreds of variables.

However, metaheuristic algorithms for MPE problems are lighter enough in order not to cause any memory-exceeding issues. Considering the proposed Cuckoo search algorithm with N dimensions (N RESs), most memory will be reserved by the initialization matrix in eq. (3). The row and columns of the matrix in eq. (3) correspond to the number of particles and the problem dimensions. A typical microcontroller can support up to eight RESs, reserving eight matrix columns. At the same time, the number of particles in

FIGURE 8. Performance comparison between (a) Jaya and (b) proposed MDC algorithm for PS2. The proposed MDC algorithm exhibits significantly fewer power fluctuations compared to the Jaya algorithm with a much faster convergence speed under PS2 condition.

the search space is generally chosen to be five, reserving five rows of the matrix. A total of forty memory positions (eight times five) can thus be reserved by a multi-dimensional algorithm. Considering one of the cheapest ATmega8 microcontrollers (around 1$ price), each memory location will reserve 8 bits corresponding to 1 byte of memory. Therefore, reserving forty memory locations will require 40 bytes of storage. In addition, certain variables in Cuckoo updating equations, like Φa, Φb, bet, etc., need to be stored and will require around 7 bytes of memory, totaling 47. Besides the 47 bytes for the Cuckoo algorithm, there are other auxiliary variable storage requirements that are involved in the execution of the algorithm, which may reserve a few more bytes. Moreover, the ATmega8 microcontroller has 8 kilobytes (KB) of memory for data storage. Thus, the overall memory reserved by the proposed algorithm cannot exceed the 8KB microcontroller memory.

A typical microntroller has limited input/output (I/O) pins and can support upto 7 renewables. Considering the above scenario with 56 renewables, the proposed integrated system

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FIGURE 9.Performance comparison between (a) Jaya and (b) proposed MDC algorithm for PS3. The proposed MDC algorithm exhibits significantly fewer power fluctuations compared to the Jaya algorithm with a much faster convergence speed under PS3 condition.

requires 8 microcontrollers for implementation, while the conventional individual system needs 56 microcontrollers.

Considering one of the cheapest AtMEGA8 microcontrollers (around 1$ cost) and assuming its implementation on a PCB reaching up to 2$ (an approximate assumption, the exact cost may differ), the microcontroller cost for the integrated system will reach around 16$ while for the individual system, it will be around 112$. The cost of the other system components is not required to be evaluated because it will remain similar. The overall savings for a 56 RES system will thus be around 96$.

In our study, we consider optimizing the power output of multiple photovoltaic strings and a fuel cell. A photovoltaic string is a connection of multiple photovoltaic modules connected in a series configuration. When photovoltaics are implemented practically on a site, on rooftops, etc., they are implemented in a multi-string configuration [42]. From each PV string, the wires are taken and connected to a multi-string inverter [42] which includes several maximum power extraction (MPE)/MPPT controllers to optimize the extracted power for each PV string. Thus, evidently the distance between different PV sources (strings) does not have any effect as wires from each string are being taken and connected to a common multi-string inverter. Considering a string inverter supporting up to three strings, two such inverters will be used for the proposed configuration (PV system with four strings and a fuel cell). In the case of a multi-inverter system, each inverter is connected just next to each other as shown in [42]. Thus, one of the inverters

will receive the outputs from three PV strings, while another inverter will receive the output from the remaining PV string and FC. In the proposed work, instead of performing MPPT with individual microcontrollers, a common microcontroller is used to make the system more cost effective. Connecting a microcontroller in the middle of the RES connection points for two inverters (e.g., Fig. 10), the microcontroller will remain very close to the connection points. In Fig. 10, considering a typical width of 72 cm for a three-string inverter (see the manufacturer’s datasheet [43]), the approximate distance between RES connection points on inverters will be around 90 cm. The microcontroller will thus be around 45 cm from each connection point, which is very small to cause duty ratio or sensor delays. To prove our work is extendable to general scenarios, through the similar method above, we have proved its feasibility for even a higher number of renewables and PV strings. Certain sites will contain wind turbines with more number of PV strings and FCs. Considering a larger system, say containing 10 PV strings, 2 FCs and 2 wind turbines, five three-string inverters will be needed to accommodate such a system. Moreover, considering a typical microcontroller can accommodate up to around seven RESs, two microcontrollers will be required.

Each microcontroller will optimize power through two RESs.

The two microcontrollers (one near the second inverter and another near fourth inverter starting from right in Fig. 10 of this document) will be approximately 90 cm from the farthest RES output which is sufficiently near to avoid duty ratio and sensor delays.

VII. Conclusion

The present paper developed an integrated duty cycle control system for Maximum Power Extraction (MPE) of a multiple-RESs system in the presence of photovoltaic panels under partial shading condition. The proposed system was developed to overcome the limitation of the conventional MPE control strategies: (a) individual MPE and (b) MPE for PV only. These methods can only extract power in an individual manner with a dedicated microcontroller for each RES. The proposed combined duty cycle control converts the problem into more complex MD-MPE non-convex issue that was solved using the improved Multi-Dimensional Cuckoo (MDC) algorithm. The proposed integrated system was compared to the individual MPE system to demonstrate that, despite being less expensive, it nevertheless extracts power similarly to the individual system. Moreover, the proposed MDC algorithm’s performance was evaluated for different complex partial shading scenarios on PV strings to prove its global convergence which other works generally do not consider. Finally, the MDC algorithm’s superiority in terms of other power tracking metrics like convergence speed and power fluctuations was proved over a Jaya algorithm proposed in the literature for a one-dimensional MPE. A potential future contribution of this work is to experiment

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Inverter 1 Inverter 2

Output from three PV

strings

Inverter 1

strings

Inverter 1 Inverter 4 Inverter 3 Inverter 5

MCU MCU MCU

MCU

strings Output from two

fuel cells and a PV string Output from two

wind turbines

90 cm

90 cm 90 cm 90 cm90 cm

90 cm 90 cm

Inverter 1 Inverter 2

MCU MCU

strings

Inverter 1

Output from a PV string and a fuel

cell

90 cm

45 cm 45 cm

(a) (b)

FIGURE 10.RES output connection for (a) two multi-string inverter system for the proposed architecture and (b) five multi-string inverter system for 10 RESs. The figure describes combining the outputs through various RESs to a common multi-string inverter irrespective of their positions on site. Due to the high vicinity among RES connection points the microcontrollers can be placed so as to minimize any sensor or duty ratio pulsing delays.

the proposed architecture on a real hardware setup to gain practical insights.

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