*Article* **Optimum Synthesis of a BOA Optimized Novel Dual-Stage** *PI* − *(1* + *ID)* **Controller for Frequency Response of a Microgrid**

#### **Abdul Latif 1,\*, S. M. Suhail Hussain 2, Dulal Chandra Das <sup>1</sup> and Taha Selim Ustun <sup>2</sup>**


Received: 3 June 2020; Accepted: 1 July 2020; Published: 3 July 2020

**Abstract:** A renewable and distributed generation (DG)-enabled modern electrified power network with/without energy storage (ES) helps the progress of microgrid development. Frequency regulation is a significant scheme to improve the dynamic response quality of the microgrid under unknown disturbances. This paper established a maiden load frequency regulation of a wind-driven generator (*WG*), solar tower (*ST*), bio-diesel power generator (*BDPG*) and thermostatically controllable load (heat pump and refrigerator)-based, isolated, single-area microgrid system. Hence, intelligent control strategies are important for this issue. A newly developed butterfly algorithmic technique (BOA) is leveraged to tune the controllers' parameters. However, to attain a proper balance between net power generation and load power, a dual stage proportional-integral- one plus integral-derivative *PI* − *(1* + *ID)* controller is developed. Comparative system responses (in MATLAB/SIMULINK software) for different scenarios under several controllers, such as a proportional-integral (*PI*), proportional-integral-derivative (*PID*) and *PI* − *(1* + *ID)* controller tuned by particle swarm optimization (PSO), grasshopper algorithmic technique (GOA) and BOA, show the superiority of BOA in terms of minimizing the peak deviations and better frequency regulation of the system. Real recorded wind data are considered to authenticate the control approach.

**Keywords:** isolated hybrid microgrid system (*IH*μ*GS*); solar tower (*ST*); biodiesel power generator (*BDPG*); frequency regulation; butterfly optimization technique (BOA); microgrid energy management

#### **1. Introduction**

Electricity consumption is increasing in parallel with population and energy demand [1]. The increasing generation capacity with conventional energy sources has negative impacts on environment [2]. Research shows that the introduction of microgrids with renewable energy resources (RERs) is an environmentally friendly solution to this energy problem [3,4].

Microgrids can provide energy in a clean and optimal way when digital control technologies are coupled with sources such as wind and solar. However, the intermittent characteristics of RERs and low inertia of inverter-interfaced systems cause control and stability issues in microgrids [5]. Hence, combining diesel generators and RERs [6–8] is one possible solution to mitigate the detrimental effects (e.g., frequency fluctuation) of hybrid power systems. Additionally, a non-toxic bio-diesel power generator (*BDPG*) can be a more environment-conscious supplementary option for frequency regulation schemes.

To overcome the frequency fluctuation in a more reliable way, different storage devices (SDs) have been considered, such as battery (BSD), fuel cell (FCSD), ultra-capacitor (UCSD) and superconducting magnetic storage system (SMSD) [9]. There are maintenance and disposal concerns for BSD, while FCSD suffers from slow response and SMSU experiences leakage of expensive helium liquid [10]. In the following, a cost-effective, carbon-neutral-based, solid-oxide fuel cell (SOFC) can be utilized for the frequency regulation of isolated hybrid microgrids (*IH*μ*GS*). In addition, different thermostatically controllable loads (TCLs) such as a heat pump (*HP*) and refrigerator (*RFZ*) are employed for smoothing the dynamic system responses. In the recent past, several studies have focused on the frequency regulation of *IH*μ*GS* [11–15]. The study in [12] framed out a mathematical modeling of a system comprised of dish-stirling, solar thermal, diesel and SDs. The authors of [13] sketched a load frequency management for a hybrid power system that includes wind, solar PV and SDs. In fact, the application of a plug-in electric vehicle (PHEV)-battery (BSD) to contain frequency fluctuation is investigated in [14].

Beside the system architectures, several works have introduced a load frequency controller such as proportional-integral (*PI*) [9], proportional-integral-derivative (*PID*) [6], model predictive controller (MPC) [16], fractional order *PID* (FOPID) [17] or PIFOD [18] for the aforementioned issues. In this work, a dual-stage, proportional-integral-one plus integral-derivative *PI* − *(1* + *ID)* controller is introduced for the provision of better system dynamics.

Several algorithmic techniques have been leveraged in order to optimally tune the controller parameters for *IH*μ*GSs*, such as genetic algorithm (GA) [9], PSO [6], firefly technique (FA) [19], cuckoo search technique (CS) [14], mine blast technique (MBA) [20], grasshopper algorithmic technique (GOA) [21]. A comprehensive review of different algorithmic techniques for a load frequency controller is presented in [22]. In this regard, this work explores the application of a butterfly algorithmic tool (BOA) for designing the parameters of a frequency controller. This algorithm was recently developed and is considered in this paper due to its high convergence rate [23].

Therefore, the scope of this work and its contributions to the current body of knowledge can be summarized as follows:


The rest of the paper is organized as follows: Section 2 details the frequency response modeling steps. Section 3 gives an overview of the BOA technique and shows its adaptation for the purposes of this work. It also presents the proposed dual-stage controller. Simulation works and their analyses are presented in Section 4. The conclusions are given in Section 5.

#### **2. Frequency Response Modeling of the Proposed Dual-Stage Controller**

The hybrid system of the proposed work consists of wind generators (1.5 MW); solar-tower-based, solar-thermal power system (1 MW), *BDPG* (800 kW), *SOFC* (200 kW); thermostatically controllable *HP*; *RFZ* elements; and demanded loads (2.2 MW). The schematic layout and abbreviation of the relevant parameters are shown in Figure 1 and Table 1, respectively.

**Figure 1.** Schematic representation of *IH*μ*GS*.



#### *2.1. Wind Generator (WG)*

The kinetic energy of the wind converts into electrical energy through the wind generator (*WG*). As wind is a highly variable source, the power output through the *WG* depends on the instantaneous speed of the wind. Equation (1) formulates how wind energy is converted to the mechanical output power of *WG*.

$$P\_{\rm WG} = 0.5 \, V\_{\rm WG}^3 \rho \, A\_{\rm bd} \, \text{Cp} \, (\lambda, \beta) \tag{1}$$

where ρ*, VWG*, *Abd*, and *CP* are, in proper order, the air density, intermittent wind speed, blade-swept area and the extractable power co-efficient. Akkanayakanpatti station's recorded wind speed data are considered and modelled in the proposed work [24]. The rate of change in real recorded wind power (ΔP*WG*) and transfer function model of the *WG* are represented as shown in Equation (2) [25]

$$
\Delta P\_{\rm WG} = \begin{cases}
0, \ V\_{\rm WG} < V\_{\rm cut-in} || \, V\_{\rm WG} > V\_{\rm cut-out} \\
0, \ V\_{\rm refLeft} \le V\_{\rm WG} \le V\_{\rm cut-out} \\
\left( \begin{array}{c}
[0.007872 \, V\_{\rm WG}^5 - 0.23015 \, V\_{\rm WG}^4 + 1.3256 \, V\_{\rm WG}^3 \\
+11.061 \, V\_{\rm WG}^2 - 102.2 \, V\_{\rm WG} + 2.33 \right] \Delta V\_{\rm WG} \end{array} \tag{2}
$$

#### *2.2. Solar Tower (ST)*

The dual-axis (vertical and horizontal) heliostats-enabled central receiver system is *ST*, placed on a surface. Here, the reflected solar radiation is focused on the central receiver of *ST* with a higher concentration ratio (500–1000) and temperature (500–850 ◦C) of fluid (steam or molten salt). The collected incident solar power (*Pin*) can be deliberated as

$$P\_{in} = \eta\_{\text{lt}} I A\_{\text{h}} \tag{3}$$

where *Ah* is the heliostats area, *I* incident solar radiation and η*<sup>h</sup>* is the system constant. By solving the state equations, the linearized transfer function model of ST can be represented as [18]

$$\mathbf{G}\_{ST}(s) = \left(\frac{\mathbf{K}\_{RF}}{sT\_{RF} + 1}\right) \left(\frac{\mathbf{K}\_{RV}}{sT\_{RV} + 1}\right) \left(\frac{\mathbf{K}\_G}{sT\_G + 1}\right) \left(\frac{\mathbf{K}\_T}{sT\_T + 1}\right) \tag{4}$$

#### *2.3. Biodiesel Power Generator (BDPG)*

The combination valve regulator and combustion-engine-based biodiesel power generation (*BDPG*) was leveraged to offer support as a backup power generation. It has inherently biodegradable and non-toxic positive characteristics, which were the main reasons to incorporate it in the suggested work. Equation (5) details the transfer function of *BDPG* [21].

$$G\_{RDPG}(s) = \left(\frac{K\_{VR}}{sT\_{VR} + 1}\right) \left(\frac{K\_{CE}}{sT\_{CE} + 1}\right) \tag{5}$$

#### *2.4. Solid-Oxide-Based Fuel Cell (SOFC)*

Through the electrochemical reaction, the fuel cell produces dc power and, by using a DC-AC converter, this power is converted into AC. With a fast charging–discharging time and higher efficiency (~80%), the *SOFC* has gained much interest in recent years among all the categories of FCSDs. In view of the above, *SOFC* was selected as the storage device in the system. Its transfer function model is given in Equation (6) [18]

$$G\_{\rm SOFC}(s) = \frac{K\_{\rm SOFC}}{sT\_{\rm SOFC} + 1} \tag{6}$$

#### *2.5. Thermostatically Controllable Loads (HP and RFZ)*

In order to manage the energy consumption and to improve the system dynamic responses (by controlling operation cycles), two thermostatically controllable loads were considered, i.e., heat pump (*HP*) and *RFZ*. The transfer function models of *HP* [19] and *RFZ* [19] could be expressed as in Equations (7) and (8)

$$\mathcal{G}\_{HP}(\mathbf{s}) = \frac{\mathcal{K}\_{HP}}{\mathbf{s}T\_{HP} + 1} \tag{7}$$

$$\mathcal{G}\_{\rm RFZ}(s) = \frac{\mathcal{K}\_{\rm RFZ}}{sT\_{\rm RFZ} + 1} \tag{8}$$

*Energies* **2020**, *13*, 3446

#### *2.6. IH*μ*GS Dynamic Model*

The instantaneous change in power (Δ*PG*) of the proposed *IH*μ*GS* can be formulated as

$$
\Delta P\_G = \Delta P\_{WG} + \Delta P\_{ST} + \Delta P\_{BDPG} \pm \Delta P\_{SOFC} - \Delta P\_{NCL} = \Delta P\_{CL} \to 0 \tag{9}
$$

where

$$\begin{aligned} \Delta P\_{\text{NCL}} &= \Delta P\_{\text{HP}} + \Delta P\_{\text{RFZ}}\\ \text{and } \Delta P\_{\text{DM}} &= \Delta P\_G - \Delta P\_{\text{CL}} \end{aligned} \tag{10}$$

The equivalent dynamic model of *IH*μ*GS* could be illustrated as

$$\mathbf{G}\_{IH\mu\text{GS}}(\mathbf{s}) = \left(\frac{\Delta f}{\Delta P\_{DM}}\right) = \frac{\mathbf{K}\_{IH\mu\text{GS}}}{D + \mathbf{s}\mathcal{M}} \tag{11}$$

Refer to Table 1 for the nomenclature and abbreviations used for *IH*μ*GS* system modelling.

#### *2.7. Objective Function Formulation*

The formulation of the objective function (*J*) has a great impact on system dynamics and the achieved results. Therefore, the proposed work considered the integral of square error (*ISE*) objective function. This could be formulated as

$$\text{Minimize } I\_{\text{ISE}} = \bigcup\_{0}^{t\_{\text{Sin}}} (\Delta f)^2.dt \tag{12}$$

*Subject to* :

$$\begin{cases} \begin{array}{l} \mathcal{K}\_{Pi}^{\min} \le \mathcal{K}\_{Pi} \le \mathcal{K}\_{Pi}^{\max} \\ \mathcal{K}\_{Ii}^{\min} \le \mathcal{K}\_{Ii} \le \mathcal{K}\_{Ii}^{\max} \\ \mathcal{K}\_{Di}^{\min} \le \mathcal{K}\_{Di} \le \mathcal{K}\_{Di}^{\max} \\ \mathcal{K}\_{Ii2}^{\min} \le \mathcal{K}\_{Ii2} \le \mathcal{K}\_{I2}^{\max} \\ \mathcal{K}\_{Di2}^{\min} \le \mathcal{K}\_{Di2} \le \mathcal{K}\_{Di2}^{\max} \end{array} \tag{13}$$

where *i* = 1, 2. The range of controller parameters is taken as (0–50).

#### **3. Optimization Techniques**

Three metaheuristic techniques were considered to optimally tune the controller parameters along with their comparative dynamic responses.

#### *3.1. Particle Swarm Technique (PSO)*

A swarm-based metaheuristic particle swarm technique (PSO) was developed by Eberhart and Kennedy in 1995 to solve the specified problem by improving the candidate solution with reference to the given measure quality [26]. The solution of PSO is termed as a particle. Every particle follows a track of coordinates in the problem space until the best solution is reached with respect to the suggested problem. The velocity of each particle is varied on the basis of best position (*Pbest*) and *Ibest* location. The optimum values obtained by optimizer are termed as *Ibest* [26].

#### *3.2. Grasshopper Algorithmic Technique (GOA)*

A metaheuristic grasshopper algorithmic technique was proposed by Saremi et al. [27]. Its characteristics depend on the swarming and foraging characteristics of grasshopper, which could be modeled to form structural algorithmic techniques. The steps involved for initialization, exploitation and exploration are depicted in [27].

#### *3.3. Butterfly Optimization Technique (BOA) and Proposed Dual-Stage Controller*

Recently, since 2018, based on the food-probing approach and mating characteristics of butterflies, a natured-inspired algorithmic technique named BOA has been developed to solve several engineering problems. The unique food-probing strategy and mating characteristics of BOA are modeled in [23].

The main idea of BOA depends on three key parameters. These are sensor modality (*Ms*), impulsive intensity (*Is*) and power component (γ). Moreover, the objective function of this technique depends on the distinction of *Is* and formation of fragrance (*P*), which could be formulated as

$$P\_i = M\_{\mathfrak{s}} J\_{\mathfrak{s}}^\gamma \text{ } i \in \text{(1, 2...N)}\tag{14}$$

where *Pi* is the fragrance magnitude of *i*th butterfly. In the following, to investigate global search stage, a dominated fitted solution *q\** could be depicted as

$$\begin{array}{l} m\_i^{t+1} = m\_i^t + \left( n^2 \times q^\* - m\_i^t \right) P\_i \\ \text{where } n \in \left[ 0, 1 \right] \end{array} \tag{15}$$

where *m* and *q\** are the solution vectors of *i*th butterfly and current best solution among all the solutions. The formulation of the social search could be illustrated as

$$m\_i^{t+1} = m\_i^t + \left(n^2.m\_\mathcal{g}^t - m\_h^t\right)P\_i \tag{16}$$

where, *mg* and *mh* are the *g*th and *h*th butterflies enabled in the search space [23]. The approximate flow diagram of BOA technique is framed out in Figure 2. All the parameters considered for algorithmic techniques are given in Appendix A.

**Figure 2.** Flow diagram of butterfly optimization technique (BOA).

To reach above control target, a novel dual-stage proportional-integral-integral-derivative (*PI* − *(1* + *ID)*) controller is deployed, as framed in Figure 3. In the following, Δ*f* is leveraged as an input signal, whereas *C(s)* is the output control signal of the controller. The control output signal and transfer function of the proposed controller are formulated as

$$\mathbb{C}(\mathbf{s}) = \Delta f.PI - (\mathbf{1} + lD) \tag{17}$$

$$G\_{\rm PI-(1+ID)}(\mathbf{s}) = K\_{\rm P} + K\_{\rm I}/\mathbf{s} - (\mathbf{1} + K\_{\rm I}/\mathbf{s} + K\_{\rm D}.\mathbf{s}) \tag{18}$$

**Figure 3.** Proposed (*PI* − *(1* + *ID)*) controller.

#### **4. Frequency Response Studies and Analysis**

In order to verify the proposed control strategy, two scenarios are simulated in a system with Core-i7-4770 CPU under MATLAB/SIMULINK (R2013a, MathWorks, Natick, USA) was environment. Three algorithmic techniques (PSO, GOA and BOA) have been considered. Furthermore, to validate the control strategy, real recorded wind speed data have been considered.

#### *4.1. Scenario 1: Performance Analysis of All Controllers during Non-Accessibility of All RERs*

In this scenario, assume that all the RERs are unavailable due to maintenance. Therefore, the extractable power forms *WG* (Δ*PWG*) and *ST* (Δ*PST*) are zero (Δ*PWG* = Δ*PST* = 0%) during the entire period. A net constant critical load demand (ΔPCL = 30%) is considered from *t* = 0 s onwards. The comparative performance of different controllers such as *PI*, *PID* and (*PI* − *(1* + *ID)*) are displayed in Figure 4, where the tuned parameters are listed in Table 2. The system dynamics assessment of the abovementioned controllers under BOA and objective function (*JISE*) and figure of demerits (*JFOD*) clearly depicts that the proposed (*PI* − *(1* + *ID)*) controller is superior to the rest. To elaborate further, the performance indicators such as peak overshoot (+OP), peak undershoot (-UP) and settling time (*TST*) are tabulated in Table 2.


**Table 2.** Comparative performance parameters of different controllers with optimal BOA-tuned gain values.


**Table 2.** *Cont.*

Bolt point out superior output.

**Figure 4.** Comparative system dynamics analysis of different controllers (proportional-integral (*PI*), *PI*-derivative (*PID*), (*PI* − *(1* + *ID)*) (**a**) deviation in system frequency (Δ*f*), (**b**) change in extractable power of bio-diesel power generator (*BDPG*) and *SOFC*, (**c**) change in extractable power of *HP* and *RFZ*, (**d**) Comparative converged objective function (*Jmin*).

#### *4.2. Scenario 2: Performance analysis of Di*ff*erent Algorithms Under Concurrent Random Changes of WG (Utilization of Real-Recorded Data), ST and Critical Load Demand*

In this scenario, the proposed system is tested under real-recorded wind (obtained from National Institute of Wind Energy, India) [25], as displayed in Appendix B. The operating condition is illustrated with 30% average power of *ST* and 50% critical load demand for the entire time duration. The wind speed and its corresponding output power is shown in Figure 5a. The results are depicted in Figure 5b-e, showing the comparative system dynamic responses of Δ*f*, Δ*PBDPG*, Δ*PSOFC*, Δ*PHP*, and Δ*PRFZ*. Figure 5b–e it clearly shows that the BOA-optimized *PI* − *(1* + *ID)* controller performed better than the other suggested PSOs, GOA-tuned (*PI* − *(1* + *ID)*) controller. The tuned values of the controller parameters are displayed in Table 3.

**Figure 5.** Comparative system dynamics analysis of different algorithmic techniques (PSO, GOA, BOA) (**a**) Real recorded wind speed and other multiple disturbances, (**b**) deviation of system frequency (Δ*f*), (**c**) change in extractable power of *BDPG*, (**d**) change in extractable power of *SOFC*, (**e**) change in extractable power of *HP* and *RFZ*.


**Table 3.** Optimal values of particle swarm optimization (PSO), grasshopper algorithmic technique (GOA) and BOA techniques tuned *PI-(1*+*ID)* controller.

#### **5. Conclusions**

The present article develops a novel frequency regulation scheme for wind-solar-tower-biodieselbased *IH*μ*GS*. A novel dual-stage (*PI* − *(1* + *ID)*) controller is enabled to investigate the system dynamics under different scenarios. A recently developed BOA technique is utilized to optimally tune the proposed dual stage (*PI* − *(1* + *ID)*) controller gains and compare the system dynamics under real recorded wind data. The comparative system dynamic responses, as well as performance parameters such as peak deviation (+OP, −UP) and settling time (*TST*), clearly indicate that the BOA-optimized (*PI* − *(1* + *ID)*) controller performs better than other classical benchmark controllers. The simulation test results prove the effectiveness of the proposed control strategy. This control scheme could be further extended by integrating different RER technologies and storage devices, as well as electric vehicles, into the microgrid.

**Author Contributions:** Conceptualization, A.L., S.M.S.H., D.C.D. and T.S.U.; Methodology, A.L., S.M.S.H., D.C.D. and T.S.U.; Software, A.L.; Validation, A.L.; Formal Analysis, A.L., S.M.S.H., D.C.D. and T.S.U..; Writing—Original Draft Preparation, A.L. and D.C.D.; Writing—Review and Editing, S.M.S.H., and T.S.U.; Visualization, A.L.; Supervision, D.C.D.; Funding Acquisition, T.S.U. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** Authors would like to thank TEQIP-III NIT Silchar for providing technical support for this work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

PSO technique: Number of population: 50, Maximum iteration (*ItrMax*): 100, Max<sup>m</sup> weight factor (Wmax): 0.9, Min<sup>m</sup> weight factor (Wmin): 0.1, Acceleration factors (C1&C2): 2.

GOA technique: Number of population: 50, Maximum iteration (*ItrMax*): 100, Maximum coefficient factor (*Cfmax*) = 1, Minimum coefficient factor (*Cfmin*) = 0.00004, attraction intensity (f): 0.5, length scale of attractiveness (l): 1.5

BOA technique: Number of population: 50, Maximum iteration (*ItrMax*): 100, Probability of switching (D) = 0.8, Power component (γ) = 0.1, Sensor modality (*Ms*) = 0.1.

#### **Appendix B**

*WG*: Date of noted data: 1st July, 2016, Minimum speed of wind: 7.4804 m/s; Maximum speed of wind: 14.08 m/s; Average speed of wind: 10.922 m/s; SD: 1.1895.

#### **References**


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