*Article* **PV/Wind-Integrated Low-Inertia System Frequency Control: PSO-Optimized Fractional-Order PI-Based SMES Approach**

**Md Shafiul Alam 1,\*, Fahad Saleh Al-Ismail 1,2,3,4 and Mohammad Ali Abido 1,2,4**


**Abstract:** A paradigm shift in power engineering transforms conventional fossil fuel-based power systems gradually into more sustainable and environmentally friendly systems due to more renewable energy source (RES) integration. However, the control structure of high-level RES integrated system becomes complex, and the total system inertia is reduced due to the removal of conventional synchronous generators. Thus, such a system poses serious frequency instabilities due to the high rate of change of frequency (RoCoF). To handle this frequency instability issue, this work proposes an optimized fractional-order proportional integral (FOPI) controller-based superconducting magnetic energy storage (SMES) approach. The proposed FOPI-based SMES technique to support virtual inertia is superior to and more robust than the conventional technique. The FOPI parameters are optimized using the particle swarm optimization (PSO) technique. The SMES is modeled and integrated into the optimally designed FOPI to support the virtual inertia of the system. Fluctuating RESs are considered to show the effectiveness of the proposed approach. Extensive time-domain simulations were carried out in MATLAB Simulink with different load and generation mismatch levels. Systems with different inertia levels were simulated to guarantee the frequency stability of the system with the proposed FOPI-based SMES control technique. Several performance indices, such as overshoot, undershoot, and settling time, were considered in the analysis.

**Keywords:** virtual inertia control; renewable energy resources; solar and wind energy; superconducting magnetic energy storage (SMES); fractional-order proportional integral (FOPI); frequency response

**1. Introduction**

Due to the continuous depletion of fossil fuels, increased government incentives, technological advancements, and price drops, the utilization of renewable energy sources (RESs) as distributed generators (DGs) has increased dramatically in recent years. In power systems, several technical issues, such as low reserve generation, fault ride through capability, inertia, and high fault current, have arisen because of high-level RES integration [1]. Thus, the frequency stability issue of high-level RES-integrated systems is greatly affected. Moreover, the two main sources of renewable energy, solar and wind, are highly unpredictable. The intermittent and unpredictable RESs can be modeled with sophisticated methods to lower the risk of instability in power systems [2]. A high share of RESs complicates grid-balancing and market operations. Several dedicated devices can be installed in a RES-integrated system to provide ancillary services such as power variations, congestion reduction, grid balancing, and primary reserve [3,4]. The technical issues of RES integration with a power system could also be handled with different cutting edge technologies such

**Citation:** Alam, M.S.; Al-Ismail, F.S.; Abido, M.A. PV/Wind-Integrated Low-Inertia System Frequency Control: PSO-Optimized Fractional-Order PI-Based SMES Approach. *Sustainability* **2021**, *13*, 7622. https://doi.org/10.3390/ su13147622

Academic Editors: Thanikanti Sudhakar Babu and Marc A. Rosen

Received: 17 May 2021 Accepted: 25 June 2021 Published: 7 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

as modern control and optimization techniques, energy storage devices including batteries and supercapacitors, and fault current limiting devices [5].

The overall inertia of a power system is decreased greatly as a result of the integration of low-inertia wind and inertia-less PV systems [6]. Power electronic converter decoupling between the wind generator and the power system is responsible for the low inertia. As a result, such a low-inertia wind system cannot properly maintain the frequency stability of the power system. Moreover, solar PV with no inertia is highly responsible for the frequency deviation of the system. Therefore, high-level PV and wind penetration reduces the total inertia and augments the rate of change of frequency (RoCoF), which are responsible for the unexpected load-shedding controller activation even at small generation–load mismatch [7]. In addition, reserve power reduction due to high-level PV/wind integration causes frequency deviation [8]. In summary, inertia emulation controllers need to be designed to improve the frequency stability of RES-integrated power systems.

In order to minimize the frequency excursion of a low-inertia system, several methods have been presented in the literature, such as the auxiliary load frequency (LFC) control technique, the inertia emulation technique, the deloading technique, the droop technique, and the energy storage-based technique [9–12]. In [13], an auxiliary LFC technique was presented to control the frequency of the Egyptian grid considering high-level PV and wind integration employing the proportional-integral-derivative (PID) controller. However, the LFC technique does not consider the detailed model of the Egyptian grid; instead, it excludes tie line power flow, which needs further investigation. In general, conventional PI and PID controllers, the parameters of which were fine-tuned experimentally or tuned by Ziegler–Nichols methods, were employed in system frequency control [14,15]. However, the conventional tuning methods of PI/PID controllers may not provide satisfactory performance. In [16], a virtual inertia support technique was presented for a low-inertia microgrid with a particle swarm optimization (PSO)-based PI controller.

The superconducting magnetic energy storage (SMES) is considered a promising device for the low-inertia issue of the microgrid system in [17]. The conventional derivative approach for the virtual inertia control loop was implemented. The detailed design of feedback and proportion gains, however, were not discussed in this work. Another energy storage, the battery, was presented in [18] for frequency support of the doubly fed induction generator (DFIG)-based wind system. The battery was connected to the DC link of DFIG and controlled with the droop technique in order to reduce frequency deviation by scheduling active power exchange during system disturbances. In [19], a self-adaptive virtual inertia fuzzy controller was adopted for a high-level renewable integrated system. The proportional virtual gain was adapted by the fuzzy system, which uses the deviation of real power and frequency as it inputs. In this scheme, however, the generalized energy storage system (ESS) was considered a simple first-order system. Since the specific ESS was neither discussed nor modeled, the presented frequency support scheme needs further improvement or investigation. The sharing of active power from different energy storage devices were scheduled based on their abilities in [20] for frequency control of renewable sources. In this capability-coordinated frequency control (CCFC) approach, the total error signal was forwarded to the primary control loop of each unit based on its capabilities. The LFC for mass-less inertia PV systems was presented in [21] with PI controllers. The parameters were optimized with the hybrid optimization technique in the case of different step load changes. In order to stabilize the low-inertia PV system, another virtual inertia synthetization using a synchronverter was reported in [22] with the learning technique. The optimized virtual inertia frequency control and protection schemes were developed in [23,24] for a low-frequency interconnected power system. The combination of SMES and thyristor-controlled phase shifters (TCPS) [25] was applied in a low-inertia utility grid with the adaptive neuro-fuzzy system (ANFIS) controller. The detailed design of SMES negative feedback and proportional gains, however, was not considered. The main advantage of SMES is the quick charging/discharging ability to react to sudden changes in system dynamics. Thus, the fast-response capability of SMES could be the most

effective countermeasure against frequency deviations in a power system. The voltage and frequency stability issues of a power system are addressed in some of the literature with SMES [26–28]. Furthermore, the transient stability issues are also handled with the application of SMES [29–31]. Based on a comprehensive literature survey on SMES device applications in power systems, it is concluded that further study on virtual inertia control topologies using SMES is imperative.

In recent years, several theoretical and applied studies have been conducted on fractional-order controllers [32,33]. Better system performance is observed with fractionalorder controllers over conventional PI controllers because the fractional-order controller involves additional real parameters [34]. However, in general, there is no hard and fast rule for tuning the parameters of fractional-order controllers. The tuning of fractional-order proportional integral (FOPI) controller parameters with the artificial bee colony (ABC) [35] technique has been presented, which is complex in objective function evaluation and low convergence speed. The parameter-tuning task of FOPI is formulated as an optimization problem and solved with the seeker optimization algorithm (SOA) in [36]. The harmony search (HS) algorithm is reported in [37] for FOPI parameter optimization to control the power-switched reluctance motor. However, there are no conclusive studies on the application of the virtual inertia technique using an SMES topology-based FOPI controller.

Based on several studies [17–19,25,38], it is identified that the detailed design of the PSO-optimized SMES is missing the FOPI controller to support virtual inertia for RESs. Thus, in this paper, we propose a PSO-optimized FOPI-SMES controller design approach for a two-area power system. The proposed approach can support the virtual inertia of the high-level renewable energy integrated system. The addition of this virtual inertia makes the system stable over a wide range of load–generation mismatches. Since the FOPI controller is superior to the conventional PI, the proposed technique performs better when reducing system frequency deviation. However, the design of FOPI is challenging compared to the conventional PI. Thus, this work introduces a detailed model of FOPI, SMES, and a two-area power system to find the design parameters. The dynamic model of the system presented along with SMES and FOPI is utilized to develop the frequency deviation-based cost function for the PSO algorithm. To validate the proposed optimized FOPI controller-based SMES, several case studies were considered and simulated for a wide range of load profile variations. The robustness of the proposed virtual inertia control scheme was tested under reduced system inertia. The proposed controller was compared with the conventional controller, where the improvements in several indices, such as total frequency deviation, overshoot, undershoot, and settling time, were observed. Furthermore, the performance of the non-optimized FOPI was compared with the PSOoptimized FOPI.

The manuscript is organized as follows. The dynamic model of the system including RESs is given in Section 2. The SMES modeling and PSO-based FOPI-SMES design techniques are discussed in Section 3. The simulation results are discussed in Section 4. Finally, the conclusions of this study are given in Section 5.

#### **2. High-Level PV/Wind-Integrated System Modeling**

The fractional-order PI controller for superconducting magnetic energy storage (SMES) is designed to virtually support inertia for a high-level solar PV- and wind-integrated twoarea power system. An interconnected power system with low inertia due to a high-level integration of PV and wind energy sources, as shown in Figure 1, is considered in this study. The areas are connected by a tie-line, and both of them consist of thermal generating units, an industrial load, a residential load, solar PV, wind, and SMES. The measured frequency and tie-line signals are accumulated in the control and monitoring center. Since the system faces low inertia, it is expected to support the inertia via the control center, which sends control signals to the controllable energy storage devices of both areas if the communication network is available. However, in absence of a communication link, local controllers such as decentralized control, primary control, and droop control can

be employed. The net power (*Pnet*) in each area in Figure 1 can be calculated using the power of (1) the thermal unit (*PTH*), (2) the solar array (*PSA*), (3) the wind farm (*PWF*), (4) SMES (*PSMES*), (5) combined industrial and other loads (*PL*), and (6) the tie-line (*Ptie*12). The expression for *Pnet* is given below.

$$P\_{net} = P\_{TH} + P\_{SA} + P\_{WF} - P\_L \pm P\_{SMES} \pm P\_{tie} \tag{1}$$

**Figure 1.** Two-area low inertia interconnected power system.

In general, higher-order models for thermal generating units, wind systems, solar PV, and converters, with nonlinearity are considered to precisely demonstrate the dynamic behaviors of the interconnected system. For large power systems with power electronic converters, however, simplified dynamic models are employed to study the frequency stability. The interested readers can find more details on such dynamic modeling in [39–41]. The simplified dynamic model of the two-area system can be developed as shown in Figure 2 for frequency stability analysis.

From the dynamic model, as shown in Figure 2, the frequency deviation for the *k*th area can be written as follows.

$$
\Delta f\_k = \frac{1}{2H\_k s + D\_k} \left( \Delta P\_{TH,k} + \Delta P\_{SA,k} + \Delta P\_{WF,k} - \Delta P\_{L,k} + \Delta P\_{\text{tie},k} \right) \tag{2}
$$

where,

$$
\Delta P\_{TH,k} = \frac{1}{1 + sT\_{t,k}} (\Delta P\_{\text{g.k}}) \tag{3}
$$

$$
\Delta P\_{\rm g,k} = \frac{1}{1 + sT\_{\rm g,k}} (\Delta P\_{A \to C,k} - \frac{1}{R\_k} \Delta f\_k) \tag{4}
$$

$$
\Delta P\_{WT,k} = \frac{1}{1 + sT\_{wind,k}} (\Delta P\_{wind,k}) \tag{5}
$$

$$
\Delta P\_{SA,k} = \frac{1}{1 + sT\_{pv,k}} (\Delta P\_{pv,k}) \tag{6}
$$

where *Hk* is the inertia constant in area *k*, *Dk* is the damping constant in area *k*, Δ*PTH*,*<sup>k</sup>* is the incremental power of the thermal unit in area *k*, Δ*PSA*,*<sup>k</sup>* is the incremental power of solar farm in area *k*, *PWF*,*<sup>k</sup>* is the incremental power of wind farm in area *k*, *Tt*,*<sup>k</sup>* is the turbine time constant in area *k*, *Tg*,*<sup>k</sup>* is the governor time constant in area *k*, *Twind*,*<sup>k</sup>* is the wind turbine time constant in area *k*, and *Tpv*,*<sup>k</sup>* is the solar system time constant in area *k*.

Two physical constraints, governor dead band (GDB) and generation rate constraint (GRC), affect the dynamic performance of the power system. The thermal units consist of rotating mass, which inherentlyhas mechanical inertia; thus, it puts a constraint/limit on the output power change, which is known as GRC. The controller designed without GRC may not perform well in practical applications. To handle this issue, GRC is considered for the virtual inertia controller design in this work, as shown in Figure 2. Furthermore, the governor cannot change its valve position within a specific range of speed variation. Due to this dead-band, the tie-line power oscillation with a natural frequency of 0.5 Hz is observed. The dead-band for governor is also taken into consideration in this study to reflect the practical implementation case. The solar PV, wind, and different loads are modeled as disturbances in the dynamic model. The interested readers are directed to the literature [39] for more details on dynamic modeling of PV/wind integrated system.

**Figure 2.** The dynamic model of low inertia system with the proposed controller.

#### **3. SMES Model with FOPI Controller**

SMES is a promising device for dynamic stability improvement of power systems. The SMES has several components: thte power conversion system (PCS), consisting of the inverter/rectifier, and the superconducting coil which is kept under extremely low temperature [25]. The PCS also consists of three-phase transformers to allow for energy exchange between the AC grid and the superconducting coil. The harmonic contents of the signals are filtered by two cascaded six pulse bridges, as shown in Figure 3. The capability of SMES to exchange huge power within a very short duration has drawn the attention of researchers in the power system application.

In normal conditions, the SMES coil charges quickly to its pre-defined peak value. As the coil temperature is maintained below the critical value, it conducts the current with nearly zero loss. During contingencies, as the power demand is initiated by the power system, the SMES discharges power through the PCS to the grid almost instantly. While the governors of the generators support the power demand after contingencies, the SMES again charges at its preset value. The inductor DC voltage is given by the equation below [25,42].

$$E\_d = 2V\_{d0} \cos \mathfrak{a} - 2I\_D R\_D \tag{7}$$

where *Vd*<sup>0</sup> is the maximum voltage of the bridge circuit, *α* is the triac firing angle, *ID* is the superconducting coil current, and *RD* is the damping resistor. Thus, the DC voltage appearing across the superconducting coil can be controlled with the variation of the triac firing angle *α*. If *α* is above 90◦, the energy stored in the superconducting coil is released to the grid. In contrast, the superconducting coil charges if *α* is below the 90◦. In this way, the superconducting coil charges and discharges through the bidirectional converter system to absorb or provide energy.

**Figure 3.** SMES basic configuration.

The detailed dynamic model of SMES for frequency stability studies along with the FOPI controller are shown in Figure 4. During excessive system loading, the load surpasses the generation, the *ED* becomes negative, while the current *ID* maintains the same direction. The incremental change in *ED* is written as

$$
\Delta E\_D = \frac{K\_{SMES} \Delta E - K\_{ID} \Delta I\_D}{1 + sT\_{DC}} \tag{8}
$$

where *KSMES* is the SMES gain, Δ*ED* is the output of the FOPI controller, *KID* is the negative feedback gain, Δ*ID* is the incremental change in superconducting coil current, and *TDC* is the converter delay time. The incremental change in inductor current *ID* is written as

$$
\Delta I\_D = \frac{\Delta E\_D}{sL} \tag{9}
$$

The active power of SMES can be derived as follows based on Equations (8) and (9).

$$
\Delta P\_{SMES} = \frac{K\_{SMES}(1 + sT\_{DC})sL}{(1 + sT\_{DC})[(1 + sT\_{DC})sL + K\_{ID}]}(I\_D + I\_{D0})\tag{10}
$$

**Figure 4.** The dynamic SMES model along with the FOPI controller.

#### *3.1. Controller Design*

This study focuses on the optimal FOPI-SMES design based on the PSO algorithm to augment the frequency stability of the two-area power system. The fractional-order calculus involves generalized differentiation and integration of non-integer order [33,34]. The fractional-order controller is applied in several engineering fields such as automatic control and power systems due to its superiority over conventional integer order controllers.

The time domain FOPI controller can be represented as

$$
\mu(t) = K\_p \omega(t) + \int\_t^\lambda K\_i \omega(t) \tag{11}
$$

where *e*(*t*) is the error signal, *Kp* is the proportional gain, *Ki* is the integral gain, and *λ* is a fractional order and real number that lies between 0 and 2. The Laplace transformation gives the following transfer function for the FOPI controller.

$$\mathcal{C}(\mathbf{s}) = \mathcal{K}\_{\mathcal{P}} + \frac{\mathcal{K}\_i}{\mathbf{s}^{\lambda}}, \lambda \in (0, 2) \tag{12}$$

The conventional integer order PI and the FOPI can be understood using Figure 5 in the *λ* axis. The integer order controller is represented by two points on the *λ* axis. However, the FOPI controller can be represented by the infinite number of points between 0 and 2. Thus, it gives more degree of freedom and flexibility over the conventional integer order controller.

**Figure 5.** PI controller (fractional order and integer order).

As presented in Figure 4, the SMES virtual inertia based on FOPI is developed in this study to support the frequency of the low-inertia interconnected system. The feedback and proportional gains of SMES along with the FOPI's proportional gain, integral gain, and fractional parameter are optimized with PSO. The following subsections describe the objective function formulation and solution system with the PSO.

#### *3.2. Description of Cost Function*

The appropriate cost function is vital in the application of nature-inspired and heuristic optimization techniques in power systems. In general, the cost function is defined to minimize or maximize some variables. In this work, several FOPI gains, fractional orders, SMES feedback gains, and proportional gains are designed based on tie-line power fluctuation and area frequency deviation. For better comprehension of the optimization process, the following cost function is considered.

$$\text{Minimize: } \operatorname{ISE} = \int\_0^T (\left| \Delta f\_1 \right|^2 + \left| \Delta f\_2 \right|^2 + \left| \Delta P\_{\text{fic}} \right|^2) dt \tag{13}$$

Decision Variables: *Kp*1, *Ki*1, *λ*1, *Kp*2, *Ki*2, *λ*2, *K*1, *K*2, *KID*1, *KSMES*1, *KID*2, *KSMES*<sup>2</sup> (14)

$$\begin{array}{l}\text{Constrainity:} \ K\_{p12\text{min}} \le K\_{p12} \ge K\_{p12\text{max}}, \ K\_{l12\text{min}} \le K\_{l12} \ge K\_{l12\text{max}}, \ K\_{1\text{min}} \le K\_1 \ge K\_{1\text{max}}\\\ K\_{1\text{min}} \le K\_1 \ge K\_{1\text{max}}, \ K\_{l1\text{D12}\text{min}} \le K\_{l1\text{D12}} \ge K\_{l1\text{D2max}}, \ K\_{\text{SMES12}\text{min}} \le K\_{\text{SMES12}} \ge K\_{\text{SMES12}\text{max}}\end{array} \tag{15}$$

where subscripts 1 and 2 are to denote area 1 and area 2 for the interconnected power system. *T* is the simulation time, Δ*f* is the frequency deviation, Δ*Ptie* is tie-line power deviation, *Kp* is the FOPI proportional gain, *Ki* is the FOPI integral gain, *KID* is the SMES negative feedback gain, and *KSMES* is the SMES proportional gain. Mainly, the upper and lower

limits of Equation (15) are selected based on knowledge/experience of FOPI and SMES applications in power system. The optimization algorithm is coded in a MATLAB script (.m files) environment and linked with the MATLAB Simulink (.slx files) environment.

#### *3.3. Solution Approach with PSO*

This study proposes a FOPI-based SMES virtual inertia approach in which the minimization problem described by Equation (13) is solved by the PSO. PSO, a heuristic optimization technique, was inspired by the sociological behavior of birds flocking [43]. In the PSO algorithm, several random particles that move in a search space to find the best minimum or maximum value of the cost function based on the minimization or maximization problem, respectively, are initially generated. The PSO shows outstanding performance compared to the other algorithms, as follows [44–46]:


In recent years, the PSO has been implemented successfully to solve several power system problems such as that presented in [47,48]. The position and velocity vectors in a multi-dimensional solution space for PSO algorithm are mainly described by two equations as follows [49]:

$$v\_i^k = c \left\{ v\_i^{k-1} + c\_1 r\_1 (p\_i^{k-1} - x\_i^{k-1}) + c\_2 r\_2 (p\_\mathcal{g}^{k-1} - x\_i^{k-1}) \right\} \tag{16}$$

$$
\mathfrak{x}\_i^k = \mathfrak{x}\_i^{k-1} + \mathfrak{v}\_i^k \tag{17}
$$

where *v<sup>k</sup> <sup>i</sup>* and *<sup>x</sup><sup>k</sup> <sup>i</sup>* are the velocities of *i*th particle for the *k*th iteration in a multi-dimension search space and the position of *i*th particle for the *k*th iteration in a multi-dimension search space, respectively; *pk*−<sup>1</sup> *<sup>i</sup>* and *<sup>p</sup>k*−<sup>1</sup> *<sup>g</sup>* are the individual best and global best, respectively, for the *i*th particle of the (*k* − 1)th iteration; *r*<sup>1</sup> and *r*<sup>2</sup> are the uniformly distributed random numbers in [0 1]; and *c*<sup>1</sup> and *c*<sup>2</sup> are the learning factors used to obtain the best solution. In addition, the *c* is the constriction factor that is calculated from the values of *c*<sup>1</sup> and *c*2, as follows:

$$\mathcal{L} = \frac{1}{\left| 2 - (c\_1 + c\_2) - \sqrt{(c\_1 + c\_2)^2 - 4(c\_1 + c\_2)} \right|} \tag{18}$$

The maximum velocity and minimum velocity of each particle can be calculated as follows:

$$
\omega\_i^{\text{max,min}} = \pm (\mathbf{x}\_i^{\text{max}} - \mathbf{x}\_i^{\text{min}}) / N \tag{19}
$$

where *vmax <sup>i</sup>* and *<sup>v</sup>min <sup>i</sup>* are the maximum and minimum velocities of the *i*th particle, respectively; *xmax <sup>i</sup>* and *<sup>x</sup>min <sup>i</sup>* are the maximum and minimum limits of the *i*th particle, respectively; and N is a number that takes a value between 5–10. The PSO solution steps for solving the optimization problem formulated in Section 3.2 is described below.

**Step 1:** Initialization of the limits of several variables and particle velocity, as described by Equations (15) and (19), respectively.

**Step 2:** Selection of the PSO initial parameters including *c*1, *c*2, maximum iteration, population size, etc.

**Step 3:** Generation of the initial population within the limits.

**Step 4:** Running the time domain simulation and determining the value of the objective function described by Equation (13).

**Step 5:** Storing the local best, the best of the current population, and the global best, the best of the total population.

**Step 6:** Updating the velocity of all populations using Equation (16).

**Step 7:** Generating a new population based on the updated particle position calculated by Equation (17).

**Step 8:** Stopping the optimization if the termination criteria are met. Otherwise, returning to step 4.

The overall flowchart for the PSO algorithm to design FOPI and SMES parameters is shown in Figure 6.

**Figure 6.** The PSO flowchart for optimizing control parameters.

#### **4. Results and Discussion**

The effectiveness and robustness of the proposed optimized FOPI controller in improving the frequency stability are presented in this section. The dynamic model of the system presented in Figure 2 is considered for analytical analysis. The system parameters listed in Table 1 are used to conduct computer simulations and to facilitate analyses. The total generation capacity of the two-area power is 55 MW. The rating of the energy storage device is 6 MW. The proposed energy storage with only 10.9% of the total plant capacity is capable of maintaining frequency stability in case of several load–generation mismatches. The simulations were conducted in MATLAB Simulink considering several scenarios such as light loading, medium loading, heavy loading, and reduced inertia. The system dynamic model was built in Simulink and linked with the PSO optimization code to optimally design the SMES and FOPI parameters. PSO algorithm convergence for the proposed cost function is depicted in Figure 7. As shown in Figure 7, the optimization algorithm converges at the iteration number 20 for several runs, and the corresponding optimized parameters are listed in Table 2.

The system was tested under several step load variations in both areas of the system. The frequency deviations in both areas were plotted for three cases such as (i) without any

inertia controller, (ii) with a conventional SMES controller, and (iii) with the PSO optimized FOPI-based SMES controller.

**Table 1.** System parameters for simulation.


**Figure 7.** The convergence of the cost function.



#### *4.1. Frequency Response Study for Step Load Change in Area 1*

In this case, the studied system is simulated for default inertia (100%), as shown in Table 1. The frequency deviations for both areas are depicted in Figure 8 for low, medium, and high step load changes in area 1. The positive effect of the proposed controller is

visualized through the reduction in frequency deviations. As visualized in Figure 8a, a step load change of 0.1 p.u. in area 1 causes a significant frequency deviation in area 1 without a virtual inertia controller. The frequency deviation is around 0.42 Hz without any auxiliary controller. The conventional controller-based SMES improves the deviation to about 0.035 Hz. However, the proposed PSO optimization-based FOPI controller for SMES greatly improves the frequency deviation in area 1, which is around 0.005 Hz. It is noteworthy that the settling time is slightly increased for conventional SMES controllers while the frequency deviation is improved. However, the proposed optimized FOPI-based SMES significantly improves all indices, such as settling time, maximum undershoot, and maximum overshoot. Likewise, the frequency deviation in area 2 is very high, around 0.02 Hz, without any inertia controller, as depicted in Figure 8b. The conventional SMES controller improves frequency deviation to some extent. However, the proposed optimized FOPI-based SMES controller reduces the frequency deviation to almost zero. It is observed that, for a large step load change (0.35 p.u.) in area 1, the system cannot maintain stable operation. As visualized in Figure 8e,f, the frequency deviations in both areas continue to increase, leading to instability in the system. The application of the conventional SMES controller can maintain stable operation with some frequency deviation. On the other hand, our proposed techniques stabilize the system with almost zero frequency deviations in both areas. Thus, the system response for several load disturbances in area 1 using the proposed controller is faster, has a very small steady-state error, and is better in terms of overshoot and undershoot compared to other control strategies. The frequency deviations for several scenarios in area 1 and area 2 are given in Table 3 to clearly show the positive impact of the proposed FOPI-based SMES controller on system performance.



#### *4.2. Frequency Response Study for Step Load Change in Area 2*

The load disturbances, ranging from the low to high levels, are also applied in area 2 with the system default inertia. It is noticed that the system frequency oscillates over a wide range without any inertia controller. In some cases, the oscillations are beyond the acceptable limits; thus, it requires the system frequency protection relay to operate. As depicted in Figure 9, the frequency deviation in area 1 is 0.395 Hz without any virtual inertia controller for a step load change of 0.1 p.u. The conventional SMES controller reduces the frequency deviation to 0.025 Hz, whereas the proposed optimized FOPI controller is capable of maintaining almost zero frequency deviation. Similarly, the frequency deviation in area 2 is 0.32 Hz without any auxiliary controller. The conventional SMES controller is capable of reducing the frequency deviation by 90.6%. However, the proposed optimized FOPI-based SMES controller reduces the frequency deviation by 96.87%. For the medium and high step load changes in area 2, at 0.2 p.u. and 0.35 p.u., respectively, the frequencies of both areas fall below the under-frequency relay operating setpoint of 59.5 Hz [50] without any virtual inertia controller.

**Figure 8.** Performance improvement with the proposed controller for load disturbances in area 1. (**a**) Area 1 frequency response for a 0.1 p.u. step load change. (**b**) Area 2 frequency response for a 0.1 p.u. step load change. (**c**) Area 1 frequency response for a 0.2 p.u. step load change. (**d**) Area 2 frequency response for a 0.2 p.u. step load change. (**e**) Area 1 frequency response for a 0.35 p.u. step load change. (**f**) Area 2 frequency response for a 0.35 p.u. step load change.

**Figure 9.** Performance improvement with the proposed controller for load disturbances in area 2. (**a**) Area 1 frequency response for a 0.1 p.u. step load change. (**b**) Area 2 frequency response for a 0.1 p.u. step load change. (**c**) Area 1 frequency response for a 0.2 p.u. step load change. (**d**) Area 2 frequency response for a 0.2 p.u. step load change. (**e**) Area 1 frequency response for a 0.35 p.u. step load change. (**f**) Area 2 frequency response for a 0.35 p.u. step load change.

However, the frequency deviation is well below the under-frequency relay operating point with the conventional SMES controller, as depicted in Figure 9c–f. In these figures, it is visualized that the proposed controller is capable of maintaining the frequency deviations in both areas at almost zero. Thus, the system stability and reliability are guaranteed with the proposed FOPI-based SMES controller. The overall frequency deviations for several cases are listed in Table 3.

#### *4.3. Controller Performance with Solar PV and Wind Power Fluctuations*

The effectiveness of the proposed controller was also tested with fluctuating solar and wind power in both areas. The intermittent solar and wind power disturbances considered in this study are depicted in Figure 10a,b, respectively. The solar and wind powers have mean values of 0.05 p.u. and 0.15 p.u., respectively. The solar power is integrated in area 1 at 50 s during the 150 s simulation time, which continues to inject fluctuating power during the entire simulation period. On the other hand, the intermittent wind generating unit is connected at 75 s, which is kept connected throughout the entire simulation period. As shown in Figure 10c,d, the connection of varying solar and wind powers has a detrimental effect on system frequency response without any auxiliary controller.

**Figure 10.** The frequency response for wind generation addition at 50 s and solar generation addition at 75 s. (**a**) Solar power disturbance. (**b**) Wind power disturbance. (**c**) Area 1 frequency response for intermittent solar and wind power. (**d**) Area 2 frequency response for intermittent solar and wind power.

The frequency of the system continues to vary during the entire simulation period and does not settle to a steady-state value. The conventional SMES controller slightly improves the system frequency response. On the other hand, the proposed controller performance is superior, in terms of settling time, overshoot, and undershoot, to the conventional SMES controller. The improvement of several performance indices is listed in Table 4 to demonstrate the superiority of the proposed controller.

**Table 4.** Improvement of the performance indices for intermittent solar and wind power integration.


#### *4.4. Frequency Response Analysis for Multiple Load Changes*

The effectiveness and robustness of the proposed control technique for virtual control of low inertia systems were also tested with multiple load change scenarios. Several step load changes were considered, as shown in Figure 11a, to investigate the system capability to bring back the frequency deviation to zero before the next changes. Better performance of the proposed FOPI-based SMES is visible from the system frequency response, as seen in Figure 11b, following the first step load change of 0.1 p.u. at 25 s. The proposed controller is faster at eliminating the frequency deviation before the beginning of the second step load change of 0.15 p.u. at 50 s compared to conventional techniques. The frequency deviations in area 1 are very high at all points of step changes without a virtual inertia controller. Although the conventional SMES controller improves the frequency response slightly, a notable improvement is achieved with the proposed technique. In this case, also, the proposed method provides a much better performance in terms of overshoot, undershoot, and settling time. The frequency response for area 2 as visualized in Figure 11c shows better performance with the proposed control technique.

#### *4.5. The Robust Performance of the Proposed Controller with the Reduced System Inertia*

In this scenario, the robustness of the proposed controller is verified with the system inertia variations. The inertia in both areas is reduced by 50%, and a step load change of 0.15 p.u. is applied in area −1 at 50 s. The frequency response for this load change is depicted in Figure 12a,b. As depicted in Section 4.1, the system is capable of maintaining stable operation with a step load change of 0.15 p.u. in the case of default inertia (100%). However, Figure 12a,b show that the frequency deviations in both areas gradually increase, leading to instability. The system without SMES requires the under-frequency relay to start operation within 1 second of the load variation since the frequency deviation goes below 0.5 Hz, as depicted in Figure 12a. Although the area 2 frequency takes a longer time to operate under frequency relay, it is also unstable, as depicted by the increasing frequency oscillation in Figure 12b. The conventional SMES controller reduces the frequency deviations and stabilizes the system. However, the proposed control method augments the system stability greatly by reducing frequency deviations to almost zero even with 50% system inertia. The model presented in Figure 2 was also tested for very low inertia with a step load change of 0.1 p.u. in area 1. As shown in Figure 13, the controller is capable of stabilizing the model of Figure 2 for these low inertia. Furthermore, the robustness of the proposed optimized FOPI controller is compared with the non-optimized FOPI controller. The frequency deviation for the system with 15% inertia is plotted in Figure 14 with the optimized FOPI and nonoptimized FOPI controller. Thus, the proposed controller is more robust compared to the conventional technique. The main limitation of the proposed technique is that the SMES is a costly solution. Further studies may be conducted on FOPI-based hybrid energy storage devices such as SMES, battery, and supercapacitor for the frequency control of low inertia PV/wind-integrated systems.

**Figure 11.** (**a**) Multiple load variations in area 1. (**b**) Frequency response in area 1. (**c**) Frequency response in area 2.

**Figure 12.** System response for 50% inertia (**a**) Area 1 frequency response. (**b**) Area -2 frequency response.

**Figure 13.** The system response for very low inertia.

**Figure 14.** The frequency response comparison for the optimized and non-optimized FOPI controllers.

#### **5. Conclusions**

In this work, an optimized FOPI-based SMES virtual inertia controller is designed for a highly renewable energy integrated system. The dynamic model of the system is developed with FOPI to facilitate analysis and design of optimal parameters using PSO. The system response was analyzed with the designed virtual inertia controller considering highly fluctuating solar PV and wind energy. The system and the associated controllers were simulated in MATLAB Simulink. Small, medium, and large load disturbances were applied in the system to prove the effectiveness of the proposed energy storage-based virtual inertia control strategy. The system with default inertia and reduced inertia were tested under single and multiple load disturbances to guarantee the robustness of the proposed controller. The simulated results show promising performance in reducing system frequency deviations and in improving the frequency stability of the system. The proposed

controller is superior to the conventional controller in reducing settling time, overshoot, and undershoot, as evident from the analysis. Moreover, the simulation outcomes prove the potential benefits of FOPI controller-based energy storage in high-level renewable energy integration and endorse the green efforts to improve sustainability. Finally, a detailed large-scale DFIG offshore wind farm model with FOPI-based hybrid energy storage virtual inertia controller can be studied as future work.

**Author Contributions:** Conceptualization, M.S.A.; methodology, M.S.A.; formal analysis, M.S.A., F.S.A.-I. and M.A.A.; writing—original draft preparation, M.S.A.; writing—review and editing, M.S.A. and F.S.A.-I.; supervision, M.A.A.; and funding acquisition, M.S.A. and F.S.A.-I. All authors have read and agreed to the published version of the manuscript.

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

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors acknowledge the support provided by King Fahd University of Petroleum & Minerals (KFUPM) through the directly funded project No. DF201022. The authors also acknowledge the funding support provided by K.A.CARE Energy Research & Innovation Center (ERIC), KFUPM, Dhahran, Saudi Arabia.

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

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### ISE Integral squared error

#### **References**


**Shabib Shahid 1,\*, Saifullah Shafiq 2, Bilal Khan 1, Ali T. Al-Awami 1,3 and Muhammad Omair Butt <sup>2</sup>**

<sup>1</sup> Electrical Engineering Department, King Fahd University of Petroleum & Minerals,


**Abstract:** Due to the recent advancements in the manufacturing process of solar photovoltaics (PVs) and electronic converters, solar PVs has emerged as a viable investment option for energy trading. However, distribution system with large-scale integration of rooftop PVs, would be subjected to voltage upper limit violations, unless properly controlled. Most of the traditional solutions introduced to address this problem do not ensure fairness amongst the on-line energy sources. In addition, other schemes assume the presence of communication linkages between these energy sources. This paper proposes a control scheme to mitigate the over-voltages in the distribution system without any communication between the distributed energy sources. The proposed approach is based on artificial neural networks that can utilize two locally obtainable inputs, namely, the nodal voltage and node voltage sensitivity and control the PV power. The controller is trained using extensive data generated for various loading conditions to include daily load variations. The control scheme was implemented and tested on a 12.47 kV feeder with 85 households connected on the 220 V distribution system. The results demonstrate the fair control of all the rooftop solar PVs mounted on various houses to ensure the system voltage are maintained within the allowed limits as defined by the ANSI C84.1-2016 standard. Furthermore, to verify the robustness of the proposed PV controller, it is tested during cloudy weather condition and the impact of integration of electric vehicles on the proposed controller is also analyzed. The results prove the efficacy of the proposed controller.

**Keywords:** photovoltaic; autonomous control; electric vehicles

#### **1. Introduction**

Most of the governments around globe have set ambitious targets for reducing carbon emissions. In order to achieve these targets, a significant amount of small and medium scale renewable energy resources need to be integrated into the power grids. Hence, the traditional power systems are observing an ongoing transition that focus on environmental concerns such as smart grid initiatives, etc. Considering the renewables as an integral part of the power grids, the concept of unidirectional flow of power is not applicable anymore. Furthermore, the solar power being available in abundance and easy to harvest energy from, is allowing prominent integration of photovoltaic (PV) generators in power systems and enabling bi-directional power flow [1].

Among various renewable energy resources, the PV panels and wind turbines (WT) are considered as most suitable options for distributed power generation. Both the PVs and WTs tend to provide an economic and environment-friendly solution, besides being readily available [2]. However, the performance of these resources is inconsistent and is highly dependent on climatic factors such as location, time of the day, weather, etc. Thus, it is highly likely that the power generated through these renewable resources will not follow

**Citation:** Shahid, S.; Shafiq, S.; Khan, B.; Al-Awami, A.T.; Butt, M.O. A Machine Learning-Based Communication-Free PV Controller for Voltage Regulation. *Sustainability* **2021**, *13*, 12280. https://doi.org/ 10.3390/su132112208

Academic Editor: Thanikanti Sudhakar Babu

Received: 20 August 2021 Accepted: 30 September 2021 Published: 5 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

power variations in load. Consequently, introducing an uncertainty in the power quality and reliability of overall power system [3–6]. A net negative demand may result in the power system, due to inclusion of large number of renewables which can lead to voltage, thermal and other technical problems [7]. Hence, a controlling mechanism is required for all the system elements along with respective participants, to ensure effective integration of renewables in the power distribution systems [8].

Different machine-learning based controllers have been developed in the recent years, which are different in scope and objectives [9–12]. Artificial neural networks (ANN) are used by researchers to demonstrate faster and more accurate maximum power point tracking for solar PVs [9]. In [10], a multi-layer feed-forward ANN is used to improve the power quality in a power system with wide-spread EV chargers. Neural network-based vector controller is designed in [11,12] for the integration of residential solar PV with a utility grid. This intelligent control mechanism has several advantages over conventional controllers. These controllers are capable of mapping non-linear relationships and provide accurate solutions for multivariable problems. Hence, ANN is used to construct the controller used in this research work.

Active control strategies can be classified into model-based [13,14] or model-free [15] from the perspective of network operation modelling. In addition, control schemes can be defined as stochastic [16] and robust [17] when the relating uncertainties from renewable generation and communication networks are taken into account. An important system aspect is observability when classifying the control strategies. In this regard, approaches can be grouped into centralized, decentralized and fully autonomous [18].

A centralized control scheme requires an extensive observation platform to remotely monitor the distribution system parameters [19], lacking by current weaker or older distribution systems. Additionally, to process this huge amount of data, higher processing computing resources are needed in the central control unit. This centrally processed data is used to calculate power of the PV units. Therefore, this strategy turns out to be suboptimal for distribution systems which lack established communication links [20]. While the decentralized control procedures rely on reduced communication linkages, they also apply less computational resources as reduced data is transacted [20]. In spite of that, the need for communication networks, make these strategies less desirable.

Contrary to the presented strategies, autonomous schemes rely on locally available information. In addition, these local controllers avoid nearby communication dependence and are fast and less expensive to deploy. Thus, these techniques are most suitable solutions pre-widespread communication dependence. Autonomous techniques also have better thermal management since the amount of power curtailment reduce system components congestions [21]. However, there is a highly non-linear relationship between PV's output and the system voltages.

In centralized and decentralized strategies, the system voltages are maintained by regulating PV's active and reactive power outputs. However, in the literature, few autonomous control schemes are discussed. For voltage regulation reference [21] employs a voltage sensitivity concept to control PVs active and reactive power outputs. Although the concept of voltage sensitivity-based regulation is promising but the sensitivity calculation method is not robust enough to adapt to the system changes. Since configuration changes occur frequently in a typical distribution system. Moreover, the PVs fail to contribute equally for voltage regulation since the farthest PVs participate unfairly. Embedded inverter features, such as volt/var and volt/watt curves, can also be put in service to regulate the voltages in the absence of communication infrastructure [22]. In [23], optimal volt-var curves are found offline for rooftop PV inverters which are connected in the system taking count of load and PV's active power scenarios. However, this approach has a major shortcoming as it cannot integrate system changes. Additionally, the present optimal volt/var curves may become worst due to resulting changes in the system configuration.

Generally, the rooftop PVs are installed to maximize the monetary profits and therefore, most of the PVs are installed with controllers that drive them towards unity power

factor [24]. However, smart inverters are required to operate within a range of selected power factors to support voltage regulation, as per the IEEE 1547 Standard for distributed energy resources (DERs) interconnection [25]. Thus, all PVs should contribute equally when system support is needed, especially during over-voltage events. In this context, similar contribution from the PVs available at disparage locations in the distribution system is called *'fairness'*. An autonomous PV controller is designed that ensures fairness among the PVs, but it is limited to a small-scale distribution system [26].

In this article, a machine learning-based autonomous PV controller framework is presented. The training data are generated for changing loading conditions to include daily, monthly and yearly load variations. Nodal voltage and its sensitivity to changes in the load are input signals to the controller and the determined output is the applicable demand. The proposed controller thresholds the active power output of the PVs to maintain the voltages within the allowable range as given by ANSI C84.1-2016 standard [27]. A noteworthy feature of the proposed controller is ensuring fairness among PVs installed at various locations in the secondary distribution system. A PV-rich test distribution system is employed to evaluate efficacy of the proposed controller. Moreover, response of the controller is further tested under cloudy weather and it fairly controls all the PVs irrespective of their locations. To further test the robustness of the PV controller, many EVs are connected in the network. Results show that the implemented controller regulates the system voltages effectively. Moreover, all the PVs fairly contribute when the system requires support. The following are specific contributions of this article:


#### **2. Proposed Methodology**

#### *2.1. PV Voltage Control*

The proposed controller adjusts the power injection of the solar PVs to keep the system voltage within an acceptable range. These PV power plants are connected at various locations in the distribution system, some are closer to and others farther away from the distribution transformer. Each of these solar PVs must be restricted to generate power not more than the upper generation limit termed as power generation cap (PGcap).

In order to circumvent the communication requirements between the distributed solar power producers, it is important to estimate the PGcap using local measurements only. Although voltage at the point of connection (POC) is an important basis for estimating PGcap, but it is not sufficient. Because voltages of the different nodes may behave differently to the power injections. Some of the nodes may violate the upper voltage limits, especially when PV generates more than the connected demand. In this case, downstream or farther nodes in the system will have higher voltages as compared to the nodes at the upstream. In fact, the downstream nodes which are farther from the feeding point are more sensitive to load/generation changes as compared to the upstream nodes. Therefore, the nodal sensitivity can be used along with the nodal voltages, to regulate the power generated by PVs. Moreover, the local voltage sensitivity can also be estimated remotely [18,20]. In addition, the method for its computation is described by Algorithm 1.

Algorithm 1 uses the local nodal voltage (*VPV*), electric load (*Pload*) and the power generated by the solar PV (*Pgen*). These inputs are used to compute the local voltage sensitivity (*δPV*) for each instant. However, in some instances when the change in *Pgennet* at a particular node is less than the threshold *β*, the sensitivity value is not updated because these events may result in the incorrect sensitivity calculations. In fact, the change in load/generation at a particular node would have more impact on the voltage of that node as compared to the other nodes. So, if the sensitivity is calculated for the node during the instances when the change in load/generation is low at that specific node, the change in the voltage at that node may have the more influence of the significant changes in load/generation at the nearby nodes. Hence, these instances may result in wrong sensitivity calculations and are ignored. A tuning parameter *β* is used to filter out these values. Note that *β* may vary from one distribution network to another.

**Algorithm 1** Proposed voltage sensitivity calculation

**Input:** *V*PV,t, *V*PV,t−1, *P*gen,t, *P*gen,t−1, *P*load,t, *P*load,t−1, *δ*PV,t−<sup>1</sup> **Output:** *δ*PV,t **Variables:** *Pgen*net,t, *Pgen*net,t−<sup>1</sup> 1: *Pgen*net,t = *P*gen,t − *P*load,t 2: *Pgen*net,t−<sup>1</sup> = *<sup>P</sup>*gen,t−<sup>1</sup> − *<sup>P</sup>*load,t−<sup>1</sup> 3: **if** *Pgen*net,t−*Pgen*net,t−<sup>1</sup> *Pgen*net,t−<sup>1</sup> ≥ *β* **then** 4: *<sup>δ</sup>*PV,t = *<sup>V</sup>*PV,t−*V*PV,t−<sup>1</sup> *Pgen*net,t−*Pgen*net,t−<sup>1</sup> 5: **else** 6: *<sup>δ</sup>*PV,t = *<sup>δ</sup>*PV,t−<sup>1</sup> 7: **End if**

The value of the voltage sensitivity coefficient at any node and the respective voltage at the POC, gives a good description of the nodes position in the distribution system. Therefore, a machine learning-based approach is designed to use these inputs to determine the PGcap fairly for all the solar power plant. Once the objective and input to the machine learning-based strategy is identified, the strategy is further grouped in offline training and an online application module as given in Figure 1.

**Figure 1.** Flow chart brief overview.

#### *2.2. Create Voltage Regulation Database*

For any machine learning algorithm to achieve good performance in online application, the training set needs to cover operation conditions in the field. In this application, this means realistic ranges of system loads (*Lsyst*) and solar power generations needs to be simulated.

To generate a required data set, load is set at all the system nodes and then the PGcap is found by an iterative process as shown in Figure 2. At the start, all the PVs are selected to generate at their maximum rated capacity. Then, the power flow analysis is performed using a simulator and subsequently power outputs of PVs are reduced to the level that all the system over-voltages are eliminated. This procedure is repeated for various conditions of electrical load in the system to simulate load variations ranging from hours to seasons. Based on the power flow results of each loading condition, the PGcap that needs to be applied at each node is determined so that the acceptable voltage profiles are obtained.

**Figure 2.** Flow chart for determining PGcap for different system loads.

Furthermore, the additional training data points are required to train the controller's response to high voltage and low voltage scenarios. The high voltages may appear in the system when the power generated by the PVs is greater than the PGcap at any particular instant. Likewise, low voltages may occur when the PV power output is less than the PGcap. These events are very common for the distribution systems with variable renewable energy sources and load excursions. To imitate these events, power generated by the PVs is varied and the power-flow is simulated for all the high/low voltage scenarios. These sub-optimal power generations are represented by (*m* × *PGcap*), where *m* is a multiplier and it is varied between *mmin* and *mmax*, as shown in Figure 1. Training data points for lowvoltage and high-voltage scenarios are obtained when *m* is less than 100% and greater than 100%, respectively. The response of the controller in these sub-optimal power generation conditions is explained in Section 2.3.

Voltages of the nodes in the distribution system change differently with the changes in power generations. For instance, consider the LV distribution system shown in Figure 3. Houses available at different levels are connected to the nearby LV transformer. Note that the transformer bus is regulated at the voltage of 1.01 p.u., as mentioned in Figure 3. In addition, note that the house at level 1 is less sensitive to the changes in load/generation as compared to the house at level 4. The voltages and sensitivities of these houses for different power generations (*m* × *PGcap*), are shown in Figure 4. Note that the Figure 4 is plotted at a specific loading condition. It can be seen that the slope of the curve for level 4 house is steeper than the curve of the level 1 house. That means, the house at level 4 is more sensitive when compared to the level 1 house. Another important fact is that

when the generation (*Pgen*) becomes equal to the load (*Pload*), the net power generation (*Pgen*net) becomes zero and the voltages of the nodes become the same as the voltage at the transformer bus (i.e., 1.01 p.u.). For a specific loading condition of this example system, *Pgen*net becomes zero when *m* = 50% as shown in Figure 4. It is important to note that this event can happen at different loading conditions for smaller/bigger distribution systems. It can also be observed from the Figure 4 that for the positive *Pgen*net (i.e., to the right of the marked circle) the nodes with higher sensitivities have higher voltages than the other less sensitive nodes.

**Figure 3.** Example distribution system.

**Figure 4.** Voltage and sensitivities in extreme conditions.

#### *2.3. Training Controller Response*

A neural network is a non-linear statistical model that endeavors to recognize underlying relationships in a set of data. It can represent the complex behaviors of natural or engineered processes. They can adapt to changing input; so, the network generates the best

possible result without needing to redesign the output criteria. Hence, a fully connected multi-layer perceptron (MLP) neural network is used to design the control formula for the PV power output. This network is trained with the generated voltage regulation database to calculate the parameters associated with MLP neural network. The concept of transfer learning is employed for optimal training of the controller.

In this ML approach, the inputs are the nodal voltages (*V*) and their corresponding sensitivities (*δ*) and the output is the desired PV power generation (*P<sup>d</sup> out*). Both the inputs *V* and *δ*, were obtained during the voltage regulation database generation. By design, the database included the input points which represent the over/under power generation (*m* × *PGcap*) instances. Now, to secure the stability of the system in these extreme scenarios, the desired outputs of the controller (*P<sup>d</sup> out*) must improve the voltages in steps. For instance, if the voltages are high then the controller is expected to reduce the power generation. Similarly, for lower voltages the power generation needs to be increased. The relationship between *P<sup>d</sup> out* and *m* × *PGcap* is calculated using (1).

$$P\_{out}^d = PGcap[1 + a\_I(1 - m)]\tag{1}$$

where

$$0 \le a\_r \le 1$$

$$m\_{\rm min} < m < m\_{\rm max}$$

*Pd out* is the desired power output, *PGcap* is the power generation cap, *m* is the multiplier and *α<sup>r</sup>* is the gradient of the controller response. Note that when the multiplier is 1, the *Pd out* becomes equal to *PGcap*. However, when the multiplier is not equal to 1, then *P<sup>d</sup> out* is adjusted accordingly to improve the system voltages.

As mentioned earlier, the output of PVs may vary since they are highly variable. Moreover, the output of neural network-based controller may vary a bit from the desired power output depending on the input data. Hence, the data points must be generated in such a way that the desired controller response is achieved. Note that *α<sup>r</sup>* is the parameter that defines the behaviour of the controller response. It is important to understand that if the value of *α<sup>r</sup>* is close to 0, then the controller output would not change significantly during the extreme voltage conditions. In other words, the controller response would be highly conservative. On the other hand, if the value of *α<sup>r</sup>* is close to 1, then the controller output would quickly respond to the changes in the load/generation but may oscillate between the extreme voltage conditions. Therefore, the best controller response would be achieved when the value of *α<sup>r</sup>* is between 0 and 1. In this work, the best controller response is achieved when the *α<sup>r</sup>* is set to 0.37. However, it may vary depending on the controller requirements.

Let us demonstrate the controller behaviour as described in (1). Figure 5 shows the relationship between *P<sup>d</sup> out*/*PGcap* and *m* (as defined in Equation (1)), with *α<sup>r</sup>* = 0.37. For example, if the multiplier *m* is 160% (i.e., point A in Figure 5), then the voltage reaches to 1.078 p.u. at the downstream bus (i.e., level 4 house) as shown in Figure 4. Since the voltage violation is severe, the controller would reduce the power output to 78%. Correspondingly, the controller will move to the point B (see Figure 5) and the voltage would become 1.028 p.u. (see Figure 4). At the subsequent instants, the controller will move to 108% (i.e., point C in Figure 5). Eventually, the controller response will reach to PGcap (point D) and regulate the system voltages within the allowed limits. It is important to note that the controller will mostly operate in the normal range, that means, the data points generated for the low/high voltages will be only followed during these extreme events.

**Figure 5.** Controller response in extreme conditions.

#### *2.4. Neural Network Structure*

In this control strategy only two inputs are used, namely, voltage and the nodal sensitivity. Therefore, a small ANN structure is sufficient to be used for effective PV power control. Figure 1 shows the general overview of the proposed control structure. The purpose of the controller is to predict the PV power output depending on the inputs.

Note that the activation function of the output layer is linear, as provided in (2). However, the sigmoid activation function, given in (3), is used in the input layer. The associated weights and biases are represented by *w* and *b*, respectively. Moreover, *N* represents the total number of neurons in the hidden layer.

$$P\_{out} = \sum\_{i=1}^{N} w\_i^{output} \times v\_i + b\_i^{output} \tag{2}$$

$$w\_i = \tanh\left(w\_{i, \text{voltage}}^{input} \times V\_{\text{PV}} + w\_{i, \text{sensitivity}}^{input} \times \delta\_{\text{PV}} + b\_i^{input}\right) \tag{3}$$

The network is obtained through training by using the Levenberg-Marquardt algorithm. The training of neural network means adjusting the weights of layers and biases to get the target values. During the training process, weights and biases are adjusted and the target values are tracked continuously until the squared error between the actual and the desired outputs is minimized. The performance function of ANN is the mean squared error (MSE), as described in (4).

$$\begin{array}{c} \text{Total} \\ \text{MSE}(v) = \sum\_{j=1}^{\text{samples}} \left( P\_{out\_{\gamma}j} - P\_{out\_{\gamma}j}^{d} \right)^{2} \end{array} \tag{4}$$

Neural networks have the ability to adapt to the distribution function and this makes them more likely to find the non-linear relationships between the input measurements and the output. Nevertheless, this ability to adapt may result in the neural network that largely overfits the training data, producing the effect called '*overfitting*' [28]. To avoid this, a split of the data must be carried out between the training model and the test model (e.g., 80%–20%), with the aim of obtaining low MSE on the test data. In this work, 80% of the data is used to train the controller while the controller is tested on the rest of the 20% data.

#### **3. Test System**

The distribution network used to test the effectiveness of the proposed PV controller is shown in Figure 6 [20,29]. This is a balanced three-phase medium voltage (MV) system with 17 primary nodes. Where each node is connected to a low voltage (LV) radial distribution system. The accumulated load and rated PV capacity at each of these LV systems is 300(60 × 5) kW and 560(140 × 4) kW, respectively. The system parameters of the primary and secondary nodes are provided in Table 1.

**Figure 6.** Test primary distribution system.



Primary nodes have a three-phase 12.47/0.22 kV secondary distribution transformer. Each transformer feeds 20 houses at each phase through five laterals, as shown in Figure 7. The PVs are installed on four buses in the secondary systems, which are labelled as SB 02, SB 03, SB 04 and SB 05 (see Figure 7). Note that the secondary systems connected to the highlighted primary nodes in Figure 6 have solar PVs installed.

**Figure 7.** Secondary distribution network topology.

The communication-free PV controller is installed with each rooftop PV. The voltage regulation database (explained in Section 2.2) is used to train the controller to their respective output values determined by Equation (1) as mentioned in Section 2.3. Since there are only two inputs and one output, a small ANN with 5 hidden neurons is chosen. This network is trained using "nntool" in MATLAB. The network is obtained through training by using the Levenberg–Marquardt algorithm. In this control strategy, the controller is trained in such a way that it can be installed at any location in the distribution system. The relationship between inputs and the output is shown in Figure 8. It can be observed that there are four different groups of data points. These groups correspond to the different levels of houses in the secondary distribution system. The red plane shown in Figure 8 shows the response of the neural network controller.

**Figure 8.** Relationship between inputs and the output.

#### **4. Results and Discussion**

The purpose of the proposed controller is to modulate the power injected by the rooftop solar PVs connected in the distribution system. These controllers are expected to regulate the system voltages within an acceptable range, defined by the ANSI C84.1- 2016 standard. Additionally, fairness among the distributed PVs is also an important

requisite for customer satisfaction. The machine learning-based PV controller presented in this article is designed to work in the absence of any communication linkages between the controllers. The trained network only uses the local voltage measurements and the sensitivity estimations as inputs (see Algorithm 1).

The test distribution system under consideration has loads on all the (17 × 5) = 85 secondary buses. A typical load profile and the average load profile of these loads are depicted in Figure 9 for illustrative purposes. It can be noticed that the load is highly variable, this is due to the on/off actions of various household appliances. These high load variations in each LV node of the system will make the voltage regulation problem more challenging and, hence, test the controller's effectiveness in the abnormal or extreme conditions.

**Figure 9.** A typical load profile.

The voltage regulation performances of different communication-free PV controllers are compared and they are arranged in increasing order of their benefits. These control schemes include, opportunistic maximum power point tracking controller, droop-based and voltage-based on-off controllers and lastly the proposed PV controller. Note that, considering space limitations, results are presented for some specific nodes. To present node-specific results, two extreme nodes, i.e., Node-10 (upstream) and Node-7 (downstream), are selected since they can provide sufficient performance details.

#### *4.1. Conventional System (i.e., without PVs)*

In order to showcase the impact of increasing the solar power penetration in the present electric power infrastructure, for comparison the test system without PVs is shown. For this case, bus voltages of the secondary system connected to Node-7 and Node-10 are shown in Figure 10.

It is clearly visible that there is not much of a difference between the voltage profiles of the upstream and downstream MV nodes. The voltages of the downstream LV system (Figure 10a) are only slightly lower than that of the upstream LV system (Figure 10b). However, there is a significant voltage difference between the upstream and downstream LV busses. Voltage of the upstream bus (i.e., SB 02) is close to 1 p.u. while the voltage at the most downstream bus (i.e., SB 05) is much lower yet within the allowable voltage range as defined by the ANSI C84.1-2016 standard. A bus connected closer to the MV/LV transformer (i.e., strong/upstream bus) is less sensitive to change in load than that connected farther from the transformer (i.e., weak/downstream node). That is why, SB 05 has the highest voltage variations. This elucidates the importance of voltage regulation for the power sources connected to the LV busses.

**Figure 10.** No PV system voltage profiles at (**a**) Node-7, (**b**) Node-10.

#### *4.2. Base Case (i.e., PVs without Any Controller)*

This case represents moderate levels of solar power integration with the system loads shown in the previous sub-section. The solar power is injected into the power system without any control. PV power profiles for a particular sunny day in the summer season is considered which is shown in Figure 11. In a sunny day during the peak sunlight hours, there is more energy being produced by the PVs than consumed by the loads. Hence, in this section the impact of this high penetration of widespread PVs in the distribution system is studied.

**Figure 11.** Real power available from the PV systems without controllers.

The base case voltage profiles are shown in Figure 12 with uncontrolled PV integration. The buses that are farther away from the transformer (i.e., SB 04 and SB 05) have voltage upper limit violations; however, buses that are closer to the transformer (i.e., SB 02 and SB 03) have the voltages within the allowable limits. It is noteworthy to observe that the voltage at the downstream bus is much higher as compared to the upstream bus. However, it was much lower as compared to the upstream bus when no PVs were installed (see

Figures 10 and 12). It is due to the fact that the downstream buses are often more sensitive to changes in the load and/or power generation when compared to the upstream buses.

**Figure 12.** Base case voltage profile at (**a**) Node-7, (**b**) Node-10.

#### *4.3. On-Off Controller*

In this case, an on/off switch controller is tested. A reference voltage, *vr* = 1.045 p.u. is selected. Based on the POC bus voltage, the controller decides to ramp down the power generation if the voltage is higher than *vr* and ramp up the power generation if the voltage is lower than *vr*. Ramp limits are selected to be 1 kW/10 s to avoid abrupt variations.

In Figures 13 and 14, the voltage profiles and power generation profiles of the secondary buses are shown. It is evident that the power is only curtailed for downstream buses (i.e., SB 04 and SB 05), whereas the upstream buses are allowed to generate all the available power. Moreover, due to the frequent switching the SB 05 bus has fluctuating voltage problem, which may lead to other power system problems [30].

**Figure 13.** On-off case voltage profile at (**a**) Node-7, (**b**) Node-10.

**Figure 14.** On-off case output power generated at (**a**) Node-7, (**b**) Node-10.

#### *4.4. Droop-Based Controller*

In this section, a prevalent control scheme based on droop characteristics is shown for comparison. This scheme relies on the static droop P-V characteristics curve of each node in the distribution system. This relationship between the voltage and the output power is defined by the piecewise linear function as provided in (5). In [31], settings are done based on the location and the system loads. However, due to system reconfigurations this scheme would require communication, which is absent in present-time distribution systems.

A simpler form of the droop-based controller is tested with same droop constants, *kd*. A critical system voltage, *vcritical*, is set to be 1.05, which is the maximum allowable voltage defined by the ANSI C84.1-2016 standard. Considering a safety margin, the controller is activated at 1.02 p.u. The droop constant, *kd*, is set at 21.

$$P\_{\rm out}(t) = P G\_{\rm available} \times \begin{cases} k\_d (v\_{critical} - v\_i(t)), & v\_i(t) \ge 1.03 \text{ p.u.} \\ 1, & v\_i(t) < 1.03 \text{ p.u.} \end{cases} \tag{5}$$

where:

$$k\_d = \frac{140\text{ kW}}{(1.05 - 1.02)(220\text{V})} = 21.2\text{ kW/V} \tag{6}$$

The system voltages are shown in Figure 15. It can be seen that all the voltages are within the allowed limits. However, the buses located downstream inject less power than the buses closer to the transformer as illustrated in Figure 16. The buses closer to the transformer can export full PV power available while the downstream buses are undesirably restricted due to their higher voltages. Thus, the PV generated revenues for these customers are lower as compared to other customers.

**Figure 15.** Droop-based controller voltage profile at (**a**) Node-7, (**b**) Node-10.

**Figure 16.** Droop-based controller power generated at (**a**) Node-7, (**b**) Node-10.4.5. Proposed voltageand-sensitivity-based controller.

The uncontrolled integration of PVs results in voltage-rise problems, as it is shown in Section 4.2. While other communication-free controllers (Sections 4.3 and 4.4) are not able to act fairly among all the PVs connected in the system. Additionally, these controllers are not able to provide a stable voltage profile at the PVs point of connection. It is because they only use voltage readings to control the power injected and there are no integral or derivative control modules.

In order to mitigate the voltage-rise problem, a machine learning-based autonomous PV controller is presented. The controller utilizes both, the nodal voltage and its sensitivity to throttle the power output of the solar PV. Each solar PV in the distribution system is controlled independently by these controllers. The resulting voltage profiles are provided in Figure 17 when the proposed controllers are implemented. It can be clearly seen that the controller is able to effectively regulate the system voltages with good system voltage stability. Throughout the day, the voltages are maintained within the permissible range, except between 8:00 A.M. and 9:00 A.M., where some negligible over-voltages are recorded. This is because of the time required by the controller to respond to the significant variations in load/generation (as shown in Figure 5 and explained in Section 2.3).

**Figure 17.** Proposed controller voltage profile at (**a**) Node-7, (**b**) Node-10.

The most interesting feature of the proposed controller is fair power curtailment, despite the fact that there is no communication among the PVs connected at various locations in the distribution network. The power generated in the presence of the proposed controller is shown in Figure 18. The proposed controller curtails similar amount of power from all the PVs when the system support is required. The daily energy produced by the proposed and the droop-based controllers are provided in Table 2. It can be observed that the secondary downstream bus (i.e., SB 05) produces around 240 kWh less energy than the upstream secondary bus (i.e., SB 02) when the droop-based controllers are utilized. However, for the proposed controller similar amount of energy is being produced at all the secondary buses in the system. These results indicate the efficacy of the proposed controller.

**Figure 18.** Proposed controller power generated at (**a**) Node-7, (**b**) Node-10.


**Table 2.** Comparison of daily energy production (kWh).

\* P represents the primary node, whereas D and U represent downstream node (i.e., Node-7) and upstream node (i.e., Node-10), respectively.

#### **5. Control Strategy Performance**

In this section, performance of the proposed voltage and sensitivity-based control strategy is further examined. Table 3 summarizes the fairness for all control modes and effectiveness of these methods to avoid voltage limit violations. Total energy produced by each primary node in a day are also included. As anticipated, the uncontrolled integration of solar power results in the maximum energy production; however, the voltage violations are extreme and persist for longer duration (i.e., for about 286 min). On the other hand, the voltages are appreciably improved for on-off and droop-based controllers, but the fairness issue was gravely compromised. It is evident that the downstream buses (SB 04 and SB 05) experience most of the energy curtailment; therefore, these control techniques are not suitable for fair power integration. However, the proposed controller fairly curtails the energy from each PV system. Moreover, it drastically improves the system voltages as compared to the uncontrolled case. Note that the proposed controller curtails a little higher amount of the generated power in comparison to the other controllers. However, this slightly higher curtailment allows all the distributed PVs to participate fairly in the voltage improvement process.


#### **Table 3.** Comparison of controller performances.

\* P represents the primary node, whereas D and U represent downstream node (i.e., Node-7) and upstream node (i.e., Node-10), respectively. The bus will be reported as a high voltage violation if the voltage exceeds 1.05 p.u. % Energy curtailed is calculated using energy produced in uncontrolled case.

> In addition, the performance of the proposed control strategy is assessed with solar resource variability. This can happen for many reasons, including the cloud covering the solar PVs. The PV's output generation is highly varied on a cloudy day compared to a sunny day, as shown in Figure 11. The voltage and power generation profiles of the secondary buses are shown in Figures 19 and 20, respectively, when the proposed controller is tested during cloudy day. The results illustrate that the controller response to fluctuating available solar power is quick. Despite that the change in output power is not restricted (no ramp limit), power is always fairly curtailed to minimize the over voltage violations.

**Figure 19.** Voltage profiles in a cloudy day at (**a**) Node-7, (**b**) Node-10.

**Figure 20.** Power generation profiles in a cloudy day at (**a**) Node-7, (**b**) Node-10.

To further assess the robustness of the proposed autonomous PV controller, it is assumed that one of every two houses has an electric vehicle (EV). Nissan Leafs having 40 kWh battery pack model [32] are used to test the proposed controller when they are connected to the secondary buses. The EVs are assumed to charge at the rate of 7 kW when plugged in. That means, each EV takes 4 h to charge the battery from 30% to 100%. EVs are expected to plug-in between 6:30 a.m. and 10:30 a.m. since the impact of EVs charging on the PV control needs to be studied. The state of charge (SOC) for the EVs connected in primary Node-10 are shown in Figure 21.

**Figure 21.** State of charge of EVs connected at secondaries of Node-10.

When two EVs get connected to a bus at any given time, the load at that bus increases by 14 kW. Consequently, the voltage at that bus changes which affects the PV power generation. Figure 22 shows the PV power output when the proposed controller is being used during these events. Note that the EVs only connected at SB 03 and SB 04 are charging during the period from 9:00 a.m. until 9:30 a.m. During this time period, the power generated at these buses is only 3 to 5 kW more than the power generated at other buses. Similarly, from 12:30 p.m. until 1:25 p.m. the EVs only connected to SB 01 and SB 05 are charging, while the others are already fully charged. During this time, the PV power output for the buses with connected EVs is only a little more than the other buses. The voltage profiles of the EVs charging points are shown in Figure 23. Note that the voltages of the buses decrease when the EVs start charging, this happens because of the instantaneous increase in the load.

**Figure 22.** Power output comparison, with EVs charging at different times.

**Figure 23.** Voltage profiles at EV connection points.

Table 4 shows the overall PV energy produced in a day at the secondary buses of Node-7 and Node-10 when the EVs are being charged. It can be seen that the daily energy production has been increased when there is extra load connected in the system (see Tables 3 and 4). In fact, the system voltages drop when more load is connected which allows the PVs to generate relatively more power. These results indicate that the proposed controller successfully balances the trade-off between high penetration of renewable energy and fair power curtailment, so that the voltages remain within the allowable range as defined by ANSI C84.1-2016 standard.


**Table 4.** Energy produced in a day with EV charging from 30% to 100% (kWh).

\* P represents the primary node, whereas D and U represent downstream node (i.e., Node-7) and upstream node (i.e., Node-10), respectively.

#### **6. Conclusions**

This paper proposes a local voltage regulation control scheme for distributed solar PVs connected in the secondary network of the distribution system. The proposed technique is aimed at fairly controlling the power injections of all the PVs without the need of any communication infrastructure. The proposed machine-learning based controller uses two local measurements as inputs, namely, the nodal voltage and its sensitivity, to determine the PV power output. The performance of the proposed controller is validated in a PV-rich MV/LV test distribution system. Even though the controllers in the system work independently, they fairly controlled the power injections of all the PVs to keep the network voltages in an acceptable range. The distinctiveness of the proposed technique is highlighted by comparing a few other communication-free controllers as presented in the previously published literature. In addition, the robustness of the controller is verified by considering a cloudy day. In addition, the electric vehicles (EVs) are integrated into the secondary distribution system to further confirm the efficacy of the proposed controller in the future distribution systems.

The contributions of the proposed approach are evident since the machine learningbased controller is relatively inexpensive yet easy to deploy solution, which only requires the local voltage measurements at the point of connection. Additionally, this method is computationally fast because of the minimal hardware requirement and there are no

communication delays. The fast computational time ensures the suitability of the approach for solving real-time voltage problems.

**Author Contributions:** Conceptualization, S.S. (Shabib Shahid), S.S. (Saifullah Shafiq) and A.T.A.-A.; methodology, S.S. (Shabib Shahid), S.S. (Saifullah Shafiq) and B.K.; software, A.T.A.-A.; validation, S.S. (Saifullah Shafiq), B.K. and A.T.A.-A.; formal analysis, S.S. (Shabib Shahid) and S.S. (Saifullah Shafiq); investigation, A.T.A.-A.; resources, A.T.A.-A.; data curation, S.S. (Shabib Shahid) and B.K.; writing—original draft preparation, S.S. (Shabib Shahid), S.S. (Saifullah Shafiq), B.K. and M.O.B.; writing—review and editing, S.S. (Shabib Shahid) and S.S. (Saifullah Shafiq); visualization, S.S. (Shabib Shahid), B.K. and M.O.B.; supervision, A.T.A.-A.; project administration, S.S. (Saifullah Shafiq) and M.O.B.; funding acquisition, S.S. (Saifullah Shafiq) and M.O.B. All authors have read and agreed to the published version of the manuscript.

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

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors would like to acknowledge the support provided by World Futures Studies Federation (WFSF), Prince Mohammad Bin Fahd University (PMU), Prince Mohammad Bin Fahd Center for Futuristic Studies (PMFCFS), Khobar, Saudi Arabia.

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

#### **References**

