Abstract
This paper aims to develop a supervisory control scheme to enhance the effectiveness and profitability of a small-rating super capacitor energy storage system (SCESS) used in load-frequency-control applications. The proposed approach, which uses one-step-ahead adaptive predictive control (APC), adeptly handles the operational limitations of the SCESS. For the purpose of online estimation of system parameters, the recursive least square (RLS) algorithm has been employed. The system can be characterized as a two input two output system, wherein the real and reactive powers required by the SCESS serve as control signals issued by the controller. The SCESS voltage is subject to constraints to limit energy trade within specific bounds. The proposed control scheme successfully maintains the voltage constraints of the SCESS while significantly reducing frequency and voltage deviations in the presence of two disturbances, viz; load disturbance and wind disturbance. The effectiveness of the proposed scheme is demonstrated through simulation experiments on an isolated hybrid wind diesel power system, which addresses several modeling and design aspects.
Introduction
Transmission of electricity to off-grid sites is one of the key problems faced by isolated communities. Because of high transmission losses, high transportation costs, sustainable supply of fuel and several other factors, the transmission of electricity to such remote locations is not only a cumbersome job but also a challenging task (Rashid et al., 2023). To meet the demand of such locations has, therefore, become the need of the hour. One of the obvious solutions to tackle this problem, provided by the researchers, is to install hybrid systems either in isolated mode or grid-connected mode. Hybrid systems are self-sufficient systems that combine renewable sources of energy with non-renewable sources of energy to maintain the reliability of the system. Due to the several advantages of wind energy, it has become the prime focus for researchers. However, the intermittent nature of wind and integration of wind energy systems through power electronic interfaces lowers the inertia of the system, thereby, adding instability in the system in terms of perturbations in power demand (Thoker and Lone, 2021).
Energy storage devices are considered as the favorable option to confront the issues of power quality. The energy storage device increases the inertia of the system, making the system immune to the perturbations like load disturbances, wind disturbances, wind park disconnection etc and hence enhancing the robustness of the system. Various energy storage technologies with distinctive features such as Superconducting magnetic energy storage (SMES), battery energy storage system (BESS), flywheel energy storage system (FESS), supercapacitor energy storage system (SCESS) etc. have been reported in the literature for tackling the intermittent nature of wind, load leveling, frequency modulation etc. Therefore, improving the dynamic behavior of wind integrated power systems can be accomplished through the implementation of an efficient method such as the addition of energy storage to the wind energy facility (Zargar et al., 2021).
Superconducting magnetic energy storage (SMES) and battery energy storage have been used to enhance the dynamic performance of power systems and for load leveling applications (Mufti et al., 2015). Unfortunately, operation of these systems and maintenance come with a number of challenges and are exorbitant. BESS has a high energy density but a low power density. However, SMES has a slightly lower storage density but is more expensive (Zargar et al., 2021). The storage density of capacitors developed with current technology is only about
The frequency control of a hybrid system that has been supported with a fuzzy-controlled battery energy storage system is the focus of research by Zhang et al. (2016). Sebastián (2016), the use of a battery as an energy storage device for frequency regulation and peak shaving in a wind-diesel system is proposed. Short-term energy distributed predictive control for a wind farm is proposed by Zhao et al. (2016). Microgrid frequency regulation with flywheels and fuel cells has been investigated by Vidyanandan and Senroy (2016). The effects of load and wind power variations can be mitigated by using the discrete control scheme reported by Nisa and Mufti (2021). But the DFIG is not involved in the primary frequency support, and neither are the DC link dynamics of SCESS taken into account. Despite this, widespread implementation of these technologies is limited for a variety of reasons, including those pertaining to technology and the economy (Syed et al., 2023; Xiong et al., 2018). Optimized and parameter-identified advanced controls result in slow computation. Thus, their use in real-time applications has become cumbersome. In addition, there is no systematic approach for the design, development, and use of Fuzzy logic Control (FLC), making it highly dependent on the designer’s expertise (Ahsan and Din Mufti, 2020; Syed et al., 2023). Mufti et al. (2007) proposed fuzzy logic-based SCS for improved AGC, but it lacked the capability to maintain SCS voltage within allowable limits.
This paper presents a simulation and modeling of a hybrid wind-diesel system that integrates an adaptively controlled SCESS energy storage device. The energy storage device is located at bus 4, the load bus. Buses 1 and 2 are connected to two synchronous generators, each of which has an automatic voltage regulator and a governor.To harness wind power, an equivalent induction machine is installed at bus 3, as depicted in Figure 1. In other words, this study aims to develop a comprehensive understanding of the hybrid wind-diesel system with SCESS energy storage, which can be valuable in enhancing the system’s overall performance and efficiency. Ultimately, this study highlights the importance of integrating energy storage devices in hybrid energy systems to improve their stability and reliability.

Hybrid wind-diesel-SCESS system.
Super capacitor energy storage system
A SCESS with a low rating has been incorporated in a hybrid wind diesel system in order to supplement frequency regulation in the event of any disturbance in the system. Figure 2(a) depicts the configuration of the power conversion system (PCS) that is used to interface the SCESS with the electric utility grid. This is accomplished by using a pair of power converters. The DC link voltage is supplied by the grid side converter (GSC), and a fast bidirectional interface is set up by a combined buck-boost DC-DC converter.

(a) Configuration of SCESS and (b) primary control loop of SCESS.
The supervisory controller directs the primary control loop to convert power commands into current commands for the supercapacitor bank (SCB), utilizing the PI controller in the inner current control loop to regulate the flow of current through the SCB via the dc-dc converter. By switching between the two modes of operation viz. the buck or charge mode and the boost or discharge mode the bidirectional dc-dc converter facilitates energy transfer bidirectionally between the input and output sides with the chopper employing modulation of the buck/boost switch for buck/boost mode. Figure 2(b) illustrates the non-linear average value model of SCESS and its primary control (Mufti et al., 2015; Syed et al., 2023). Moreover, the DC link voltage,
where,
Problem formulation
Controller formulation and parameter identification
An adaptive predictive control scheme has been introduced for an isolated wind-diesel power system. This scheme utilizes a one-step ahead approach based on the SCESS unit. The system has been specifically designed to proficiently manage any uncertainties that may arise within the system. It is well-suited for nonlinear and time-varying systems. In the event of any unexpected changes, the system automatically updates itself to ensure optimal performance. The advanced on-line identification technique employed for parameter estimation is depicted in Figure 3. This method generates a control signal using a pre-assigned model order that can be aptly characterized by an autoregressive discrete time model as (Mufti et al., 2015; Zargar et al., 2021):

Representation of TITO and MISO systems.
For a system with two inputs and two outputs, equation (2) may be expressed as follows:
Here,
The main objective of the controller is to reduce the voltage and frequency deviations whenever the system is subjected to disturbances which can be achieved by defining a cost function for the controller. The purpose of the cost function is to regulate the system output and prevent the excessive control as well (Mufti et al., 1996).
The cost function is formulated as follows:
Here,
The performance index is calculated as:
Where,
The control law is obtained by setting equation (4) to zero (Zargar et al., 2021). For formulation of optimal control law, expression for
Minimizing (4) with respect to
Expanding (7) and (8) by substituting
Equation (9) in a general form can be written as (10) which is the control law for achieving an optimal control.
Two MISO approach is preferred for n-step ahead identification, with TITO system splitted into two MISO system as shown in Figure 4.

Representation of (a) TITO and (b) MISO systems.
The application of optimal control signal
where
The recursive algorithm for parameter estimation is expressed through a set of equations as (Mufti et al., 1996):
where the caret denotes the estimated values and
Constraints on SCESS energy level
The power command for a SCESS device must always be within the limits of the converter rating. In order to adhere to the prescribed energy exchange limits between the wind-diesel system and the SCESS unit, constraints are placed on the energy transfer by the power conversion system. A minimum stored energy level must be enforced on the SCESS unit for continuous control (Iqbal et al., 2009; Zargar et al., 2021). To ensure profitable operation and uninterrupted control, the voltage/energy of the SCESS must always remain within the upper and lower limits. By discretizing time into discrete intervals, the discrete-time model is used to represent the relationship between the energy level and the voltage of the storage unit as depicted in Figure 5, which takes into account the time constant of the SCESS unit

Prediction for energy level of SCESS.
An imperative factor that holds great significance in the realm of supercapacitors is the discharge factor
where
For
In order to ensure that the energy limits are not surpassed, as outlined by equations (5) and (6), a judicious implementation of the power directive at the
To this end, a Simulink model has been developed, that imposes these constraints on the SCESS energy, based on the equations (2)–(6).
Implementation of proposed scheme on SCESS unit
The present section encompasses the execution of the control and identification algorithm derived in section “Controller formulation and parameter identification.” The SCESS unit under consideration is a two input two output system, where
Specifically,
For continuous control operation, the second term in (19) is incorporated, enabling the SCESS voltage to restore to its nominal value after tackling a disturbance. In the condition of a steady state, it is observed that both the frequency and SCESS voltage deviations are rendered null. It is imperative to exercise judiciousness in selecting the value of
Time domain simulation results
The hybrid wind diesel test-bed system is initially presumed to be in a steady state. However, upon being subjected to a combination of load and wind disturbances, this balance is disrupted, leading to a deviation from its steady state values. To augment the system power quality under such scenarios, an adaptively controlled SCESS unit is proposed.
Load disturbance
Due to the low inertia of the systems, load perturbation is a typical sort of perturbation that appears in hybrid wind power systems. As the bus admittance matrix adapts to the new load requirement, the system experiences frequency and voltage fluctuations (Rashid et al., 2023; Thoker and Lone, 2021). We assume that the system’s initial load was 260
Load description for an alteration in reactive/active load power.
Figures 6 and 7 show the simulation findings for this case study. The results show that SCESS is able to keep the system power quality dynamics stable by lowering the maximum voltage and frequency fluctuations.

System frequency deviation trajectory under load disturbance.

Dynamic power system and SCESS responses for load disturbance.
Wind disturbance
The second scenario for which the developed strategy has been assessed is wind disturbance. To determine how effectively SCESS improves the system power quality, the test-bed system is operated for a total of 14 seconds under wind turbulence. In the beginning, the wind turbines are only producing 36 kW of power, but it is anticipated that the load demand will be 260 kW and 182 kVAR. For

System Frequency deviation profile for wind disturbance.

(a) Wind speed trajectory and (b) wind power output.

Dynamic power system and SCESS responses for wind disturbance.
The simulation results are summarized as follows:
The application of the proposed framework not only leads to the elimination of persistent undesirable oscillations but also results in a notable reduction in both frequency and voltage deviations as illustrated in Figures 6–8 and 10 for both cases respectively. Through the utilization of the proposed control scheme to regulate the SCESS, a significant decrease in the frequency and voltage deviations is observed. This demonstrates that the suggested framework is quite effective at containing peak frequency and voltage variations.
The proposed methodology compels the SCESS to function in close proximity to its limitations, thereby successfully and efficiently mitigating power-system oscillations.
The SCESS converter is consistently able to manage a power that never surpasses the rated value of the converter, equivalent to 0.07 p.u. of power.
The voltage of the SCESS consistently sustains itself within the permissible limits, both in the upper and lower thresholds.
After addressing a perturbation, the SCESS obtains its designated voltage level, thereby accumulating energy and persisting in a prepared state to confront additional load disruptions.
From the obtained results, it can be inferred that the adaptive predictive controller is proficient in generating the dynamic power constraints with satisfactory outcomes. This establishes the justification for the utilization of the aforementioned controller in the SCESS based wind diesel power system.
Conclusion
This paper presents the application of a one-step ahead adaptive control scheme based on a SCESS unit to mitigate power quality issues caused by the random nature of wind. A discrete-time model of the storage unit is utilized to generate a suitable power command for the unit. System parameters are estimated using a two-input, two-output system that is split into two two-input, single-output systems. The recursive least square algorithm is used for parameter estimation and a separate model is applied to impose constraints on the SCESS energy/voltage level. By incorporating these constraints into the controller formulation, significant reductions in frequency and voltage deviations are observed, and the SCESS voltage/energy limits are always within the prescribed limits. The proposed methodology has undergone testing for disturbances belonging to two distinct categories, namely continuous wind perturbation and higher magnitude load disturbance. Despite the presence of such disturbances, the SCESS constraints are always upheld while simultaneously minimizing the deviations in frequency and voltage. The adaptive controller-based SCESS unit, as conferred in this study, has the potential to be a more favorable choice for power systems that rely on renewable sources. The selection of the regulated parameter under consideration compels the SCESS to operate as a highly efficient damping mechanism, thereby augmenting the efficacy of Load Frequency Control (LFC).
Footnotes
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
