Smart Integration of Renewable Energy Sources Employing Setpoint Frequency Control—An Analysis on the Grid Cost of Balancing

Abstract

The increasing installation of Renewable Energy Sources (RES) presents significant challenges to the stability and reliability of power systems. This paper introduces an advanced control method to mitigate the adverse effects of intermittent generation from RES on the power system frequency stability. The proposed approach emphasizes the critical role of Battery Energy Storage Systems (BESS) and RES in enhancing the resilience of modern power networks. The Generation Export Management Schemes (GEMS) are employed to curtail the excessive export of RES, thereby contributing to improved frequency stability. This research involves a comprehensive analysis of the dynamic behavior of the network under various operational scenarios, particularly focusing on power exchanges between RES, BESS, and synchronous generation units. Furthermore, this paper focuses on the economic implications of integrating RES into the grid, with a detailed cost of balancing (COB) modelling and analysis conducted to assess the financial viability of the proposed frequency management solutions. The analysis encompasses both short-term and long-term perspectives, providing insights into the development of economically sustainable smart power networks that effectively integrate renewable energy and storage technologies while maintaining system stability.

1. Introduction

The energy sector is a major source of greenhouse gas emissions that is committed to reaching net zero by 2050 [1]. This means that the total greenhouse gas emissions emitted during power generation would be equal to the emissions removed from the atmosphere during power generation, aiming to limit global warming and climate change effects [2]. The government aims to reduce all direct emissions from public sector buildings by 50% and 75% by 2032 and 2037, respectively [3]. The drive for net zero is prompting a new push for cleaner and more sustainable forms of power generation, thus the switch from the switch of Synchronous Generators (SGs), which are fueled by fossil fuels, to Renewable Energy Sources (RES). Figure 1 shows a continuous rise in RES while non-RES installation is on the decline.

In traditional power systems, SGs provide transient energy on the network in the form of inertia, which is required for network stability [4]. The inertia support from SGs refers to the energy stored in the rotating mass within the generator to maintain system frequency during sudden changes in electrical load or disturbances in the power grid [5]. The key component is the rotor, which rotates at a constant speed, synchronous with the frequency of the grid [6]. This kinetic energy provides inertia support to the system, i.e., if there is an increase in load demand or a sudden loss of generation elsewhere in the system, the rotational speed of the SG will change to maintain the stability of the grid [7]. Losing SG means the network is more susceptible to frequency variation as demand and supply changes, as the transient energy stored in the rotor is not slowly declining because of the switch to RES rather than SG.

Figure 1. Global growth of RES from 2001 to 2021 [8].

Figure 1. Global growth of RES from 2001 to 2021 [8].

Inertia support works in conjunction with other control mechanisms, such as governor action and automatic generation control (AGC), to stabilize system frequency when there is a sudden increase in load, for example, the speed of the generator’s rotor decreases momentarily because of the increased mechanical load. The energy stored in the rotating mass helps to resist this change, allowing time for other control mechanisms to adjust the output of the generator to match the new demand and restore the system frequency to its nominal value [9].

The push for net zero presents both technical and economic challenges for the power systems. The technical challenge originates from the transition from SGs to RES. The nominal function of RES is to increase the green energy generation to offset carbon footprint, and thus, it is not designed to take part in frequency control. These RES can participate if the controllers are altered to respond to frequency fluctuation. Wind turbines (WTs) use pitch and speed control to contribute to inertia. RES energy production fluctuates constantly, as the output is determined by nature [10]. The decline in SG generators on the electrical grid coupled with the installation of non-synchronous RES generation causes the grid to have faster oscillation. RES are designed for cheaper and more reliable energy, as such a solution is for the RES to provide inertia response. In this solution, the controller of the RES would need to be altered to participate in inertia control or frequency control [11].

To address the technical challenges from RES, Energy Storage Systems (ESS) are included in the mix of generation, as the ESS can absorb excess energy produced from RES in the network by charging and discharging shortage/excess energy when required in times of high and low demand, respectively. The most popular form of ESS deployed globally is the Battery Energy Storage System (BESS). BESS technology has drawbacks, such as low energy density, high maintenance cost, and high installation cost [12].

The adoption of RES can potentially increase the cost of balancing (COB) of the grid. The variability of RES means that grid operators need to balance the supply of electricity more frequently, which can lead to increased costs. In addition, the integration of RES can require significant upgrades to the existing grid infrastructures, which can also increase costs. Figure 2 represents the increase in COB in the grid in the UK from the year 2020 to 2022. The total COB for the network for the year 2020 was GBP 1.7 B, and it increased to GBP 4.2 B in 2022, i.e., an increase of 247% within two years [13].

In a power system with multiple types of energy generation, frequency control is critical to the system’s stability, and thus, it has been investigated in the literature. The majority of studies are on demand-side management. Demand-Side Response (DSR) is a measure used to manage the demand for electricity by incentivizing consumers to reduce their energy consumption during periods of high demand or low supply. This is accomplished by offering consumers financial incentives to reduce energy consumption during peak periods [14]. In ref. [15], a DSR constraint model was developed based on three flexible loads, namely Electric Vehicles, BESS, and air conditioning clusters, to reduce electricity costs and improve the cost of operation. The model considered day and night to schedule the flexible loads to shift loads where RES had a surplus generation, and as a result, the cost of energy was reduced. DSR can give customers the strategic opportunity to adjust electricity consumption to reduce electric costs, by reducing load at peak times [16]. Two customer incentive plans are detailed in the literature, namely the Price-Based Demand Response (PBDR) and Incentive-Based Demand Response (IBDR). PBDR can shift the load distribution of users and has the effect of “cutting peaks and filling valleys”, while IBDR cannot shift the load distribution of users, but the effect of load reduction during the peak period of users is better than PBDR [17].

Optimal scheduling of VPP operation considering the intermittent supply of RES forecast on the day-ahead and real-time scale using both the PBDR and IBDR to form a two-stage optimal scheduling of a VPP supporting DSR is presented in ref. [18]. During the first stage, the impact of the PBDR and IBDR is studied with the objective of minimizing the cost of operation of the VPP. The next stage uses the regulation characteristics of IBDR and real-time power fluctuation of the VPP during operation to ensure stability in power flow on the VPP. The proposed VPP two-stage optimal scheduling model can effectively smooth out the power fluctuation caused by the day-ahead prediction error and ensure the reliability of system operation [18].

A Multiple Linear Regression (MLR) model was built to estimate the effects of direct loads on customers’ average hourly demand [19]. The average reduction in hourly demand from residential load with the use of smart meter data is utilized. The MLR model found, during the summer and winter seasons, that the controlled appliances could contribute to DSR. A real-time control-based method based on export limits was implemented on a roof-top PV system [20]. The low-voltage feeder controller utilizes a two-stage decision-making process to reduce the assigned export from the PV on the LV feeders on the distribution network. The real-time control algorithm solves a minimization problem, to assign 5 min export limits for households while ensuring that network constraints are not violated.

Generation Export Management Scheme (GEMS) is a measure for the management of electricity generation by controlling the output of the generator [21]. GEMS operates by reducing the output of RES during periods of low demand or high supply, which helps to avoid surplus generation on the grid and ensures that the supply of electricity matches the demand. GEMS can be used in conjunction with other measures, such as energy storage systems and demand response (DR) programs, to help balance the grid and ensure reliable and stable operation.

Despite the extensive body of research exploring Demand-Side Response (DSR) and its potential to address network instability and operational costs, significant gaps remain concerning the diverse energy generation types and their involvement in frequency control. Also, another shortcoming in the existing literature is the insufficient focus on COB. While many studies emphasize the operational cost reduction capabilities of DSR strategies, such as Price-Based Demand Response (PBDR) and Incentive-Based Demand Response (IBDR), they often fail to provide a comprehensive analysis of COB, especially in systems with high penetration of Renewable Energy Sources (RES). The balancing costs, which include expenditures on ancillary services to maintain system equilibrium amid variable RES output, are underexplored, limiting the understanding of DSR’s true economic impact.

This paper examines the integration of the Generation Export Management Scheme as a strategy for power system control to mitigate both the cost of balancing (COB) and the Rate of Change of Frequency (ROCOF). While numerous studies have concentrated on Demand-Side Response (DSR) as a remedy for network instability, this research addresses this gap by exploring generation control as an alternative approach to addressing instability and the increasing cost of balancing by proposing a load frequency control (LFC) simulation model and formulating the cost of balancing when GEMS is employed. Specifically, a Set-Point Control algorithm is proposed in the LFC model to assess the impact of GEMS on COB and ROCOF.

The novelty of the methodology lies in the unique introduction of the Setpoint Control to the Maximum Power Point Tracking (MPPT) Mode within the GEMS framework. This integration enhances the responsiveness of renewable energy sources and improves frequency stability, which has not been explored in previous studies. This study focuses on generation control and demand response at the same time, offering a fresh perspective that contributes to the development of more resilient and economically efficient power systems.

To demonstrate the benefits of this work, a case study of a mini-grid is presented with cross-comparisons between the traditional control method using the MPPT and the proposed Set-Point Control. The analysis reveals that the Set-Point Control significantly reduces COB and mitigates ROCOF more effectively than traditional control strategies. This research not only provides a viable alternative to existing solutions but also opens new avenues for integrating renewable energy sources more effectively into the grid.

The remaining part of this paper is organized as follows. Section 2 presents the theoretical framework and methodology employed in this research, including the development of the LFC simulation model with the Set-Point Control algorithm. Section 3 presents detailed descriptions of the mathematical models for energy not supplied (ENS) and COB of the grids. Section 4 outlines a microgrid study with data sources, simulation environment, and experimental design utilized to evaluate the impact of GEMS on the cost of balancing (COB) and Rate of Change of Frequency (ROCOF). This section also discusses the results of the simulations, analyzing the effectiveness of GEMS and Set-Point Control in reducing COB and improving frequency stability. Section 5 summarizes this work and provides recommendations for future research.

2. Load Frequency Control Model

Load Frequency Control (LFC) is a critical mechanism in power systems designed to maintain the system frequency within acceptable limits despite variations in load demand and generation [7]. The primary goal of LFC is to keep the system frequency close to its nominal value by balancing power supply and demand in real time. This is achieved by automatically adjusting the output of generators in response to frequency deviations caused by changes in load or generation.

2.1. Schematic Diagram of LFC Simulation

In this paper, a simulation model for Load Frequency Control (LFC) of power systems with a variety of Distributed Energy Resources (DERs) is presented to model the power system frequency control and estimate the system cost of balancing. Figure 3 shows a schematic diagram of the LFC model.

The LFC model simulates frequency change as a function of network power; thus, the LFC model assumes network demand is always met. In the base model, the BESS was implemented as a secondary frequency regulation technology. The model is susceptible to a range of operational conditions, including abrupt supply shortages and surpluses, because of the intermittent characteristics of the RES.

The discharge frequency is based on the standard operating frequencies of the power systems. The frequency and power of the BESS are inverted since the BESS control is specifically engineered to discharge frequencies that indicate supply loss. Conversely, the BESS will generate a charge to eliminate any surplus power on the network when the frequencies indicate a supply surplus.

In this paper, the model is designed to be universal and adaptable to any country’s grid frequency. The example is given for the UK power system context (f = 50 Hz). However, it can be easily adapted for other countries with different frequencies, e.g., 60 Hz for North America. The frequency variations considered are within the typical operational ranges of different power systems globally, ensuring that the model is applicable and can be tailored to various national grid standards.

The model presented in Figure 3 is designed and tested in MATLAB/Simulink 2023a. The HOMER Pro 3.16.2 [22] is used to produce an input dataset of photovoltaic (PV) and wind turbine (WT) power for the LFC Model.

2.2. Set-Point Control

The RES operating in economy mode will utilize Maximum Power Point Tracking (MPPT) [23]. However, in frequency mode, the RES will utilize an LFC controller to activate and deactivate based on a frequency constraint rather than an MPPT controller. Figure 4 provides a visual representation of the RES’s transition between frequency mode and MPPT mode, which is determined by the frequency magnitude.

When the RES detects a frequency deviation from the nominal level, specifically a threshold above the Set-Point Control Frequency threshold, the operating mode of the RES will switch to Frequency Mode. In this mode, the system employs a Load Frequency Control (LFC) mechanism, critical for maintaining grid stability. LFC adjusts the RES’s output to help balance supply and demand, aiming to keep the frequency within an acceptable range to prevent grid instability. For instance, if the grid frequency exceeds the setpoint control frequency threshold, indicating an over-supply of power or reduced demand, the RES will activate a Frequency Setpoint Controller. This controller prioritizes frequency regulation by modulating the RES output based on real-time frequency data rather than maximizing power generation. Conversely, when the frequency threshold is not breached, the RES reverts to MPPT mode, resuming focus on optimizing energy production.

The setpoint controller (SC) operates in two modes: MPPT mode and frequency mode. Under normal conditions, the RES operates in MPPT mode. However, when the frequency dips or rises above the setpoint frequency set by the system operator, the frequency controller sends a feedback loop to the RES to initiate generation turn down. Therefore, the RES will transition between power supply and frequency control modes. Refer to the picture illustrating the feedback control system used in the study for frequency regulation. The flowchart for the SC is represented in Figure 5.

In Figure 5, the SC continuously monitors the grid frequency and compares the measured frequency against the setpoint thresholds defined by the system operator. Based on this comparison, the SC decides whether the RES should remain in MPPT mode or switch to the Setpoint Frequency Control mode. If a frequency deviation is detected, the SC sends a control signal to the RES to adjust its power output, initiating generation turn down or ramp-up as necessary. The SC continues this monitoring and adjustment cycle, modifying the RES’s operation until the frequency returns to within acceptable limits. By incorporating Load Frequency Control (LFC) into the RES operation through the SC, the system effectively balances its objectives of maximizing renewable energy production and maintaining grid stability. This integration of control mechanisms ensures that the RES not only contributes to energy generation but also plays a vital role in supporting the overall reliability of the power system.

3. Mathematical Formulation

Energy Not Supplied (ENS) and cost of balancing (COB) are critical parameters in the mathematical modelling of power system operations, particularly in networks with high integration of Renewable Energy Sources (RES). This section presents detailed formulations for ENS, COB and their relationship with the rate of change of power.

3.1. Energy Not Supplied and Cost of Balancing

Energy Not Supplied (ENS) is the amount of energy that is restricted because an RES is being used for frequency regulation. ENS denotes the cost incurred by RES when participating in frequency support. This study examines the ENS by focusing on the RES running in Maximum Power Point Tracking (MPPT) mode, which is the primary mode of operation for the RES. Equation (1) displays the ENS calculation.

$$\mathrm{E}\mathrm{N}\mathrm{S}={\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{P}\mathrm{V}}_{\mathrm{M}\mathrm{P}\mathrm{P}\mathrm{T}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)-{\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{P}\mathrm{V}}_{\mathrm{F}\mathrm{C}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)+{\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{W}\mathrm{T}}_{\mathrm{M}\mathrm{P}\mathrm{P}\mathrm{T}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)-{\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{W}\mathrm{T}}_{\mathrm{F}\mathrm{C}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)$$

(1)

where WT_MPPT and PV_MPPT represent the power produced when WT and PV are operating in MPPT mode.

Essentially, Equation (1) calculates the total energy that could have been supplied if the RES were operating solely in MPPT mode, minus the actual energy supplied when the RES is participating in frequency regulation mode. This difference represents the ENS, which relates to the opportunity cost associated with RES participation in frequency support.

The cost of balancing (COB) refers to the total cost associated with maintaining the balance between electricity supply and demand in the grid, which is particularly significant in power systems with high RES penetration. In this study, the COB includes costs from various sources of energy generation and storage, as well as the cost associated with energy not supplied due to frequency regulation activities.

The equation for COB for a traditional grid is shown in Equation (2).

$${{\mathrm{C}\mathrm{O}\mathrm{B}}_{\mathrm{H}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{R}\mathrm{E}\mathrm{S}\_\mathrm{G}\mathrm{r}\mathrm{i}\mathrm{d}}=\mathrm{c}}_{\mathrm{t}}^{\mathrm{S}\mathrm{G}}{\int }_0^{\mathrm{t}}{\mathrm{P}}_{\mathrm{S}\mathrm{G}\left(\mathrm{t}\right)}\mathrm{d}\left(\mathrm{t}\right){+\mathrm{c}}_{\mathrm{t}}^{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}}\underset{0}{\overset{\mathrm{t}}{\int }}{\mathrm{P}}_{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}\left(\mathrm{t}\right)}\mathrm{d}\left(\mathrm{t}\right)+{\mathrm{c}}_{\mathrm{t}}^{\mathrm{e}\mathrm{n}\mathrm{s}}\mathrm{E}\mathrm{N}\mathrm{S}$$

(2)

where ${\mathrm{c}}_{\mathrm{t}}^{\mathrm{S}\mathrm{G}}{\mathrm{c}}_{\mathrm{t}}^{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}},{\mathrm{c}}_{\mathrm{t}}^{\mathrm{S}\mathrm{C}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{c}}_{\mathrm{t}}^{\mathrm{e}\mathrm{n}\mathrm{s}}$ are the costs of balancing the grid per unit of energy generated (GBP/MWh) by synchronous generator and battery, respectively, and ${\mathrm{c}}_{\mathrm{t}}^{\mathrm{e}\mathrm{n}\mathrm{s}}$ is the cost of a unit of energy not supplied.

Substitute the formulation from Equation (1) into Equation (2) to represent the formulation for COB for a grid with high RES penetration, shown in Equation (3).

$$\begin{array}{cc}\hfill {\mathrm{C}\mathrm{O}\mathrm{B}}_{\mathrm{H}\mathrm{i}\mathrm{g}\mathrm{h}\_\mathrm{R}\mathrm{E}\mathrm{S}\_\mathrm{G}\mathrm{r}\mathrm{i}\mathrm{d}}& = {\mathrm{c}}_{\mathrm{t}}^{\mathrm{S}\mathrm{G}}\underset{0}{\overset{\mathrm{t}}{\int }}{\mathrm{P}}_{\mathrm{S}\mathrm{G}\left(\mathrm{t}\right)}\mathrm{d}\left(\mathrm{t}\right)+{\mathrm{c}}_{\mathrm{t}}^{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}}\underset{0}{\overset{\mathrm{t}}{\int }}{\mathrm{P}}_{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}\left(\mathrm{t}\right)}\hfill \\ & + {\mathrm{c}}_{\mathrm{t}}^{\mathrm{P}\mathrm{V}}\underset{0}{\overset{\mathrm{t}}{\int }}\left({\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{P}\mathrm{V}}_{\mathrm{M}\mathrm{P}\mathrm{P}\mathrm{T}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)-{\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{P}\mathrm{V}}_{\mathrm{F}\mathrm{C}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)\right)\hfill \\ & + {\mathrm{c}}_{\mathrm{t}}^{\mathrm{W}\mathrm{T}}\underset{0}{\overset{\mathrm{t}}{\int }}\left({\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{W}\mathrm{T}}_{\mathrm{M}\mathrm{P}\mathrm{P}\mathrm{T}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)-{\int }_0^{\mathrm{t}}{\mathrm{P}}_{{\mathrm{W}\mathrm{T}}_{\mathrm{F}\mathrm{C}\left(\mathrm{t}\right)}}\mathrm{d}\left(\mathrm{t}\right)\right)\hfill \end{array}$$

(3)

3.2. ROCOF and Power Balance Equation

Power imbalance is caused by the difference in demand and supply. A sudden increase in net demand will cause the frequency to drop and vice versa; a sudden decrease in demand will cause the frequency to rise. This can be shown in Equation (4), where the relationship between the rate of change of frequency (ROCOF) and rate of change of power (ROCOP) is mathematically derived [24]:

$${\displaystyle \frac{\partial f}{\partial t}}=\left({\displaystyle \frac{\Delta P}{2H}}\right).f_0$$

(4)

where H is the inertia constant of the network, $\Delta P$ is the ROCOP and $f_0$ is nominal network frequency. Thus, the frequency of the network can be calculated by adding the ROCOF to the nominal frequency. To effectively mitigate frequency deviations, it is essential to clarify the complex relationship between power and frequency. By optimizing power exchange during grid operation, frequency curtailment is achievable. Equation (5) is the power balance equation on the grid considering the SG, PV, WT and BESS configuration.

$$\mathsf{\Delta }P\left(s\right)=\mathsf{\Delta }{P}_{\mathrm{gen} }\left(s\right)+\mathsf{\Delta }{P}_{\mathrm{wind} }\left(s\right)+\mathsf{\Delta }{P}_{\mathrm{solar} }\left(s\right)+\mathsf{\Delta }{P}_{\mathrm{battery} }\left(s\right)$$

(5)

where $\mathsf{\Delta }{P}_{\mathrm{SG} }\left(s\right)$ is the rate of change of power from the SG, $\mathsf{\Delta }{P}_{wind}\left(s\right)$ is the rate of change of power from the WT, $\mathsf{\Delta }{P}_{Solar}\left(s\right)$ is the rate of change of power from the PV, and $\mathsf{\Delta }{P}_{Battery}\left(s\right)$ is the rate of change of power of the battery.

4. Results and Discussion

This section presents a mini-grid case study to compare the setpoint control to the base model that represents the current practice with SG and BESS. A mini-grid or microgrid is an aggregation of loads and one or more energy sources operating as a single system providing electric power independently or in synchronization with the main grid [25]. The integration of RES and energy storage systems aims to provide reliable power to a designated community or area, enhancing energy access and resilience. The mini-grid supports both autonomous operation and grid-connected configurations, allowing for optimized energy management and improved stability in power supply [26].

The proposed model with Set-Point Control is compared against a general benchmarking model, called the base model, which employs the SG with MPPT control mode [23,27]. It is noted that the MPPT control model in refs. [23,27] is mainly for the PV system, and in this research, we also extend this to the WT system to compare and demonstrate the effectiveness of the proposed setpoint control against the existing models in the literature.

In addition, to demonstrate that the proposed model operates under conditions that closely mirror real-world scenarios, the mini-grid case study utilizes real-life data for wind and solar energy input, generated from HOMER Pro 3.16.2 [28], which is a widely used software in academia and industry, as it includes historical real-life data.

It is assumed that the microgrid is subject to excess supply and loss of supply from the RES.

Table 1. Microgrid parameters for study.

Turbine Time Constant	0.5	sec
Governor Time Constant	0.2	sec
Governor Inertia constant	5	sec
Governor Speed Regulation	0.05	sec
PV Size	50	kW
Wind Size	50	kW
BESS Size	50	kW
Cost of WT for COB	25	£/kWh
Cost of PV for COB	25	£/kWh
Cost of BESS for COB	25	£/kWh

presents the specifications of the microgrid described in this paper.

4.1. Base Model Results

The primary method of providing frequency support in the base model is from the SG. The BESS was deployed as a secondary form of frequency regulation. The model has various operating conditions such as sudden shortages or surpluses in supply, due to the intermittent nature of the RES. The BESS charge and discharge is controlled by frequency magnitude; thus, the BESS will discharge to frequencies ranging from 49.5 Hz to 50 Hz, which indicates a loss of supply. However, frequencies ranging from 50.05 Hz to 50.5 Hz indicate an excess supply of electricity. In this situation, the BESS will charge to remove excess power from the network. This mode of operation will persist until the frequency exceeds the deadband threshold of 50 Hz.

See Figure 6 for the visual depiction of the system dynamics from the base model. During the time interval from 0 to 5 s, the frequency experiences a decline to 49.8 Hz because of a reduction in the supply from the RES connected to the network. In order to offset this loss of supply, the BESS exports the stored energy into the grid. Excess supply and low demand conditions in the system lead to a sharp increase in frequency to 50.3 Hz within a time frame of 30–40 s. As a result, the BESS will import the excess power on the network. The total cost for network balancing is approximately GBP 18 k.

4.2. Setpoint Control Model Results and Comparison

This model is influenced by various operating conditions, such as loss and surplus generation produced by the intermittent nature of RES. The link between frequency and BESS power is inversely proportional. The BESS control system is designed to respond to frequencies within the range of 49.5 Hz to 50.05 Hz by exporting power, as this signifies a deficit in the power supply. On the other hand, frequencies ranging above 50.05 Hz to 50.5 Hz indicate a surplus of supply; thus, the BESS will charge to extract surplus power from the grid. This process persists until the frequency approaches the threshold of 50 Hz, known as the dead-band point. The setpoint frequency is set to 50.2 Hz, resulting in a reduction in the overall power output of the RES to about 0 kW. The difference may be observed in Figure 7, particularly when comparing subplot 1 and subplot 2. The graphic in Figure 7 depicts the switching of RES from MPPT mode to frequency control mode. Specifically, between 10 and 20 s, the controller restricts the power from the RES to 0 kW as the frequency has reached the setpoint of 50.2 Hz. The setpoint control is applied within the time of 30–40 s as the RES power is restricted to 0 kW, and subsequently, MPPT mode operation returns as the frequency drops to 49.8 Hz at 50 s.

The diagram in Figure 7 illustrates the impact of the BESS when the frequency decreases to 49.8 Hz during the time frame of 0–5 s. During this period, there is a reduction in the power supply from the RES on the network. To offset this loss of supply, the BESS discharges energy into the network. The system encounters an excess of supply, resulting in a sudden increase in frequency to 50.2 Hz during the time of 30–40 s. Consequently, the Battery Energy Storage System (BESS) charges itself to absorb the extra power in the network. The base model depends exclusively on the BESS and SG for maintaining network equilibrium, whereas the SC model utilizes the RES to maintain frequency stability. The network balancing incurs a total cost of around GBP 18.07 k.

For a better interpretation of the setpoint control, see Figure 8, where the established frequency threshold of 50.2 Hz serves as a critical operational boundary.

The top graph in Figure 8 provides a detailed representation of grid frequency dynamics, fluctuating within the narrow range of 50.1995 Hz to 50.2005 Hz over a short temporal window. Notably, at approximately 13.6 s, the grid frequency breaches the 50.2 Hz threshold, marking a significant point. The bottom graph, depicting the total RES power output, exhibits a direct and immediate response to this frequency breach. Once the frequency exceeds 50.2 Hz, the RES power output undergoes a sharp curtailment, dropping to zero; this is the effect of the Setpoint Frequency control. This behavior strongly suggests the setpoint control mechanism designed to safeguard grid stability by curtailing renewable generation during over-frequency events. The coordinated response between grid frequency and RES output reflects a deliberate operational strategy aimed at mitigating the risks of frequency excursions, thus ensuring the system remains within secure operational limits.

Figure 9 provides a clear comparative analysis of the grid frequency behavior and total renewable energy source (RES) power output under the base case and the setpoint frequency control. This comparison presents a valuable insight into the operational differences and their implications on system stability.

In the upper graph of Figure 9, the base case exhibits a gradual decline in frequency, starting just above 50.2 Hz and tapering toward 50 Hz. While this decline suggests a natural rebalancing of generation and load within the system, the base case is marked by inherent oscillations, which could potentially destabilize the grid under certain conditions. In contrast, the 50.2 Hz setpoint control imposes a more stringent regulation, maintaining the frequency within a narrower and more controlled range near the 50.2 Hz threshold. The comparison also demonstrates a frequency swing of 0.3 Hz between both cases. unlike the base case, where the frequency is allowed to fluctuate, the setpoint control effectively mitigates these deviations, thereby ensuring a more stable frequency profile. This behavior is critical in maintaining grid reliability and avoiding over-frequency conditions that can strain system components.

In the lower graph of Figure 9, the total RES power output further illustrates the operational impact of the setpoint frequency control compared to the base case. Under the base case, RES output would likely continue to be curtailed, contributing to frequency oscillations and the risk of breaching acceptable operational limits. However, with the setpoint control active, RES output is drastically curtailed during the 30 to 40 s window, remaining close to zero. This sharp reduction in renewable power generation is a direct consequence of the setpoint control’s response to elevated frequencies, particularly as the frequency approaches the 50.2 Hz mark. This deliberate curtailment serves as a safeguard, preventing further contributions to frequency elevation from RES, which, in turn, assists in maintaining overall system stability. The coordinated response between the controlled reduction in RES power and the stabilization of grid frequency reflects the efficacy of the setpoint frequency control in managing over-frequency events.

4.3. Sensitivity Analysis

The setpoint control is applied to various frequency limits to estimate the COB and ENS if the control is applied to an electrical grid. The frequencies at which the setpoint control is tested vary from 49.5 Hz to 50.5 Hz as the nominal operation for the UK grid. See

Table 2. Results on frequency swing, ENS and COB sensitivity analysis.

Setpoint Frequency (Hz)	Frequency Swing (Hz)	ENS (kWh)	COB (GBP/kWh)
49.5	0.5	915	42.74
49.6	0.5	825	42.776
49.7	0.5	810	42.776
49.8	0.3	760	34
49.9	0.2	600	32.5
50	0.1	362	20.433
50.1	−0.3	209	14.008
50.2	−0.4	97	9.336
50.3	−0.5	22	6.2
50.4	−0.56	10	5.278
50.5	−0.6	5	5.278

for the detailed sensitivity analysis results for the setpoint control.

From Table 2, the frequency swing is constant at 49.5 Hz–49.7 Hz, which indicates the system experiences similar power exchanges, as the SC would not have been utilized, as the frequency did not go above the setpoint limit. However, from frequency 50.1 Hz to 50.5 Hz, the frequency swing increases to suppress the over-generation from RES because of the setpoint control. The effect of setpoint control is observed in that the frequency swing drops as the setpoint frequency control limit increases.

The setpoint control sensitivity analysis for the ENS gives a different perspective as to why the operational frequency band is between 49.5 Hz and 50.5 Hz. The ENS has an inverse relationship with frequency. In terms of the COB, it reduces as the setpoint frequency increases. However, the COB is constant for frequencies at 50.4 Hz and above. This is interesting, as it implies that there is a limit on the setpoint frequency control at which no benefit in terms of COB is obtained.

The sensitivity analysis for the COB indicates that the COB has a similar trend to the ENS, which indicates the direct relationship between ENS and COB. The ENS is less between 50 and 50.5 Hz, as the RES setpoint control is used less within these frequencies, as overgeneration from RES can be accommodated with the higher frequency band. In lower frequencies from 49.5 Hz to 49.9 Hz, both the ENS and COB are higher because the frequencies band is too tight, and as such, the setpoint control would be utilized to minimize frequency swing.

The comparative analysis of control strategies based on the metrics of frequency swing, ENS and COB, clearly demonstrates that the 50.5 Hz setpoint control strategy outperforms the 49.5 Hz setpoint control strategy and the base case. The 50.5 Hz setpoint control strategy exhibits a marked improvement in the frequency stability with a frequency of −0.6 Hz, which is significantly lower than the 0.6 Hz observed in the base case and the 0.5 Hz setpoint in the 49.5 Hz Setpoint Control. This indicates a superior capacity for frequency regulation, which is critical for the reliable operation of power systems, especially under high renewable energy penetration.

In relation to ENS, the 50.5 Hz Setpoint Control strategy achieves a reduction of 5 KWh in the ENS compared to 915 KWh seen in the 49.5 Hz Setpoint Control strategy scenario. The substantial decrease in ENS highlights the 50.5 Hz Setpoint Control strategy efficiency in aligning generation with demand, thereby minimizing frequency variation and enhancing system reliability. The significant reduction in the ENS underlines the strategic advantage of employing a higher setpoint control, as this method mitigates the negative impacts of supply–demand mismatch.

In terms of the COB metric, the 50.5 Hz Setpoint Control strategy is the most effective, with a COB of GBP 5.278/kWh, significantly outperforming both the base case (GBP 18/kWh) and the 49.5 Hz Setpoint Control strategy (GBP 42.74/kWh). This analysis indicates that the 50.5 Hz Setpoint Control strategy not only stabilizes system frequency more effectively but also reduces the COB of operating the microgrid. This ability to achieve lower balancing costs is a critical factor with more RES installed on the network.

Table 3. Summary of results.

Control Strategy	Difference in Frequency Swing (Hz)	ENS (kWh)	COB (GBP/kWh)
49.5 Hz Setpoint Control (Worst Case)	0.5	915	42.74
50.5 Setpoint Control (Best Case)	−0.6	5	5.278
Base Case	0.6	N/A	18

compares the worst- and best-case scenarios of the setpoint control sensitivity analysis against the base case of the microgrid considering three factors, namely the COB, frequency swing and ENS.

From Table 3, the COB is estimated at GBP 42.74 k and GBP 5.278 k for the worst- and best-case scenarios for setpoint control; subsequently, these scenarios perform better than the base case system, which did not include control of the RES but solely relied on the SG and BESS for maintaining frequency within the operational limits. The difference between the cost of balancing is attributed to the ENS not being supplied in both models; the ENS is the difference between the RES operating in MPPT and FC mode, and thus, there is a direct relationship between the ENS and COB. However, the base case model does not have an ENS magnitude, as this model does not utilize the RES for frequency control.

5. Conclusions and Recommendations

This research presents the need to highlight a growing problem with RES integration from both the power system stability and economic perspectives. The cost of balancing the grid while considering generation management as an alternative method with DSR is investigated to improve the system stability. To achieve the results, a mathematical model for COB, ENS and network frequency is implemented on an LFC simulation model using setpoint control to consider these variables.

The relationship between setpoint frequency, Energy Not Supplied (ENS), cost of balancing (COB), and frequency swing (an indicator of the Rate of Change of Frequency, ROCOF) provides critical insights into optimizing power system performance, especially with high integration of Renewable Energy Sources (RES). The innovative aspect of this research lies in the strategic adjustment of setpoint frequencies and the dynamic switching between Maximum Power Point Tracking (MPPT) and modes—a method that extends beyond traditional approaches found in the existing literature.

From the case study results, the higher setpoint frequencies facilitate better accommodation of RES overgeneration, resulting in lower ENS and COB. Specifically, as the setpoint frequency increases from 49.5 Hz to 50.5 Hz, ENS decreases significantly, and COB reduces correspondingly. Additionally, the frequency swing decreases at higher setpoint frequencies, indicating improved frequency stability and reduced ROCOF.

In principle, the network balancing cost is influenced by the magnitude and duration of frequency deviations, the costs associated with using SG, BESS and RES for energy transactions during balancing actions. In the case study, the period of the balancing cost is a 60 s simulation duration, capturing the dynamic interactions between RES variability, demand fluctuations, and frequency control actions. The sensitivity analysis for the proposed setpoint control reveals that the setpoint frequency also influences the cost of balancing and it could significantly reduce the COB, as demonstrated in Section 4.3.

This demonstrates that the innovative control strategy not only enhances economic outcomes but also strengthens system stability. The setpoint control strategy with frequency limit of 50.5 Hz demonstrates the best performance in terms of the COB while maintaining low-frequency swing and minimal ENS cost, making it the preferred choice for frequency management and cost-effective grid operation compared to the traditional model. By significantly enhancing frequency stability, reducing ENS, and minimizing COB, this strategy offers a robust solution for modern power systems challenged by the need for efficient integration of renewable energy sources and maintenance of grid stability. Our simulation results demonstrate that our proposed method offers significant enhancements over traditional LFC approaches. For instance, Figure 2 and Figure 3 show a reduction in frequency overshoot and a faster return to nominal frequency compared to the base scenario. This indicates improved system resilience and effectiveness of our control strategy. Finally, all the COB, ENS and frequency metrics for the setpoint control compared to the base scenario are detailed in Table 3.

Future work should explore the scalability of this approach for real-world power grids with further economic evaluation and grid conditions and its integration with other grid management technologies to further enhance system resilience and operational efficiency. This work can also be further expanded to consider other factors such as the State of Charge for hybrid energy storage systems, and subsequently the use of machine learning to ensure that the best control strategy is utilized to achieve the lowest cost of balancing based on RES prediction.