
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12958-1
10.1016/j.heliyon.2024.e36927
e36927
Research Article
A comprehensive study on energy management, sensitivity analysis, and inertia compliance of feed-in tariff in IEEE bus systems with grid-connected renewable energy sources
Behera Sadasiva sadasiva.behera@miet.ac.in
a
Das Sumana dassumana12@gmail.com
b
Ganesh Pardhu B.S.S. pardhu4all@gmail.com
c
Vais Ram Ishwar ramismdhanbad@gmail.com
d
Babu Naladi Ram rambabu.nits@yahoo.com
c⁎⁎
Bhagat Sanjeev Kumar sksanju1070@gmail.com
e
Alharbi Mohammed mohalharbi@ksu.edu.sa
f
Mbasso Wulfran Fendzi fendzi.wulfran@yahoo.fr
g⁎
a Department of Electrical Engineering, Meerut Institute of Engineering and Technology, Meerut, India, 250005
b Department of Electrical and Electronics Engineering, MLR Institute of Technology, Dundigal, Hyderabad, India, 500043
c Department of Electrical and Electronics Engineering, Aditya University, Surampalem, East Godavari, Andhra Pradesh, India, 533437
d Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, UP, India
e Department of Electrical Engineering, Sandip University, Sijoul, Madhubani, Bihar, India, 847235
f Department of Electrical Engineering, College of Engineering, King Saud University, Riyadh, 11421, Saudi Arabia
g Laboratory of Technology and Applied Sciences, University Institute of Technology, University of Douala, PO Box: 8698, Douala, Cameroon
⁎ Corresponding author. fendzi.wulfran@yahoo.fr
⁎⁎ Corresponding author. rambabu.nits@yahoo.com
26 8 2024
15 9 2024
26 8 2024
10 17 e3692711 4 2024
15 8 2024
24 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
The need to incorporate renewable energy generators (REGs) into the electrical grid has become increasingly crucial due to the push for a more sustainable environment. This study advocates an innovative strategy for optimizing inertia-integrated generation and transmission expansion planning (GTEP) to implement feed-in tariffs (FiT). The application of the GAMS CPLEX solver to the model, which tested on an IEEE 6/IEEE 16 system, reveals that using FiT results in a 12.1 % drop in system cost ($599 million to $526 million) and a 7.91 % rise in total system inertia. Sensitivity analysis highlights the correlation between increased REG integration and FiT payment reduction at 50 % penetration. The model outperforms soft computing optimization techniques, showcasing rapid convergence and computational efficiency. The proposed model's validated superiority in rapid convergence and computational efficiency is demonstrated by comparing its results with those obtained from other soft computing optimization techniques.

Keywords

Energy management
Emission reduction
Energy consumption
Feed-in tariff
Renewable energy generators
CPLEX solver
==== Body
pmc1 Introduction

Renewable energy sources (RES) are increasingly used since fossil fuels are becoming more harmful daily [1]. So, according to the Paris proposal, it targets net zero carbon emissions by 2050 [2]. By 2030, renewable energy generators (REGs) will make up 60 % of the grid in certain countries [3]. However, according to the International Energy Agency (IEA), wind power is approximately reaching (8020 TWh) and solar power is (7000 TWh), which covers 2030 [4]. However, FiTs, like other existing related Renewable Portfolio Standards (RPSs) tariffs, Renewable Energy Certificates (RECs), Renewable Electricity Production Tax Credits (RETCs), Investment Tax Credits (ITCs), Residential Energy Credits (RECs), and Tradable Green Certificates (TGCs), etc. are approved nationwide to promote RES development and help meet the high-RES target [5]. Fig. 1 shows the various FiT systems grouped by methodology and electricity market structure. China, Japan, the USA, the UK, Italy, Thailand, Iran, Malaysia, and Germany have successfully implemented comparable economic incentive systems. One of the best method-based RES incentives is the FiT. It assures a long-term price per kWh for REs-produced electricity, relieving investors and fostering sustainable REs growth [6]. Thus, acceptable FiT rates provide adequate returns to attract RES technology investors [7]. The most common is the market-independent fixed price FiT model, whose price depends on the REs technology's infrastructure cost. When converter based REGs replace synchronous generators (SGs), system inertia decreases. During system contingency, the grid's instability makes it more sensitive to frequency issues [8]. The rapid rate of change of frequency (RoCoF) and nadir frequency are most used in RES systems to perform stability. Furthermore, these ideas have drawbacks regarding the limited renewable energy generation (REG) adoption. To overcome this, it is suggested to utilize fast-dynamic-responding energy storage systems (ESSs), hybrid fast-dynamic-responding energy storage systems (HESS), and REGs with a converter scheme. This approach aims to tackle the frequency stability problems faced by low-inertia power grids [9] and power management. Several countries like Australia, Ireland, Great Britain, and the Nordic countries have imposed limitations on minimum inertia limitation for RoCoF in RES penetration [10,11]. So far, RE investors and sustaining grid inertia to promote RE technology advancement are crucial. Generation, transmission, GEP/TEP, and combined expansion planning (GTEP) studies exist. This power system planning methods make the network bigger to handle more energy use and technical problems with the grid. Few growth planning models consider system inertia. Such developed grid inertia and CO2 emission will generate a very low-carbon expansion planning model [12]. New generators were introduced in the model without transmission expansion plans. Model planning excluded incentives. The incorporation of power with natural gas systems was GTEP by Ref. [13] using decreased system frequency restrictions. Planning power system expansion for inertia demands specialized equipment. This study didn't examine the effects of economic incentive schemes on planning (see Fig. 2).Fig. 1 Functions of smart EMS.

Fig. 1

Fig. 2 FiT classifications.

Fig. 2

These power systems, GEP, TEP, and GEP/TEP planning models, enlarge the network for rising energy demand and grid challenges. Few expansion models have inertia [14], which created grid inertia and CO2 emission-based low-carbon producing expansion models. Planning model errors stem from ignoring inertia and CO2 emissions. The model lacks transmission expansion plans after adding generators. Model planning lacks incentives. GTEP was done on a low-frequency integrated power and natural gas system. Inertia planning requires unique equipment. This research didn't analyze the planning consequences of economic incentive schemes.

Renewable energy incentives receive more attention in studies than power system growth planning models' economic incentives [15]. However, the FiT's impact on Chinese PV power output was studied. They found FiT boosts PV investment. The model's expanded planning excluded inertia and emission. GTEP model [16] minimizes system cost and CO2 emissions while boosting FiT. Which can increase REG energy usage and reduce CO2 emissions, but the grid inertia didn't increase FiT in this model. However, we have summarized the aforementioned articles in a tabular format for enhanced clarity in Table 1.Table 1 Past research information on FiT objectives, along with the outcomes and future scope of each article.

Table 1Ref.	Outcomes	Future Scopes	
[4]	The presents a charging navigation strategy for electric vehicles that optimizes charging times based on time-of-use pricing, reducing costs for users.	Further research could explore integrating real-time traffic data and renewable energy sources to enhance the efficiency and sustainability of the charging navigation system.	
[5]	The study finds that the feed-in tariff policy significantly reduces the curtailment of wind power in China.	It could investigate the long-term economic impacts of feed-in tariffs and their integration with other renewable energy policies.	
[6]	It demonstrates that a centralized energy management system for isolated microgrids improves operational efficiency and reliability by using feed-in tariff policy.	Future scope can explore the integration of advanced forecasting techniques and adaptive control strategies to further enhance the performance of centralized energy management systems.	
[8]	It reveals that reductions in feed-in tariffs and the implementation of renewable portfolio standards significantly influence the growth of distributed photovoltaic generation in China.	Future research may examine the combined effects of various policy measures and technological advancements on the long-term sustainability and scalability of distributed photovoltaic systems.	
[9]	The study evaluates different feed-in tariff models for photovoltaic systems in Thailand, providing insights into their effectiveness based on empirical evidence.	Further such objectives can focus on optimizing feed-in tariff structures and incorporating market dynamics to enhance the adoption and efficiency of photovoltaic systems in Thailand.	
[10]	It explores the effectiveness of payback-year based feed-in tariff mechanisms in Australia, finding that they can significantly accelerate the payback period for renewable energy investments.	Future research could investigate the long-term impacts of these mechanisms on market stability and renewable energy adoption rates, as well as their applicability in different regional contexts.	
[11]	It provides an overview of the challenges associated with inertia requirements in modern grids powered by renewable energy sources, highlighting the need for improved grid stability.	By developing advanced control strategies and storage solutions to enhance grid inertia and ensure reliable integration of renewable energy sources cab be applicable for future study.	
[12]	It review provides an updated overview of current solutions and emerging challenges in power system frequency control, highlighting advancements and areas needing improvement.	Further investigate novel control methodologies and technologies to address the increasing complexity and dynamic behavior of modern power systems, especially with high renewable energy integration.	
[13]	The study highlights that fast-acting reserves can effectively augment system inertia in power systems with high penetration of wind power, enhancing grid stability.	Future research could explore the integration of various fast-acting reserve technologies and their economic feasibility in different power system configurations.	
[14]	Authors presented the impact of increasing renewable energy integration on system rotational inertia in the European power system, identifying potential stability challenges.	Future research could focus on developing strategies and technologies to mitigate the negative effects on rotational inertia, ensuring stable and reliable grid operation amidst growing renewable energy penetration.	
[15]	It assesses how inertia and reactive power constraints influence generation expansion planning, highlighting their critical role in ensuring grid reliability and stability.	May explore integrated planning approaches that optimize generation expansion while considering inertia and reactive power requirements to support increased renewable energy integration.	
[16]	The study presents a stochastic planning approach for integrating power and natural gas networks, incorporating simplified system frequency constraints to enhance operational reliability.	It could investigate more advanced modeling techniques and real-time data integration to further refine the accuracy and robustness of integrated energy network planning under stochastic conditions.	
[17]	New evidence on how feed-in-tariff subsidies influence renewable energy investments in China at the firm level, highlighting their impact on market dynamics.	Further investigation could delve into the long-term sustainability of feed-in-tariff policies and their interaction with other regulatory mechanisms to optimize renewable energy investment strategies in China.	
[18]	Developed a software program to determine the open-circuit voltage and fill factor of photovoltaic cells based on the one-diode equivalent circuit model.	The program could be adapted to assess the impact of feed-in tariff (FiT) policies on the economic performance and efficiency of photovoltaic systems.	

The authors are unaware of any GTEP optimization models that account for FiT and grid inertia application point of view. Very few articles are found. This study recommends using a FiT inertia integrated GTEP model to boost RES development and grid frequency stability. GTEP's system inertia and FiT combination distinguish it from new energy management system model models, which are shown in Table 2. Common important features of FiT tariffs in the recently published articles are shown in Table 3. The mathematical programming-based optimization approach provides quick convergence to the global optimal solution with reduced processing time, improved stability, and accurate results obtained by this FiT approach.Table 2 Common important features of FiT tariffs in the recently published articles.

Table 2	New features	Applications	
FiT [[1], [2], [3], [4], [5], [6], [7]]	• This approach is suited for unreliable solar or wind power production. It manages frequency or voltage fluctuations to fulfill environmental regulations and accommodate electric vehicle usage's unpredictable patterns.

• Compatible with EVCSs near wind farms, solar farms, or high-traffic regions.

• This tariff mechanism helps the power system address the problems of variable power production from wind and solar energy.

• It indicates the de-carbonization of the transportation and energy sectors.

• It enables the use of the fluctuating nature of renewable energy through Vehicle-to-home (V2H).

	• Electric vehicle charging stations (EVCS) and electric vehicles (EVs) encourage the de-carbonization of the power and transportation sectors by increasing the use of renewable energy.

• EVs and EVCSs solve renewable energy integration issues.

	

Table 3 Evaluation of the proposed model about multiple power system models that have been reviewed.

Table 3Ref.	Analysis of the system- inertia	FiT analysis	Consideration of the CO2 emission	TEP considerations	GEP considerations	GTEP considerations	
[11]	×	✓	×	×	×	×	
[19]	✓	×	✓	✓	✓	✓	
[20]	✓	×	×	✓	✓	✓	
[21]	×	×	✓	✓	✓	✓	
[22]	×	×	✓	✓	✓	✓	
[23]	×	✓	✓	✓	✓	✓	
[24]	×	×	✓	✓	✓	✓	
[25]	×	×	×	✓	×	×	
[26]	×	✓	×	✓	✓	✓	
[17]	×	✓	×	✓	✓	✓	
Proposed article	✓	✓	✓	✓	✓	✓	
✓: considered ⨯: Not-considered.

The novelties of the article are as follows:• To develop a FiT incentives-based inertia combined generating and transmission expansion model.

• Analyze the impact of including system inertia and FiT in GTEP decision-making while considering the financial and environmental implications.

• Compare these outcomes to a fictitious situation in which these elements are not considered.

• To assess the upshot of FiT spurs on the cohesive GTEP model under diverse levels of REG penetration and examine the correlation between RES penetration and system inertia.

The subsequent sections of the paper follow the same organization as Section 2, which deals with the precise mode of the cohesive FiT with inertia GTEP. The implementation and developed simulation models are described in Section 3. The results and discussion are described in Section 4. Analysis of the dynamic behavior of the studied model is presented in section 5. Section 6 examines the proposed Sensitivity Analysis and Result Discussion. Section 7 presents the study's conclusion along with suggestions for future research.

2 Mathematical formulation of a GTEP model that incorporates both FiT and inertia

This research presents a unique model of the GTEP system that includes inertia and a Feed-in Tariff (FiT) mechanism. The CPLEX solver in GAMS software is described as a mixed integer quadratic constrained programming (MIQCP) model. The model's main goal is to reduce the system's total cost, reduce CO2 emissions, enhance FiT incentives for renewable energy, and improve system inertia for technical stability. It describes the integrated model formulation, and Fig. 1 depicts the flowchart of the proposed GTEP model steps. Table 3 comprehensively compares other relevant works, considering various constraints.

2.1 Formulation of the system inertia objectives

Power grid stability and resilience depend on system inertia. The term “inertia” pertains to the rotational energy that is stored within the rotor of synchronous generators (SGs). This energy helps to maintain system frequency stability, particularly during unexpected events or contingencies [8]. Thus, this subsection's issue aims at system inertia maximization. So, the expression for the maximum inertia function is given as in Eq. (1) [19].(1) Max(H)=(∑i=1NHi.Si+∑Hes=1NHesHhes.Shes.λ1hes+∑j=1NjHj.Sj.λ2j+∑k=1NkHk.Sk.λ3k∑i=1NSi+∑Hes=1NHesShes.β1hes+∑j=1NjSj.β2j+∑k=1NkSk.β3k)

where Hi, Hhes,Hj, Hk are the inertial constants of the different generators, howeverthe generators' apparent power is being referred to Si, Shes,Sj, Sk, and N, NHes, Nj, Nk are the number of generators respectively. λ1hes, .λ2j, λ3k, β1hes, and β3k decide the potential of HES, solar PV and wind turbine respectively with the help of binary decision variables.

2.2 Proposed mathematical modeling

The model also reduces system operating cost, the system cost includes operating, asset, and economic incentive costs. Operational costs include thermal generator fuel, wind turbine O&M, and thermal generator pollutants. The investment cost includes purchasing and installing new solar power plants, wind turbines, HES, and conduction lines. In contrast, the government's entire FiT cost on renewable energy providers' electricity is the monetary incentive price. This model's incentive is a fixed FiT scheme. Eq. (3) states that one issue aim is to minimize the model's overall system cost and maximize the FiT incentive.

2.3 Formulation of environmental (CO2) objective

In this proposed methodology, minimizing CO2 emissions to the lowest possible level is a primary concern, as detail describe in Eq. (2), which gives the mathematical formulation of environmental (CO2) emission objective.(2) Min(CO2)=min({α∑i=1NeiCO2(Pi)})︷CO2emissions∀i∈I

in this unique objective function, the power output of thermal generators (Pi) is the key decision variable, acting as a throttle for CO2 emissions. By adjusting the power output, we can precisely regulate the amount of emissions released into the atmosphere.

2.4 Formulation of a proposed model that considers multiple objectives

According to Eq. (1), the GTEP becomes a multi-objective problem when inertia and FiT are added and the proposed objective is described in Eq. (2). However this issue is expressed in details mathematically as in Eq. (3). Moreover the resultant multi-objective issue maximizes system inertia while minimizing economic expense and carbon dioxide emissions (technical objective). Eq. (4) illustrates the process of converting a multi-objective problem into a single objective function using the weighted-sum method, whereby the relative importance of each goal is determined by multiplying it by an equal factor. Objectivity requires a system of weights to rank the relative importance of its many goals. This research uses uniform weighting parameters to avoid favoring one goal function over another. In this study, we utilize Eq. (5) [22], to assign a weight of 0.33 to each objective function due to the fact that there are three of them.(3) Min(Cost)=min[α[∑i=1N[ai(Pi)2+bi(Pi)+ci]+[∑iNλiCO2⋅eiCO2(Pi)]+∑jNjCOjom(Pj)⋅λ2j]⏟operationalcost+∑HesNHesCOhesinv⋅λ1hes+∑jNjCOjinv⋅λ2j+∑kNkCOkinv⋅λ3k+∑clNcCOclinv⋅λ4cl⏟investmentcost+max{∑t=1t=α[∑j=1j=NjPjmax⋅CFj⋅FiTj⋅λ2j+∑k=1k=NkPkmax⋅CFk⋅FiTk⋅λ3k]⏟Economicincentive}]

where ai,bi,ci are the coefficients mentioned in Ref. [21] are utilized to express the thermal generators' fuel cost ($/hr) as a quadratic function of their producing power, Pi [20]. The emission cost is determined by the product of the carbon tax λiCO2 ($/tonCO2), emission factor eiCO2 (tonCO2/kWh), and the power from thermal unit is expressed as (kWh), the maintenance, operating cost of wind power generation is expressed as in dollars. Where, the maintenance costs COjom ($/kWh), and the active power (Pj) of the wind turbine. COhesinv,COjinv,COkinv, and COclinv are the HES potential. Whereas λ1Hes,λ2j,λ3k,λ4cl are helps to take the decision in order to invest in various power generation resources.

When selecting this specific technology for installation, the decision variable is assigned a value of 1, and 0 otherwise. The decision variables stand in for the power production of wind turbines and thermal generators Pi and Pj respectively. During the planned horizon, this is the highest possible number of potential transmission lines that can be built. That represents the fixed FiTj and FiTk incentives rate in $/kWh and denotes the rates to find the precise outcomes of the power of a solar PV plant and a wind turbine, respectively. Moreover, the Pjmax (wind turbine) and Pkmax (solar PV) maximum capacity. For both plant capacity factor is assigned by as CFj and, CFk respectively. The cumulative yearly operational duration of the power generation units are measured in hours. Hence, the study utilizes FiT incentive of 0.00240 US $/kWh for wind turbines and 0.00750 US $/kWh for solar PV systems.

2.5 Proposed model constraints

2.5.1 Constraints on FiT incentives

Feed-in Tariff (FiT) rates must be appealing, offering a substantial return on investment without putting an excessive financial strain on the government. Hence, the constraints on FiT utilized in the model [23] are defined by Eqs. (6), (7). Eq. (6) provides a definition for the total annual Feed-in Tariff (FiT) payment received for generating electricity from Renewable Energy Generators (REGs). This payment is determined by the FiT rate per technology (expressed in dollars per kilowatt-hour. The capacity factor of Renewable Energy (RE) generators and the capacity of each technology are expressed in kilowatts. According to equation (7), the total yearly Feed-in Tariff (FiT) incentive payment made to investors in renewable energy cannot exceed the budget allocated for renewable energy. The budget cap is the highest monetary limit BUres established for the acquisition of new RE generators.(4) TFiTtotal=∑t=1t=α[∑j=1NjPjmax(t)⋅CFj⋅FiTj(t)⋅λ2j+∑k=1k=NkPkmax(t)⋅CFk⋅FiTk(t)⋅λ3k]

(5) TFiT≤BUres

2.5.2 Constraint on power equilibrium

In this contest, the power equilibrium in Eq. (6) provides the power balance constraint for the model, which is derived from Kirchhoff's current law. According to the statement, the combined power output of the thermal generator, the potential of HES, solar PV plants, wind power, and the overall load demand must be met or exceeded by the net electricity flowing via current and future transmission lines [24] at any given node. PFijext+, PFijext− is The real or active power flow that enters and leaves the existing transmission line. PFijcl+, PFijcl− is The active power entering and exiting the identified conduction lines, and total load demand (LODi) is the at bus.(6) ∑gnPg+∑hesnhesPhes⋅μ1hes+∑wnwPw⋅μ2w+∑snsPs⋅μ3s+∑l∈rlPFijext+−∑l∈slPFijext−+∑l∈rlPFijcl+⋅μ4cl−∑l∈slPFijcl−⋅μ4cl≥∑iLODi

∵∀g∈G,∀s∈S,∀w∈W,∀hes∈HES,∀cl∈CL,∀ext∈EXT,∀rl∈RL,∀i∈I

2.5.3 Constraint on power flow

Power flow limitations are established via equation (7) through [16] using Kirchhoff's voltage law's DC approximation. These formulas are used to control power transmission for both the current system, which includes the lines that are currently in place, and any future extensions that may be necessary [25]. However, PFmaxext, PFij,maxcl are represent the upper limits of power flow in the current transmission lines (TL) and potential candidate lines, respectively. Bijext, Bijcl represents the bus susceptance of lines connected among ith and jth, respectively. θirl, θisl, θircl, θiscl represents angles corresponding to voltage form sending to receiving ends transmission line. Moreover, it θi represents the angle associated with voltage at the specified bus.(7) −PFmaxext≤PFijext≤PFmaxext∀ext∈EXT

(8) −μ4cl⋅PFij,maxcl≤PFijcl≤μ4cl⋅PFij,maxcl∀cl∈CL

(9) PFijext=Bijext(θisl−θjrl)∀ext∈EXT

(10) −(1−μ4cl)M≤PFijcl−Bijcl(θiscl−θjrcl)≤M(1−μ4cl)∀i∈I,∀cl∈CL

(11) −π4≤θi≤π4∀i∈I

(12) μ4cl∈[0,1]∀cl∈CL

(13) ∑clμ4cl≤nc∀cl∈CL

Eq. (9) determines the maximum power flow allowed on current transmission lines, while Eq. (10) specifies the maximum power flow permitted on potential transmission lines. The equation for DC power flow on existing transmission lines, outlined in Eq. (11), describes the susceptance and the voltage angles for both ends of the line. Newly built transmission lines, which include the Big-M variables, have their DC power flow Eq. described by Eq. (12).). However, M encompasses every conceivable value since it is a huge integer. No voltage angle greater than the one specified by Eq. (13) should be allowed on the bus. The decision variable that is used to decide whether a new line is to be added is defined by Eq. (14) and is 1 if the line is to be built and 0 otherwise. A maximum of one hundred candidate TL may be built within the planning horizon, according to Eq. (15).

2.5.4 Constrained and limitations on power generation

Eq. (16) through [23] govern the operational aspects of existing and potential renewable energy generators. Eq. (16) sets the maximum power output for existing thermal generators, while Eqs. (17), (18) determine the allowable production capacities for potential wind turbines and solar PV facilities, respectively. So far, Eq. (19) presents a binary decision variable determining the choice of potential wind turbines and solar PV facilities, considering their maximum power ratings and capacity factors, which reflect the intermittent characteristics of renewable energy sources. Since, Eq. (20) prevents concurrent investment in both solar PV facilities and wind turbines by establishing a binary investment decision for each bus. Equations (21), (22) place restrictions on the total number of PV units and wind turbines that can be built throughout the planning horizon.(14) Pgmin≤Pg≤Pgmax∀g∈G

(15) 0≤Pw≤Pwmax.CFw∀w∈W

(16) 0≤Ps≤Psmax⋅CFs∀s∈S

(17) μ2w,μ3s∈[0,1]∀w,s

(18) μ3w+μ4s≤1

(19) ∑wμ2w≤nw

(20) ∑sμ3s≤ns

2.5.5 Limitation of HES

When it comes to inertia response, conventional power systems rely entirely on the kinetic energy that SGs' rotors emit. But with the right virtual inertia controllers, HES can also respond to inertia and main frequency in today's power systems. However, in order for the current power grid to be stable, it is necessary to carefully choose and appropriate size HES [27,28]. A combination of high-power super capacitor energy storage (SCES) and high-energy batteries is employed to give the required main frequency response and inertial response. According to [29], Eq. (23)–(30) characterizes the functioning of the HES.(21) PRmin≥k⋅∑iLODi

(22) ∑hesnhesPhes≥PRmin

(23) Phesmin≤Phes≤Phesmax

(24) Phes=ηv⋅Pv+ηsces⋅Psces

(25) Pv≥z⋅Phes

(26) ∑hesnhesz⋅Phes≥[Khes.fo]×[ΔPOF]

(27) ∑hesnhesz⋅Phes≤q.[Khes.fo]×[ΔPOF]

(29) SChesmin≤SChes≤SChesmax

(30) μ1hes∈[0,1]∀hes∈HES

The power system's principal frequency response, as defined by Eq. (23), should be at least 5 % of should ideally be at least 5 % of the entire load demand at the bus, and preferably more. According to Eq. (24), the combined power capacity of all potential HESs must be more than or equal to the main reserve minimum. Eq. (25) sets upper and lower bounds on the power that HES can supply. If we add together the electricity from the BES and the SCES sources, we get the total power provided by the HES, as stated in Eq. (26). As per Equation (27), 80 % of the overall capacity of the Hybrid Energy System (HES) must be allocated to Battery Energy Storage (BES) within the HES configuration. Eq. (28) delineates the lowest capacity necessary for BES within the HES composite to prevent storage capacity overflow, factoring in the power-frequency characteristics of the model. However, Eq. (29) establishes the maximum BES capacity required within the HES composite to avoid excessive storage. Moreover, Eq. (30) imposes constraints on the states of charge for potential HES units. But Eq. (31) introduces a binary decision variable determining whether a new HES is to be installed at a specific bus; a value of 1 denotes selection, while 0 signifies non-selection.

2.5.6 Constraint on the flexibility of renewable energy sources

Eqs (32), (33), (34) provide restrictions on the integration of RES into the power grid, ensuring that it remains within a predetermined limit in accordance with the renewable energy (RE) goal set by the suggested model [12]. The desired levels for the penetration of RES are set at 25 %, 50 %, 75 %, and 100 %. Eq. (32) imposes limitations on the overall power production from RES by using a versatile parameter f, expressed as a proportion of the entire load need. Eq. (33) restricts the maximum power output from thermal generators, which cannot exceed (1- f) percent of the total load demand. This requirement ensures that f percent of the power production comes from renewable energy sources [12,30]. Eq. (34) establishes the permissible values for the variable parameter, f, in order to restrict the amount of RE source penetration within the range of 25 %–100 % of the overall load demand.(31) [∑s=1nsPs⋅μ3s+∑w=1nwPw⋅μ2w]≤f⋅[∑iLODi]

(32) [∑g=1nPg]≤(1−f)⋅[∑iLODi]

(33) f∈[0.25,0.5,0.75,1]

2.5.7 Limitation of inertia

Inertia plays a crucial role in preserving the stability of the power system after a transitory incident. It is crucial to make sure that the virtual inertia energy from RE generators and storage units can equal the kinetic energy provided by the decommissioned synchronous generators (SGs) to replace the current SGs with these virtual inertia-providing units and storage units [11]. The suggested model ensures frequency stability by the inertia constraint formulation, which is given by Eqs (35), (36), (37), (38), (39), (40), [31]. Eq. (35) provides the defined limit for the total system inertia constant, as stated in [8]. Eq. (36) restricts the frequency of the system to a permissible limit according to the grid code of South Africa [32]. The system's RoCoF is limited by Eq. (37) to a reasonable range. The above perturbation data constrained analyses [33], which contain all of in Eq. (38). Likewise, Eq. (39) accurately calculates the total inertia energy produced by all wind turbines, solar photovoltaic plants, and hybrid energy systems (HES) that are currently in operation. Eq. (40) states that the overall inertia energy produced by the hybrid energy system (HES) and all online renewable energy sources must exceed or equal the minimum threshold of inertia energy set. As per Eq. (41), to reimburse for the discrepancy in kinetic energy, the cumulative inertia energy derived from the HES must exceed or equal the rotational energy dissipated by the heat generator(s) during a contingency event. The model stipulates 49 Hz as the minimum permissible frequency [34].(34) Hmin≤H≤Hmax∀g∈G,∀s∈S,∀p∈P,∀w∈W,∀v∈V

(35) frmin≤fr≤frmax∀g∈G,∀s∈S,∀p∈P,∀w∈W,∀v∈V

(36) −RoCoFmax≤RoCoF≤RoCoFmax

(37) IEmin=ΔP⋅fo2⋅RoCoFvmax+ΔP⋅Hgl

(38) IEhes,w,s=∑s=1nsHsSs+∑w=1nwHwSw+∑hes=1nhesHhesShes

(39) IEhes,w,s≥IEmin

(40) ∑hesHhes⋅Shes≥ΔP⋅Hgl

3 Implementing and simulating models implementation

The suggested model is applied to an IEEE 6-bus system for efficacy evaluation, followed by model validation through various case studies. Both solar photovoltaic (PV) and wind turbines are considered, categorized as Class I and Class II, as potential installation options. Class II PV plants and Class II wind turbines are anticipated to be capable of providing virtual inertia, while Class I PV plants and Class I wind turbines lack this capability. Additionally, it is presumed that the demand for each bus will rise by 50 % to meet growing power demands and facilitate financing for new transmission lines (TL) and renewable energy generation units. Concurrently, the determined capacity of every conduction line is halved from its early construction capacity (see Fig. 3).

3.1 Implementation of the IEEE 6-bus system

The IEEE 6-bus test setup used for model validation is shown in Fig. 4. The system consists of four load points, six TL that are now in use, ten TL that are planned, four Hydroelectric Systems (HES), four possible wind turbines, and four possible solar PV plants. Two TL per corridor are allowed, and Big-M is set to 103. Under consideration are 100 MW Renewable Energy Generators (REGs) for buses 2 and 5, which have the greatest load demand. Due to variable renewable energy sources, 50 MW Hybrid Energy Systems (HES) at buses 2 and 5 are considered. Table 4 lists the study's system data, including a mean load demand of 1140 MW [35] despite a cumulative thermal production capacity of 1400 MW. Additional system data is provided [[17], [18], [26], [36], [37], [38]], and Bus 1 is slack. The IEEE-16 bus test system may be analyzed similarly.Fig. 3 Comparing the REG outcomes in 2020 with the predicted future REGs by 2030.

Fig. 3

Fig. 4 Flowchart for standard procedure.

Fig. 4

Table 4 Aggregate inertia over many case studies.

Table 4Case study	System inertia constant [s]	Total inertia energy [MWs]	
Synchronous inertia	Virtual inertia	Total inertia	
Case-1	5.681	8500.0	1400.0	9900.00	
Case-2	5.566	8500.0	1200.0	9700.00	
Case-3	6.140	8500.0	2200.0	10700.0	

4 Simulation results and analysis

The outcomes of the simulated model will be discussed and studied here.

4.1 Consideration of the System's inertia

The total system inertia for the various case studies is shown in Table 4. With a total inertia constant of 6.139s—or 10,700 MWs in inertia energy—Case Study 3 has the highest value. With a constant of 5.565 s and associated inertia energy of 9700 MWs, case study 2, on the other hand, exhibits the lowest total system inertia. The incorporation of inertia into the model formulation leads to an increase in inertia energy in case study 3, which impacts investment decisions. Cases 1 and 2, on the other hand, have lower inertia energies since inertia is not taken into account during the planning stage.

4.2 Decisions on system costs and investments

Table 5 shows the cost analysis and expansion plans for additional HES, transmission lines, and REGs for each study instance. Case 1 has the highest investment and system cost, whereas case 3 has the lowest. Investment choices in both scenarios explain the cost discrepancy. Case 3 had an 11.94 % and 8.86 % drop in system cost and a 44.9 % and 38 % decrease in investment cost compared to examples 1 and 2. However, scenario 2 had the greatest yearly FiT payment since solar PV facilities had higher FiT rates than wind turbines, as in cases 1 and 3. The FiT effectively influences scheduling choices. Due to FiT inducements and the optimum choice to invest in fewer TL (3 lines) than case 1 (6 lines) and case 2, case 3 had the lowest overall system cost (5 transmission lines).Table 5 Thorough evaluation of expenses and investment choices in various research scenarios.

Table 5Metrics	Study cases	
Case study1	Case study 2	Case study 3	
How Much fuel cost required [$]	1.78131E+08	1.67839E+08	1.7747E+08	
Estimated wind power plant [$]	9.29206E+06	–	9.3206E+06	
Emission cost [$]	2.39342E+08	2.39342E+08	2.4432E+08	
Overall expense [$]	4.194E+08	4.191E+08	4.31E+08	
The overall expense of the investment [$]	1.75E+08	1.58E+08	9.64E+07	
Earned FiT total (including PV and wind turbine) [$]	–	3.29E+06	1.5978E+6	
Total cost [$]	5.99E+08	5.76E+08	5.26E+08	
Record of wind turbine investments	2 [WT1, WT3]	–	2 [WT2, WT4]	
The sum of all investments in solar PV	–	2 [S3, S4]	–	
Total number of investments on HES	2	2	2	
Funding for transmission cables	(2–6) (×2)
(3–5) (×2)
(4–6) (×2)	(4–6) (×2)
(2–6) (×2)
(3–5)	(4–6)
(3–5)
(2–6)	

4.3 Variation in generation capacity and CO2 emissions

After planning, CO2 emissions and capacity mix for each producing technology are shown below. Table 6 shows thermal generator CO2 emissions and capacity mix for each research instance. Table 6 shows that instance 3 emits 2.2 % less CO2 than case study 2. The integrated model that included FiT (cost), system inertia and emission reduce CO2 emissions by 0.226 million tons. Because wind turbines have a larger capacity factor than solar PV facilities, scenario 3 has the largest producing capacity. Case 2 has the largest thermal generator CO2 emissions compared to case studies 1 and 3. However, for the variation in generation capacity and CO2 emissions, whereas in Fig. 5 illustrates the IEEE 6-bus test system schematic is shown, with blue dashed lines representing transmission lines, candidate HES, and REGs (see Table 7).Table 6 Variation in CO₂ emissions and generating capacity across all cases.

Table 6Identities	Study cases	
Case 1	Case 2	Case 3	
Total CO2 emissions [tonsCO2]	9.7367E+6	0.9999E+7	9.7729E+6	
The sum of all thermal generator output powers [MW]	963.9	989.9	967.5	
Total electricity produced through wind power plant [MW]	76	–	76	
Output power from PV systems [MW]	–	50	–	
Total power generation [MW]	1039.9	1039.9	1043.5	

Table 7 Frequency response dynamics under contingency conditions for the various situations investigated.

Table 7Case study	System inertia [s]	Drop in frequency	Nadir frequency range	
Case-1	5.5980	1.0478	48.9623	
Case-2	5.4965	1.0605	48.9496	
Case-3	6.0941	0.9978	49.0012	

Fig. 5 The IEEE 6-bus test system schematic is shown, with blue dashed lines representing transmission lines, candidate HES, and REGs. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5

5 Analysis of the dynamic frequency response of the model

The dynamic behavior of the frequency response is analyzed for every research scenario. An examination has been conducted after the failure of the largest 600 MW synchronous generator. Table 5 displays the system frequency variation caused by disturbances in several study scenarios. In instances 1 and 2, where system inertia was not accounted for in the proposed model, the frequency nadir was found to be 47.9396 Hz and 48.9523 Hz, respectively. The frequency of nadir readings falls below the permissible limit set by the research. When system inertia is taken into account in scenario 3, the lowest frequency, known as the frequency nadir, is 49.002 Hz. This value is within the allowed frequency range. Therefore, the model improves the existing grid's ability to withstand and recover from disruptions.

6 The proposed sensitivity analysis and result discussion

By applying various RES penetration levels to the model, FiT and system inertia are analyzed. Then, system inertia and total FiT change.

6.1 Analyzing the sensitivity of FiT

Generally, four scenarios are proposed to analyze the sensitivity of FiT incentives in relation to different degrees of RES penetration. A model with a 25 % penetration of RES in the base scenario. Scenario 2: RES adoption at 50 %. Scenario 3: The level of RES penetration is 75 %. In scenario 4: Model with 100 % renewable energy penetration. Table 8 shows the composition of energy production based on the level of RES penetration. Additionally, it presents the whole investment expenditure and Feed-in Tariff (FiT) payment for any Renewable Energy Source (RES) penetration scenario. The FiT payment substantially decreased investment expenses. Fig. 6 illustrates the proportion of investment costs that are financed by the FiT payment. The sensitivity analysis, using data from Table 9 and Fig. 6, demonstrates that when the penetration of renewable energy sources (RESs) increases, both the total system cost and the total FiT received likewise increase. Nevertheless, once the 50 % RES penetration threshold is reached, the ratio of FiT payment to the overall investment cost diminishes, despite maintaining steady FiT rates.Table 8 Assortment of capacities for various degrees of RES integration.

Table 8The power output of each installed generator technology in (MW)	RES Penetration level (%)	
25	50	75	100	
Thermal	1400	800	400	0	
Wind	400	400	800	1200	
Solar	–	600	600	600	
Investment cost on new REGs ($)	3.2000E+07	8.76E+07	1.17E+08	1.46E+08	
Accrued total FiT ($)	3.1956E+06	1.31E+07	1.62E+07	1.94E+07	

Fig. 6 A proportion of the investment cost is financed by the overall FiT payments.

Fig. 6

Table 9 Inertia coefficients correspond to different levels of renewable energy integration.

Table 9Percentage of Renewable Energy Integration (%)	System inertia	
Scenario 1	Scenario 2	
Inertia constant [sec.]	Inertia energy of the Synchronous generator [MWs]	Inertia energy from RES and HES [MWs]	Total inertia energy [MWs]	Inertia constant [s]	Synchronous inertia energy [MWs]	Inertia energy from RES and HES [MWs]	Total inertia energy [MWs]	
25	5.333	8499	1100	9600	6.827	8500	3400	11900	
50	2.6890	3999	800	4800	4.8179	4000	4600	8600	
75	2.1176	1999	1600	3600	4.5938	2000	6200	8200	
100	1.4860	0000	2400	2400	4.2105	0	6800	6800	

6.2 Explore the impact of variations in system inertia through a sensitivity analysis

The sensitivity analysis looked at how the combined GTEP model's total system inertia changed with different percentages of RES. In order to do the sensitivity analysis, two possible outcomes were examined, with varying degrees of RES penetration assumed in each. The assumption of virtual inertia by REGs and HES was made in Scenario 1. Scenario 2 included the use of virtual inertia by REGs and HES. The consequences of the sensitivity analysis are displayed in Table 9, Fig. 7, Fig. 8. In all situations, there is a decline in overall system inertia as the proportion of renewable energy sources (RESs) increases (as shown in Table 9 and Fig. 7). More precisely, Scenario 1, which fails to consider the virtual inertia capacity of RE generators and HES, demonstrates a more significant decrease rate in comparison to Scenario 2. In Scenario 1, the total inertia constant drops from 5.333 s to 1.4860 s, resulting in a reduction of 72.1 %. This information can be found in Table 9 and visually represented in Fig. 8. In contrast, in Scenario 2, there is a decrease from 6.827s to 4.2105s (a drop of 38.3 %). Furthermore, the inertia constant limit set in Eq. (35) imposes a restriction on the maximum permissible RES penetration level, limiting it to less than 50 % in Scenario 1 and up to 100 % in Scenario 2. However, even though Scenario 2 allows for 100 % RES penetration without breaching the inertia limit, the substantial reduction in the total inertia constant raises concerns about the grid's stability. The examination of grid stability becomes crucial at 100 % RES penetration, warranting further analysis.Fig. 7 RES penetration changes in multiple scenarios were investigated with respect to changes in synchronous inertia and total inertia energy.

Fig. 7

Fig. 8 Changes in the system inertia constant across various levels of Renewable Energy Sources (RES) penetration.

Fig. 8

6.3 Details elaboration of the results

The simulation results show that the cost, system inertia, and CO2 emissions were considerably affected by the addition of parameters including inertia, emissions, and FiT in the GTEP model (case 3). In particular, compared to case-2, the total system cost dropped by 8.86 %, CO2 emissions declined by 2.2 %, and the system inertia constant increased by 10.3 % (from 5.565s to 6.139s) when these aspects were taken into account throughout the model design process (case 3). Case 3 also made better transmission line planning selections than case-1 and case-2. Case-3 installs three transmission lines, whereas case- 1 and 2 install six and five, respectively, increasing transmission line investment costs. In scenario 3, two virtual inertia wind turbines (W2, W4) are installed to balance cost and model inertia. In contrast, example 1 (W1, W3) recommends installing two wind turbine units without any virtual inertia. The maximum FiT of 3.29 million USD was attained in case-2. This is explained by the purchase of a solar power plant, which provided greater FiT rates than wind turbines while having a lower inertia constant. Case 3 got 1.5978 million USD in FiT, significantly less than case 2, although grid inertia was included in the planning. Thus, the GTEP (case 3) model that incorporates inertia, emissions, and The FiT boost improved system performance by leveraging the highlighted metrics, aiding power system planners in making informed decisions regarding expansion planning.

In terms of calculation time, Table 10 compares the mathematical programming model to soft-computing optimization approaches. Compared to the Genetic algorithm (GA), Slap swarm algorithm (SSA), and other soft-computing optimization methods, the provided mathematical approach obtained global optimum solutions quicker and with less computation time. Therefore, the suggested technique saves processing time. The trade-off relationship between total system cost, CO2 emissions, and system inertia is depicted by the Pareto optimal graph in Fig. 9.Table 10 Computing time comparison of the suggested mathematical method to previous soft-computing optimization strategies.

Table 10Method of solving	Processing duration [sec.]	
Proposed method utilizing (MILP)	16.359	
Using (NSGA-II) [18]	18.61	
Using GA	33.76	
Using of Multi-objective Harris Hawks optimization	253.8	
Using ALO	353.1225	
Using SSA	384.7674	
Using an improved PSO called IBPSO	3096	

Fig. 9 The relationship between system inertia and both total system cost and total emissions using a Pareto chart.

Fig. 9

7 Conclusions and future study

This article concludes that the integrated Feed-in Tariff (FiT) application within the inertia-based GTEP optimization technique has been successfully implemented on the IEEE test system. Leveraging the CPLEX software, the proposed model effectively minimizes the total system cost and CO2 emissions while optimizing system inertia through FiT incentives. The model is based on the IEEE 6/IEEE 16-bus test system, and the GAMS CPLEX solver is used to solve it. Three distinct research scenarios were employed to evaluate the efficacy of the suggested approach. These hypothetical situations were created to investigate FiT and system inertia at various penetration levels of Renewable Energy Generation (REG). The following is an explanation of the thorough study results:• In order to promote increased utilization of Renewable Energy (RE), particularly solar photovoltaic (PV) systems, which tend to have higher costs compared to wind turbines, it is recommended that the Feed-in Tariff (FiT) rate be set at a level greater than 0.24$/Wh. This higher FiT rate serves as an incentive, encouraging greater adoption of solar PV systems by making their economic viability more attractive to users. By offering a competitive FiT rate, policymakers aim to stimulate the growth of solar energy projects and bolster the overall shift towards sustainable and renewable energy sources.

• Notable improvements were obtained when FiT, emissions, and system inertia were incorporated into the GTEP model, especially in Case-3. These improvements encompassed a substantial decrease in total system cost (11.94 % lower compared to case-1), a significant boost in system inertia (8 % increase compared to case-1), and a reduction in CO2 emissions (2.2 % decrease compared to case-2). Moreover, the GTEP model exhibited superior performance compared to alternative soft-computing optimization techniques, requiring less processing time for its computations.

• The combined model's larger inertia constant value improved frequency stability after system contingency.

• A considerable influence on the supply of virtual inertia by REGs and HES is revealed by the shift from a 25 % to a 100 % penetration level of RES. A significant 72.1 % reduction in the total system inertia occurs when REGs and HESS are unable to provide virtual inertia in the absence of support. Nonetheless, the overall system inertia drops to 38.3 % when RES penetration is raised from 25 % to 100 % with the help of REGs and High-Efficiency Synchronous Systems (HESS) that provide virtual inertia. In order to maintain system inertia levels during the shift to increasing RES penetration, it is imperative that planning methodologies consider both RES and High-Efficiency Storage Systems HESS that can provide virtual inertia.

• The proposed analysis indicates that as the penetration of RES increases, both the overall system cost and the total FiT received also increase. However, once renewable energy (RE) penetration exceeds 50 %, the proportion of FiT received in relation to the total investment cost decreases.

• As per the designated limit for the inertia constant in the model Eq. (31), investing in renewable energy (RE) technology and hybrid energy storage systems (HESS) cannot provide sufficient virtual inertia when the RE penetration level exceeds 50 %. This violates the inertia limit. However, when using renewable energy generators (REGs) and HESS, the inertia limit is not exceeded even at RE penetration levels of up to 100 %.

The future work will expand the model to a bigger test system by studying grid stability improvement by considering island/grid mode of operations at 100 % RESs and energy storage penetration.

Data availability statement

The data are available from the corresponding author upon request.

CRediT authorship contribution statement

Sadasiva Behera: Writing – original draft, Formal analysis, Data curation. Sumana Das: Resources, Formal analysis, Conceptualization. B.S.S. Ganesh Pardhu: Validation, Software, Investigation. Ram Ishwar Vais: Project administration, Methodology, Investigation, Kareem M. AboRas, Writing – review & editing, Supervision, Project administration. Naladi Ram Babu: Visualization, Validation, Investigation. Sanjeev Kumar Bhagat: Visualization, Software, Data curation. Mohammed Alharbi: Software, Methodology, Data curation. Wulfran Fendzi Mbasso: Writing – review & editing, Supervision, Methodology.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work was supported by the Researchers Supporting Project number (RSP2024R467), King Saud University, Riyadh, Saudi Arabia.
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