Profit enhancement and grid frequency control by energy level scheduling of CAES system in wind-connected electrical system

Abstract

The maintenance of power balance poses significant challenges in renewable combined deregulated power systems due to the unpredictable nature of renewable energy sources. This situation leads to economic instability within the system. However, an energy storage system can help maintain energy supply and control system stability for renewable incorporated thermal power plants. Unlike in regulated markets, energy prices in deregulated markets are not fixed by any government body or particular company. Instead, the Independent System Operator (ISO) serves as the main entity in the electrical market, gathering tenders from Generation Companies (GENCOs), Distribution Companies (DISCOs), and Transmission Companies (TRANSCOs). The market controller regulates energy prices using Nodal Pricing (NP), which provides economic benefits to both GENCOs and DISCOs. However, the unpredictability of renewable sources often results in a decline in system profit due to the production of an imbalance price (CostIMC) caused by a mismatch in contracted power generation from the renewable power plant. To address these issues, this study proposes a novel combined system that utilizes a suitable scheduling technique for the optimum operation of a wind farm-compressed air energy storage (CAES) system to maximize profit and revenue while maintaining grid frequency. The CAES system’s energy level is divided into four different levels, and an optimal strategy has been developed to efficiently utilize the CAES system to maintain grid frequency. This work has been conducted in both regulated and deregulated environments using a modified IEEE 30-bus system. The proposed method has been compared with an existing approach and has yielded better results in all aspects.

Keywords

Frequency control CAES wind farm EVs energy level control economic sustainability nodal pricing

Introduction

In the last few decades, monopoly electrical systems have been replaced by transparent electrical systems. This transformation has ushered in a shift from regulated to deregulated environments. As a result of this shift, the deregulated electrical environment has become a hotbed of competition among market participants, including GENCOs, DISCOs, TRANSCOs, retailers, and more. Fortunately, this competition has yielded numerous benefits for customers, including improved power quality and enhanced economic sustainability. While renewable energy incorporation with existing thermal power plants is an incredibly multifaceted process, it has the potential to create some instability within the system. In the electricity market environment, the primary objective of any system must be to maximize economic stability in all situations, regardless of whether they are normal or faulty. As we continue to navigate this ever-evolving landscape, we must remain vigilant in our efforts to promote stability and sustainability within the electrical marketplace.

As the energy system undergoes decarbonization, there is an escalating proportion of electricity generation derived from intermittent renewable sources, such as wind and solar. While energy storage’s significance in a renewables-intensive energy system is frequently discussed, the necessity of frequency stability in the supplied alternating current is often overlooked. The preservation of a consistent frequency is crucial for the secure and reliable operation of the infrastructure that distributes electricity, as well as for the equipment that is connected to it. The present-day grids depend heavily on the inertia of the large rotating turbines and generators in traditional power plants to provide frequency stability. As these sources are supplanted by renewables that lack this rotating inertia, alternate techniques for maintaining frequency stability will be required. The integration of sustainable energy sources into the thermal power plant creates a day-ahead electric network environment. Within this framework, renewable energy generators are required to provide the power supply bid to the electric system operator at least 1 day in advance of operations. The electric system operator, in turn, establishes the power schedule for both thermal and renewable sources according to the bid submitted by the renewable energy producers. However, the variable attributes of sustainable energy sources prevent the electric network from adhering to the fixed power scheduling conditions established by the system operator. Wind farms and solar photovoltaic systems are frequently utilized among all sustainable energy sources due to their widespread availability and efficient properties. Due to a possible mismatch between the forecasted and actual renewable power generation, there is a likelihood of creating a surplus or deficit power condition in the electrical grid. The electrical network parameters, including power demand and generation, are constantly changing within the thermal power system. As a result, grid frequency is in a state of fluctuation within the thermal system. Incorporating the renewable system with the thermal system results in even more fluctuating and unstable conditions for the grid frequency. Therefore, maintaining grid frequency control is of utmost importance for the renewable incorporated system to ensure system stability and security. In this situation, the optimal functioning of the energy storage system can play a critical role in maintaining system frequency by providing additional power to mitigate the difference between the actual and forecasted renewable power. Pumped storage hydro (PSH), compressed air energy storage (CAES), and battery systems have been employed as reverse energy sources worldwide over the last few decades.

Bazdar et al. (2022) have conducted a comprehensive survey regarding the application and characteristics of CAES systems in the integrated energy network. The authors have also presented the optimal sizing and integration classifications of the CAES systems. In paper Sarmast et al. (2023), a methodology (i.e. coverage-percentage method) has been proposed for determining the optimal sizing of the CAES system to achieve the optimal operation of the power grid of Ontario. Lemofouet and Rufer (2006) have introduced a hybrid model of supercapacitor and compressed air energy storage to maximize the system’s efficiency using the maximum efficiency point tracking method. The installation of energy storage devices in the power sector enhances the efficiency and stability of the system, but it can harm economic operation due to the additional installation cost of storage devices. Swider (2007) describes an electricity model that minimizes the energy production cost of a power network by proper hybrid operation of CAES and wind farms. Due to the varying nature of renewable energy sources, the incorporation of energy storage has always played a pivotal role in maintaining electricity market contacts within a day-ahead competitive power environment. The optimal placement of energy storage and energy-producing units is of paramount importance in achieving economic and sustainable operation, given the interconnected condition of the electricity grid. In this context, Ghofrani et al. (2013) and Li and Hedman (2015) have proposed a system designed to determine the ideal position of an energy storage device for a wind-associated competitive power system, with the authors also presenting the impact of different wind penetrations. The profits generated by power-generating units are dependent upon the revenue earned from selling power to customers and the cost of energy production. Opportunities exist to exploit profit by reducing energy production costs, maximizing revenue earned, or both. Numerous research works are currently underway to fulfill these power system conditions and maximize the economic profit of the system. Saadat et al. (2014) has developed a high-level controller for the CAES system, which incorporates a wind turbine to maximize system revenue and further improve the economic profit of the hybrid system. Cleary et al. (2015) have assessed the economic sustainability of the CAES system to alleviate wind curbing in a renewable-storage hybrid energy system. The author Kokaew et al. (2016) has focused on electric generation through air pressure, with maximum power tracking in an individual small-scale CAES system. The concept of uncertain transmission connection of the turbine drive shaft with an air compressor in the latest hybrid wind turbine system has been proposed in Krupke et al. (2017). Chen et al. (2016) and Wang et al. (2017) have briefly discussed the basic principles, classifications, technologies, development, and operation modes of the CAES system. Information gap decision theory (IGDT) and Look-ahead optimization models have been proposed in Khatami et al. (2020) and Shafiee et al. (2016) for commercial CAES systems in real-time and day-ahead power markets. The author Attarha et al. (2018) depicts a self-scheduling model that is specifically designed for a wind plant twin through a CAES system in the deregulated market. Calero et al. (2019) presents a scientific model for the diabetic-CAES system, while Azizivahed et al. (2020) examine the multi-area economic dispatch (MAED) issues considering the uncertain nature of wind farms and integrating CAES into the system.

Nourollahi et al. (2022) has developed a hybrid three-stage stochastic framework using a mixed-integer linear programing model. This framework seeks to coordinate the operations of wind producers and CAES. Additionally, two mathematical formulations have been presented in de Souza et al. (2021a) to investigate the unpredictable model for scheduling of price taker CAES system. Moreover, Aldaadi et al. (2021) examines the combined energy system consisting of the CAES and wind power plant in the power market as a private owner and presents their views on the commercial prospects in the power market. In another paper de Souza et al. (2021b), presents a stochastic optimization model to increase the profit of the CAES system under uncertain pricing conditions. Furthermore, a proposal for the implementation of a small-scale CAES for energy storage purposes on a day-to-day basis in an active distribution system has been presented in Ghadi et al. (2021). In addition, Rahimi et al. (2022) discusses a virtual power plant that includes a thermal generator, solar PV panels, wind farm, energy storing device, and controllable loads in the real-time and day-ahead market. Finally, the author of Bhattarai et al. (2019) elaborates on the usage and advantages of CAES in wind-integrated transmission-constrained systems, while Xie et al. (2021) designed an optimization technique for the CAES system to minimize the uncertain constraints and to gain the bidding curve for contributing to the energy system. Malakar et al. (2014) proposes a formulation for maximizing the operational profit of a micro grid-connected hybrid system with a wind farm and a pumped storage unit in a frequency-based pricing environment for a day-ahead energy market. Mahmoud et al. (2023a) presents a comprehensive study and application of various optimization techniques that can be employed to tackle power quality issues in the distribution segment of the grid. Mahmoud et al. (2023b) seek to facilitate the deployment of Fault Ride-Through Capability technologies and offer valuable insights for wind power research on grid integration. In Mahmoud et al. (2022), a comparison of the effectiveness and performance of photovoltaic and wind turbine systems as sources of renewable energy to power a polymer electrolyte membrane electrolyzer is conducted under varying conditions. Ewais et al. (2023) investigates the use of an adaptive controller that is based on a hybrid Jaya-Balloon optimizer (JBO) for frequency oscillation mitigation in a single-area smart G system. In Kamel et al. (2023), a novel isolated microgrid structure is proposed to reduce voltage and frequency instabilities and enhance the system’s dynamic performance.

Through an extensive review of the literature, it has been observed that various forms of research have been conducted involving the integration of storage devices in renewable energy systems. However, to the best of the author’s knowledge, no methodology has been proposed for maintaining grid frequency and increasing system profitability in the presence of imbalance prices by utilizing the energy levels of the CAES system, as has been accomplished in this study. The present work proposes an effective operating methodology for the thermal-wind-CAES hybrid system, which is distinct from the approach recommended in Malakar et al. (2014). While the operation suggested in Malakar et al. (2014) was performed with a pumped storage hydro system, the present study follows the same logic for the CAES system and aligns all parameters according to Malakar et al. (2014). Subsequently, the proposed operating strategy is implemented and a comparison is drawn between the old logic (Malakar et al., 2014) and the proposed approach. It is important to note that the evaluation is solely focused on the operating strategy of energy levels of the CAES system, and the effective procedure and limitations are completely different from Malakar et al. (2014). The primary objective of this work is to optimize system profitability and maintain grid frequency through proper operation and management of the energy level of the CAES reservoir tank. The concept of imbalance price is also deliberated for calculating system profit. The entire work is conducted in both regulated and deregulated electrical systems, and a comparison is drawn between these two electrical environments.

The proposed hybrid system’s schematic representation is displayed in Figure 1, where the control station plays a crucial role. It receives power from the wind farm, thermal power station, and CAES system, and controls the grid frequency to transfer power to energy consumers. The present study highlights the following key aspects:

The considerations of imbalance price for measuring the system profit in a renewable associated deregulated electrical system is very crucial. This imbalance price is caused by the mismatch between forecasted and actual wind speed, which leads to market contracts being prepared at least 1 day before operation.

To mitigate the harmful impact of an imbalance price, this work proposes the use of a storage device to supply additional power to the grid and maintain market contracts.

The CAES system is suggested as a hybrid solution for the wind farm and thermal power system to maintain power demand and availability ratios and sustain grid frequency.

The novelty of this work lies in the distribution of the energy level of the CAES reservoir (EL_CAES,max, EL_CAES,opt, EL_CAES,low, EL_CAES,min), which operates based on actual and forecasted wind power conditions along with the present grid frequency.

This approach maximizes system profit and maintains the grid frequency in both regulated and deregulated power environments.

To execute and function the proposed approach, a modified IEEE 30-bus system is utilized, and the optimal power flow (OPF) is solved using a sequential quadratic programing (SQP) approach.

Figure 1.

Illustrative diagram of the proposed hybrid power plant.

This is structured as follows: In Section 1, the background study is presented, along with the literature review and main highlights of the work. Section 2 describes the various mathematical formulations employed to evaluate the performance of the proposed configuration. Section 3 establishes the objective functions associated with the constraints for optimization. In Section 4, the proposed method for assessing the system economy and societal benefit of deregulated systems while maintaining the grid frequency is outlined. Section 5 combines the results obtained for the different scenarios with the integration of wind energy sources and the CAES system. Comparative studies on system revenue, profit, and CAES reservoir energy level using SQP algorithms have been conducted, and finally, the conclusions of the work are presented.

System modeling

System modeling is considered to be a vital stage before executing the process, objective, simulation, and output. Wind farm-based power generation and compressed air energy storage systems have been formulated to achieve the desired objective function.

Wind farm-based power generation

The sporadic, and unpredictable behavior of wind creates a hurdle for the incorporation of a wind farm in the existing thermal plant. This work focuses on wind speed forecasting and its effects in terms of economic sustainability in a competitive power market. The power generation based on the available wind speeds is calculated by the wind characteristics graph shown in Figure 1. The generation of electricity through a wind turbine that is, WGP(s) is formulated as follows (Dawn et al., 2019):

WGP (s) \frac{1}{2} . D_{A} . A_{WT} . η_{WP} . {V_{W, dh}}^{3}

(1)

Here, $D_{A}$ is the density of air, $A_{WT}$ is the rotor sweep area of a wind turbine, $η_{WP}$ is the overall wind plant efficiency, $V_{W, dh}$ is the wind velocity at h meter height from ground level. The assumptions taken for this work are as follows: $D_{A}$ = 1.225 kg/ $m^{3}$ , $η_{WP}$ = 0.49, and turbine rotor radius = 40 m.

Figure 2 shows the power generation characteristics of the wind farm where cut-in speed, rated speed, and cut-out speed play an important role. In between the region of cut-in speed, and rated speed the wind power is produced based on the equation (1). From 0 to the cut-in speed region, there will not be any wind power whereas after the cut-out speed, there will be no production of wind power. In this work, the wind power generation capacity of the system has been measured based on the wind power characteristics shown in Figure 2. In this paper, wind speed prediction has been performed for a day-ahead electrical system. It is assumed that the system cut-in speed, rated speed, and cut-out speed as 3.5, 16, and 25 m/s.

Figure 2.

Power generation characteristics of a wind farm.

Compressed air energy storage

A CAES system is one of the most efficient storage devices and it is mainly used for the large power system. This system can alleviate the unpredictability of a wind farm by providing additional power to the grid as per their requirement. A CAES system can be operated in three different modes that is, compressor mode, turbine operating mode, and idle mode. The CAES system is operating in turbine mode when there is a requirement for power in the system grid, at the other end this is operating in compressor mode when there is excess power available in the grid. This system stores the energy during the compressor mode operation for running the CAES in the turbine mode. In the wind-incorporated competitive power system, the wind farm is anticipated to maintain the bidding power. In this situation, CAES will operate in different modes to maintain the contracted power in the electrical grid. Controlling the energy level of the CAES system tank is crucial for its operation because the charging and discharging of the CAES system depend on the CAES energy levels. The energy level of the CAES tank ( $χ_{g (t)}$ ) at a time “t” is expressed as:

χ_{g (t)} = χ_{g (0)} + P_{e (com)} η_{com} t_{c (c)} - \frac{P_{e (gen) t_{c (t)}}}{η_{tur}}

(2)

χ_{g (in)} = P_{e (com)} η_{com} t_{c (c)}

(3)

χ_{g (out)} = \frac{P_{e (gen)} t_{c (t)}}{η_{tur}}

(4)

γ_{CAES} = η_{com} η_{tur}

(5)

Here, $P_{e (com)}$ , $P_{e (gen)}$ is the power requirement and supply for the CAES system at compressor mode and turbine mode respectively. $χ_{g (0)}$ is the energy level of the CAES system at an initial stage. $η_{com}$ and $η_{tur}$ are the efficiency of the CAES system in compressor and turbine mode operation respectively whereas $γ_{CAES}$ is the overall CAES system efficiency. The CAES tank energy levels in compressor mode and turbine mode are $χ_{g (in)}$ and $χ_{g (out)}$ . The operating times of the CAES system in turbine and compressor modes are given by $t_{c (t)}$ and $t_{c (c)}$ correspondingly.

Nodal pricing (NP)

Nodal pricing has played a significant task in finding the optimal selling price of power in a competitive electrical system. This price consists of marginal and optimal power generation cost, the cost for the losses of power, and transmission congestion cost. This price is changing for the different nodes present in a system. The mathematical expression of the nodal pricing is as follows:

NP = {MOC}_{G} + {MOC}_{L} + {MOC}_{TLC}

(6)

Here MOC_G, MOC_L, and MOC_TLC are the marginal cost of generation, cost of losses, and cost of transmission line congestion.

Objective function

In the deregulated electrical network, the fulfillment of the market contracts is very much essential otherwise some economic penalties can be imposed on the power producers by the market controllers for violating the contracts. An electrical grid can be sustained and maintain stability and security if there is a proper balancing of generated power and customer demand while maintaining the frequency of the grid. Here, an electrical network has been considered with N_B overall buses, N_D demand buses, and N_G generators. The main objective of this work is to enhance the economic profit of the wind-thermal hybrid system by proper utilization of the CAES energy storage system while maintaining the grid frequency. The objective of the proposed method has been obtained by anticipating the actual and forecasted wind speed data, the frequency of the grid, and the reservoir energy level of the CAES system. In a renewable integrated system, if the actual (AWS) and forecasted wind speeds (FWS) vary, once the GENCOs & DISCOs enter into a power contributing agreement based on a wind speed estimation, the ISO may penalize or give reward to the GENCOs for their shortfall or excess in power delivery. So, to cut the unhelpful effects of cost imbalances, GENCOs are functioning to close the power gap between actual and forecasted wind power. An energy storage system is the most successful way to crack this power emergency. Storage systems in a universal energy marketplace can reduce power discrepancies and the load on thermal power plants, enabling the financial return to be realized. The mathematical expression of the system economic profit (SEP(s)) with the consideration of imbalance price (Cost_IM(s)) is as follows:

Maximize, SEP (s) = TRC (s) + Cos t_{IM} (s) - TGC (s)

(7)

Here, TRC(s) and TGC(s) are the total revenue earned by the GENCOs and the total system generation cost of the wind-CAES hybrid system at the time “s” respectively. The total system revenue is comprised of two parts that is, revenue from the thermal power plant ( ${TRC}_{Thermal} (s)$ ) and revenue from the hybrid wind-CAES system ( ${TRC}_{WF - CAES} (s)$ ). Now, the expression of total system revenue is as follows:

TRC (s) = {TRC}_{Thermal} (s) + {TRC}_{WF - CAES} (s)

(8)

{TRC}_{Thermal} (s) = \sum_{i = 1}^{N_{G}} GP (i, s) . NP (i, s)

(9)

{TRC}_{WF - CAES} (s) = ({TRC}_{CAES} (s) + {TRC}_{WF} (s) - {TRC}_{SL} (s))

(10)

Here, GP(i,s) is the generated power from i-th thermal generator at a time “s.” NP(i,s) is the nodal price of i-th thermal generator. TRC_CAES(s), TRC_WF(s), and TRC_SL(s) are the total revenue cost of CAES, wind farm, and system loss respectively at time “s.”

{TRC}_{CAES} (s) = {TRC}_{tur} (s) - {TRC}_{com} (s)

(11)

{TRC}_{tur} (s) = P_{tur} (s) . NP (s)

(12)

{TRC}_{com} (s) = P w_{com, w} (s) . Cos t_{WG} + P w_{com, g} (s) . NP (s)

(13)

{TRC}_{WF} (s) = P_{WF - g} (s) . NP (s)

(14)

{TRC}_{S L} (s) = ω . NP (s) . [P_{grid} (s) - P_{WF - g} (s) - P_{tur} (s)]

(15)

Here, ${TRC}_{tur} (s)$ and ${TRC}_{com} (s)$ are the revenue of the CAES system in turbine and compressor operating modes at time “s.” $P_{tur} (s)$ is the generated power with the turbine mode operation of CAES. $P w_{com, w} (s)$ is the power for the compressor mode from a wind farm whereas $P w_{com, g} (s)$ is power for the compressor mode operation of CAES purchased from the electric grid. $Cos t_{WG}$ is the generation cost of wind power. $P_{WF - g} (s)$ is the quantity of wind power delivered to the electrical grid. ω is the system penalty factor. $P_{grid} (s)$ is the total scheduled power to be delivered to the grid from the WF-CAES hybrid plant.

The system imbalance price is measured based on the forecasted and actual wind speed data. The deficiency rate (DR) and excess rate (ER) have produced the system imbalance price. The imbalance price is “–ve” when the penalty is imposed on GENCOs whereas it is “+ve” when the award is given to GENCOs. The imbalance price is zero when there is no disparity between AWS and FWS. The “+ve” imbalance price boosts the system profit whereas the “−ve” imbalance price reduces the system economic profit. So, it is desirable to maintain the contact power in the grid by providing the additional power supply from the CAES (if needed). The system imbalance price of a wind-associated electrical network is as follows:

Cos t_{IM} (s) = \sum_{i = 1}^{N_{G}} (ER (s) + DR (s) . {(\frac{FWP (i, s)}{AWP (i, s)})}^{2}) . (AWP (i, s) - FWP (i, s))

(16)

DR (s) = (1 + β) . NP (i, s), ER (s) = 0 if FWP (i, s) > AWP (i, s)

(17)

ER (s) = (1 - β) . NP (i, s), DR (s) = 0 if FWP (i, s) < AWP (i, s)

(18)

ER (s) = DR (s) = 0 if FWP (i, s) = AWP (i, s)

(19)

The excess and deficiency rates of the wind plant at time “s” are represented by ER(s) and DR(s). The produced wind power for the i-th unit is represented by FWP(i,s) and AWP(i,s) depending on projected and actual wind speed. $β$ is the price imbalance coefficient. The overall cost of system generation is given as:

TGC (s) = {GC}_{Ther} (s) + {GC}_{WT} (s)

(20)

{GC}_{Ther} (s) = \sum_{i = 1}^{N_{G}} (a_{i} + b_{i} . AWP (i, s) + c_{i} . AWP {(i, s)}^{2})

(21)

Here, ${GC}_{Ther} (s)$ and ${GC}_{WT} (s)$ are the power production costs of thermal plants and wind farms at a time “s.”a_i, b_i, and c_i are the price coefficient of the thermal power plant. Some limits must be addressed for the hybrid power system to operate optimally. The following are the limitations of the CAES system and constraints for solving the OPF problem:

Constraints for the CAES system

P_{com} (s) = P w_{com, w} (s) + P w_{com, g} (s)

(22)

P_{com}^{\min} \leq P_{com} (s) \leq P_{com}^{\max}

(23)

P_{tur}^{\min} \leq P_{tur} (s) \leq P_{tur}^{\max}

(24)

{EL}_{CAES} (s + 1) = {EL}_{CAES} (s) + [(P_{com} (s) . η_{com}) - (P_{tur} (s) / η_{tur})]

(25)

{EL}_{CAES}^{\min} \leq {EL}_{CAES} (s) \leq {EL}_{CAES}^{\max}

(26)

Here, $P_{com} (s)$ is the total compressor load of the CAES system. $P_{com}^{\max}$ , $P_{com}^{\min}$ , $P_{tur}^{\max}$ , and $P_{tur}^{\min}$ are maximum and minimum limits of compressor mode and turbine mode operation of the CAES system. ${EL}_{CAES} (s)$ is the energy level of the CAES reservoir at the time “s.” ${EL}_{CAES}^{\max}$ and ${EL}_{CAES}^{\min}$ are the minimum and maximum energy levels of the CAES system.

Constraints for solving of problem

\sum_{i = 1}^{N_{G}} {GP}_{i} + WGP - {PL}_{TL} - P_{Demand} = 0

(27)

{Vol}_{i}^{\min} \leq Vo l_{i} \leq {Vol}_{i}^{\max} i = 1, 2, 3 \dots N_{B}

(28)

\emptyset_{i}^{\min} \leq \emptyset_{i} \leq \emptyset_{i}^{\max} i = 1, 2, 3 \dots N_{B}

(29)

{TL}_{l} \leq {TL}_{l}^{\max} l = 1, 2, 3 \dots N_{TL}

(30)

{GP}_{real, i}^{\min} \leq {GP}_{real, i} \leq {GP}_{real, i}^{\max} i = 1, 2, 3 \dots N_{B}

(31)

{GP}_{react, i}^{\min} \leq {GP}_{react, i} \leq {GP}_{react, i}^{\max} i = 1, 2, 3 \dots N_{B}

(32)

Here, ${PL}_{TL}$ and $P_{Demand}$ are the transmission line loss and power demand. $Vo l_{i}$ and $\emptyset_{i}$ are the voltage magnitude and voltage angle whereas ${Vol}_{i}^{\min}$ , ${Vol}_{i}^{\max}$ , $\emptyset_{i}^{\min}$ , and $\emptyset_{i}^{\max}$ are their minimum and maximum limit. ${TL}_{l}^{\max}$ is the thermal limit of the transmission line. $N_{TL}$ is the number of transmission lines present in the power network. ${GP}_{real, i}$ and ${GP}_{react, i}$ are the active and reactive power generation whereas ${GP}_{real, i}^{\min}$ , ${GP}_{real, i}^{\max}$ , ${GP}_{react, i}^{\min}$ , and ${GP}_{react, i}^{\max}$ are their minimum and maximum limit.

Application of the proposed approach

The technique given here is for the correct exploitation of the CAES reservoir energy level and their optimal operation depending on the state of real wind speed, anticipated wind speed, and grid frequency. For the correct operation of the CAES system, six scenarios were evaluated in this work. Figure 3 depicts the proposed operating strategy of the CAES power plant, where P_com,min and P_com,max are the lower and maximum limits of power when CAES is used as a compressor. P_tur,min and P_tur,max are the lower and higher power restrictions while CAES is in turbine mode. P_wind is the wind farm’s electricity supply to the electrical grid. Figure 3 shows that the operating policy has a total of 11 operating criteria that cover all of the considered six cases. This approach can be applied to any practical system to maintain the grid frequency by proper use of the CAES system when a threat comes into the system due to the mismatch between the actual and predicted wind speed.

Figure 3.

Indicating flow-chart of the presented method.

Scenario 1: awp ≥ fwp; (f_g > 50 Hz)

In this condition, actual wind power deriving from the wind power plant is more than the forecasted power. This surplus power is available in the grid due to the excess frequency already available in the grid. The nominal frequency in India is considered to be 50 Hz. The electricity pricing is comparatively low as the availability of power is more compared to the power demand. The excessive electricity in the power grid (for being f_g = 50 Hz) can be utilized in an economical method by operating the CAES in compressor mode up to the maximum energy limit stated in the first operational state of the flowchart shown in Figure 3.

Scenario 2: awp ≥ fwp; (49.7 Hz ≤ f_g ≤ 50 Hz)

Similarly, as the first condition actual wind power is in excess as compared to the forecasted power and the frequency range is between 49.7 and 50 Hz. The pricing of the power is also low as the actual power is more than the forecasted power. In this case, the CAES operates in operational state 2. The dedicated power is instantly delivered to the power grid and the excessive power that occurs due to the actual and forecasted wind speed is utilized to operate the CAES as the compressor mode.

Scenario 3: AWP ≥ FWP; (f_g < 49.7 Hz)

At this condition, the actual wind power is more than the predicted power but the frequency is lower than 49.7 Hz. This specifies the scarcity of power in the grid. In this scenario, there are three operational states, according to the energy level among the maximum and minimum of CAES (EL_CAES,max) and (EL_CAES,min) is additionally split into two levels (EL_CAES,opt) and (EL_CAES,low).

As soon as the energy level of CAES reaches less than (EL_CAES,low), the issue should be considered as a threat that the use of CAES as a generator must continue only in an emergency to avoid the breakdown of the grid due to a drop in frequency. When there is a moderate amount of air pressure in CAES then the level of energy is below EL_CAES,opt and if the level of energy in CAES is more than EL_CAES,opt then there is excess air pressure than required. Hence, generation can be conducted at any time to increase the system profit of the wind-AES hybrid system. CAES energy level is been investigated after the frequency survey. As per operational stage 3, actual wind-generated power will be supplied to the power grid to get a better frequency, if the level of energy in CAES is lower than EL_CAES,low. When the level of energy is more than EL_CAES,low but lower than EL_CAES,opt then the grid requires power, hence the electricity pricing will be high. Hence, to maximize the revenue of the wind-CAES power plant, the CAES works as a turbine to generate power by generation restricted to half of the maximum generation limit of the CAES plant displayed in state 4. Another condition is present, where the level of energy in CAES is more than EL_CAES,opt. Hence there is an excess depleted air reservoir in CAES, due to this the electricity pricing is also high in the power market. So, CAES is operated as a turbine with maximum power-producing capacity at operational stage 5.

Scenario 4: AWP < FWP; (f_g > 49.7 Hz)

At this condition, forecasted wind power is more than the actual wind power and the frequency is more than 50 Hz. The power supplied to the grid is less than the forecasted amount; the grid has surplus power as the frequency is more than 50 Hz, hence there is no purpose to operate CAES at turbine mode to deliver the forecasted power as it will further increase the frequency. The CAES will work as a compressor in this case which stores the energy in the system and also maintains the grid frequency at the nominal value of 50 Hz. Depending upon the energy level of CAES, two operational states have come up considering two separate compressor limits. The compressor limit of CAES is adjusted to its maximum value (as in state 8) once the level of energy is less compared to the EL_CAES,opt compressor will work half of the extreme compressor limit as in operational state 9. The electricity for the compressor operation drive is provided by a wind power plant rather than buying from the power grid for both cases as electricity from wind energy sources is economical. The excessive power available after storing the energy is sold to the power grid.

Scenario 5: awp < fwp; (49.7 Hz ≤ f_g ≤ 50 Hz)

At this condition, forecasted wind power is more than the actual wind power and the frequency is between 49.7 and 50 Hz. In this scenario, the CAES works in turbine mode to mitigate the imbalance between the actual and forecasted power. As in state 8, concentrating on the level of energy of CAES, two operational states have been suggested. When the level of energy in CAES is less than EL_CAES,opt then CAES acts as a turbine and delivers lagging power which occurs due to the mismatch of actual and forecasted power (as in operational state 10), or else the CAES operates as a turbine with adjusting its maximum value to CAES generation and its minimum value is adjusted to the difference between forecasted and actual power of CAES as displayed in operational state 11.

Scenario 6: AWP < FWP; (f_g < 49.7 Hz)

In this condition, forecasted wind power is more than the actual wind power and the frequency is less than 49.5 Hz. As the frequency is less, the power demand is comparatively very high but the hybrid system is not able to fulfill the demand and then the CAES plant acts in turbine mode. When the present level of energy is less than EL_CAES,low, then CAES operates as a turbine to deliver power at least the mismatch between the actual and forecasted power (as in operational state 6). If the level of energy is more compared to EL_CAES,low, then CAES will adjust the minimum generated power level at the difference between the actual and forecasted amount however the maximum generation power level is adjusted to the maximum generating capacity of CAES (as in the operational state 7).

Results and discussions

A modified IEEE 30 bus test system is been considered to observe the effect of hybrid thermal power plants, wind farms & CAES systems in regulated as well as deregulated environments by controlling the grid frequency. In the modified IEEE 30 bus test system, bus no. 1 is chosen as the slack bus and the MVA limit of this system is 100 MVA. It has six generators, 19 loads, and 41 transmission lines, and all the bus, branch, and generator data are taken from Singh et al. (2022). The intended system consists of 20 wind farms each having a capacity of 3.5 MW, so a total capacity of 70 MW wind farms is considered in the chosen system. In a wind-incorporated system, the electric network operation is reliant on the actual and forecasted wind speed data. The optimal, economic, and stable performance of the renewable-connected system depends on the frequency of the grid, forecasted, and actual wind speed.

At first, the hourly basis actual and forecasted wind speed data are collected for a day as illustrated in Figure 4. The wind speed data has been collected for a randomly chosen place Vijayawada (India Meteorological Department, 2023). The forecasted wind speed data for 15th March 2023 is taken on 10th March 2023 and the actual wind speed data for 15th March 2023 is taken on 16th March 2023. From the collected actual and forecasted wind speed data, it has been observed that there is a mismatch between actual and forecasted wind speeds in maximum hours. This is occurred due to the unpredictable behavior of wind flow.

Figure 4.

Actual and predicted wind speed for a day.

In a renewable integrated network, grid frequency control is a vital aspect as it encourages the system’s stability and safety. The Electricity Grid Code (IEGC) has stated the minimum operating frequency of the Indian power grid as 50 Hz and the tolerable frequency range is between 49.5 and 50.2 Hz. Figure 5 depicts an hourly grid frequency scenario for a selected place that has been considered randomly to verify the efficiency of the proposed method.

Figure 5.

Grid frequency for a day.

The power system’s profit is mostly reliant on generation cost and system revenue at an instant time. The system revenue for an electrical network is determined by the generated power and nodal pricing (equation (9)) of that particular location. The main objective of this work is to achieve the system profit and maintain the grid frequency with appropriate operating and management of the energy level of the CAES reservoir in a wind-incorporated system. And profit maximization is an objective function in the appearance of imbalance pricing. Initially, the wind generator placement is conducted in bus no. 4 in the modified IEEE 30 test bus system. Bus no. 4 has been chosen for wind placement because bus no. 4 contains maximum electrical demand. So, the impact of the wind farm placement will be very high in the system. The maximization of the system profit is gained by maintaining and controlling the frequency of the network and the appropriate scheduling of the energy level of the CAES reservoir tank. The considered energy level of the CAES reservoir is shown in Table 1. Initially, some power is required to start the operation of the CAES system. Here, the initial energy level of the CAES (EL_CAES,ini) is been considered as 32 MWh in the operation starting hour. An ideal approach has been suggested to use the CAES system effectively. The proper distribution of the energy level of the CAES chamber is crucial as the charging and discharging depend on the energy level. The proposed scheduling of the CAES energy level (shown in Figure 3) provides an economically stable system. This work has been performed in both regulated and deregulated system environments. Several steps are involved to conduct the proposed work which are depicted as follows:

Case 1: System performance in a regulated power network.

1.1 Calculation of system imbalance price, revenue, and profit.

1.2 Measurement of system economic parameters after the implementation of the proposed method.

1.3 Comparative studies of system revenue, and profit between the proposed method and existing method.

Case 2: System performance in a deregulated power network.

2.1 Calculation of system imbalance price, revenue, and profit.

2.2 Measurement of system economic parameters after the implementation of the proposed method.

2.3 Comparative studies of system revenue, and profit between the proposed method and existing method.

Table 1.

Considered energy level of CAES reservoir.

EL_CAES,max	EL_CAES,Opt	EL_CAES,low	EL_CAES,min	EL_CAES,ini
70 MWh	30 MWh	15 MWh	8 MWh	32 MWh

Case 1.1: Calculation of system imbalance price, revenue, and profit in a regulated system

The wind velocity has been adjusted based on the acquired dataset to execute the suggested method. Subsequently, the integration of the wind generator into the current thermal power plant using optimal power flow is done to determine the highest economic benefit concerning the imbalance pricing, system profit, and revenue. Following that, the wind velocity is modified on an hourly basis, and the imbalance pricing, system revenue, and profit are calculated by consecutively performing OPF solutions.

Table 2 illustrates the impact of imbalanced pricing on the electrical network. A negative imbalance pricing signifies that GENCOs have failed to meet the power demand as per their commitment. Consequently, GENCOs are penalized due to the shortage of power supply. Conversely, a positive imbalance pricing indicates the availability of excess power. GENCOs are rewarded accordingly. Thus, it is evident from Figure 4 and Table 1 that the system’s profit is maximized when the negative effect of imbalance pricing is minimal, and the difference between actual and forecasted wind speed is also minimal.

Table 2.

Imbalance price and profit of WF-thermal hybrid systems in regulated systems.

Hour	Revenue ($/h)	Imbalance price ($/h)	Profit($/h)	Hour	Revenue ($/h)	Imbalance price ($/h)	Profit($/h)
1	13,091.94	−1640	1104.89	13	12,891.73	−1405.4	1657.709
2	12,891.73	0	3063.109	14	12,621.7	48.05	3514.035
3	12,711.45	67.23	3409.059	15	12,786.09	55.7	3280.072
4	13,165.92	−2926.7	−308.241	16	12,711.45	67.23	3409.059
5	12,621.7	20.18	3486.165	17	13,091.94	−2501.2	243.6899
6	12,621.7	33.93	3499.915	18	13,165.92	−2926.7	−308.241
7	12,786.09	41.74	3266.112	19	12,621.7	0	3465.985
8	12,987.39	25.89	2939.452	20	12,621.7	57.35	3523.335
9	13,165.92	−2470.2	148.2591	21	12,621.7	0	3465.985
10	13,091.94	−2501.2	243.6899	22	12,711.45	18.5741	3360.403
11	12,621.7	0	3465.985	23	12,891.73	0	3063.109
12	12,621.7	57.35	3523.335	24	13,091.94	−566.8	2178.09

Case 1.2: Measurement of system economic parameters after the implementation of the proposed method in a regulated system

The intended proposal of a hybrid CAES system has been implemented to increase the system profit and diminish the risk of imbalance pricing by maintaining the frequency of the grid. Figure 3 represents the flow chart of the projected method where the operational mode of CAES has been controlled to fulfill the contracted power in the electricity market to raise the system’s profit and revenue. Turbine mode plays a vital role in optimal power flow problems.

A comparison analysis has been undertaken for the hourly revenue of the WF-CAES hybrid power plant, the revenue of the system under imbalance pricing, the generation cost of the system, and the overall profit. These results are presented in Table 3. From Tables 1 and 2, it has been seen that the system revenue and profit have enhanced in the maximum hours after the implementation of the proposed method. In the results obtained in Table 3, the impact of the imbalance prices is also included. So, if the effect of the imbalance price is not present in the system then the system profit will get much more. The proposed method entails dividing the CAES reservoir into four parts according to energy levels. To charge and discharge the CAES system, real-time data on both actual and forecasted wind power, as well as grid frequency, are utilized. The proposed method also identifies the parameters for operating the CAES in generating or pumping mode while considering the energy level for charging or discharging. The cost coefficient for all generators in power plants is obtained from Singh et al. (2022). The optimum power flow offers the least generation pricing for the generation re-scheduling in a thermal power plant. Figure 6 exhibits the generated thermal power and the corresponding nodal price for all the generators in 24 hours after implementing the proposed scheduling approach in the hybrid system.

Table 3.

Comparative study of revenue and profit of the hybrid system (proposed method) in regulated systems.

Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance cost ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)	Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance cost ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)
1	1986.019	14,927.7661	11,608.59	3319.17349	13	2606.097	15,345.4615	11,530.29	3815.17142
2	2039.638	15,536.334	12,041.46	3494.87386	14	2660.935	16,048.998	12,043.87	4005.12802
3	2989.508	16,467.8553	12,072.36	4395.49275	15	2359.361	15,917.2251	12,102.55	3814.67271
4	1105.506	14,123.4031	11,646.78	2476.62062	16	2989.508	16,467.8553	12,072.36	4395.49275
5	2533.292	15,840.1946	12,005.26	3834.93462	17	−49.2282	13,456.3219	11,962.58	1493.73931
6	4423.377	16,892.6328	11,474.71	5417.92283	18	1105.506	14,123.4031	11,646.78	2476.62062
7	3729.632	16,436.0452	11,523.8	4912.24279	19	3133.372	15,750.1975	11,516.32	4233.8775
8	1711.567	15,193.2444	11,988.92	3204.31949	20	2931.225	16,319.336	12,043.87	4275.46602
9	−925.652	13,025.7429	12,323.13	702.61039	21	2715.822	15,933.418	11,968.02	3965.39799
10	1527.608	14,469.355	11,608.59	2860.76239	22	2566.443	15,627.6174	11,778.72	3848.89486
11	3133.372	15,750.1979	11,516.32	4233.8779	23	2474.509	15,361.1192	11,580.8	3780.31912
12	1856.284	15,450.6786	12,164.38	3286.29856	24	2552.291	15,494.0379	11,608.59	3885.44529

Figure 6.

(a) Generated thermal power (MW) and (b) nodal price ($/MWh) of the hybrid system (proposed approach) in regulated system.

The efficient use of the energy level of the CAES reservoir holds significant importance for ensuring the economic and stable functioning of the hybrid system. Figure 7 demonstrates the range of power for the compressor and turbine modes of operation of the CAES system, following the application of the recommended approach. Notably, the power span is nil during the 19th and 23rd hours, indicating that the CAES remains in an idle state.

Figure 7.

Operating range of CAES system (in MW) in regulated system.

Case 1.3: Comparative studies of system revenue, and profit between the proposed method and existing method for a regulated system

Contracts between GENCOs and DISCOs have been signed based on the forecasted wind speed in the WF-CAES hybris system. The CAES system will operate in different modes, such as turbine, compressor, or ideal mode, depending on the actual and forecasted wind power to maintain the bidding power. The proposed approach is executed in both regulated and deregulated environments, and the integration of the WF-CAES system will enhance socio-economic well-being. Furthermore, the incorporation of the WF-CAES system helps reduce congestion in the network. Table 4 provides a comparative study of the system revenue and profit of the hybrid system with the existing method (Malakar et al., 2014).

Table 4.

Comparative study of revenue and profit of the hybrid system (existing method (Malakar et al., 2014)) in deregulated system.

Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance price ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)	Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance price ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)
1	1986.019	14,927.77	11,608.59	3319.173	13	2606.097	15,345.46	11,530.29	3815.171
2	2039.638	15,536.33	12,041.46	3494.874	14	2660.935	16049	12,043.87	4005.128
3	2989.508	16,441.79	12,072.36	4369.432	15	2359.361	15,917.23	12,102.55	3814.673
4	1105.506	14,123.4	11,646.78	2476.621	16	2989.508	16,467.86	12,072.36	4395.493
5	2533.292	15,840.19	12,005.26	3834.935	17	−727.124	13,146.57	12,269.66	876.9109
6	3581.207	16,198.03	11,516.32	4681.713	18	1105.506	14,123.4	11,646.78	2476.621
7	3297.836	16,076.2	11,548.86	4527.333	19	3133.372	15,729.2	11,516.32	4212.878
8	1711.567	15,193.24	11,988.92	3204.319	20	2931.225	16,317.4	12,043.87	4273.528
9	−925.652	12,016.09	12,323.13	−307.038	21	2715.822	15,933.42	11,968.02	3965.398
10	1527.608	14,469.36	11,608.59	2860.762	22	2566.443	16,993.61	11,778.72	5214.885
11	3133.372	15,750.2	11,516.32	4233.878	23	2474.509	15,391.12	11,580.8	3810.319
12	1856.284	15,452.66	12,164.38	3288.279	24	2233.196	15,228.22	11,627.67	3600.542

This section of the work presents the comparative studies of system revenue, profit, and average nodal price between the existing logic (Malakar et al., 2014) and the proposed logic. There were some limitations in the operation of the energy storage device’s energy level in the existing logic which has been diminished in the proposed methodology. Figures 8 and 9 depicts the comparison between the proposed and existing logic in term of WF-CAES and Thermal-WF-CAES hybrid system respectively.

Figure 8.

Comparative studies of WF-CAES hybrid system revenue ($/h) in regulated system.

Figure 9.

Comparative studies of thermal-WF-CAES hybrid system revenue ($/h) in regulated system.

The revenue generated by the WF-CAES system has been illustrated in Figure 8, excluding the revenue obtained from the thermal power plant, which is incorporated in Figure 9. The earnings acquired through the CAES system are bifurcated into two categories—compressor cost and turbine revenue. The compressor cost can be deemed as negative revenue as it entails a fee that needs to be paid to the electrical grid for acquiring power from the grid in order to execute the compressor mode operation. On the other hand, the turbine mode operation generates the power from CAES and supplies this to the grid for selling to the customer. So, it is very obvious that the operation of CAES in compressor mode can put an extra burden on the system economy. So, proper operation of the energy level can only provide better economic sustainability of the system. Figure 10 shows the comparative studies of system profit between the existing and proposed logic. From Figures 8 to 10 it has been seen that the proposed approach gives better results in all economic system aspects as compared to the existing approach.

Figure 10.

Comparative studies of thermal-WF-CAES hybrid system profit ($/h) in regulated system.

The system revenue got as 54,155.99$/h for the entire day using the proposed approach whereas it was 51745.03 $/h by the existing approach for the WF-CAES hybrid system. This scenario is also can be seen in the case of WF-CAES-thermal hybrid system revenue and profit. The hybrid system revenue and profit were 369,958.4 and 86,129.36$/h using the proposed logic whereas these values are 366,667.7 and 82,445.83 $/h using the existing logic. These scenarios can only be possible due to the advancement of the system nodal pricing. The system nodal pricing comparison between the proposed and existing methods is displayed in Figure 11. The proper scheduling of the energy levels of CAES as well as the efficient operation of the WF-CAES system provides the improved nodal price in the system which gives the economic benefit to the energy producers.

Figure 11.

Comparative studies of thermal-WF-CAES hybrid system’s average NP ($/MWh) in regulated system.

Case 2.1: Calculation of system imbalance price, revenue, and profit in a deregulated system

In this part of the work, the economic impact of the hybrid operation of the WF-CAES system has been investigated in the deregulated power environment. The restructured electrical system always gives financial benefits to the consumers due to the competition among the market participants. In this work, one demand-side bidding has been considered from bus no. 7. In a deregulated system, ISO clears the market at a price that is, nodal price, in which all the market players get the benefit. Based on the nodal price, system revenue, and system profit are measured. Table 5 shows the system profit and revenue while considering the system imbalance price in a deregulated system. From the results, it has been seen that some hours imbalance prices are zero which provides the maximum system profit.

Table 5.

Imbalance price and profit of wind-incorporated thermal hybrid systems in deregulated system.

Hour	Revenue ($/h)	Imbalance price ($/h)	Profit ($/h)	Hour	Revenue ($/h)	Imbalance price ($/h)	Profit ($/h)
1	12,631.39	−1623.2	775.4174	13	12,436.13	−1392	1324.27
2	12,436.13	0	2716.27	14	12,172.12	45.5633	3163.461
3	12,257.6	62.84	3054.642	15	12,333.2	53.0887	2930.457
4	12,704.92	−2899	−625.143	16	12,257.6	62.8446	3054.646
5	12,172.12	19.67	3137.568	17	12,631.39	−2476.5	−77.8826
6	12,172.12	32.6725	3150.571	18	12,704.92	−2899	−625.143
7	12,333.2	40.2274	2917.596	19	12,172.12	0	3117.898
8	12,529.26	25.344	2592.159	20	12,172.12	53.73	3171.628
9	12,704.92	−2446.6	−172.743	21	12,172.12	0	3117.898
10	12,631.39	−2.4765	2396.141	22	12,257.6	18.17	3009.972
11	12,172.12	0	3117.898	23	12,436.13	0	2716.27
12	12,172.12	53.7347	3171.633	24	12,631.39	−561.05	1837.567

In the economic price study of the system’s base operational conditions, it has been observed that the system’s profit is at its lowest in a deregulated environment. This is a clear indication of the improved profit margins for electricity consumers, which is the primary objective of implementing deregulation in the power system.

Case 2.2: Measurement of system economic parameters after the implementation of the proposed method in a deregulated system

Like the regulated system, in this case, the optimal scheduling operation of the WF-CAES system has been performed to maximize the system’s profit and revenue while maintaining the grid frequency. The system’s economic parameters after implementation of the proposed logic are shown in Table 6. As compared to the base case (shown in Table 5) and CAES system operation (shown in Table 6) it is observed that the system’s economic sustainability has been enhanced by the optimal operation of the CAES reservoir energy level. The system profit is maximized in every case with the proposed approach which is desirable for any stable and efficient power system.

Table 6.

Comparative study of revenue and profit of the hybrid system (proposed method) in deregulated system.

Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance cost ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)	Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance cost ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)
1	1967.52	14,451.58	11,498.11	2953.47	13	2581.54	14,869.02	11,425.03	3443.99
2	2021.48	15,053.11	11,926.53	3126.58	14	2632.45	15,558.46	11,931.67	3626.79
3	2957.40	15,971.10	11,957.90	4013.19	15	2333.56	15,424.77	11,986.08	3438.69
4	1095.78	13,654.82	11,534.30	2120.52	16	2957.40	15,971.10	11,957.90	4013.19
5	2508.72	15,339.65	11,895.04	3444.61	17	−49.12	12,961.26	11,842.70	1118.56
6	4397.86	16,480.35	11,375.74	5104.61	18	1095.78	13,654.82	11,534.30	2120.52
7	3694.40	15,950.22	11,418.84	4531.38	19	3104.58	15,273.33	11,413.06	3860.27
8	1693.68	14,709.17	11,870.51	2838.66	20	2899.996	15,826.01	11,931.67	3894.33
9	−919.15	12,556.49	12,196.43	360.06	21	2691.823	15,452.71	11,859.96	3592.75
10	1513.75	13,998.53	11,498.11	2500.42	22	2541.283	15,629.54	11,669.14	3960.40
11	3104.58	15,273.33	11,413.06	3860.27	23	2451.675	14,882.60	11,470.75	3411.85
12	1835.53	14,911.11	12,046.94	2864.17	24	2528.059	15,012.84	11,498.11	3514.73

The optimal power flow solution provides the most ideal results including line flow, power generation capacity, NP, and bus voltages for a power network. Figure 12 displays the generated power capacity and their corresponding nodal pricing for the proposed approach in a deregulated environment.

Figure 12.

(a) Generated thermal power (MW) and (b) nodal price ($/MWh) of the hybrid system (proposed approach) in deregulated system.

Case 2.3: Comparative studies of system revenue, and profit between the proposed method and existing method for a deregulated system

The contracts between GENCOs and DISCOs have been signed depending on FWS in the WF-CAES hybrid system. Based on AWP and FWP, the CAES system will operate in a different mode to maintain the scheduled power. The incorporation of the WF-CAES system helps in the reduction of congestion in the network as well as gives additional security to the system by mitigating the power deficiency in the grid. Table 7 illustrates the comparative studies of system revenue and profit of the hybrid system with the existing method (Malakar et al., 2014).

Table 7.

Comparative study of revenue and profit of the hybrid system (existing method (Malakar et al., 2014)) in deregulated system.

Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance cost ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)	Hour	WF-CAES hybrid plant revenue ($/h)	Total system revenue including imbalance cost ($/h) (A)	System generation cost ($/h) (B)	Profit ($/h) (C = A − B)
1	1967.522	14,452.31	11,498.11	2954.195	13	2581.541	14,869.02	11,425.03	3443.991
2	2021.488	15,051.17	11,926.53	3124.636	14	2632.452	15,558.46	11,931.67	3626.795
3	2957.402	15,971.1	11,957.9	4013.2	15	2333.567	15,424.78	11,986.08	3438.695
4	1095.782	13,654.83	11,534.3	2120.523	16	2957.402	15,971.1	11,957.9	4013.2
5	2508.727	15,356.62	11,895.04	3461.577	17	−722.398	12,677.4	12,145.03	532.3664
6	3547.892	15,716.65	11,413.06	4303.589	18	1095.782	13,654.79	11,534.3	2120.483
7	3267.188	15,594.56	11,441.52	4153.039	19	3104.58	15,273.34	11,413.06	3860.278
8	1693.68	14,709.18	11,870.51	2838.665	20	2899.996	15,826.01	11,931.67	3894.339
9	−919.151	12,556.5	12,196.43	360.0672	21	2691.823	15,452.72	11,859.96	3592.758
10	1513.752	13,998.54	11,498.11	2500.426	22	2541.283	15,145.82	11,669.14	3476.681
11	3104.58	15,273.34	11,413.06	3860.278	23	2451.675	14,882.6	11,470.75	3411.852
12	1835.539	14,964.17	12,046.94	2917.234	24	2212.326	14,748.07	11,515.46	3232.612

This section showcases a comparison of the revenue, profit, and energy levels of the CAES reservoir between the existing approach (Malakar et al., 2014) and the proposed approach. The proposed method has yielded greater system revenue and profit due to the limitations of the existing method. Figures 13 and 14 depict a comparison between the proposed and existing logic in terms of WF-CAES and thermal-WF-CAES hybrid systems, respectively.

Figure 13.

Comparative studies of WF-CAES hybrid system revenue ($/h) in deregulated system.

Figure 14.

Comparative studies of thermal-WF-CAES hybrid system revenue ($/h) in deregulated system.

The system revenue for the WF-CAES system has been shown in Figure 13 whereas the revenue received from the thermal along with the WF-CAES system has shown in Figure 14. The revenue earned for the CAES system is divided into two parts that is, compressor cost and turbine revenue. The operation of CAES in compressor mode can put an extra burden on the system economy. So, proper operation of the energy level can only provide better economic sustainability of the system. Figure 15 shows the comparative studies of system profit between the existing and proposed logic. From Figures 13 to 15 it has been seen that the proposed approach gives better results in all economic system aspects as compared to the existing method.

Figure 15.

Comparative studies of thermal-WF-CAES hybrid system profit ($/h) in deregulated system.

In this study, the primary role was played by the energy level of the CAES reservoir. The novelty of this research lies in the scheduling of the CAES energy level to maintain grid frequency in the presence of wind uncertainty. As shown in Figure 16, the energy level comparison between the proposed and existing methods for the deregulated environment reveals that the energy level utilization in the proposed method is efficient. Unlike the existing method, the proposed method never recommends charging the CAES system to achieve full charging conditions. Based on the detailed result verification, it can be concluded that the proposed method is superior and efficient for grid frequency control through optimal operation of the WF-CAES hybrid system.

Figure 16.

Comparative studies of CAES reservoir energy level (MWh) in deregulated system.

Conclusions

A systematic approach for enhancing the profit and revenue of the thermal-WF-CAES incorporated hybrid system in both regulated and deregulated environments has been recommended in this work. The frequency of the grid is also maintained through optimal scheduling of the CAES system’s energy level. The proposed CAES system operates differently from the existing one. The storage system’s energy level usage is restricted in the existing method and is only utilized for ultimate savings during peak demand hours. However, the proposed CAES system is suggested to operate to compensate for the power deficit caused by unpredictable wind power to fulfill the commitment. The CAES system in this study is not only utilized to compensate for the power difference between actual and forecasted wind power but also to improve the hybrid system’s profit. The proposed method’s outcome is compared with the existing method (Malakar et al., 2014). The evaluation is conducted using MATLAB-IPM to solve the optimal power flow problem. The proposed approach yields more favorable results for all cases, as can be seen from the outcome. The simulation is conducted hourly, with loads changing at each bus every hour. The result shows that the CAES reservoir is utilized effectively in the proposed approach, resulting in good revenue.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jayendra Kumar

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Profit enhancement and grid frequency control by energy level scheduling of CAES system in wind-connected electrical system

Abstract

Keywords

Introduction

System modeling

Wind farm-based power generation

Compressed air energy storage

Nodal pricing (NP)

Objective function

Constraints for the CAES system

Constraints for solving of problem

Application of the proposed approach

Scenario 1: awp ≥ fwp; (fg > 50 Hz)

Scenario 2: awp ≥ fwp; (49.7 Hz ≤ fg ≤ 50 Hz)

Scenario 3: AWP ≥ FWP; (fg < 49.7 Hz)

Scenario 4: AWP < FWP; (fg > 49.7 Hz)

Scenario 5: awp < fwp; (49.7 Hz ≤ fg ≤ 50 Hz)

Scenario 6: AWP < FWP; (fg < 49.7 Hz)

Results and discussions

Case 1.1: Calculation of system imbalance price, revenue, and profit in a regulated system

Case 1.2: Measurement of system economic parameters after the implementation of the proposed method in a regulated system

Case 1.3: Comparative studies of system revenue, and profit between the proposed method and existing method for a regulated system

Case 2.1: Calculation of system imbalance price, revenue, and profit in a deregulated system

Case 2.2: Measurement of system economic parameters after the implementation of the proposed method in a deregulated system

Case 2.3: Comparative studies of system revenue, and profit between the proposed method and existing method for a deregulated system

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Scenario 1: awp ≥ fwp; (f_g > 50 Hz)

Scenario 2: awp ≥ fwp; (49.7 Hz ≤ f_g ≤ 50 Hz)

Scenario 3: AWP ≥ FWP; (f_g < 49.7 Hz)

Scenario 4: AWP < FWP; (f_g > 49.7 Hz)

Scenario 5: awp < fwp; (49.7 Hz ≤ f_g ≤ 50 Hz)

Scenario 6: AWP < FWP; (f_g < 49.7 Hz)