2.1. VPP Bidding in DA-Ahead (DA) and Real-Time Markets

Recent research in optimal bidding strategies for electricity markets has concentrated on VPP components, addressing the challenges of extensive data forecasting. Various studies have explored VPP participation in DA and real-time markets. A key development is a bilevel stochastic mixed-integer linear programming (MILP) optimization model for technical VPP to trade in energy market [7]. This model perceives the DA energy market as the wholesale market and utilizes the multicarrier structure of the TVPP to compete with other electricity producers. Moreover, a two-stage bidding procedure for a price taker was analyzed, evaluating the DA energy and real-time market alongside a two-stage bidding approach for price-takers in DA and real-time markets, which exclude ancillary services [8]. Alongside these developments, numerous papers have highlighted the significance of managing uncertainties in VPP operations and scheduling, proposing innovative methods such as stochastic and local optimization in demand response (DR) programs [9–11]. The extensive body of research conducted to date has made a considerable contribution to the exploration of optimal control operations and bidding strategies for VPP. Such literature often employs optimization methodologies in their investigations. For instance, Hadayeghparast et al. proposed a noteworthy energy management model that leverages two-stage stochastic programming, taking into account the existence of renewable energy resources, to manage the operational scheduling of a VPP [12]. On the other hand, a unique combination of stochastic and adaptive robust optimization techniques to model uncertainties, particularly for the expansion planning problem related to generation and transmission, has been carried out in [13].

2.2. Risk Management Approaches for VPP

Risk management constitutes another significant research area for VPP bidding, scheduling, and seeking informed decisions. Notable studies in the literature have come up with distinct methodologies addressing risk-associated problems, for instance, risk-based VPP operation in [2, 14] and risk-averse VPP strategies in [15, 16]. These studies propose advanced stochastic optimization models to tackle uncertainties in market prices, renewable generation, and demand. Study [2] incorporates CVaR and Markov Chain Monte Carlo (MCMC) to optimize risk-based operations, while authors in [14] introduce a multiobjective programming model with p-robust stochastic programming to balance operational costs and risk regret levels. Similarly, in [15], a two-stage stochastic mixed-integer linear program is employed with CVaR to mitigate low-profit risks and maximize the generation companies’ expected profit in DA and balancing markets. Moreover, the literature in [16] further extends this framework by addressing real-time and spinning reserve markets, formulating a risk-constrained stochastic problem that integrates DERs, ESSs, and demand-side flexibility to maximize VPP profits. Nevertheless, many risk control strategies predominantly emphasize CVaR or boundary constraints in the optimization process, leaving other significant risk measures such as value at risk (VaR) and shortfall probability (SP) relatively underexplored. In [17], the authors address this gap by proposing a risk-averse stochastic decision-making framework that incorporates multiple risk metrics (CVaR, VaR, and SP) for energy trading in a wind-storage system within an electricity market. By embedding these metrics in a scenario-based risk-aware stochastic optimization model for wind-storage energy trading, the study demonstrates how this integrated approach can effectively manage uncertainties and accommodate the needs of multitype risk-averse decision-makers in electricity markets.

2.3. Role of Ancillary Services, Frequency Regulation, and Scenarios-Oriented Approaches for VPP

Although VPPs have been increasingly investigated in DA and real-time markets, however, despite this wealth of research, a notable gap persists in studies addressing their collective participation in DA energy and frequency regulation reserve markets (FRRM). This oversight, largely attributed to the complexities of accurately modeling uncertainties in DERs, limits the development of effective electricity market bidding strategies. With the added uncertainties in generation, demand, and market prices, the problem of electricity market bidding becomes even more critical in the ancillary services market (regulation and reserve services) compared to the DA energy market. Thus, the ancillary services market, particularly the frequency regulation reserve market referred to as FRRM, presents an untapped potential for leveraging the fast-ramping capabilities of DERs, potentially yielding higher profits and reduced operational costs [18]. Consequently, we found research scarcity involving the integration of slow-ramping resources (e.g., CHP, boiler, and thermal storage) with faster ramping renewables (such as BESS) within a VPP context. Since they have the capability of offering flexibility to the power system, we thus speculate that they are somehow ignored in the operational scheduling modeling of VPP taking into account multienergy market scenario. In this respect, some research studies have tried to address this issue through the inclusion of these slow-ramp resources in a VPP, thereby considering different electricity market environments. Notable exceptions include studies exploring optimal bidding strategies of CHP-DH and RES generators in DA and imbalance markets [19], and the operational scheduling of a coupled combined heat and power-virtual power plant (CHP-VPP) comprising heterogeneous DERs based on the electric power network and the district heating network thoroughly studied considering DA profit maximization and minimizing operational cost in the real-time market [20]. However, these studies fall short in incorporating a comprehensive VPP model that includes CHP, boiler, and thermal resources in a multienergy market setting, particularly the FRRM. Also, we noticed a similar research in [21]; however, it offers no applicability to the VPP concept. Hence, our paper aims to bridge this gap by integrating slow-ramping resources (CHP–EiB–thermal) with the fast-ramping resources (BESS) within an aggregated VPP, while allowing them to trade their capacities in DA market and FRRM. This approach also accommodates a hybrid energy storage (HES) system such as BESS and thermal storage, enhancing the flexibility and market benefits of various DERs [5]. Moreover, FRRM proved to be more suitable, effective, and flexible for various DERs due to their higher market benefits and stability offering to the balancing of the power system. To improve the social welfare, revenue maximization, and controlling operational costs, various scenarios-oriented modeling techniques have been developed in earlier literature which focuses on benefiting the market participants.

Although we might see a wide variety of research conducted previously on the scenario-oriented modeling techniques, while beneficial for market participants, they often struggle with accurate forecasting of demand and generation, computational efficiency, and market prices [22–24]. As per our understanding, we relate this discrepancy due to ineffective scenario generation and simultaneous reduction methods, which leads to inaccuracies in prediction, slower computation and execution, as well as a higher computational burden. Thus, to address these challenges, we introduce the fast forward selection and simultaneous reduction (FFS&SR) algorithm, designed for efficient and rapid processing of large-scale datasets. Our study also expands on the limited focus of the existing literature on FRRM-specific strategies for VPPs [25–28] and harnesses advancements in artificial intelligence and machine learning to improve forecasting and operational risk evaluation. A variety of approaches based on deep learning (DL), reinforcement learning (RL), long short-term memory (LSTM), and bidirectional long short-term memory (B-LSTM) have been investigated in published papers that help in superior uncertainty handling and higher financial benefits compared with scenario-based scheme [29, 30]. Besides, the current literature often overlooks the role of key resources, the evaluation of operational risk during bidding strategies, and the limitation to a single market operator. For instance, FRRM problem is addressed in [29] taking ESS, wind power (WP), EV, and DG as DERs, yet it lacks other key resource participations, lack of evaluating operational risk during bidding strategies, and limitation to a single market operator. To overcome these limitations, we turn to scenario-based research methodologies, which have proven to be more mature and precise in handling uncertain DER parameters.

In response to the identified research gaps, the pressing need is to develop and rigorously analyze sophisticated bidding strategies for VPP in multiple electricity markets, such as the DA market and FRRM. Our study proposes a stochastic optimization-based bidding strategy, focused on scenario counts, to assist VPP operations in these dual-energy markets. While our approach does not currently incorporate real-time bidding strategies, it remains applicable within the context of the balancing market. The FRRM, in particular, offers unique advantages in managing capacities for both upward and downward regulations, aligned with the precise dispatching of secondary frequency regulation signals [31]. In the context of performing regulation based on the automatic generation control (AGC) signal response, different electricity markets have adopted varying rules. For instance, the California ISO (CAISO) in the United States treats upward and downward regulation as distinct entities for regulation performance [32]; consequently, the PJM grid operator in the United States treats it as a single regulation entity [33]. These variations highlight the complexity and need for robust frameworks that can cater to multiple regulations simultaneously.

Our primary objective is to equip VPP operators with a flexible, robust, and realistic strategic bidding framework for market participation. This aims to maximize social welfare and economic benefits through efficient DER utilization and establish a more risk-averse VPP framework that effectively reduces uncertainties. Considering both upward and downward regulation services in our model allows for the full exploitation of DER capacities. The core of our work facilitates VPP participation in multiple energy markets, optimizing potential profits in dual-bidding scenarios. We achieve this by aggregating various DERs into a unified VPP, enabling its participation in both the DA market and the ancillary services market, particularly the FRRM, as depicted in Figure 1.

2.4. Summary of the Relevant Literature

The current literature on VPP bidding in energy markets demonstrates advanced methodologies for DA and real-time engagement, utilizing stochastic techniques. In the field of risk management, research has mostly focused on risk-based or risk-averse techniques, especially utilizing CVaR or boundary limitations, while neglecting measures like VaR and SP. While these strategies are essential for alleviating uncertainty in energy markets, their efficient integration with slow-ramping and fast-ramping resources across various market circumstances is a significant difficulty. Although there are many potential advantages to ancillary services markets, especially FRRM, there are not many thorough studies that include both slow-ramping resources (like CHP, boilers, and thermal storage) and fast-ramping resources (like BESS) in multienergy contexts. The existing scenario-based and AI/ML-driven models confront intricate uncertainties, although they often have trouble with forecasting inaccuracy, computing demands, and a limited emphasis on individual market operators or narrow risk metrics. Thus, there is an urgent requirement for a cohesive, risk-averse VPP architecture that can combine various DERs, complex risk metrics, and different market configurations. The subsequent sections expand on these observations, pinpointing the gaps and outlining our proposed solution.

6.1. Two-Stage Stochastic Programming Method

In this paper, we have proposed a two-stage stochastic programming method tailored for optimizing operational decisions and scheduling of a VPP within a multienergy market context. This approach is specifically designed to address scenario ω, with the focus on generating units g at temporal instance t. The proposed stochastic optimization model aims to maximize revenue and minimize costs for a VPP, considering two distinct stages of the bidding market, as highlighted in prior research [11]. The first stage involves the VPP submitting supply offers or demand bids in the DA energy market. Simultaneously, the second stage requires the VPP to provide both upward and downward regulation supply offers for the ancillary services market, particularly under the framework of pay-for-performance (PFP). This strategy is critical for ensuring precision and responsiveness to the dispatched AGC regulation signal. In the PFP model, market participants are compensated based on the regulation capacity offered and the extent of adjustments made to their dispatch set points following the system operator’s directives. Furthermore, rewards are contingent upon the degree of adherence to regulation signals, aligning with the standards set by established guidelines [36]. This two-pronged approach not only aligns with market demands but also enhances the operational efficiency and profitability of the VPP in a complex multimarket environment.

6.2. Objective Function

The initial segment (i) of the aforementioned objective function, indicated as (2a), is devoted to defining the intricacies of the energy market problem (DA). Conversely, the subsequent segment outlines the second-stage problem (ii) which explicates the workings of the regulation market (FRRM). In order to streamline this process further, we distinguish between functions within the objective function (2a) that are scenario-dependent and those that are not. For the first portion of the second stage (ii), we operate under the presumption that capacities remain constant and are not contingent on the specified scenarios. However, the second portion, specifically pertaining to the regulation market (within the second stage), is scenario-sensitive. This part takes into account factors such as mileages, operational costs, and risk assessment. The decision variable in the initial stage (i) is designated as $$, with $$ symbolizing the corresponding price. The decision variables in the succeeding stage (ii) are $$ and $$, which offer regulation capacity to the market, with the capacity available for both up- and downregulation. The (μ^MLG)Δt is utilized as a mileage factor, signifying the average distance to be covered within the time frame of Δt. The final component showcases a risk-aversion measurement, CVaR, which computes the expected profit for a given confidence level α in the worst scenarios. Equation (2b) refers to the operational costs of the participating resources, including CHP systems, BESS, and EiB. The operational cost of CHP includes both start-up and shut-down expenses, in addition to fuel costs tied under binary variables signifying the ON and OFF states of the CHP, respectively. Moreover, it is important to recognize that the operational costs of these generators fluctuate based on the distinct scenarios. Constraints (2c) is the representation for imbalance power in which $$ is the power to purchase (to cover the demand shortage), whereas $$ shows the excess power to be sold (maximum profit) in the energy market. Constraints (2d) shows that both the positive and negative power imbalances are non-negative. We have articulated all of the operational limitations for the generating units or resources within the VPP during the first stage (DA stage). This is achieved through submitting a number of bids—actions we classify as “here-and-now” decisions. Subsequently, contingent upon the outcomes of the first stage, decisions for the second stage (recourse decision) are formulated by dispatching the generating units and managing power exchange—decisions; we categorize as “wait-and-see” actions [37]. It is significant to note that certain types of resources, specifically WP and photovoltaic (PV), are listed as types that will not engage in the FRRM.

6.3. DA Energy Market and Its System Constraints (Stage 1)

6.3.2. CHP Unit Constraints (Equations (5a)–(5f))

The problem of unit commitment (UC) in the context of CHP systems has been extensively investigated in the past. However, it is speculated that the coupled energy networks associated with a CHP-VPP have received limited attention in the existing literatures [38]. Consequently, this paper aims to construct a coordinated dispatch strategy for the CHP-VPP framework, with the objective of achieving controlled decision-making capabilities, heightened flexibility, and increased economic advantages. In order to realize this, we initially establish feasible operation regions (FORs) for the CHP unit, considering both its electrical and thermal power output under different scenarios. Then, we develop its market environment model by factoring in its participation in the DA and FRRM [21]. The FORs for a CHP unit, which defines the boundaries for power and heat generation, comprise five viable regions, forming a polygon. This polygon accommodates electrical power output $$ and thermal power output $$, for CHP unit g at time t carrying scenario ω, and is bounded by the curve denoted by the alphabetical sequence ABCDE, which represent the extreme points of the designated area. The gradients of the four vertices of the lines AB, BC, CD, and DE are represented as a_ba, a_cb, a_dc, a_ed [38] graphically depicted in Figure 3:

$$ ()

$$ ()

$$ ()

$$ ()

$$ ()

$$ ()

Constraints (5a)–(5d) represent the operational constraints applicable to the CHP units denoted as g, where index e represents the number of extreme points under a designated operation area (ABCDE) with its respective coordinates $$ and $$. The set of extreme point is denoted as ∂^CHP; however, $$ denotes the combination coefficient of e − th extreme point of the g − th CHP unit. The X_g,ω,t is binary variable condition for generator ON and OFF status. Constraint (5e) signifies the linear operation cost associated with a CHP unit, and $$ denotes operation cost at the e − th extreme point for g − th unit of CHP. Constraint (5f) lays out the stipulations for net power generation $$ by a CHP unit. This constraint represents the power traded (selling power) $$ in the energy market, and the capacity reserved $$ instantaneously in the DA market for trading in the frequency regulation market.

6.3.3. EiB Unit Constraints (Equations (6a)–(6d))

A boiler constitutes a type of energy conversion device, adept at transforming electrical energy into distinct thermal energy, to fulfill industrial needs and domestic heating requirements. The operational principle of a boiler, as considered in this research, is such that if the CHP unit fails to accommodate the thermal load capacity, the boiler can function as a supplementary solution, depicted in Figure 4. This research, therefore, presents an innovative concept of EiBs that displays immense potential to enhance system flexibility, swift regulation capabilities, and optimize surplus power usage [39]:

$$ ()

$$ ()

$$ ()

$$ ()

Given that a CHP unit can function as a boiler, constraint (6a) represents the EiB, specifying the permissible limits for the input power of boiler unit g. Equation (6b) shows that the thermal power output for boiler unit g at time t under scenario ω is equal to the product of the input of electrical power and energy conversion efficiency of boiler. Constraint (6c) restricts the heat production of the boiler, a necessity due to the boiler’s finite heat storage capacity, which could potentially be exceeded by accumulated heat. The $$ serves as a generic representation of the efficiency, illustrating the ratio of total energy output to total energy input for a boiler. Finally, equation (6d) represents the operational cost of the EiB.

6.4. FRRM and Its System Constraints (Stage 2)

Decisions within the FRRM are contingent upon the determinations made in the first stage (Stage 1). Subsequent are the system constraint models for those resources poised to deliver regulation services, which are based on the decisions made during the first phase of the two-stage stochastic model.

6.5. WP and PV Power Forecasting Error Calculation (Equations (15a) and (15b))

Equation (15a) formulates the forecasted error as the discrepancy between the actual power output and forecasted power, divided by both the installed WP and PV capacity. In (15b), B(a, b) is the beta function that normalizes the probability density function (PDF), where “a” and “b” are the shape parameters employed in the beta PDF to generate PDFs for different beta distributions. This equation signifies that under a given WP and PV forecast power condition, both the PV and WP forecast error follows the beta distribution. The analysis on scenario generation sets is carried out in Section 8.1, as demonstrated in Figures 5, 6, and 7. The generation and reduction of scenario sets employ the FFS&SR algorithm, and the forecasted errors are eliminated by the beta PDF distribution. The scenario generation set analysis builds future predicted possible scenarios that closely resemble the original set.

6.6. Risk Aversion CVaR Embedded in the Objective Function (Equations (16a)–(16c))

The first component of the multiobjective decision-making function, as demonstrated in (16a), represents the anticipated revenue accrued by the VPP, while the CVaR index is exhibited in the second term of the equation. Additionally, β serves as a weighting parameter that allows the VPP to manifest the balance between risk (CVaR) and anticipated profit (revenue), where β ∈ [0, 1]. The selection of β is directly tied to risk aversion decisions. For instance, a larger β value signifies a more risk-averse VPP. Generally, a risk-neutral VPP, which seeks to maximize its profit without considering risk factors, sets the β value to zero. The η denotes the VaR, while ζ_ω is an auxiliary variable. Constraints (16a) and (16b) fulfill the requirements for the linear formulation of the CVaR metric incorporation into the model.

8.1. Scenario Generation Settings

For this study, data including market prices were sourced from the PJM electricity market operator, encompassing DA and FRRM pricing, historical forecasts of wind and solar PV generation, and dispatched regulation signals under Reg-D. To predict next-day (D0 + 1) prices, we generated 13,000 random scenarios using April 2022 data [49]. Additionally, random scenarios for PV outputs and wind generation were derived from probabilistic historical data of April 2022 [50, 51], reflecting the inherent uncertainty in PV units and wind turbines. The large number of scenarios for our stochastic parameters, including renewable generation, demand, and pricing, represents the uncertainty inherent in decision-making problems. However, such a high number of scenarios renders the optimization problem complex and challenging to navigate. To achieve tractability and an optimal solution closely resembling the original problem, this study proposes the use of the fast forward scenario selection and reduction technique (FFS&SR). This approach streamlined the initial set of 13,000 DA scenarios to a more manageable 200 and then to 20, likewise, the random scenarios of PV and wind generation to 20. For a 24-h planning horizon, we selected these 20 reduced scenarios of market prices, PV, and WP production, focusing on the most likely occurrences in the uncertainty set. The probability of occurrence for these scenarios was set at 0.05. Figures 5, 6, and 7 illustrate the market price scenario generation and reduction process, and the output power production scenarios for wind and PVs, along with their reduced scenario set.

8.2. Case Settings

The operational parameters of our proposed aggregated VPP model, accommodating diverse heterogeneous resources, are detailed in Tables 1, 2, 3, and 4. It features three CHP units (each with a 30-MW maximum output, 16-MW/h ramp-up, 12-MW/h ramp-down limits), while a BESS unit with 40-MWh capacity and 20-MW charging/discharging power at 90% efficiency, based on data derived from [52]. Initially, CHP units start in an OFF state, activating with the bidding market. EiB and thermal/heat storage data, sourced from [53], include a 12-MW EiB unit at 90% efficiency and a 10-MWh thermal storage with 0.9 efficiency. Load profiles cover electrical (up to 320 MW) and thermal demands (up to 160 MW), with the VPP’s energy consumption set at 150 MWh. Additional resources are WP and PVs, with 450 and 400 MW capacities, respectively. Their operation is based on historical data reflecting inherent uncertainties. The maximum power for DA market trading is 800 MW, and for FRRM, it is 200 MW. The specific parameters for these resources are comprehensively listed that are employed in our VPP model, in the mentioned Tables 1, 2, 3, and 4.

8.3. Discussion on Proposed Fast Forward Scenario Generation and Simultaneous Reduction

The process of scenario reduction is an essential advantage for electricity market problem-solving, as it enables tractability within a large set of scenarios. The resultant reduced set appropriately characterizes the uncertainties involved, which are crucial for making informed market decisions [48].

8.3.1. Index-Based Comparative Analysis of Various Scenarios

The proposed FFS&SR technique comparatively performs better showing robustness in scenario generation and simultaneously reducing for large number of scenarios. However, we find out that the critical problem lies in deciding a criterion of selecting the exact number of scenarios that could lead to an optimal solution. Thus, we present index-oriented criteria for choosing various number of scenarios. We have performed comparative analysis for different scenarios (20, 30, 40, and 50) to calculate the index of probability similarity and Kantorovich distance for different scenarios. In this course, we executed several numbers of iterations against the value of the index which led to some interesting and convincing results as illustrated in Figure 9. We noted that with the increasing number of scenarios, the index value greatly reduces. For instance, the value of the probability similarity index (difference of similarity between an original and reduced set of scenarios) in Figure 9(a), 9(b), 9(c), and 9(d) shows a downward trend with the increased number of iterations for various scenarios, depicting a close relationship of similarity between reduced and original scenarios. The increased number of scenario generations will lead to greater similarity of probability between the reduced sets and original ones. On the other hand, the comparison has also been established based on the Kantorovich distance metric for distinct scenarios to evaluate the value of indexes. The Kantorovich distance characterizes spatial features between original and reduced scenarios. From Figure 9, we can argue that the greater number of scenario generations results in a declining value of Kantorovich distance due to relatively lower distance among respective scenarios.

8.3.2. Comparative Analysis Based on FFS&SR’s Robustness and Optimality Gap

The proposed fast forward selection and reduction algorithm in this paper (detailed in Section 7) is further compared with existing scenario generation and reduction techniques previously examined and studied in the literature [47, 54–56]. This comparison is based on two critical differentiating factors: (1) the duration of computation during the scenario selection and reduction process and (2) the overall optimality gap. The duality gap was set at 1.0% for this analysis, which estimates the minimum number of scenarios required to achieve solution stability with reduced computational burden and a lower optimality gap. The findings in [47] indicate that solution stability is reached only when approximately 30 scenarios are considered. However, this approach employs a risk-neutral cost function, enabling a stable solution with a reasonably sized scenario set. In contrast, the risk-averse case tried in this work led to additional computational challenges due to the complexity of the cost function. The study in [54] compares various scenario reduction techniques based on operating costs and the computational time required for stochastic UC. The uncertainty model in scenario-based stochastic UC generates a single schedule for a given scenario set, aiming to minimize the expected operating cost over all scenarios. Unlike our study’s outcome, the extreme scenarios with low probabilities in this paper contributed to higher optimality gaps and increased computational time, as these scenarios emphasize minimizing operating costs for more probable, less extreme scenarios. The cost function proposed by Dupačová et al. in [55] demonstrates broad applicability across various problem settings but performs inadequately in stochastic environments. The resulting median computation time ranges from 50 to 60 s, and the method often fails to converge to the optimal solution, leaving optimization incomplete. Similarly, the study in [56] advocates using minimal information distance for best approximation methods, emphasizing close probability relationships in scenario generation, reduction, and optimality gap minimization. While this approach suggests higher convergence rates and faster computation, its numerical findings do not substantiate the theoretical and mathematical claims. Moreover, their method is better suited for smaller scenario counts (5 to 10), as it relies on stability estimates derived solely from problem-specific data without broader informational constraints.

Within the context of the two-stage stochastic optimization method, our results are simulated under the assumption of 20 random scenarios related to the total operational cost, as shown in Figures 10 and 11. Figures 10(a) and 10(b) depict the production and simultaneous reduction of scenarios from the initial 20 random scenarios, demonstrating superior efficiency in comparison with other scenario generation and reduction techniques [47, 54–56] in terms of lower computational time and computational burden, as well as diminished operational costs. A substantial optimality gap was observed between the total operational cost and the expected cost when other scenario selection and reduction techniques were utilized, as illustrated in Figure 11. In contrast, our proposed method displayed superior performance by minimizing the optimality gap, more accurately capturing the range of operational cost against the expected cost. In summary, the FFS&SR technique excels in generating and simultaneously reducing scenarios, achieving the least expensive actual operating cost, the fastest solution time, and the lowest computational requirements to reach optimality. Its performance surpasses existing methods by ensuring solution stability with fewer scenarios and reduced computational overhead.

8.4. Discussion on Optimal Operation and Bidding Strategy of VPP

The historical real-time operation data of the Reg-D signal from PJM (September 2020) [57] have been utilized to simulate the VPP resources’ response. Frequency regulation capacity in FRRM involves reserving a specific capacity by a resource to follow AGC signals, earning capacity payments for reserved capacity, and mileage payments for actual delivery. Our simulations across various scenarios over a 24-h period indicate an optimal VPP performance, with a total expected profit of $22,456. This profit results from all DERs actively participating, generating social welfare in both the DA energy market and FRRM. However, this approach is more suited to less risk-averse VPPs (risk-neutral), which overlook potential risks in revenue generation linked to scheduling decisions. In contrast, more risk-averse VPP, considering worst-case scenarios and CVaR, are discussed further in Section 8.6. It can be noticed that VPP in the proposed risk-averse environment yields a total expected profit of $21,383 respecting potential risks while generating profits linked to scheduling decisions.

8.5. Comparative Results for VPP’s Optimal Bidding Strategy in DA and FRRM

The bidding strategy in this problem is mounted on a two-stage stochastic programming problem. (1) First-stage (here-and-now) bidding decisions: It utilizes the average price and power values to determine the optimal DA bidding decisions. (2) Second-stage (wait-and-see) recourse decisions: After the determination of the first-stage bidding decisions, the recourse decisions in the second stage are undertaken. For simplicity, we denote operating day with D0, and DA bidding with D0 + 1. The comparative bidding results are premised on the optimal power exchange in the DA energy and FRRM markets (up and down), across a 24-h timescale.

8.5.1. DA Bidding

In order to get the optimal bidding decisions for VPP in DA energy market, we have further compared and differentiate the bidding results on two aspects, that is, deterministic bidding (D0) power for a single operating day and scenario-oriented stochastic programming (SOSP) bidding power (D0 + 1). The comparison has been drawn by taking the average values of market prices (PJM market results) which are assumed to be predicted through the price predictor. The deterministic bidding result for the single day (focuses on first-stage decision) has been illustrated in Figure 12(a) showing the average values of market prices as an input parameter to determine the deterministic bidding power. We notice relatively higher market prices and deterministic bidding power results in the evening hours (16:00–21:00) due to peak energy consumption. Additionally, the SOSP bidding decisions for the next bidding day (D0 + 1) have been conducted for each scenario. As explained earlier in this paper, we have generated and reduced large set of scenarios by utilizing FFS&SR. The SOSP is a recourse decision stage which predict and determine the bidding decision for next day. The comparative DA bidding results for the VPP are demonstrated in Figure 12(b). The deterministic bidding power stays higher for the whole 24 h compared with the SOSP bidding power. We can notice higher stochasticity in prices for SOSP to perform bidding decisions in the next operating day.

8.5.2. FRRM Regulation DN

A fully operational VPP responds to the reserve request signal from the independent system operator (ISO), deploying its reserved capacity to meet the actual scenario requirements. Key periods for maximum downregulation are identified as (08:00 to 11:00), (14:00), and (19:00–23:00), exemplifying the best instances for downregulation (Reg-DN) in a 24-h span. During these times, the VPP manages overproduction and surplus load by regulating downward, thereby maintaining optimal power levels. In response to the Reg-D signal, VPP resources participating in FRRM reduce their power production (increasing consumption) to fulfill the downregulation requirement. This process is illustrated in Figure 13(a). The storages such as BESS and thermal (heat) begin their charging; meanwhile, EiB and CHP units maintain their operational status for consistent power output. Notably, market prices tend to peak in the evening (19:00 to 23:00), offering a lucrative opportunity for the VPP to sell energy in the DA market, thereby maximizing profits.

8.6. Risk Assessment Under CVaR

These conclusions underscore the importance of risk consideration in VPP operational strategies, particularly when engaging in energy market transactions.

8.7. Computation Efficiency

The proposed optimization problem is formulated as MILP model and solved in GAMS commercial software (version 24.3.3) [58] utilizing high-performance IBM CPLEX solver (12.6.01). The experimental results of the proposed two-stage scenario-based stochastic optimization model are executed through a PC with Intel (R) Core (TM) i7-9700 CPU 3.60 GHz processor with 32 GB of memory. The time required for computational execution is approximately 5 s, for efficient solution of the proposed model framework.

9.1. Summary of Key Findings

This study presented a risk-averse two-stage stochastic optimization model designed for VPP operations in the DA and FRRM. Significant contributions encompass the incorporation of slow-ramping resources (e.g., CHP, EiB, and thermal storage) alongside fast-ramping resources (e.g., BESS) into a cohesive framework. The suggested approach utilizes the adaptability of various DERs to improve operational efficiency and market profitability, tackling significant issues encountered by VPP operators in multienergy markets.

A distinctive feature of this study is the FFS&SR algorithm, which emerged as a critical methodological innovation. This algorithm guarantees computational efficiency in handling extensive uncertainties in DER operations. It provides a streamlined approach to scenario reduction, preserving essential variability while minimizing computational burdens. The simulation results validated the proposed model over a 24-h planning horizon period across multiple scenarios, yielding a total expected profit of $21,383 through the optimal utilization of aggregated resources. Furthermore, the analysis revealed that the proposed model not only improved computational efficiency but also ensured scalability for larger systems with the higher number of scenarios, all while retaining performance within reasonable timeframes. The trade-off between risk aversion and profit maximization was evident; as with increasing values of the risk aversion parameter, expected profits showed a decline, but the CVaR value consistently increased, demonstrating enhanced risk mitigation. For example, under higher risk aversion, profits declined by a quantifiable amount, while the CVaR value aligned more closely with operators’ reliability expectations, underscoring the adaptability of the framework to varying risk preferences.

Moreover, the model demonstrated superior performance in dual-market environments, effectively optimizing bidding strategies for both DA and FRRM participation. The comparison between the risk-neutral VPP framework and the proposed risk-sensitive approach highlighted the latter’s ability to adapt to varying levels of risk aversion while preserving operational efficiency. Specifically, the model showed a marked improvement in flexibility, enabling operators to adjust resource allocation dynamically to respond to market fluctuations. The findings provide critical insights into how integrating diverse DER types and tailoring bidding strategies to specific market conditions can offer significant economic and operational benefits. By fully utilizing the strengths of aggregated resources, the framework supports an adaptive and resilient energy management strategy. These results lay the groundwork for a robust framework that enables VPP operators to navigate complex and uncertain energy markets with increased confidence and adaptability, providing a practical roadmap for enhancing grid reliability and market profitability.

9.2. Practical Recommendations for Engineers and Decision-Makers

This study’s findings offer practical insights for VPP operators, market regulators, and policymakers.

9.3. Applications for Real-World Decision-Making

This research provides VPP operators with a strategic roadmap for navigating dual-market participation. By integrating the FFS&SR algorithm, operators can streamline computational efforts while maintaining high levels of accuracy in forecasting and decision-making. The methodology’s flexibility makes it suitable for diverse operational contexts, such as integrating RESs or expanding HES solutions. Furthermore, this approach allows for more efficient utilization of DERs in markets with fluctuating demand, allowing operators to synchronize their plans with immediate opportunities and enduring sustainability objectives.

For market regulators and policymakers, the study highlights the importance of enabling frameworks that support risk-averse decision-making and resource integration. Specifically, incentivizing the adoption of slow-ramping resources alongside fast-ramping assets can improve grid stability while ensuring economic viability. Additionally, policymakers are urged to establish common protocols and market regulations that enable the seamless involvement of VPPs across diverse markets. The proposed approach further aligns with global efforts to transition to low-carbon energy systems advocating for effective DER usage, improving energy security, and diminishing greenhouse gas emissions. Moreover, the integration of scenario-based optimization tools like FFS&SR provides actionable insights for addressing regulatory complexities, especially in regions with diverse energy policies. By incorporating these strategies, decision-makers can bridge the gap between theoretical optimization models and practical implementations, driving the adoption of innovative energy solutions at scale.

9.4. Limitations of the Study