1 Introduction↩︎

Coordinating diverse distributed resources has become essential for enhancing grid flexibility and enabling broader participation in electricity markets. In this context, the rvpp emerges as a framework that unifies drs, ndrs, and fd, leveraging digital infrastructure, advanced forecasting, and decentralized energy management [1]. By aggregating small-scale and distributed assets—often excluded from markets on their own—the rvpp facilitates the integration of res into wholesale markets, thereby potentially providing additional revenues [2]. It also enhances operational flexibility for energy trading and reserve provision [3]. Recent reforms in Spain’s electricity market—such as integration with the European PICASSO platform [4] and the expansion of demand response participation—have reshaped opportunities for rvpp engagement [5]. These developments open new pathways for participation in the dam, srm, and idm [6]. To exploit these opportunities, optimization models must represent the technical, operational, and economic characteristics of rvpps, while also accounting for uncertainties in multi-market participation.

In contrast to traditional power systems—where thermal power plants dominate generation and fossil-fuel units provide the main source of flexibility—modern grids increasingly rely on ndrs. Their weather-driven variability, which leads to forecast errors and limited dispatchability, introduces greater stochasticity compared to conventional portfolios [5]. Achieving carbon-neutral targets therefore requires integrating clean flexibility on both supply and demand sides [3]. Recent studies highlight the role of flexible resources in improving rvpp operation [1], [2], [7], [8]. Approaches include integrating distributed generation and dispatchable loads to enhance dam participation of ndrs under uncertainty [1], using controllable sources such as ess and hydropower to mitigate forecast errors [2], [7], and combining csp with ts to improve dispatchability in wind-dominated vpps [8].

The economic viability of flexible resources strongly depends on the rvpp’s multi-market participation strategy and the role of each technology in shaping profitability. Ancillary service markets, such as the srm, ensure reliability by securing sufficient reserve capacities in advance [9]. Several studies propose multi-market bidding and pricing strategies that integrate demand response, ess, and electric vehicles to improve vpp profitability and enhance the scheduling of ndrs [10]–[12]. Since day-ahead participation are increasingly affected by renewable uncertainty, idms have emerged as complementary markets that allow continuous bid revisions based on updated forecasts [13]. Building on this link, recent works design scheduling, congestion management, and bidding mechanisms across the dam, srm, and idms, leveraging demand flexibility, corrective actions, and rescheduling to reduce forecast errors, renewable curtailments, and exposure to market risks [14]–[16].

Different methods have been proposed to allocate vpp profits among members. Simple schemes, such as equal allocation and proportional sharing, divide profits uniformly or by unit size [17], but fail to capture the real value of heterogeneous resources. To address this, contribution-based approaches such as the sv and mc have been developed. sv-based methods allocate profits by quantifying each unit’s marginal impact on coalition performance and have been applied in energy, balancing, and regulation markets to better reflect unit contributions [18], [19]. The mc method instead measures a unit’s importance by the profit reduction when it is excluded, offering computational simplicity and coalition stability. Recent works demonstrate its practicality by applying mc-based allocation to distribution network operator–vpp models and cost–benefit sharing under distribution constraints [20], [21], making it especially appealing for real-world implementations where fairness and transparency are critical [17].

Although several studies have examined different aspects of vpp operation in electricity markets—such as uncertainty modeling and profit-sharing mechanisms—a comprehensive analysis of how various flexible resources affect rvpp profitability across multiple markets (including the dam, srm, and idms) under multiple sources of uncertainty is still lacking. To address this gap, this paper examines an rvpp composed of diverse flexible resources, including drs (hydropower and biomass plants), csp with ts, and fd, which together support the integration of ndrs such as wf and solar pv. Uncertainty-handling strategies ranging from optimistic to pessimistic are analyzed within a two-stage ro framework to demonstrate the impact of flexible resources on rvpp profitability in multi-market participation. Furthermore, a mc-based profit-allocation method is employed, as it balances fairness and practicality by reflecting the actual contribution of each technology to energy and reserve provision and to the overall viability of the rvpp. Accordingly, the major contributions of this study include:

• To evaluate the trading strategy and the energy and reserve scheduling of rvpp units under different uncertainties—including renewable energy production, demand consumption, and multi-market electricity prices—and to assess the impact of a wide range of decision-making strategies, from optimistic to pessimistic, on trading and scheduling performance.

• To analyze the multi-market participation of rvpp, including the dam, srm, and idms, and to evaluate the role of each market in the overall viability of the rvpp.

• To investigate the effect of various flexible resources and unit combinations—such as drs, ndrs, csp, and fd—along with different levels of demand flexibility on rvpp profitability, and to develop a comprehensive profit-allocation strategy using mc that accounts for the joint effects of market participation and uncertainty, thereby ensuring a fair distribution of profits according to the flexibility provided by each technology.

The paper is organized as follows: Section 2 defines the the problem scope, while Section 3 presents the optimization framework for rvpp multi-market participation. The validation of the model through case studies is presented in Section 4, and final insights are summarized in Section 5.

2 Problem Description↩︎

Figure 1 illustrates the schematic of the rvpp participating in dam, srm, and idm. The figure comprises three levels. At the asset level, multiple drs, ndrs, csp, and fd units are integrated into the rvpp to enhance energy and service provision. At the rvpp operator level, technical and forecast data are collected from units and markets to optimize scheduling and multi-market participation. The operator allocates profits among technologies according to their contribution in each market and the uncertainty-handling strategy adopted. The optimization framework provides bidding strategies for the relevant markets in which the rvpp participates, as shown in the electricity market level. Depending on bidding gate closures, updated forecasts, and delivery times, the operator may co-optimize multiple products or fix the cleared results of previous markets in the optimization problem by adjusting the objective function. For instance, the operator can co-optimize energy and reserve before the dam gate closure but only submit an energy bid to the dam. Once the dam is cleared, the operator can re-optimize participation in the srm using updated forecasts and fixed energy bids from the dam. The rvpp is modeled as a price-taker, submitting zero-price bids to reflect its relatively small scale compared to the system. After receiving market-clearing results, the operator communicates dispatch instructions to its internal units.

The additional profit generated through aggregation, relative to independent operation, is allocated using the mc method, enabling the contribution of each technology to be quantified by excluding it from the coalition. This paper focuses on technologies rather than individual units, aiming to identify which technologies—or their combinations—are most beneficial for the rvpp operator. Unit-level allocation can also be performed if a more detailed comparison is required. The bidding strategy of the rvpp depends on its degree of conservatism toward uncertain parameters, which significantly affects profit allocation, particularly between dispatchable and non-dispatchable units. To address multiple uncertainties in multi-market participation under varying conservatism levels, this paper employs a two-stage ro approach. This framework is suitable as it provides the operator flexibility to conduct multiple simulations in a computationally efficient manner.

3 Formulation↩︎

In this section, the deterministic model for rvpp participation in the dam, srm, and idms is first developed [12]. Then, recognizing that price volatility, as well as generation and demand uncertainties, impact market outcomes, the model is extended to account for these uncertainties. Finally, the mc method used for profit allocation between rvpp units is explained. In 1 –?? , index \(t \in \mathscr{T}\) denotes time periods; \(r \in \mathscr{R}\) refers to ndrs; \(\theta\! \in\! \Theta\) to csps; \(c\! \in\! \mathscr{C}\) to drs; \(d \in \mathscr{D}\) to fds; \(m\! \in\! \mathscr{M}\) to load profiles; and \(u\! \in\! \mathscr{U}\) to rvpp units. Parameters \(\lambda\), \(P\), \(R\), \(C\), \(T\), \(K\), \(\eta\), and \(\Delta t\) represent market prices, electrical or thermal power capacity, reserve ramp rate, operating costs, reserve activation time, start-up multiplier, efficiency, and the duration of time periods, respectively. Decision variables \(p\), \(r\), and \(e\) correspond to electrical or thermal power, reserve, and energy, respectively, while \(u\) and \(v\) are binary variables indicating the status and start-up of units. Superscripts and subscripts \(E\), \(R\), \(\uparrow\), \(\downarrow\), \(SF\), \(TS\), \(\bar{A}\), and \(\underaccent{\bar}{A}\) denote the energy market (dam and idm), reserve market (srm), upward and downward regulation, the sf of csp, the ts of csp, and the upper and lower bounds of variables or parameters, respectively.

3.1 Deterministic Problem↩︎

3.1.1 Objective Function↩︎

The rvpp objective function 1 maximizes total profit in the energy and reserve markets, while accounting for the operating expenses of its units. The terms in 1 represent, respectively: revenues from energy market bids; revenues from upward and downward srm participation; and operating costs of ndrs, csps, and drs.

\[\begin{align} \label{RVPP:32Obj95Deterministic} &\mathop{\max }\limits_{{x \in X}} \sum\limits_{t \in \mathscr{T}} { {\lambda _t^{E}p_t^{E}\Delta t } } + \sum\limits_{t \in \mathscr{T}} {\left[ {{\lambda _t^{{R, \uparrow}}r_t^{R,\uparrow} } +{\lambda _t^{{R, \downarrow}}r_t^{R,\downarrow} } } \right]} \\& - \sum\limits_{t \in \mathscr{T}} {\!\sum\limits_{r \in \mathscr{R}} {C_rp_{r,t}\Delta t} } \!- \sum\limits_{t \in \mathscr{T}} {\!\sum\limits_{\theta \in \Theta} {C_{\theta}p_{\theta,t}\Delta t} } \!- \sum\limits_{t \in \mathscr{T}} {\!\sum\limits_{c \in \mathscr{C}} { {{C_c}p_{c,t}\Delta t } }} \nonumber \end{align}\tag{1}\]

The objective function 1 can be adapted to each market session described in Section 2. When dam+srm is solved jointly, both energy revenues \((\lambda_t^{E} p_t^{E})\) and reserve revenues \((\lambda_t^{R,\uparrow} r_t^{\uparrow}\) and \(\lambda_t^{R,\downarrow} r_t^{\downarrow})\) are active. In the srm alone, only reserve revenues are considered, while energy revenues are fixed by dam outcomes. For idm#1–idm#3, only energy trading terms apply and reserve terms are omitted. Cost terms are always included across all sessions.

3.1.2 Supply–Demand Constraint↩︎

The supply–demand constraint of the rvpp units is expressed in 2 . This constraint contemplates, in a compact way, the expected real-time activation scenarios: upward, downward, and no activation [12]. To capture this, reserve state vectors are introduced as \(\boldsymbol{r}_{t}^{R}=\{r_{t}^{R,\uparrow},-r_{t}^{R,\downarrow},0\}\) for the rvpp and \(\boldsymbol{r}_{u,t}=\{r_{u,t}^{\uparrow},-r_{u,t}^{\downarrow},0\}\) for each unit \(u\in\mathscr{U}\), covering ndrs, csps, drs, and fds. As a result, 2 expands into three distinct equations corresponding to the three activation scenarios.

\[\begin{align} &\!\sum\limits_{r \in \mathscr{R}} \left[ p_{r,t} \!+ \boldsymbol{r}_{r,t} \right] \!+ \!\sum\limits_{\theta \in \Theta} \left[ p_{\theta,t} \!+ \boldsymbol{r}_{\theta,t} \right] \!+ \!\sum\limits_{c \in \mathscr{C}} \left[ p_{c,t} \!+ \boldsymbol{r}_{c,t} \right] \nonumber \\& - \sum\limits_{d \in \mathscr{D}} \left[ p_{d,t} - \boldsymbol{r}_{d,t} \right] = p_{t}^{E}+ \boldsymbol{r}_{t}^{R}~; & \forall t \label{cons:Supply-Demand1} \end{align}\tag{2}\]

3.1.3 Dispatchable Unit Constraints↩︎

Constraints 3 and 4 define the upper and lower bounds of drs production based on the commitment binary variable \(u_{c,t}\). The minimum up/down time (\(UT_c\)/\(DT_c\)) constraints are given in [22] and are omitted here for brevity.

\[\begin{align} &p_{c,t} + r_{c,t}^{\uparrow} \leq \bar P_{c} u_{c,t}~; & \forall c, t \tag{3} \\ & \underaccent{\bar}{P}_{c} u_{c,t} \leq p_{c,t} - r_{c,t}^{\downarrow}~; & \forall c, t \tag{4} \end{align} \tag{5}\]

3.1.4 Non-dispatchable Unit Constraints↩︎

Constraint 6 defines the upper bound of ndrs production using a fixed value for the uncertain parameter \(P_{r,t}\). Constraint 7 specifies the lower bound on energy and reserve outputs [12].

\[\begin{align} & p_{r,t}+r_{r,t}^{\uparrow} \leq P_{r,t}~; & \forall r,t \tag{6} \\ & \underaccent{\bar}{P}_{r} \le p_{r,t}-r_{r,t}^{\downarrow}~; & \forall r,t \tag{7} \end{align} \tag{8}\]

3.1.5 Concentrated Solar Power Plant Constraints↩︎

The csp turbine converts thermal input from both the sf and ts into electricity as formulated in 14  [23]. Constraint 9 limits the thermal output of the sf. Constraint 10 ensures the balance between the turbine’s electrical energy output and its thermal energy input, accounting for sf thermal power, ts charging/discharging, and startup losses, while incorporating the turbine conversion efficiency \({\eta_{\theta}}\). Constraints 11 –12 restrict the csp’s electrical output and reserves based on capacity limits and the binary commitment variable \(u_{\theta,t}\). Constraint 13 represents the thermal energy balance of the ts over time, updating the energy level according to charging and discharging power together with their efficiencies. Minimum up/down time constraints for the csp follow [22] and are omitted for brevity.

\[\begin{align} & 0 \leq p_{\theta,t}^{SF} \leq {P}_{\theta,t}^{SF}~; & \forall \theta, t \tag{9} \\ & \frac{p_{\theta,t}}{\eta_{\theta}} = p_{\theta,t}^{SF} + p_{\theta,t}^{TS, -} - p_{\theta,t}^{TS, +} - K_{\theta} v_{\theta,t} \bar P_{\theta}~; &\forall \theta, t \tag{10} \\ &p_{\theta,t} + r_{\theta,t}^{\uparrow} \leq \bar P_{\theta} u_{\theta,t}~; &\forall \theta, t \tag{11} \\ &\underaccent{\bar}{P}_{\theta} u_{\theta,t} \leq p_{\theta,t} - r_{\theta,t}^{\downarrow}~; &\forall \theta, t \tag{12} \\ & e_{\theta,t}^{TS} = e_{\theta,t-1}^{TS} + p_{\theta,t}^{TS,+} \eta_\theta^{TS,+} \Delta t - \frac{p_{\theta,t}^{TS,-} \Delta t}{\eta_{\theta}^{TS,-}}~; &\forall \theta ,t \tag{13} \end{align} \tag{14}\]

3.1.6 Flexible Demand Constraints↩︎

The demand flexibility in this work enables the rvpp to adapt its fd behavior by either switching among profiles or adjusting within the limits associated with the chosen profile [24]. Constraint 15 establishes the minimum allowable load for fd, accounting for profile-based variability. Constraint 16 guarantees that only one profile is activated at a time. Meanwhile, the feasible domain for fd operation—covering both consumption and reserve contributions—is assigned by 17 and 18 .

\[\begin{align} & p_{d,t} \geq \sum_{m \in \mathscr{M}} \left[ {P}_{d,m,t} u_{d,m} \right]~; & \forall d,t \tag{15}\\ & \sum_{m \in \mathscr{M}} u_{d,m} = 1~; & \forall d \tag{16} \\ & \underaccent{\bar}{P}_{d} \le p_{d,t} - r_{d,t}^{\uparrow}~; & \forall d,t \tag{17} \\ & p_{d,t} + r_{d,t}^{\downarrow} \le \bar P_{d}~; & \forall d,t \tag{18} \end{align} \tag{19}\]

3.1.7 Reserve Provision Constraints↩︎

Constraints ?? and ?? define the upward and downward reserves of rvpp units based on their ramp-rate capabilities and the secondary reserve activation time.

\[\begin{align} & r_{u,t}^{\uparrow} \le T^{R} R_{u}^{\uparrow}~; & \forall u,t \label{Deterministic:32Reserve1} \\ & r_{u,t}^{\downarrow} \le T^{R} R_{u}^{\downarrow}~; & \forall u,t \label{Deterministic:32Reserve2} \end{align} \label{Deterministic:32Reserve}\] {#eq: sublabel=eq:Deterministic:32Reserve1,eq:Deterministic:32Reserve2,eq:Deterministic:32Reserve}

3.2 Robust Problem↩︎

The robust rvpp problem extends the deterministic formulation by accounting for uncertainties in market prices, renewable and solar-thermal generation, and demand. A two-stage ro framework is adopted: in the first stage, the operator determines scheduling and market participation, while in the second, the worst-case realizations of uncertain parameters within prescribed sets are considered. The compact formulation is presented in 23  [12].

\[\begin{align} & \max_{x \in X} \; \min_{\xi \in {\Xi}(\Gamma)} f(x,\xi)~; & \tag{20} \\ & h(x) \leq 0~; & \tag{21} \\ & g(x,\xi) \leq 0~; & \forall \xi \in {\Xi}(\Gamma) \tag{22} \end{align} \tag{23}\]

Where \(x\) denotes first-stage decision variables, \(\xi\) represents the uncertain parameters \({ \lambda_t^{E}, \lambda_t^{R,\uparrow}, \lambda_t^{R,\downarrow}, P_{r,t}, P_{\theta,t}^{SF}, P_{d,t} }\), and \({\Xi}(\Gamma)\) is the corresponding uncertainty set with budget \(\Gamma\). The budget \(\Gamma\) limits the number of deviations from nominal values, balancing robustness and conservatism: \(\Gamma=0\) recovers the deterministic model, while the maximum \(\Gamma\) provides full protection against all deviations. Each budget is an integer from 0 to 24 for each hour, allowing the conservatism level to range from optimistic to pessimistic. The function \(f(x,\xi)\) in 20 accounts for both first-stage decision variables in 1 and uncertain parameters related to electricity prices. The function \(h(x)\) in 21 includes only deterministic decision variables and corresponds to the constraints in 2 –?? that are unaffected by uncertainty. Finally, the function \(g(x,\xi)\) in 22 represents the constraints with uncertain parameters related to ndrs electrical generation, csp thermal production, and demand in 6 , 9 , and 15 .

The two-stage problem 23 is reformulated as a single-level milp using the standard strong duality principle [25], whose detailed formulation is omitted for brevity.

3.3 Profit Sharing via Marginal Contribution↩︎

The mc method is adopted for profit allocation in the rvpp [21]. This approach is attractive because it reflects the actual role of each unit (or technology) across markets: units that contribute more value to the coalition receive a larger share of the additional profit. Thus, the allocation balances fairness and practicality while considering both unit capacity and realized contribution. We denote by \(\Pi^{\mathrm{RVPP}}\) the total rvpp profit with all units included, by \(\Pi_u^{\mathrm{solo}}\) the profit of unit \(u\) when it participates individually in the market, and by \(\Pi^{\mathrm{RVPP}\setminus u}\) the rvpp profit when unit \(u\) is excluded. Based on these definitions, the mc-based allocation is given in 27 .

\[\begin{align} & \rho_u = \frac{\Pi^{\mathrm{RVPP}} - \Pi^{\mathrm{RVPP}\setminus u}}{P_u}; && \forall u \tag{24} \\ & \Delta \Pi = \Pi^{\mathrm{RVPP}} - \sum_{u \in \mathscr{U}} \Pi_u^{\mathrm{solo}}; && \tag{25} \\ & \Pi_u^{\mathrm{alloc}} = \Pi_u^{\mathrm{solo}} + \frac{\rho_u P_u}{\sum_{u \in \mathscr{U}} \rho_u P_u} \Delta \Pi; && \forall u \tag{26} \end{align} \tag{27}\]

Equation 24 defines the normalized marginal contribution of each unit (\(\rho_u\)), i.e., the reduction in overall rvpp profit when that unit is removed, scaled by its capacity. Equation 25 captures the incremental (\(\Delta \Pi\)) profit that the rvpp achieves relative to the sum of units acting individually. Finally, Equation 26 specifies the unit profit allocation (\(\Pi_u^{\mathrm{alloc}}\)): each unit receives its standalone profit plus a share of the incremental profit, weighted by \(\rho_u P_u\). These weights ensure that larger units with higher marginal contributions receive proportionally greater allocations. Moreover, the proposed mc method is budget-balanced, i.e., \(\sum_{u \in \mathscr{U}} \Pi_u^{\mathrm{alloc}} = \Pi^{\mathrm{RVPP}}\).

4 Case studies↩︎

This section presents simulation results based on the proposed framework to evaluate the impact of uncertainties and flexibility resources on rvpp scheduling and profitability across electricity markets. Simulations are performed on a Dell XPS (i7-1165G7, 2.8 GHz, 16 GB RAM) using the CPLEX solver in GAMS 39.1.1. The case study considers an rvpp in Southern Spain consisting of a hydro plant, a biomass unit, a wf, a solar pv plant, a csp with ts, and a fd. Forecast data are modeled using bounds from historical records: solar pv and csp from CIEMAT Spain [26], and the wf from Iberdrola Spain [27]. To avoid overly conservative solutions, bounds are set between the 20th and 80th percentiles. Forecast ranges for production and consumption are shown in Figure 2. fd forecasts are based on three demand profiles from [24], each with a 10–30% flexibility margin allowing demand to deviate above or below nominal levels. Electricity price forecasts for the dam, srm, and idm rely on historical data from [28] and are illustrated in Figure 3. Note that forecast bounds for idms prices tighten as bidding time approaches delivery, reflecting improved forecast accuracy. The updated forecast bounds for ndrs units in the idms are omitted here to avoid cluttering the figures. Technical specifications of all units are listed in Table 1 [24]. Table 2 presents the predefined budgets associated with the different uncertain parameters used in the case studies. Based on these budgets, we define three uncertainty-handling strategies for the rvpp operator: optimistic, balanced, and pessimistic. Since solar pv generation and thermal output of the csp are zero at night, their budgets are assigned smaller values. The budget for the idm#3 session, which spans fewer than 24 hours, is also proportionally reduced. This ensures a consistent share of uncertain hours across the simulation horizon for all parameters.

Three case studies assess the impact of different components and multi-market participation on rvpp performance:

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4.1 Case 1↩︎

Figure 4 shows the energy generation and consumption schedules of the rvpp units, as well as the total reserve of the rvpp in the dam+srm, under different strategic approaches adopted by the rvpp operator. The results show that when moving from optimistic to more conservative (balanced and pessimistic) strategies, the utilization of renewable units—particularly the wf and solar pv—generally decreases during several hours. This occurs because the operator adopts a more cautious scheduling approach to hedge against forecast uncertainty, reducing reliance on variable generation and increasing the contribution from more controllable units. For instance, in the optimistic case, energy fluctuations of the wf occur in hours 9, 11, 12, and 20. In contrast, in the balanced and pessimistic cases, these fluctuations occur during hours 7, 9–12, 17, 20, and 21, and during hours 1, 7–13, 17, 18, 20, and 21, respectively. Although uncertainty in the thermal input energy of the csp is considered, the csp can effectively mitigate these fluctuations with the support of its ts, resulting in only marginal impacts on its final electrical energy output. Additionally, the hydro plant plays a crucial role in compensating for energy shortages from ndrs. For example, in hour 18, the wf generates energy in the optimistic and balanced cases but not in the pessimistic case. This shortage in the pessimistic case is offset by higher energy generation from the hydro plant at that hour.

Figure 5 details the reserve provided by rvpp units participating in the dam+srm under different strategic approaches of the rvpp operator. The results show that adopting more conservative strategies leads to a reduction in the total upward reserve provided by rvpp units. For example, in the pessimistic case, the provision of upward reserve decreases during hours 1–7, 10–12, and 18 compared to the optimistic case. These reductions occur because greater uncertainty negatively impacts the production of ndrs and the consumption of demand, requiring drs to compensate for energy shortages and thereby reducing their availability for reserve provision. In all cases, the hydro plant and csp provide the largest share of upward reserve due to their inherent flexibility. Specifically, the hydro plant contributes significantly during hours 1–7, while the csp supplies reserve efficiently between hours 9–19 when it is available. Notably, although the fd provides upward reserve in the optimistic case, it does not do so in the balanced and pessimistic cases, as its flexibility is primarily allocated to compensate for the energy reduction of ndrs.

4.2 Case 2↩︎

Figure 6 shows the traded energy and reserve of the rvpp across different electricity market sessions under various strategic approaches of the rvpp operator, with the values in each session reflecting cumulative trades that include all previous sessions. The rvpp is primarily an energy seller in the optimistic, balanced, and pessimistic cases, except during hours 8–9. In the optimistic case, where uncertain parameters are allowed to deviate to their worst-case values in only a limited number of hours, changes in total traded energy are observed up to idm#3, with the most significant changes occurring in idm#1. In idm#1, the rvpp acts as an energy seller during hours 8–13 and 17–20, and as an energy buyer during hours 2–3, 15–16, and 21–24. This leads to an increase in total energy sold during hours 10–13 and 17–20, and a decrease in both the energy sold during hours 2–3, 15–16, and 21–24, and the energy bought during hours 8–9, compared to the dam session. In the balanced case, uncertain parameters are allowed to deviate in a greater number of hours. As a result, the energy sold by the rvpp in the dam decreases compared to the optimistic case, particularly in hours 7, 10–18, and 21. Additionally, the up reserve provided by the rvpp is reduced in hours 19–22 compared to the optimistic case. Moreover, changes in the traded energy of the rvpp are observed in all idm sessions, and these changes are of higher magnitude than in the optimistic case. This is because, with increased uncertainty, greater fluctuations in the production of ndrs are considered, making the role of the idm in adjusting the rvpp’s energy more critical. In the pessimistic case, higher uncertainty budgets are applied compared to the previous optimistic and balanced cases. This leads to further reductions in the energy sold and reserves provided across more hours, along with an increase in energy purchased during hours 8–9 to supply internal demand. Additionally, more substantial changes in the traded energy of the rvpp are observed across the idms compared to the earlier strategies.

Table 3 presents the economic results across different multi-market sessions under various uncertainty strategies. The main income of the rvpp is derived from energy and reserve provision in the dam and srm, while the idms primarily serve for energy adjustments. Under more conservative strategies, rvpp revenue in the idm sessions increases compared to the optimistic case. For example, the revenue change in idm#1 between the optimistic and the balanced and pessimistic strategies is 13.4% and 85.8%, respectively. These results indicate that when more uncertainty is considered, the role of the idms in energy adjustment becomes more significant. The total profit across all market sessions, however, is lower in the conservative cases. This is because under a conservative strategy, the rvpp submits lower bids in the energy and reserve markets, which reduces total revenue, while the costs associated with electricity price uncertainty increase. For instance, the profit of the rvpp in the balanced and pessimistic cases decreases by 70.4% and 128.6%, respectively. The corresponding reductions in total revenue are 7.2% and 12.1%, whereas costs rise by 7.1% and 14.4%.

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4.3 Case 3↩︎

Table [table:Economic95Robust95WO95Unit] presents the profit for different rvpp configurations in the dam+srm, where individual technologies are excluded. The total profit (or cost) of the rvpp when all units are included is 8.75 k€, –1.67 k€, and –10.67 k€ under the optimistic, balanced, and pessimistic strategies, respectively. In general, technologies with larger capacity shares, lower operating costs, and dispatchable characteristics have the greatest impact on rvpp profitability. Excluding all drs (hydro and biomass plants) reduces total profit by 40.73 k€ (= 8.75 \(-\) (-31.98)), 39.22 k€, and 38.55 k€ in the optimistic, balanced, and pessimistic cases, respectively. By contrast, removing the fd (treating demand as inflexible) decreases profit by only 7.42 k€ (= 8.75 \(-\) 1.33), 7.78 k€, and 7.44 k€, since just 10% of demand is flexible. Excluding ndrs (solar pv and wf) reduces profit by 30.44 k€, 24.17 k€, and 19.31 k€. Because the rvpp includes a significant share of ndrs (50 MW each of wf and solar pv) and these units have low operating costs, their exclusion leads to notable profit differences compared to drs. However, the contribution of ndrs is more volatile under conservative strategies due to their stochastic production. To enable fair comparison, the normalized contribution of each technology (\(\rho_u\)) is reported. The results indicate that drs have the highest normalized contribution across all strategies, with \(\rho_u\) reduced by only 4.4% and 5.9% in the balanced and pessimistic cases relative to the optimistic case. This confirms that excluding drs strongly affects energy and reserve provision. The fd makes the second-largest normalized contribution after drs, as it provides cost-effective balancing by shifting demand. The csp has a smaller normalized contribution than drs, since its thermal input is subject to uncertainty, unlike drs. For example, in the optimistic, balanced, and pessimistic cases, \(\rho_u\) for the configuration without csp is 44.1%, 46.1%, and 50.0% lower, respectively, than for the configuration without drs. Nevertheless, csp makes a higher normalized contribution than ndrs, as its ts allows it to effectively manage uncertainty and enhance profitability. Notably, the \(\rho_u\) of the configuration without ndrs decreases by 20.0% and 36.6% in the balanced and pessimistic strategies, respectively, compared to the optimistic case, highlighting the strong effect of uncertainty on the normalized contribution of ndrs.

The results in Table [table:Economic95Robust95WO95Unit] also show the profit allocation for each technology (\(\Pi_u^{\mathrm{alloc}}\)), and the profit each technology would earn if participating in the market individually (\(\Pi_u^{\mathrm{solo}}\)). For the drs, the proposed model increases profits by 21.4%, 36.0%, and 52.9% in the optimistic, balanced, and pessimistic cases, respectively. Consequently, the drs achieve a stable profit between 43.34 k€ and 44.97 k€ across all uncertainty-handling strategies, which is reasonable given the flexibility they provide to the rvpp. The corresponding profit increases for the ndrs are 23.0%, 36.0%, and 55.5%, respectively. However, the allocated profit for the ndrs, ranging between 21.83 k€ and 30.56 k€, is more volatile than that of the drs across different uncertainty-handling strategies due to their stochastic production characteristics.

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In the previous case studies, only 10% demand flexibility was considered, and although its direct impact on the rvpp profit was modest, the fd showed a substantial contribution to profit improvement. Therefore, additional simulations are performed to assess how higher flexibility levels influence rvpp performance under different uncertainty-handling strategies. In this regard, Table 5 presents the rvpp profit in the dam+srm for different levels of demand flexibility. The results show that increasing demand flexibility generally leads to higher rvpp profit, with the effect being more pronounced under conservative strategies. For instance, when flexibility increases from 0% to 30%, profit rises by 14.36 k€, 15.87 k€, and 16.70 k€ in the optimistic, balanced, and pessimistic cases, respectively. These findings highlight the importance of fd in enhancing the energy and reserve provision of the rvpp, particularly when uncertainties strongly affect its performance.

5 Conclusions↩︎

This paper analyzes the impact of different flexible resources, including drs, csp, and fd, on the multi-market participation and profitability of an rvpp with a high share of ndrs. The analysis incorporates uncertainties in energy and reserve market prices, renewable generation, and demand consumption using a two-stage robust approach. A marginal contribution method—accounting for each unit’s actual contribution to energy and reserve provision as well as the final profit of the rvpp—is applied to allocate the additional profit of the rvpp (compared to individual unit participation) among its units. Simulation results show how the rvpp operator schedules units and submits energy and reserve bids under optimistic, balanced, and pessimistic strategies. More conservative strategies reduce energy sold and increase energy purchased, providing robustness against worst-case scenarios. Furthermore, in the balanced and pessimistic cases, changes in the traded energy of the rvpp across idm sessions are greater than in the optimistic case, highlighting a stronger need for adjustments in the idm and reinforcing their importance. Additionally, the hydro plant and csp compensate for energy shortages from ndrs under more conservative strategies, which in turn reduces their reserve provision. The results also show that drs and fd make the highest normalized contributions to rvpp profitability, and these contributions remain relatively stable across different uncertainty-handling strategies. By contrast, ndrs make smaller normalized contributions with greater volatility under conservative strategies, since their output is strongly affected by generation stochasticity. The csp provides a moderate normalized contribution: although its production is influenced by thermal uncertainty, its thermal storage effectively mitigates this impact.

References↩︎