Vertical farming - energy market integration: opportunities and challenges

1 Introduction

Vertical farming offers a promising solution to local urban food production in highly controlled indoor environments, resilient to extreme weather, land, water, and resource scarcity (Kozai et al., 2019). Despite its potential, the high capital and operational costs, particularly energy expenses, pose significant barriers to the economic viability of vertical farming. The high energy consumption is primarily due to the heavy reliance on artificial lighting needed to grow plants indoors. The extensive use of artificial lighting makes Vertical Farms (VFs) less energy-efficient compared to greenhouses (Butturini and Marcelis, 2020). The recent energy crisis has highlighted the impact of these energy costs, leading to the bankruptcy of major vertical farming companies in the United States and Europe (Pennisi et al., 2025). Indeed, the high energy-related costs have significantly restricted the current application of vertical farming to high-value crops such as herbs, microgreens, leafy greens, and strawberries (Harbinson and Taylor, 2025). Improving the energy efficiency of vertical farming crops is fundamentally constrained by the practical maximum photosynthetic efficiency of plants, which is typically less than 5% (Li et al., 2023).

At the same time, the global energy grid is undergoing a transformative change with increasing renewable energy production (Hassan et al., 2024). This transformation entails more challenging grid stability due to the rising variability and uncertainty on both the supply and demand sides (Jones, 2017; Impram et al., 2020), but also an increasing democratization of market mechanisms maintaining that stability, aimed at recruiting more assets to help solve the problem. This shift creates opportunities for flexible energy consumers, such as vertical farms, to participate in various Electricity Markets (EMs), including day-ahead, balancing, and flexibility markets–and obtain economic benefits while contributing to grid stability (Lund et al., 2015; Li et al., 2021; Luciani et al., 2024). This participation has the potential to establish a symbiotic relationship between food production systems and the renewable energy grid. VFs can actively contribute to balancing energy supply and demand while receiving substantial economic benefits from participation in EMs.

In natural environments, plants exhibit remarkable energy flexibility, adapting to intermittent sunlight and variable temperature and humidity, both on short and long duration variations. Although in a VF, cultivars differ from those in open-field systems, all crops inherently possess some level of flexibility in light energy utilization due to their adaptation to shading by clouds and canopy (Long et al., 2022). Numerous preliminary studies have demonstrated that, by carefully scheduling lighting adjustments, VFs can both reduce energy costs and maintain crop health and productivity (Robbiani and Törn, 2024; Avgoustaki et al., 2022, 2021; Kaiser et al., 2024). For example, experimental trials on lettuce that adjusted light intensity according to Day-Ahead Market (DAM) (spot) market prices achieved lighting energy cost savings ranging from 13.5% to 20% by shifting consumption to intervals with lower prices, without compromising yield (Blom et al., 2024; Robbiani and Törn, 2024; Arabzadeh et al., 2023). These promising results highlight the potential of optimizing lighting schedules in response to electricity price variations.

The existing studies have primarily focused on reducing energy costs in the DAM (spot) market (Kaiser et al., 2024; Avgoustaki et al., 2022; Robbiani and Törn, 2024). A direct application of it involves aligning the VF daytime photoperiod with the lowest-price electricity hours, effectively selecting the cheapest hours of the day that are equivalent to the operational “day period” of the VF. However, a greater value of energy flexibility lies in participating in energy balancing and flexibility markets, as it can provide additional income that is more than the savings from reducing the energy cost in the DAMs. Achieving this requires modeling the energy flexibility of VFs and developing formal strategies for their optimal integration into EMs. We aim to highlight this opportunity of VF-EM integration while also underscoring the challenges and necessary research efforts, particularly within the horticultural community, to realize its full potential. We formulate the underlying decision-making problem that describes VF-EM integration and discuss critical factors for successful implementation. We also review the existing literature and identify key knowledge gaps that must be addressed to realize the economic benefits of this integration. Finally, we support our discussion with small-scale laboratory experiments, demonstrating the challenges of VF-EM integration.

In addition to lighting, flexibility in VFs may also be derived from temperature control, humidity regulation, CO₂ injection, and irrigation systems; however, these offer limited flexibility compared to lighting. Moreover, the flexibility of building thermal control has been extensively analyzed in the energy literature. Insights from this body of research can be applied to VFs, provided the operational ranges for temperature, humidity, and CO₂ in vertical farming are well defined (Li et al., 2021). Since lighting represents the largest share of energy consumption in VFs, we focus our discussion primarily on that aspect; the complementary climate-control flexibility is beyond the scope of this paper. The rest of the paper is organized as follows:

• Section 2 provides an introduction to suitable energy markets for VF-EM integration and the potential for economic gains.
• Section 3 reviews the state of the art on plant photophysiological responses to variable lighting schedules.
• Section 4 outlines the proposed VF-EM integration framework at an abstract level.
• Section 5 identifies the knowledge gaps on realizing VF-EM integration and discusses directions to address them.
• Section 6 presents a set of experiments demonstrating the effect of variable lighting induced by VF-EM integration on crop yield in VFs.
• Section 7 concludes the paper with a short discussion of experimental findings and final remarks.

2 Demand-side flexibility & energy markets

2.1 Demand-side flexibility

Traditionally, maintaining a real-time balance between supply and demand (grid balancing) in the power grid was achieved through supply-side flexibility. Dispatchable power plants such as gas turbines, CHP systems, and hydropower plants adjusted their production to match demand in real time. However, the integration of weather-dependent renewable energy sources (RES), such as wind and solar, has significantly reduced the controllability of supply. In this context, demand-side flexibility has therefore emerged as a valuable resource in grid balancing (Impram et al., 2020). Demand-side flexibility refers to the ability of energy consumers to adjust their power consumption in response to external signals such as price changes or grid conditions (Junker et al., 2018). In the context of VFs, LED lighting and climate control systems represent significant sources of flexibility. By adapting energy consumption in response to price signals or grid needs, VFs can optimize operating costs while supporting ancillary services and contributing to decarbonization targets (Miskiw et al., 2025).

2.2 Energy markets

In addition to primary wholesale electricity markets such as the DAM and the intraday market, modern power systems increasingly rely on a range of additional market mechanisms designed to procure such flexibility and ancillary services from both supply- and demand-side resources (Burger et al., 2017). Reserve and balancing markets, in particular, enable flexible consumers to monetize their ability to adjust electricity consumption in response to system needs. From the demand side, this adjustment can take the form of up-regulation, where electricity consumption is reduced during periods of system scarcity, or down-regulation, where consumption is increased to absorb surplus generation. For VFs, LED lighting loads provide a natural source of flexibility: lighting intensity can be temporarily reduced to provide up-regulation during grid deficits, or increased during periods of excess renewable generation to provide down-regulation. Through these mechanisms, large- to medium-scale loads such as data centers and VFs can actively participate in grid balancing by offering demand response as a tradable balancing service rather than acting solely as passive consumers.

A central component of this market structure is the Day-Ahead Market (DAM), in which energy is traded on an hourly or quarter-hour basis for delivery on the following day. In the DAM, market participants submit supply and demand bids that are cleared to establish a uniform market price for each delivery interval. For large electricity consumers, including VFs, participation in the DAM primarily determines the baseline energy procurement schedule against which subsequent balancing actions are evaluated. While the DAM does not explicitly procure flexibility, it plays a critical role in shaping consumption patterns and establishing the reference operating point for participation in reserve and balancing markets.

Regarding reserve and balancing markets, taking the European energy grid balancing framework as an example, it consists of multiple market products that differ in activation speed and delivery duration. This includes, (i) Frequency Containment Reserve (FCR) that must respond within approximately 30 seconds and fully deliver the reserve power for at least 15 minutes; (ii) automatic Frequency Restoration Reserve (aFRR) responds within 2 minutes and delivers power for at least one hour; (iii) manual Frequency Restoration Reserve (mFRR) responds within 12.5 minutes and delivers power for at least 15 minutes. Additionally, Fast Frequency Reserve (FFR), capable of responding in 1 second and delivering power for 5–30 seconds, is procured specifically for handling low-inertia situations in power systems with high renewable penetration (Hameed et al., 2023).

Among the four types of markets, we consider mFRR as the primary candidate for VFs. The mFRR market typically exhibits higher price volatility, partly driven by its ongoing liberalization and increasing accessibility, which creates significant potential for economic gains. Second, although aFRR and Frequency Containment Reserve (FCR) operate closer to real time and respond faster to frequency deviations in the grid, they impose extremely stringent technical and operational requirements on participating assets. Consequently, mFRR markets are often considered a practical entry point for incorporating demand-side flexibility. Based on these considerations, the remainder of this discussion focuses on mFRR markets. Nevertheless, other reserve and balancing markets may also be suitable for VFs, depending on the specific regulatory framework of the local electricity market. Therefore, focusing on mFRR does not exclude participation in other market products within the VF–EM integration framework. The concepts presented in this paper are transferable to such markets, potentially requiring modifications to the decision-making framework to account for differences in market design and operational requirements.

2.3 mFRR market

The specific products and market mechanisms within mFRR vary across countries and regions; therefore, we focus our discussion on the mFRR market of the Nordic power system, which serves as the reference system for this study (Khodadadi et al., 2020). mFRR provides tertiary control by manually activating reserve capacity to correct power imbalances and restore system balance. Participation in mFRR by demand-side resources such as VFs is realized through a bidding process in which balancing service providers (BSPs) offer the availability of upward or downward regulation capacity for predefined market time units (MTUs). Each bid specifies the regulation direction (up or down), the offered volume (MW), the bid price (C/MWh of reserved capacity), and the divisibility type, which determines whether the bid may be partially accepted or must be accepted in full (Nordic Balancing Model, 2025b). For VFs, such bids correspond to their ability to temporarily reduce or increase electricity consumption in response to activation signals from the Transmission System Operator (TSO). In the Nordic power system, mFRR is organized into two tightly coupled markets: the Capacity Market (CM) and the Energy Activation Market (EAM). TSOs contract the availability of reserves through CMs, and subsequently activate the required balancing energy from these (and other) bids in real time through the EAM to correct system imbalances.

The CM is a forward-looking market in which BSPs such as VFs are remunerated for committing a specified amount of flexible capacity in advance, thereby guaranteeing its availability to the system operator, irrespective of whether activation ultimately occurs (Nordic Balancing Model, 2023b). The CM is cleared shortly before the closure of the DAM energy market, to secure sufficient reserve capacity for the entire operating day. In the CM, bids are submitted in the DAM time frame, with gate closure occurring at 07:30 on the day before delivery, and the market is cleared shortly thereafter to secure sufficient reserve capacity for the operating day. Bid selection in the CM is primarily driven by price, with bids sorted and accepted in order of increasing cost until the required reserve volume is procured. The market is pay-as-clear, i.e. selected BSPs are remunerated at the market-clearing price for the reserved capacity in each MTU, independent of whether activation ultimately occurs, and no physical adjustment of power consumption is required at this stage. The primary function of the CM is therefore to ensure the availability of adequate balancing capacity prior to real-time operation, with strict compliance requirements to guarantee that committed capacity can be reliably delivered upon call. The current minimum bid size requirements for CM is 1MW.

In contrast, the EAM is a real-time market that determines the actual deployment of reserved flexibility to resolve supply–demand imbalances closer to delivery time. Participation (submitting bids) in the CM entails an obligation to submit accepted bids to the EAM, which is cleared close to delivery (approximately 45 minutes before the corresponding Market Time Unit (MTU) in Nordic mFRR EAM and 25 minutes in Manually Activated Reserves Initiative (MARI)). Figure 1 illustrates the chronological order of these markets for a VF acting as a demand-side flexibility provider. mFRR markets apply dual pricing structures with availability payments (reservation fees) for the CM and utilization payments (activation fees) for the EAM, allowing providers to generate revenue while ensuring that system operators have access to committed resources. The Nordic mFRR EAM is planned to be integrated with the MARI, the European mFRR activation platform, enabling harmonized clearing across EU member states (Nordic Balancing Model, 2025c). From here on, we focus on the MARI framework for the EAM. The minimum bid size requirement for MARI is 1MW.

In the MARI-EAM, BSPs submit activation bids with a structure similar to the capacity market—direction, volume, price, and divisibility, indicating the amount of upward or downward regulation they are willing to provide. Bids are submitted ahead of gate closure, occurring approximately 25 minutes before the start of each 15-minute MTU. Following gate closure, the TSOs’ activation optimization function used in MARI platform selects bids across participating regions to maximize overall social welfare, subject to network and operational constraints, and instructs the respective TSOs on which bids to activate (ENTSO-E, 2023; Nordic Balancing Model, 2024, 2023a). As illustrated in Figure 2, TSO sends activation orders to BSPs 7.5 minutes before the MTU start. MARI EAM requires activated BSPs to deliver power following a standardized trapezoidal activation profile consisting of a 10-minute linear ramp up that starts 5 minutes before the MTU, reaching at least 50% of the activated volume by the start of the MTU, a 5-minute sustained delivery plateau, and a 10-minute linear ramp down, spanning 25 minutes from 5 minutes before to 20 minutes after the MTU start. This delivery shape is a binding obligation under the Electricity Balancing Guideline put in effect through BSP implementation guides issued by the Nordic TSOs. Once the activation orders are dispatched, BSPs effectively have 2.5 minutes to prepare ramping and 12.5 minutes to reach full activation. Although the up and down ramp lasts 10 minutes, the dispatch profile is defined with 1-minute resolution, where the ramping rate is set to one-tenth of the bid volume. For example, a 1MW activation is implemented in 10 steps of 100 kW ramp-up increments and 100 kW ramp-down decrements each minute. For demand-side resources such as VFs, this corresponds to a gradual adjustment of controllable loads by smoothly reducing or increasing LED lighting intensity relative to a predefined baseline. Compliance with the activation profile is mandatory, and deviations from the instructed ramping or delivered volume may result in penalties.

Remuneration in the MARI-EAM is awarded at the regulation price, which is equal to the EAM clearing price for up- or down-regulation, depending on the activation direction (eSett, 2025). For a demand-side flexibility provider, up-regulation results in direct revenue, whereas down-regulation represents a reduced electricity cost, since additional energy must be purchased at the down-regulation price. Nevertheless, Balancing Service Providers (BSPs) still profits economically from down-regulation, as the down-regulation price is less than the DAM clearing price by design.

Participation in mFRR markets requires pre-qualification of technical capabilities, communication systems, and compliance with grid codes (Nordic Balancing Model, 2025a). VFs can participate in mFRR markets individually or through aggregators, depending on the volume of flexibility they can provide. VF aggregators must satisfy requirements such as being a certified BSP with the respective TSO, linking to a balancing responsible party (BRP) for imbalance settlement, passing pre-qualification tests, providing real-time telemetry and dispatch capability, delivering full committed capacity, and complying with technical linking and resting time constraints. Typical pre-qualification requirements include installing real-time communication systems, ability to log real-time measurements, activate remotely, verify activation response, and operate control center with staff when bids are active.

In particular, VFs are well suited to products characterized by higher response times (on the order of a few minutes), shorter delivery duration (15 minutes), a lower minimum bid volume requirement (1 MW), higher price volatility, day-ahead clearing for CM, and near real-time gate closure for EAM.

2.4 Baseline

While providing flexibility services, a baseline is needed to estimate the reference profile of consumption or generation that reflects normal, non-incentivized behavior (Lind et al., 2024). As a general requirement for participation in mFRR in the Nordic countries, this baseline consumption or production plan must be submitted to the respective TSO, specifying the expected consumption or production for each MTU of the following day (Nordic Balancing Model, 2020). The final baseline plan may be updated until 45min before the start of the operational MTU in MARI, thereby allowing bidding outcomes from capacity or intraday markets to be incorporated. In the event of bid activation in the EAM, the BSP (here, the VF) is authorized by the TSO to deviate from the submitted baseline plan. Remuneration and penalty payments are calculated based on the measured deviation from the baseline. Deviations not covered by an activation are settled as imbalances and subject to imbalance fees (eSett, 2025). Baselines can be derived from the nominal energy requirements of the demand process, for example from the nominal LED lighting load in a VF (Ziras et al., 2021).

2.5 Economic analysis of VF-EM integration

This section presents an upper-bound economic analysis of a hypothetical vertical farming facility participating in Nordic reserve capacity and energy activation markets. We focus on the mFRR-type markets in particular. We consider a VF with an installed lighting capacity of 1MW, which is assumed to be fully flexible. In practice, this corresponds to a typical VF dedicated to the cultivation of leafy greens covering a growth area of approximately 5000m². The objective of this analysis is to estimate the potential revenue under a set of simplifying assumptions that are unlikely to fully hold in practice.

2.5.1 Assumptions

The analysis assumes perfect knowledge of market-clearing prices. Under this assumption, bids submitted to the CM are selected such that they are accepted, and the same bid volumes are transferred to the EAM. This assumption ensures that CM obligations are fulfilled and that deviations from the baseline operating plan arise only from authorized EAM activations. We evaluate two assumed activation scenarios:

• Optimistic (upper-bound) case: all bids accepted in the CM are fully activated in the EAM within the same MTUs, with identical volumes.
• Realistic case: only 20% of submitted bids are activated, based on observed activation-to-reserved volume data.

Both analyses neglect the possibility that CM bids may be rejected or may not be activated in the EAM. Additionally, the optimistic analysis does not account for cases in which only a portion of the accepted bids are activated in the EAM.

We assume that the baseline energy usage profile is generated by optimizing against the spot market. While this assumption is reasonable, there is no strict regulation requiring the baseline to be constructed in this way. In principle, higher earnings could be achieved by not constraining the lighting schedule based on spot market optimization and instead prioritizing participation in mFRR markets. However, given the lack of clear rules for baseline construction, optimizing against the spot market provides a robust and practical reference, as this would typically represent the natural operating strategy of a VF even when participating in mFRR markets.

We assume that the VF cannot use more energy in any MTU than the nominal load of 1MW. In practice, this constraint could be relaxed to allow higher lighting intensities during certain MTUs, enabling the VF to increase electricity consumption and potentially generate additional revenue from down-regulation services.

Additionally, the economic analysis considers the gross remuneration received by the BSP for capacity procurement and activation without any aggregator fees. Transaction costs and other operational costs associated with market participation are not included in the calculations. These costs depend strongly on the specific implementation and market participation model and are therefore outside the scope of this conceptual analysis.

2.5.2 Strategy

First, we establish a reference case in which the VF operates under a fixed-intensity lighting schedule with a 16-hour photoperiod: lighting is set to 80% of installed capacity (1 MW) for 16 hours per day, followed by an 8-hour dark period. This schedule is independent of the DAM price variations and represents a simple, commonly used operating strategy. The corresponding energy cost is computed by applying DAM prices to hourly electricity consumption in each Nordic bidding zone. Next, we quantify cost savings from DAM participation by rescheduling lighting to the 16 cheapest hours of each day, consistent with previous studies (Avgoustaki et al., 2022; Robbiani and Törn, 2024). To estimate the additional value of mFRR participation, we use the DAM-optimized schedule as the baseline and select the most profitable time intervals for mFRR, while preserving the vertical-farming constraint of 16 hours of lighting at constant intensity. Specifically, we select 16 hours (64 MTUs) for potential up-regulation and 8 hours (32 MTUs) for potential down-regulation, and then identify the hours with the highest economic value for activation to obtain an upper-bound estimate of additional revenue. For both the DAM and mFRR analyses, the total daily accumulated lighting intensity is constrained to match that of the reference case.

2.5.3 Data

DAM data (Fraunhofer Institute for Solar Energy Systems ISE, 2024), CM data (NUCS, 2025), and EAM data (Nord Pool Group, 2025) from all Nordic bidding zones are considered for the period from 15th February 2024 to 15th February 2025, covering a full calendar year of available data.

2.5.4 Results

Figure 3 shows the reduction in energy costs from each market per bidding zone. Figure 3 illustrates the revenue potential across the different Nordic bidding zones. Bidding zone SE1 in Sweden shows the highest potential, driven by a combination of high clearing prices in both balancing markets and relatively low DAM prices. In contrast, other zones exhibit lower clearing prices, higher DAM prices, or both, which reduces the achievable economic benefits. The results support previous findings that cost reductions achieved from DAM alone amount between 5-20% (Robbiani and Törn, 2024), while higher savings are obtained through participating in the CM and EAM which is between 15-32% with 20% activation probability in EAM. Notably, EAM contributes the largest share of total cost reduction in Denmark and Finland, whereas CM earnings dominate in Norway and Sweden.

3 Plant responses to variable lighting

This section provides background on key photobiological principles essential for understanding how plants respond to the variable lighting conditions required by VF-EM integration. Additionally, it provides a brief review of the existing literature on the effects of variable lighting on plants. A list of notations used in this Section is provided in Table 1.

Table 1. List of photosynthetic symbols and notation.

3.1 Photobiological factors in VF-EM integration

This section provides some key concepts to discuss the effect of light variations on crop growth.

3.1.1 Photosystem II

When studying the effects of variable lighting at the leaf level, PSII is among the most important components of the photosynthetic apparatus (Vass et al., 1992). As one of the two core complexes responsible for photochemical reactions (Caffarri et al., 2014), PSII plays a central role in capturing and utilizing light energy. Light absorbed by the leaf is either used for photochemical activity or dissipated as excess energy. The efficiency with which PSII utilizes the absorbed light is quantified by the effective quantum yield of PSII, denoted as Φ_PSII (Maxwell and Johnson, 2000).

3.1.2 ETR

ETR, derived using Φ_PSII represents the number of electrons transported through the photosynthetic chain. ETR serves as a proxy for estimating total CO₂ assimilation (denoted as A) in crops. Under controlled laboratory conditions, a linear relationship exists between ETR and CO₂ assimilation, making ETR a reliable indicator of overall photosynthetic activity (Maxwell and Johnson, 2000). However, this relationship tends to deteriorate under field conditions or when crops are exposed to stress (Fryer et al., 1998). Given that variable lighting schedules may induce physiological stress, it is likely that the linearity between ETR and CO₂ assimilation weakens under such conditions. A schematic representation of this relationship is provided in Figure 4.

3.1.3 Stomata

Stomata are the microscopic pores on the leaf surface which regulate both the uptake of atmospheric CO₂ and the loss of water through transpiration (Matthews et al., 2018). A closely related physiological parameter is stomatal conductance (denoted as gs), which quantifies how easily gases pass through the stomata. In general, a higher stomatal conductance facilitates increased CO₂ assimilation, but also results in higher water loss (Matthews et al., 2018). Conversely, lower stomatal conductance values restrict both CO₂ assimilation and transpiration. Under steady-state conditions, CO₂ assimilation and stomatal conductance are typically positively correlated due to stomatal regulation that balances CO₂ uptake for photosynthesis against water loss through transpiration. However, during transient phases, such as when lighting conditions change, this relationship can exhibit hysteresis. Importantly, this effect does not represent a static hysteresis in the equilibrium relationship between assimilation and conductance, but rather a dynamic phenomenon arising from mismatched response times (Vialet-Chabrand et al., 2017b; McAusland et al., 2016).

In particular, photosynthetic CO₂ assimilation responds rapidly to changes in light via photochemical processes, whereas stomatal opening and closure evolve more slowly, leading to a temporary decoupling between assimilation and stomatal conductance (Vialet-Chabrand et al., 2013). The dynamics of stomatal behavior are primarily influenced by incident light intensity and the Vapour Pressure Deficit (VPD) between the leaf interior and the surrounding air (Matthews et al., 2018; Vialet-Chabrand et al., 2013). In general, stomatal opening increases with increasing light intensity, underscoring the importance of light-driven regulation in plant gas exchange. Both the PSII and stomata exhibit transient responses when light is applied. However, in the presence of variable light conditions, stomatal responses are typically an order of magnitude slower than the PSII responses (Matthews et al., 2018).

3.1.4 Acclimatization to light

Plants are capable of adjusting to variations in light intensity; however, the effectiveness of this adjustment depends on the degree of acclimatization. Acclimatization in plants refers to physiological processes that enable leaves to optimize photochemical efficiency while minimizing the risk of photodamage from excess light energy (Vialet-Chabrand et al., 2017a). Different lighting regimes influence the acclimatization process and, consequently, the ability of a plant to utilize light energy efficiently. Notably (Vialet-Chabrand et al., 2017a), demonstrated that exposure to variable light conditions led to higher photosynthetic activity across a range of light intensities, suggesting that such regimes promote more flexible and adaptive acclimatization responses.

3.1.5 Light use efficiency and saturation effect

The efficiency of PSII is primarily influenced by the applied light intensity. At lower intensities, leaves can utilize light energy efficiently, but as intensity increases, efficiency declines because excess energy exceeds the processing capacity of the photosynthetic apparatus (Maxwell and Johnson, 2000). This effect is observable in rapid light curves. Figure 5 shows a rapid light curve measured using a Micro-PAM fluorometer, where Φ_PSII and ETR are recorded under increasing light intensities. Figure 6 illustrates the theoretical photosynthetic light response curve, which describes how the rate of photosynthesis changes with increasing light intensity. At low light levels, photosynthesis increases almost linearly with irradiance as light is the limiting factor. However, as the light intensity continues to rise, the rate gradually approaches a plateau, known as the light saturation point, beyond which additional light no longer enhances photosynthesis. At these high intensities, the photosynthetic apparatus becomes saturated, and excess absorbed light energy is dissipated as heat or fluorescence to prevent photodamage, as shown in Figure 6. The light saturation point for lettuce depends on environmental factors and cultivar, however (Yudina et al., 2023), suggests 200–250 µmolm⁻² s⁻¹ as the saturation point for dry weight accumulation. Similar findings by (Fu et al., 2012) report 200 µmolm⁻² s⁻¹ as optimal for light use efficiency and 600 µmolm⁻² s⁻¹ for maximizing crop yield.

The saturation of the photosynthetic apparatus is a key consideration for optimal light use in VF, as increased light generally enhances ETR and growth, but photosynthetic efficiency declines beyond a certain threshold. Consequently, most VFs operate within the linear range of the photosynthetic response curve (below saturation) as shown in Figure 6, where energy use is most efficient. However, in the context of VF-EM integration, it may be advantageous to operate in the non-linear or saturation range to enable substantial down-regulation over shorter time periods.

3.1.6 Effect of high light intensity

High-intensity light applied for short periods can promote growth, but prolonged exposure may induce stress in plants (Shao et al., 2020; Fu et al., 2012). In one study, biomass production increased when one hour of high-intensity light at 500 µmolm⁻² s⁻¹was added to a 16-hour constant light period. However, extending the duration of high-intensity light led to reduced biomass and stress symptoms (Shao et al., 2020). Light energy drives chemical processes in the leaf, and sustained high intensity may reduce the photosynthetic capacity, requiring recovery, an effect known as photoinhibition (Nath et al., 2013; Tyystjärvi, 2013). For instance, light levels of 600 µmolm⁻² s⁻¹and 800 µmolm⁻² s⁻¹over a 14-hour photoperiod have been shown to cause mild and severe stress, respectively, in lettuce (Fu et al., 2012).

High-intensity lighting can also cause irreversible photodamage (Hideg and Murata, 1997). Therefore, the use of high light intensities can be advantageous for VF-EM integration, provided it is carefully managed to prevent photoinhibition or stress-induced damage to the plants.

3.1.7 Metric for photochemical activity

The Daily Light Integral (DLI) is the industrial standard metric used in Controlled Environment Agriculture (CEA) to quantify the total amount of photosynthetically active radiation delivered to plants over a 24-hour period. It measures the cumulative light received by the crop and serves as a practical control variable for regulating crop growth. However, the DLI represents only the integrated photon input and does not explicitly capture the photochemical processes occurring within the plant. Recent studies have introduced an alternative metric, the Daily Photochemical Integral (DPI), defined as the accumulated photochemical activity over a day, computed by integrating the ETR across the photoperiod (Elkins and van Iersel, 2020; Weaver and van Iersel, 2019; Weaver et al., 2019). DPI captures the nonlinear relationship between photosynthesis and absorbed light (Weaver et al., 2019). Since electron transport is more closely linked to actual photosynthetic activity than photon input alone, the DPI has been proposed as a more informative aggregate measure of plant photochemical performance under dynamic lighting conditions. In addition to DLI and DPI, other integrative light metrics have been proposed in the literature. For example, the Weekly Light Integral (WLI) aggregates photon exposure over longer time horizons and has been suggested as a useful descriptor for crop development over extended cultivation periods (Kim and Kubota, 2025).

3.2 Tip burn and variable lighting

Tip burn is a common physiological disorder in lettuce and other leafy vegetables that reduces marketable yield, causes significant food losses, and leads to postharvest problems (Brandl, 2008; Saure, 1998). It is a complex disorder influenced by multiple factors, including root and shoot microclimate, nutrient imbalances, genetic background, and oxidative stress (Assimakopoulou et al., 2013; Birlanga et al., 2021; Carassay et al., 2012). Tip burn appears as necrotic spots or lesions on the tips and edges of mature outer leaves (outer tip burn) and on young, unexpanded inner leaves (inner tip burn) during cultivation. Local calcium (Ca) deficiency has long been recognized as a primary cause of inner tip burn (Cox, 1980; Johnson, 1991). Calcium transport occurs mainly via bulk flow in the xylem and apoplast, so tissues with low transpiration, such as young unexpanded leaves, receive less Ca than older leaves with higher transpiration rates (Epstein, 1961). Tip burn is more common in hydroponic systems and VFs than in field-grown crops, likely due to microclimates with high humidity and limited airflow around the shoot apex (Barta and Tibbitts, 1991; Yu et al., 2024). Studies show that increasing airflow enhances transpiration and Ca translocation to young leaves, reducing tip burn incidence (Goto and Takakura, 1992; Yu et al., 2024). Inner tip burn has also been linked to rapid growth rate and increased Ca demand during accelerated development, such as under high light intensity (Cox et al., 1976; Xu et al., 2020).

There is limited research addressing the effects of variable lighting on tip burn. However, based on current understanding of tip burn mechanisms, variable lighting will likely increase the risk of tip burn. Several reports indicate that variations in irradiance or DLI, can increase tip burn incidence, likely due to imbalances in Ca distribution between young and old leaves (Saure, 1998). For example, Sago (Sago, 2016) while found that increasing light intensity (150→300 µmol m^{− 2} s⁻¹) enhanced Ca transport to outer leaves, while inner leaves remained Ca-deficient and developed tip burn. Large variations in lighting will probably also induce light stress, leading to increased production of reactive oxygen species (ROS), which may cause cellular damage; ROS involvement in tip burn under abiotic stress has been reported previously (Carassay et al., 2012). On the other hand, plants may acclimate to variable lighting over time, enhancing antioxidant capacity and protection against oxidative stress (Bechtold et al., 2025). These responses will depend on the cultivar (Fu et al., 2012; Miao et al., 2023), and those adapted to low light are generally more susceptible to tip burn (Ertle and Kubota, 2023).

Optimizing light spectrum may offer a strategy to reduce tip burn risk under variable lighting, but this topic remains understudied. Changes in light quality could influence stomatal and transpiration dynamics such that Ca distribution between older and younger tissues improves, or spectral treatments may mitigate light stress. For instance, blue light is known to open stomata, increase transpiration, and enhance antioxidant capacity in lettuce (Naznin et al., 2019). This could, in theory, detoxify ROS and increase Ca uptake. A study adding blue light at nighttime increased whole-plant transpiration but did not increase Ca translocation to tissues prone to tip burn (Ertle and Kubota, 2025). Far-red light may mitigate light stress by balancing PSI/PSII excitation, improving photosynthetic efficiency, and reducing ROS formation (Kono et al., 2017). However, recent work reports increased tip burn risk under far-red lighting (Van de Velde et al., 2025). Both the far-red and blue light studies were conducted under constant light. How far-red and blue light interact with variable lighting in relation to tip burn risk remains an open research question.

3.3 Effect of variable lighting

The naturally varying light levels caused by clouds and canopy shading have motivated earlier studies on stomatal dynamics under variable lighting. Most commonly used growth models are based on steady-state responses (Vialet-Chabrand et al., 2013), in which stomatal conductance and CO₂ assimilation rate are assumed constant relative to light and other environmental factors. However, steady-state models neglect the slow temporal response of stomata and may therefore inaccurately predict stomatal conductance and CO₂ assimilation under variable lighting (Vialet-Chabrand et al., 2013). Figure 7 illustrates the temporal lag in photochemical activity and the gap between steady-state models and actual measurements (Matthews et al., 2018). emphasizes the asynchrony between stomatal conductance and CO₂ assimilation, finding that stomatal conductance typically responds slower and is often a limiting factor on CO₂ assimilation. Under variable lighting conditions, this dynamic response can limit photosynthesis during light transitions. As a result, there is considerable focus on developing accurate models of stomatal dynamics to better predict and optimize plant responses under variable lighting regimes (Vialet-Chabrand et al., 2013). developed a model to predict stomatal conductance under natural light variations, and this was further extended to accurately model both stomatal conductance and CO₂ assimilation at the leaf level under natural light variations (Vialet-Chabrand et al., 2016). Lighting variations induced by VF-EM integration can be more abrupt and pronounced than those arising under natural conditions, motivating the need for models that explicitly capture plant and stomatal dynamics under such externally driven and highly nonstationary lighting regimes.

Acclimation plays a significant role in shaping plant responses to variable lighting. For example (Kaiser et al., 2018), found that plants acclimated to variable light performed better when later exposed to similar variations than crops previously grown under constant light, indicating improved adaptability through acclimation. This supports the feasibility of using variable lighting schedules in VFs, as crops may become more efficient under such conditions over time. Another study on plant acclimation to lighting and shading found that the values of Φ_PSII and ETR measured across a range of light intensities were higher in plants grown without shade or partial shading (Zhen and van Iersel, 2017). Short-term acclimation effects have also been studied in vertical farming settings. For example (Nam et al., 2025), observed within-day changes in Non-Photochemical Quenching (NPQ), a protective mechanism that dissipates excess light energy as heat, together with changes in Φ_PSII. These effects were attributed to short-term acclimation that increased photosynthetic efficiency under feedback-controlled lighting. The study aimed to maintain reference levels for Φ_PSII and ETR and found that, within the first day, the lighting intensity required to maintain the desired ETR decreased as Φ_PSII increased. These studies suggest that plants can adapt well to different lighting conditions, including variable and high-intensity lighting.

The effect of variable light levels was studied more concretely by (Bhuiyan and Van Iersel, 2021), who investigated the time required for plants to reach steady-state CO₂ assimilation under lighting that alternated between two fixed intensities every 15 minutes. All crops were exposed to this variable lighting throughout their growth, likely leading to acclimation to frequent light variations. The study found that intensity differences up to 240 µmolm⁻² s⁻¹ had no significant impact on yield, whereas a difference of 320 µmolm⁻² s⁻¹ reduced dry weight by approximately 22% (Bhuiyan and Van Iersel, 2021). This was attributed to increased adjustment time under larger intensity variations, delaying the attainment of steady-state photosynthetic efficiency, similar to what is illustrated in Figure 7. These findings underscore the importance of understanding and modeling efficiency losses induced by variable lighting to fully leverage the inherent flexibility of VF systems. Additionally, it has been observed that continuous 24-hour light treatments on lettuce do not adversely affect plant health or growth, provided excessive DLI is avoided (Zha et al., 2019). This finding opens up possibilities for varying the photoperiod.

While existing studies indicate that plants exhibit substantial flexibility to variable lighting conditions, the underlying photobiological mechanisms governing these responses are still not fully understood. However, precise mechanistic modeling of these effects is complex, and it may not be essential for addressing the VF-EM integration problem described in Section 4. Instead, a phenomenological model that captures the relative changes in growth rate or photosynthetic efficiency under variable lighting could be sufficient to inform the impact of variable lighting on optimal bidding strategies. In the next section, we discuss chlorophyll fluorescence as a practical approach to developing such models.

3.4 Long-term acclimation effects on plant morphology

It is well known that plants also exhibit long-term acclimation to light levels. Under low light, they develop thin, large leaves, whereas under high light, they develop smaller, thicker leaves with higher maximal photosynthesis on a leaf area basis. This acclimation may be important for plant performance under variable light. Optimal crop growth is therefore a trade-off between a high photosynthetic capacity (measured as a high Φ_PSII) and a high leaf area that maximizes light absorption under low light. Crop growth is often analyzed with classical growth analysis. Relative Growth Rate (RGR) of plants is the product of Leaf Area Ratio (LAR) (leaf area per DM) and Net Assimilation Rate (NAR) (DM increase per leaf area). NAR is closely related to CO₂ uptake. Under low light, RGR is most dependent on LAR because of a large leaf area, whereas under high light, NAR becomes more important because the plants must utilize the higher light levels (Lambers et al., 2008).

The trade-off between photosynthesis per unit leaf area (NAR) and leaf area (LAR) will probably change throughout the cultivation period. A large leaf area may be most important for growth in small plants that do not cover the entire growing area, whereas photosynthetic capacity may be more important in late growth stages when the whole growing area is covered, and all light is absorbed. Therefore, leaf area may, in addition to Φ_PSII, be an important parameter for optimizing light level. Leaf area can be estimated non-destructively by using projected area in pictures as a proxy for leaf area. The light level required for optimal RGR will probably increase throughout the cultivation period.

3.5 Chlorophyll fluorescence

Chlorophyll fluorescence measurement is a promising approach for understanding the effects of variable lighting on plants. When light is applied to a leaf, it is absorbed by chlorophyll, and the energy is directed to drive photochemical activity. Excess energy is re-emitted as either heat or light, with the latter known as chlorophyll fluorescence, hereafter referred to simply as fluorescence. By applying light pulses and measuring the resulting fluorescence, it is possible to estimate the fraction of light used in photosynthesis, yielding the effective quantum yield Φ_PSII, which can be used to compute the ETR. There are different measurements of fluorescence depending on whether the leaf is dark-adapted or not (Maxwell and Johnson, 2000). Dark adaptation is achieved by keeping the leaf in darkness, typically for at least 15 minutes (Maxwell and Johnson, 2000). In the dark-adapted state, all PSII photochemical processes are relaxed. Applying a saturating light pulse from the fluorometer then yields the maximum fluorescence level, F_m, and then applying a weak measuring light that does not induce photochemistry provides the minimal fluorescence level, F_o (Maxwell and Johnson, 2000). These two values allow the calculation of the ratio.

FvFm=Fm−FoFm ,

which represents the maximum quantum efficiency of PSII. In healthy, non-stressed plants, Fv/Fm typically ranges from 0.78 to 0.85 (Maxwell and Johnson, 2000). A reduction in this ratio indicates that PSII efficiency is impaired due to stress factors such as excessive light (photoinhibition), nutrient deficiency, drought, or temperature stress (Maxwell and Johnson, 2000; Baker, 2008). Thus, lower Fv/Fm values serve as an indicator of photoinhibition induced by high-intensity light and other environmental stress factors.

When a leaf is exposed to light, it transitions out of the dark-adapted state, and the fluorescence signal reflects ongoing photochemical activity. Under actinic light, the steady-state fluorescence level is denoted as Ft, while a subsequent saturating light pulse provides the maximum fluorescence in the light-adapted state, Fm' (Maxwell and Johnson, 2000). These values are used to calculate the effective quantum yield of PSII (Φ_PSII), which represents the proportion of absorbed light energy being used for photochemistry under the current light conditions (Maxwell and Johnson, 2000; Baker, 2008):

ΦPSII=Fm'−FtFm' .

Φ_PSII parameter reflects the dynamic efficiency of PSII in light and provides insight on how plants regulate photosynthetic energy allocation in response to environmental conditions. The ETR (J) can then be calculated from Φ_PSII with the following equation:

J=0.5 · ΦPSII · PDFa ,

where PDFa refers to the amount of absorbed light, and the factor 0.5 accounts for the assumption that energy is divided equally between Photosystem I (PSI) and PSII. Saturating light pulses applied by modern fluorometers to measure maximum fluorescence temporarily saturate PSII, and studies have shown that frequent application may stress plants and induce photoinhibition (van Iersel et al., 2016). Therefore, such pulses are typically not applied more often than once every 15 minutes, limiting how frequently the plant state can be assessed.

Chlorophyll fluorescence has been widely used to assess crop status, with fluorescence measurements serving as a biofeedback for controlling lighting intensities (van Iersel et al., 2016; Urschel and Pocock, 2018; Nam et al., 2025). Recently (Nam et al., 2025), employed chlorophyll fluorescence-based feedback control to maintain stable Φ_PSII and ETR levels over a 16-hour period. The study showed that both Φ_PSII and ETR based lighting control were feasible, but the ETR-based strategy stabilized more quickly within 30–45 minutes compared to the Φ_PSII-based approach. They also observed a gradual increase in Φ_PSII due to short-term dynamic acclimatization, which reduced the light input required to maintain stable ETR, improving energy efficiency.

3.6 Plants quality assessment

In VFs, assessing the quality of the harvested crop is essential, as market acceptance depends not only on biomass production but also on visual appearance, nutritional composition, and sensory characteristics. Plant quality assessment therefore includes a combination of external morphological traits, physiological indicators, biochemical composition, and consumer-relevant attributes.

External quality is typically evaluated through morphological indicators such as plant height, internode length, leaf elongation, leaf number, and the size of the largest leaf. These characteristics determine the compactness and visual uniformity of the crop, which are important commercial attributes in leafy vegetables produced in VFs. Additional structural descriptors such as leaf area and projected leaf area are also commonly used. Projected leaf area, obtained from overhead imaging, provides a convenient proxy for canopy development and overall plant vigor.

Visual inspection is another widely used method for assessing plant quality. Growers often employ visual scoring systems (commonly on a 1–5 scale) to evaluate traits such as leaf color, tip burn, yellowing, shoot appearance, root appearance, and the presence of disease symptoms such as gray mold. In addition, certain visual attributes can also be quantified objectively using imaging or physiological measurements; for example, leaf color may be related to chlorophyll content or nitrogen status, while root browning is commonly used as an indicator of root stress.

Internal quality assessment focuses on the biochemical composition of the plant and consumer-relevant attributes. This includes the concentration of macro- and micronutrients (e.g., N, P, K, Ca, Mg, Fe, Mn, Zn, Cu), nitrate accumulation, and levels of health-related compounds such as antioxidants. Pigment concentrations, including chlorophyll and carotenoids, provide further insight into physiological stress and nutritional value. Taste and flavor profile, although subjective, can be evaluated through structured sensory analysis protocols.

In the context of VF–EM integration, these quality indicators are particularly important because rapid variations in lighting conditions may influence both plant morphology and physiological stress responses. Table 2 summarizes the most relevant post-harvest measurements used to evaluate crop quality in vertical farming systems.

Table 2. Metrics used to assess crop quality in vertical farming systems.

4 Vertical farming - energy market integration

Now, with the necessary details on EM and plant flexibility presented in Sections 2 and 3, respectively, in this section, we formalize the integration of VF with electricity markets as a sequential decision-making problem under uncertainty. While the economic analysis in Section 2.5 illustrates the revenue potential of VF–EM integration, it relies on perfect knowledge of prices and market outcomes, which is not available to vertical farming operators in practice. To address this, we use the structure and rules of the mFRR market in Section 2.3 to formulate a decision-making framework that explicitly accounts for uncertainty in electricity prices, flexibility availability, market-clearing outcomes, and crop growth dynamics. The proposed VF-EM integration problem involves participation in mFRR-type markets, with the VF providing balancing flexibility ahead of time on the CM and committing to it just in time on the EAM, while acting as a price-taking load on the DAM. Although the focus here is on mFRR-type markets, the formulation presented in this section can be similarly applied to other flexibility products that feature separate reserve and activation markets, such as aFRR.

4.1 Structure of the VF-EM integration problem

The different timescales of the CM (cleared one day before operation) and the EAM (cleared 25 minutes before operation, see Figure 1), allow for a natural decomposition of the decision-making framework into two hierarchically solved problems. At the first level, the CM is addressed as a daily capacity-planning problem, in which a bidding plan is determined together with a corresponding daily lighting schedule for the VF before the DAM prices are released. This schedule is designed to preserve sufficient operational margins to ensure the feasibility of activation of the procured capacity during the subsequent day. Furthermore, the resulting schedule is submitted to the TSO as a baseline plan, against which deviations arising from EAM activations are validated. Unlike large-scale market participants, whose baseline plans commonly stem from price-responsive participation in DAM and intraday markets, the VF considered here is modeled as a passive, price-taking load in the DAM. Consequently, since participation in the EAM requires a baseline plan (cf. section 2.4), the schedule obtained from the daily capacity planning problem directly serves as the TSO baseline.

At the second level, the EAM is addressed as a near real-time balancing problem, which submits voluntary bids, next to legally binding bid submissions from CM obligations, for the upcoming MTUs and implements real-time adjustments to the lighting schedule in response to market activations and the revealed DAM price. While the capacity-planning layer allocates the total available flexibility of the VF across the day, the real-time layer determines instantaneous power consumption based on updated information about the crop state and prevailing market conditions. The following subsections describe the general vertical farming problem and how it can be incorporated into the proposed decision-making framework, and provide details about its main ingredients. A list of notations used in this Section is provided in Table 3.

Table 3. List of notations for the VF-EM decision-making problem.

4.2 Vertical farming system

We consider a VF consisting of n zones, each of which can be characterized by distinct crop types and growth stages. Crop within the VF is modeled using an energetic model that relates the input energy in the form of light intensity to crop growth, measured in fresh weight (g/plant). For a decision-making scheme that optimizes lighting schedules, it is critical to understand the impact of a given light input on crop growth. Therefore, we consider a general crop growth model f as a function of its current growth state and applied light intensity:

xt+1,i=f(xt,i,ut,i),

where xt,i and xt+1,i are the fresh weight per plant in zone i at current time step t and the predicted fresh weight at next time step t+1, respectively, and ut,i is the applied light intensity in zone i at time t measured in µmolm⁻² s⁻¹ (Photosynthetic Photon Flux Density (PPFD)). The applied light intensity is derived from the electrical load Pt,i(MW) allocated to lighting in zone i at time t via the following mapping:

ut,i=1kPPt,i, where kP=0.217·AcropηLED·106.

where A_crop denotes the illuminated crop growth area, ηLED is the LED efficiency, and 0.217J µmol⁻¹ corresponds to the average photon energy in the PAR range.

An example of a crop growth model in CEA is a deterministic model developed by Van Henten et al. Van Henten (1994) and adapted for vertical farming through minor modifications, most notably by Talbot and Monfet (2024) and Graamans et al. (2017). The complete dynamic model is provided in Appendix A. However, modeling crop growth directly through (4) is challenging in practice. Therefore, DLI is often used as a proxy for such a model. The DLI in zone i up to time t can be expressed as:

DLIt+1,i=∑τ=0tuτ,i,

where uτ,idenotes the light intensity applied at time step τ in zone i. To ensure stable growth conditions, the lighting schedule in each zone should maintain the DLI within a predefined acceptable band.

DLIimin≤DLIt,i−DLIt−24,i≤DLIimax, ∀i, t∈{24, 48,…,N},

where DLI_i^min and DLI_i^max are zone-specific bounds on the DLI and the discrete-time index t corresponds to an hourly time step.

In addition to total biomass production, the plants must also satisfy a set of quality requirements specified in Section 3.6. We introduce a crop quality state variable denoted by σt,i, which represents a set of quality indicators associated with the crop in zone i at time t. These indicators correspond to the quality metrics described in Section 3.6. Similar to crop growth model (4), we consider a generic crop quality model that predicts how the quality state is influenced by the applied lighting schedule:

σt+1,i=g(σt,i,ut,i),

where ut,i denotes the applied light intensity. Function g(·) captures the cumulative effects of lighting intensity, variability, and photochemical exposure on crop quality.

A crop quality model as a function of lighting conditions remains highly challenging and currently does not exist in a form suitable for practical use. In practice, crop quality is typically maintained indirectly by constraining properties of the lighting schedule, such as maximum light intensity, spectral composition, and photoperiod. Therefore, both the crop growth and quality models considered in this section are treated as generic functions used to describe the VF-EM integration problem at a high level. This abstraction allows us to formulate the underlying decision-making problem while acknowledging that the development and calibration of such models remain important topics for future research. In practice, these models can be realized through phenomenological models or heuristic proxies such as the dli. This is discussed further in Section 5.

4.2.1 System constraints

Following the crop growth and quality models, we now introduce three key constraints that a VF must satisfy when participating in EMs.

The first constraint ensures that the target biomass Qtarget is achieved at the end of the cultivation cycle:

xN,i≥Qitarget, ∀i .

Secondly, similar to the biomass requirement, crop quality must satisfy a target set of specifications at the end of the cultivation cycle, consistent with the quality metrics described in Section 3.6:

σN,i∈M , ∀i .

Finally, the total electrical power consumption at any time is limited by the net capacity of the farm Pi,max determined by the maximum electrical power of the installed LEDs in each zone:

Pt,i≤Pi,max , ∀t,i

where Pt,i= kP ut,iis the electrical power consumed by zone i at time t, with kP being the conversion factor mapping PPFD to W (5).

4.3 Capacity planning problem

A daily capacity-planning problem is defined to determine the submission of up- and down-regulation bids to the CM, jointly with a baseline lighting schedule for the VF over the subsequent operating day. Bid volumes are selected in coordination with the nominal energy consumption planned in the DAM, such that crop growth requirements and the operational constraints defined in Section 4.2.1 are satisfied while enabling revenue generation in the CM and exploiting DAM price variations. This requires a price forecasting mechanism for both the DAM and the CM over the entire plant cultivation cycle. The problem is solved repeatedly on a daily basis throughout the cultivation period and yields a consumption plan for the following day. The resulting schedule defines the nominal demand for each MTU and ensures that the extreme scenario—where all obligatory bid submissions from procured capacity are activated, remains within the feasibility region defined by the biological and operational constraints in Section 4.2.1. However, this does not render the VF independent of EAM clearing outcomes, since a scenario in which none of the mandatory bids are activated may also challenge feasibility and may require voluntary bid submissions in the EAM. Nevertheless, by bounding the capacity planning problem at this extreme case, the reliance on voluntary bid activations can be reduced.

Let the capacity market bids be drawn from Bt,iCM, denoting the set of all submitted reserve bids for zone i at time t. Each bid k∈Bt,iCM is characterized by a volume vt,i(k), a direction dt,i(k)∈{up,down}, and a bid price λt,i(k). Out of these, Nt,i bids are accepted by the system operator, indexed by j=1,…,Nt,i. The corresponding procured volumes in each direction are then:

Rt,iup=∑j=1dt,i(j)=upNt,ivt,i(j), Rt,idown=∑j=1dt,i(j)=downNt,ivt,i(j).

The resulting projected load P^t,i for the vf depends on the baseline load Pt,inom acquired from the DAM, as well as the accepted bids specified by the volume of procured up- and down-regulation capacity. The projected load for lighting P^t,i is then computed as:

P^t,i=Pt,inom−Rt,iup+Rt,idown,

where Rt,iup/down is the procured reserve volume, which is assumed to be fully activated on the EAM. We represent the net income of the VF from the CM as reward rCM. It is defined as the revenue from capacity procurement minus the combined costs of executing the projected baseline plan in the DAM and the expected reduction in crop value due to yield loss and stress, summed over all zones.

rtCM=∑i=1n(ptCM,upRt,iup+ptCM,downRt,idown−ptday−aheadPt,inom−Qloss(st,i)).

Where ptday−ahead denotes the day-ahead clearing price at time t – assumed to be known from an accurate forecast – ptCM,up and ptCM,down are the predicted reserves market clearing prices for up- and down-regulation, respectively, and Qloss is a function mapping the crop state to an expected economic loss due to yield reduction, quality degradation, or violations of predefined thresholds on plant state variables, in particular the lighting-induced stress state σt,i. This function can be quite complicated to construct in practice.

The net income earned over the planning horizon Tplan (ideally till the end of the cultivation period) is defined as the sum of stage rewards, where each stage t corresponds to one MTU of 15min in the Nordic DAM:

J=∑t=0Tplan−1rtCM ,

where rtCM is the net income of the VF for each time step t.

The daily CM planning problem consists of selecting the sequence of reserve bids and DAM baseline loads for each day over the planning horizon Tplan that maximizes the cumulative reward. Formally, the optimal sequence of decisions can be derived by solving:

{Pt,inom, Rt,iup, Rt,idown*}t=0,…,Tplan−1i=1,…,n=arg maxPt,inom, Rt,iup, Rt,idown(19)t=0,…,Tplan−1, i=1,…,n J .

4.4 Real-time activation market problem

The real-time activation market problem that follows the daily cm planning problem concerns the optimal bidding strategy on the mFFR-EAM and is structured similarly to the capacity planning problem in Section 5.3. The problem is solved repeatedly over short decision horizons prior to the gate closure of each MTU throughout the day, enabling timely adjustments based on updated system and market information. The crop growth model is the same as for the capacity planning problem and given in (4) with the difference that the input is derived from Pt,i, which denotes the actually applied lighting load resulting from the baseline plan Pt,inom together with all activated bid volumes for up- and down-regulation. The corresponding light intensity ut,i is obtained via (5). Pt,i can be computed as:

Pt,i=Pt,inom−At,iup+At,idown,

where At,iup/down are the activated volumes on the EAM, determined by the probability of grid imbalance at time t as well as the probability of activation of offered voluntary bids and obligatory bids resulting from CM participation.

The decision for each zone i and time instant t consists in determining the set of bids Bt,iEAM to submit to the eam for up- and down-regulation. Each bid k∈Bt,iEAM is characterized by a volume vt,i(k), a direction dt,i(k)∈{up,downs}, and a bid price λt,i(k). Out of these, Nt,i bids are accepted and activated by the system operator, indexed by j=1,…,Nt,i. The corresponding activated volumes in each direction are then:

At,iup=∑j=1dt,i(j)=upNt,ivt,i(j), At,idown=∑j=1dt,i(j)=downNt,ivt,i(j).

The income (reward) rEAM is defined as the difference between revenue from bid activations and the costs for the actual consumed energy Pt,iand crop-state-related penalty costs, summed over all zones:

rtEAM=∑i=1n(ptEAM,upAt,iup+(ptday−ahead−ptEAM,down)At,idown−ptday−aheadPt,i−Qloss(st,i)) ,

where ptday−ahead denotes the day-ahead clearing price at time t, ptEAM,up and ptEAM,down are the predicted activation market-clearing prices for up- and down-regulation, respectively. The term Qloss(st,i) represents the expected economic loss due to yield reduction, quality degradation, or violations of predefined thresholds on plant state variables.

Note that, for demand-side market participation, up-regulation generates direct revenue paid by the TSO, whereas down-regulation corresponds to additional consumption at a reduced price (ptday−ahead≥ptEAM,down). In this formulation, since all consumption is settled at the dam price, the vf effectively receives the price difference as revenue from down-regulation.

The cumulative income over the balancing horizon Tbal is defined as the sum of rewards at every time step t, where each step corresponds to one 15-minute MTU on the EAM:

J=∑t=0Tbal−1rtEAM ,

where rtEAM is the net income of the VF in each MTU considered over the balancing horizon.

The real-time EAM problem consists of selecting the optimal sequence of bids for each MTU over the balancing horizon that maximizes the cumulative income. Formally, the optimal sequence of decisions can be derived by solving:

{Pt,i, At,iup, At,idown*}t=0,…,Tbal−1i=1,…,n=arg maxPt,i, At,iup, At,idownt=0,…,Tbal−1, i=1,…,n J ,

subject to the three constraints in Section 4.2.1, as well as further mandatory constraints on bid volumes associated with reserve market participation, given by:

∑j=1Nt,ivt,i,jup≥Vt,iCM,up, ∑j=1Nt,ivt,i,jdown≥Vt,iCM,down, ∀t,i .

4.5 Components of VF-EM decision-making framework

This section discusses the central aspects of the proposed VF-EM decision-making framework, except for the predictive crop model, which is discussed in detail in Section 5.1.

4.5.1 Multi-market participation

Participation of a VF in multiple electricity markets, such as the DAM, CM, and EAM markets, constitutes a sequential decision-making problem with new information revealed in stages as discussed in Sections 4.3 and 4.4. The sequence is governed by the chronological order of market closures and clearings, whereby bids submitted in earlier markets constrain the feasible space of bids in subsequent ones, as shown in Figure 1. To manage the resulting temporal and structural coupling, hierarchical and decomposition-based optimization approaches can be employed. For instance, Model Predictive Control (MPC) provides a temporal decomposition, with a separate finite-horizon optimal control problem defined for each market (Rawlings et al., 2017). Each problem is solved over a receding horizon and updated at the market-specific control interval dictated by the market-clearing frequency.

The structural complexity of multi-market participation can be addressed using techniques such as Benders decomposition (Seyyed Mahdavi and Javidi, 2014). In this context, the master problem typically determines strategic decisions, such as which zones or how much capacity participate in each market, while subproblems enforce operational feasibility and compute detailed market outcomes for each market. Such a decomposition allows the VF to efficiently coordinate decisions across multiple markets, separating high-level bidding commitments from detailed operational recourse while preserving consistency between markets.

4.5.2 Market forecasting

Accurately forecasting flexibility demand and electricity prices across different market segments remains a key challenge in energy markets. This problem has been extensively studied in both academic research and commercial settings (Weron, 2014; Laitsos et al., 2024). The prices and flexibility requirements are influenced by a wide range of stochastic factors, including regional weather patterns, fuel costs, renewable generation forecasts, and transmission constraints among interconnected regions (Keles et al., 2016). In recent years, Machine Learning (ML) methods have become increasingly prevalent for developing high-performance forecasting models, and their accessibility and effectiveness continue to improve (Hong and Fan, 2016; Nowotarski and Weron, 2018). Given the inherently uncertain and time-varying nature of market dynamics, probabilistic forecasting approaches are often employed to characterize the distribution of possible future outcomes rather than single-point estimates (Nowotarski and Weron, 2018).

4.5.3 Treating uncertainty and risk

The decision-making problem for VF-EM integration inherently involves uncertainty arising from both stochastic energy market dynamics and uncertainty in crop growth responses to variable lighting. Properly accounting for this uncertainty is crucial for quantifying the risks associated with crop states and bidding strategies. In this context, risk refers to potential economic losses, which may arise from unfulfilled bid obligations leading to imbalance fees, or from reductions in crop value due to stress-induced quality loss. Key sources of uncertainty include price forecasts, market-clearing outcomes, bid activation probabilities, and plant responses to variable lighting.

Incorporating these uncertainties into the decision-making problem enables the use of risk-sensitive formulations. Depending on the desired level of conservativeness, approaches can range from robust optimization methods (Ben-Tal et al., 2009) to stochastic or risk-aware strategies that leverage probabilistic forecasts and formal risk measures such as Conditional Value at Risk (CVaR) (Birge and Louveaux, 1997; Rockafellar and Uryasev, 2000).

In decision-making problems within the VF-EM decision-making framework formulated in Sections 4.3 and 4.4, uncertainty enters indirectly through the expected procured and activated bid volumes, thus affecting the applied load for lighting in the system. The expected value of activated bid volumes is obtained by considering the probabilities of a grid imbalance requiring up- or down-regulation, bid acceptance by the system operator, and full activation of an accepted bid.

4.5.4 Feedback

Considering the sequential nature of the bidding process, leveraging feedback from realized outcomes can significantly inform and improve future decisions, even in the presence of imperfect predictive models. However, a major challenge arises from the limited observability of certain feedback signals, particularly biological variables such as crop growth and stress, which are difficult to measure accurately and therefore reduce the reliability of the state information. The feasibility of measuring such biological feedback signals is discussed in Section 3.5.

A further challenge stems from the delayed feedback inherent in EMs. In several markets (e.g., reserve procurement), bids must be committed well in advance of their delivery, rendering parts of the decision- making process inherently planning-oriented. Nevertheless, given the relatively long crop growth horizon, information revealed through past market outcomes can still serve as valuable feedback for adapting future bidding strategies.

4.5.5 Computational complexity

Computational complexity is a key performance bottleneck for large multi-stage stochastic optimization problems, such as those arising in VF-EM integration, as the number of scenarios grows exponentially with the length of the prediction horizon. This scenario explosion is further exacerbated when complex system models are employed, due to nonlinear interactions among uncertain parameters. In addition, mixed-integer formulations arising from bid volume granularity or from bidding-curve optimization with both price and quantity as decision variables (Herding et al., 2023) often render the problem computationally intractable or severely limit the length of the prediction horizon. Consequently, simpler approaches such as certainty-equivalent formulations can remain practically relevant, as they help contain problem size and maintain computational tractability.

5 Challenges and knowledge needs

This section discusses the knowledge needed for an effective VF-EM integration, and outlines potential solutions and research directions to overcome the associated challenges. Central to this integration is understanding plant responses to variations in lighting (both intensity and spectrum), alongside the development of phenomenological models that accurately capture the effects of lighting dynamics on crop growth.

5.1 Predictive crop modeling

A predictive model of crop growth and quality is indispensable for optimization-based VF–EM market strategies, as it enables forecasting future crop states, whether for the next day or over an entire cultivation cycle. These predictions allow an optimization scheme to evaluate potential future scenarios and select the most favorable one. As an example (Kaiser et al., 2024), demonstrated in a simulation study that using mechanistic dynamical models (Vialet-Chabrand et al., 2013, 2016, 2021) for integration with DAMs at a 1-hour resolution is feasible, and showed that a 12% reduction in lighting costs could be achieved without loss in modeled CO₂ assimilation. However, the model does not incorporate short-term acclimation responses or whole-plant physiological dynamics. The feasibility of applying these optimizations in practice has yet to be validated experimentally. While these results highlight the potential of hourly optimization, no predictive crop models accurately capture the effects of variable energy input at the 15-minute resolution required by energy markets. In the context of variable lighting schedules, bidding markets can introduce sudden and large variations in light intensity as demonstrated in Section 6. However, it remains unclear how physiological limitations, such as the slow dynamics of the stomatal opening, affect CO₂ assimilation under these rapid 15-minute variations in light intensity, and how such effects can be captured in the crop state model defined in (4) within the VF–EM integration problem proposed in section 4.

Quantifying the relationship between chlorophyll fluorescence parameters and CO₂ assimilation enables the use of non-invasive fluorescence measurements to estimate photosynthetic efficiency and growth in real time. Chlorophyll fluorescence indicators such as ETR, Φ_PSII, F_v/F_m, and NPQ provide insights into photochemical efficiency and plant stress responses, making them attractive candidates for studying plant responses to variable lighting regimes. Since CO₂ assimilation is more directly linked to biomass accumulation than ETR, as illustrated in Figure 4, several studies have investigated the coupling between fluorescence-derived parameters and net CO₂ assimilation rates (Perera-Castro and Flexas, 2023; Flexas et al., 2002). The correlation between CO₂ assimilation and ETR weakens outside controlled conditions (Fryer et al., 1998), motivating the use of advanced modeling techniques. Recent studies have explored machine learning to model this relationship. One study (Zhang et al., 2020) showed that fluorescence data, combined with environmental inputs, can be used in a particle swarm optimization back-propagation (PSO-BP) neural network to accurately predict CO₂ assimilation in cucumber leaves. Similarly (Pappert et al., 2025), used a machine learning model (XGBoost) to predict assimilation in basil and maize from fluorescence data under variable lighting, with high accuracy. However, the reliability and transferability of such models across species, cultivars, and growth environments remains uncertain.

While chlorophyll fluorescence-based measurements provide valuable insights into plant stress responses, these measurements are typically difficult to acquire continuously in real-time commercial VFs. As a result, although fluorescence-derived variables are useful for laboratory analysis of plant responses to variable lighting (as discussed in Section 3), their direct use as state variables in operational VF–EM frameworks is currently impractical. For practical implementations, it may therefore be more appropriate to develop phenomenological crop models that capture the aggregate effects of variable lighting schedules on plant growth and quality. Such models could rely on more easily measurable quantities, such as cumulative photochemical exposure metrics (e.g., DPI) or statistical descriptors of the applied light schedule.

The structure of such a predictive model can range from simple light integrators to detailed digital twins. These models may be mechanistic (e.g., Van Henten, 1994; Vialet-Chabrand et al., 2013, 2016, 2021), purely data-driven neural networks, or hybrid combinations of both. Mechanistic approaches provide high fidelity and interpretability by embedding biological and biophysical parameters to represent leaf- and canopy-level dynamics; however, they require extensive parameterization, calibration, and domain expertise. In contrast, empirical models infer relationships directly from sensor and operational data, making them easier to deploy and adapt across diverse growing conditions, though often at the expense of interpretability and the risk of overlooking key physiological processes. While a detailed photobiological model may not be necessary for effective VF–EM integration, a phenomenological representation is still required to capture how variable energy inputs influence crop growth and quality. From the perspective of VF-EM decision-making, these models should be designed to support optimal decision-making (bidding) rather than focusing solely on their predictive precision, as emphasized in recent decision-making literature (Anand et al., 2024, 2025). This distinction influences the model development process, ensuring that the models prioritize actionable insights and decision-relevant outputs over purely descriptive accuracy.

In addition to crop-growth models, VF-EM integration can benefit from detailed climate models of VF facilities, which combine crop growth dynamics with environmental control variables. This is particularly important when flexibility is provided not only through lighting adjustments but also via controlled variations in temperature and humidity. While modeling crop growth responses presents significant challenges, macro-scale climate dynamics in buildings are well established (Harish and Kumar, 2016) and have been successfully extended to CEA settings (Van Beveren et al., 2015a, b) due to high levels of insulation and controlled air exchange. Accurately representing microclimatic variation at the canopy or even leaf scale, however, remains significantly more complex. Nevertheless, capturing these fine-scale microclimates can provide valuable insights for optimizing local growing conditions and improving overall energy-use efficiency (Graamans et al., 2017).

5.2 Metric for photochemical activity

A standard metric in VF under variable light schedules is the DLI, typically maintained at a fixed value based on constant lighting intensity and photoperiod. This ensures consistent daily light exposure and is generally assumed to correlate linearly with growth (Weaver et al., 2019). Most studies on variable lighting for DAM participation assume a fixed DLI (Avgoustaki et al., 2022; Robbiani and Törn, 2024). However, this may be neither necessary nor optimal for VF-EM integration. First, short-term (e.g., 15-minute) variations in light intensity can influence plant acclimation and photosynthetic efficiency, as illustrated in Figure 7. Second, operating at higher intensities, even when photosynthesis is in the less efficient and saturated region of the light response curve (Figure 6), may be advantageous in order to increase the available range for down-regulation. In such cases, the reduced photosynthetic efficiency associated with leaving the linear region is not captured by a fixed DLI formulation, suggesting that a more variable lighting strategy may be preferable.

Unlike DLI, which does not account for in-leaf photochemical activity, DPI serves as a more physiologically relevant quality metric. Studies have shown that increasing the photoperiod while keeping DLI constant can improve crop yield (Nam et al., 2025). This is likely due to higher DPI at longer photoperiods, as Φ_PSII is higher at lower light intensities, improving efficiency and promoting growth (Nam et al., 2025). In addition, DPI may change throughout the cultivation period, because Φ_PSII is typically lower for small, thin leaves at the beginning of the cultivation period than for larger, thicker leaves later in the cultivation cycle. Therefore, the optimal light level may be lower at the beginning of the cultivation period than at later stages. Φ_PSII and DPI may therefore be useful for optimizing the light level throughout the cultivation period.

In existing work using DPI for biofeedback and lighting control, ETR is typically measured at 15-minute intervals and assumed to remain constant within each interval (Weaver and van Iersel, 2019). However, this assumption may not hold under variable lighting conditions in VF–EM integration, due to the transient response of photochemical activity, as illustrated in Figure 7. Accurately estimating DPI in such settings, therefore, requires dynamic models of ETR, as discussed in Section 5.1, and appropriate temporal integration to account for rapid changes in lighting. Thus, DPI may serve as a more suitable metric than DLI for designing lighting schedules in VF–EM integration, although further research is needed to fully establish and validate this approach.

5.3 Effect of light quality

Optimization of lighting in controlled environments has largely focused on light intensity and scheduling; however, the spectral composition of light also represents a valuable dimension for enhancing crop growth. In particular, blue light has been shown to influence stomatal dynamics, potentially accelerating the transition to photosynthetic steady state and improving overall CO₂ assimilation (Vialet-Chabrand et al., 2021). investigated whether increasing the proportion of blue light in the light spectrum could enhance stomatal responsiveness (the speed and magnitude of stomatal opening), thereby improving photosynthetic efficiency. Their findings revealed strong species dependence: crops such as wheat, soybean, and rice exhibited increased stomatal conductance under blue light, whereas others, including tomato, potato, and tobacco, did not show such responses. The response of leafy greens, particularly lettuce, remains underexplored in this context. Given that blue light is a known regulator of stomatal opening through phototropin-mediated pathways (Kinoshita and Shimazaki, 1999), further investigation into how lettuce stomata respond to blue-enriched spectra could yield insights into enhancing stomatal efficiency and growth performance under dynamic lighting conditions. Incorporating better control of light quality, particularly increasing the proportion of blue light, may offer a strategy to accelerate stomatal responses and reduce loss of photosynthetic activity under variable lighting (Vialet-Chabrand et al., 2021). However, increasing the proportion of blue light may also have adverse effects, such as changes to plant and leaf morphology that may alter overall plant LUE (Wang et al., 2016).

5.4 Crop monitoring and health

Effective autonomous real-time crop monitoring is critical for enabling practical VF–EM integration, particularly during early deployment stages. Traditional assessments of crop growth and quality, such as harvested weight, visual inspections, or biological testing, are typically conducted at or near harvest and thus fail to provide actionable information during cultivation. However, in sequential decision-making frameworks for VF–EM integration, real-time estimation of crop state and early detection of physiological stress development are highly useful. Such information helps compensate for the limited accuracy of predictive models and supports the optimization of energy bidding and lighting decisions. For instance, knowledge of whether crops are underdeveloped or stressed due to recent high-intensity lighting (from up-regulation events), or whether they have exceeded typical growth expectations under low-light conditions (from down-regulation), can significantly influence future bidding decisions.

Achieving such real-time feedback depends on integrating advanced sensing technologies. Common measurement techniques include assessing canopy size using RGB cameras or LiDAR systems, and estimating biomass through computer vision approaches (Shasteen and Kacira, 2023). Hyperspectral and multispectral imaging can detect light-induced stress responses and physiological variations (Taha et al., 2024; Lowe et al., 2017; Mahlein, 2016), while additional parameters such as leaf temperature and nutrient uptake can be monitored using thermocouples (Halbritter et al., 2020) and sap flow sensors (Ferreira et al., 2012). Despite their potential, the widespread deployment of comprehensive, real-time sensing infrastructures in commercial VF systems remains limited by cost and integration complexity. However, recent advancements in low-cost sensors, edge computing, and machine learning–based state estimation have made the prospect of automated, scalable crop monitoring increasingly viable (Liakos et al., 2018; Soussi et al., 2024; Jackulin and Murugavalli, 2022; Kamilaris et al., 2017). These technologies could pave the way for advanced closed-loop control systems that continuously adjust environmental variables based on plant responses, a key requirement for robust VF–EM integration.

5.5 Crop breeding for flexibility

Crop breeding specifically for vertical farming is relatively new (Teo and Yu, 2024; Bhattarai et al., 2025). Although crops used in vertical farming are typically bred for yield, morphology, or taste, there is growing evidence that improving dynamic photosynthetic traits—such as faster stomatal responses and quicker photosynthetic induction—can substantially increase carbon gain under variable lighting. Studies have shown large natural variation in these traits across genotypes and demonstrated that accelerating photosynthetic induction can improve assimilation under dynamic lighting (Sakoda et al., 2020; Yamori et al., 2020; Kimura et al., 2020; Basso et al., 2022; Nazari et al., 2024). Such traits are directly relevant for VF-EM integration. A complementary direction is breeding for phenotypic plasticity, enabling crops to maintain growth and quality despite variability in light, temperature, or nutrient conditions. Research in major field crops has identified genetic architectures underlying plasticity (Gratani, 2014), and advanced controlled-environment phenotyping now allows similar approaches for leafy greens and herbs (Fahlgren et al., 2015; Kaya, 2025). These developments suggest that future cultivars could be specifically bred for energy-flexible operation in line with VF–EM integration.

6 Experimental analysis

This section presents three sets of experiments with light schedules generated from a simulated VF-EM integration scenario, and a control experiment using a fixed light schedule as a reference. The presented experiments neither validate the proposed VF-EM framework (Section 4) nor provide statistically significant conclusions regarding crop growth under variable lighting conditions. Instead, the objective of these experiments is to provide a preliminary analysis of the impact of variable light schedules on crop growth induced by the proposed VF-EM integration, without explicitly accounting for the physiological effects of variable lighting on the plants. Experiments are conducted using simulation outcomes based on historical market data from bidding zone NO3 (Central Norway) over the period 2024-01–01 to 2024-01-18. Figure 8 shows the DAM price evolution over the considered period.

6.1 Laboratory setup

The experiments were conducted in an ebb-and-flow hydroponic vertical farming laboratory (Robbiani and Törn, 2023). Figure 9 shows the crops at the end of the cultivation period. The system is equipped with fixed-spectrum white LED lighting, delivering neutral broad-spectrum light, which allows for continuous variation in intensity within the range of 0µmolm⁻² s⁻¹ to 250µmolm⁻² s⁻¹ (PPFD) at canopy level. Figure 10 shows the normalized light spectrum at 200PPFD, measured at ground level using a spectroradiometer.

Table 4 summarizes all environmental parameters, setpoints, and setup details common to all experiments. All experiments are conducted with Iceberg lettuce (Lactuca sativa), cultivar Great Lakes 118. The pH and electrical conductivity are controlled around the indicated setpoints with hysteresis. Temperature is actively controlled by a heating and ventilation system. Although humidity is not actively controlled, it remains consistently high at 50% to 65% due to evaporation from the drainage tank within the growth chamber.

Table 4. Experimental setup and growth conditions.

For germination, seeds are placed in a pre-soaked growth medium and kept in darkness at room temperature. After four days, once cotyledon emergence is observed in the majority of seeds, the floater is transferred to the growth chamber. All successfully germinated seeds are retained for the growth phase; no selection or exclusion of seedlings is carried out. Following 18 days of light treatment, crops are harvested and subjected to post-harvest measurements. These include the total number of plant shoots and their spatial distribution within the floater, leaf count and length per plant, a visual quality assessment, and individual fresh weight. Furthermore, we measure the energy consumed for lighting using an energy meter installed in the laboratory.

6.2 Experiment protocol

Here we provide the details of all three sets of experiments, describing the light schedules used.

1. Fixed Day-Night Schedule: The first (control) experiment is conducted with a fixed photoperiod of 16 hours followed by an 8-hour dark period. This experiment serves as the reference case for evaluating the effects of market-driven variable lighting. The top row of Figure 11 illustrates the applied light intensity over the 18-day cultivation period, expressed as a fraction of the maximum PPFD indicated in Table 4. The fixed schedule operates at 80% of this maximum, corresponding to 140PPFD during the 16-hour photoperiod, which results in a DLI of 8.06molm⁻² d⁻¹. This experiment is repeated only once.

2. DAM Optimal Schedule: Two experiments were conducted to simulate optimal participation in the DAM. The experiments differ in the temporal resolution at which the controller adjusts light intensity: the first uses an hourly resolution, corresponding to the previously standard MTU in the Nordic DAM prior to October 2025, while the second uses a 15-minute resolution, matching the MTUs currently implemented in the Nordic DAM and the MARI-EAM. Both light schedules were generated by solving the optimization problem defined in (40), using step sizes of 60min and 15min, respectively. The resulting light schedules minimize energy costs relative to the DAM price while satisfying biological constraints on yield (44c) and DLI (44a), where the DLI constraint is enforced with a tolerance of ±10%. The reference values for both constraints are adopted from the fixed day-night schedule experiment. The second and third rows of Figure 11 show the applied light schedules. A full formulation of this problem is provided in Appendix B.1.

3. MARI-EAM Optimal Schedule: Two growth experiments were conducted using an identical light schedule generated from optimal participation in the MARI-EAM. The schedule was obtained by sequentially solving the DAM optimization (Appendix B.1) and the EAM bidding problem (Appendix B.2), minimizing energy costs by shifting loads to low-price periods and generating earnings from bid activations, while satisfying the biological constraints on yield (57) and dli (55) with a ±10% tolerance on the latter. An ideal mfrr participation scenario is assumed, consistent with the optimistic case considered for the economic analysis in Section 3.5, with perfect knowledge of DAM prices, market-clearing prices, and activation volumes. All bids are submitted at the clearing price and are assumed to be fully activated whenever historical data shows activation in the corresponding direction. While this neglects uncertainty in the system and deviates from the multi-market participation framework described in Section 4, it provides a scenario with the high variability in lighting expected from balancing market participation, as opposed to sole load shifting according to the DAM. The resulting schedule, shown in the bottom row of Figure 11, is visibly more variable than the DAM-optimal schedule.

6.3 Results

Table 5 summarizes the results of the experiments. Since the optimization problems (40) and (46) impose a terminal constraint on fresh weight per plant shoot (44c), we use this as the primary yield metric. The average fresh weight per plant is comparable between the fixed and the DAM-optimal schedules. A small increase in yield can be observed for the DAM experiment with hourly resolution. This observation aligns with previous reports on leafy greens subjected to intermittent lighting (Robbiani and Törn, 2024; Avgoustaki et al., 2022) stating that a moderate level of variability in lighting does not negatively affect yield. The DAM-experiment with 15-minute resolution yielded slightly less than the hourly resolution experiment. However, given the limited experimental data available, it is unclear whether this difference stems from biological variability or the small differences between the two light schedules.

Table 5. Summary of results from the five conducted experiments.

Clear differences in yield were observed for the two MARI-EAM experiments, suggesting that the higher variability of the EAM light schedule negatively impacts yield. This is a notable finding, as it hints at a threshold level of variability beyond which crop growth is affected. DAM-induced lighting appears to remain below this threshold, whereas MARI-EAM participation generates excessive variability. The two trials yielded mean fresh weights of 1.54g and 1.80g per plant shoot, respectively, indicating notable variability between runs. Whether this variability is attributable to biological variance alone or is reinforced by the variable light schedule cannot be determined from the available data and requires further investigation.

Energy consumption is similar across experiments, with minor variations arising from the ±10 tolerance on the DLI constraint (44a), which allows the daily electrical load for lighting to deviate from the reference value. By tightening this constraint, energy consumption can be forced closer to the fixed-schedule reference. Interestingly, the MARI-EAM experiments exhibit considerably higher energy consumption, as the DLI constraint is exploited at its upper bound to accommodate additional load through the provision of down-regulation services. In contrast, DAM driven light schedules merely shift periods of high intensity to low-price MTUs, resulting in comparable total consumption to the fixed schedule.

7 Discussion & conclusions

Our experimental findings show that conventional metrics such as DLI are insufficient when lighting varies on short timescales relevant for VF-EM integration. The MARI-EAM experiments with slightly higher DLI showed significant yield reductions. These results indicate that DLI alone is an insufficient metric for constraining crop growth under highly variable lighting. Metrics that integrate photochemical activity, such as the DPI, may better capture the physiological impact of variable light schedules. However, using DPI effectively requires dynamic models of ETR rather than static or steady-state approximations. Further, the relationship between ETR and CO₂ assimilation is not always linear under stress conditions, motivating the use of additional measurements such as gas-exchange analyses to properly characterize when linearity holds (Bhuiyan and Van Iersel, 2021). Additionally, yields from experiments with similar (the two-DAM experiments) or even the same (two MARI-EAM experiments) light schedules show notable variability. Further experiments are needed to clarify whether this variability arises from variable light or from natural biological variation in plant biomass.

Chlorophyll fluorescence measurements offer a promising phenomenological approach to monitoring the real-time photochemical state of crops under variable lighting. Modern fluorometers can measure Φ_PSII and derive ETR at high temporal resolution, generating rich data for understanding crop photophysiological responses phenomenologically. Nonetheless, slow stomatal dynamics introduce transient inefficiencies under rapid light variations (Lawson and Blatt, 2014), suggesting that models must explicitly capture non-steady-state responses. In addition, it would be valuable to identify the lighting conditions under which the linear ETR–CO₂ assimilation relationship holds, and to describe the relationship nonlinearly in regimes where this assumption does not apply. This is beneficial because it allows the model to directly estimate CO₂ assimilation, which is more closely related to biomass accumulation and therefore to the quantities that are ultimately meaningful for VFs.

To conclude, we highlighted both the potential and the challenges of integrating VFs as flexibility service providers within EMs. Such VF-EM integration can lower operational energy costs for VFs and create new revenue streams, thereby enabling urban food production systems to benefit from the ongoing renewable energy transition. However, realizing this potential in practice requires further research to understand how variable energy inputs, particularly lighting, affect crop growth. This knowledge, together with market forecasts and suitable optimization methods, can support the design of optimal bidding and operational strategies for VFs in EMs. Additionally, achieving this in practice may require a flexibility aggregator, depending on the energy consumption of the VF and the local market regulations. Successful VF-EM integration positions VFs not only as an urban food production system, but also as distributed, responsive assets that contribute to the resilience and efficiency of future power grids.

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Footnotes

Edited by: Tiejun Zhao, Niigata Agro-Food University, Japan

Reviewed by: Jesus Lopez Santiago, Polytechnic University of Madrid, Spain