Energy Management Model in Controlled Environment Agriculture: A Review

Abstract

Controlled environment agriculture (CEA) has emerged as a vital solution to address the escalating global food demand amidst urbanization and diminishing arable land. However, the high energy consumption of CEA poses significant challenges for sustainable development. This paper provides a comprehensive review of the energy management models within CEA. The basic models of environmental factors such as light, temperature, humidity, and CO₂ concentration are introduced, highlighting their impact on plant growth and energy use. This paper elaborates on the coupling relationships between plant physiological activities and environmental control, facility environment and energy systems, and energy consumption and carbon emissions. Applications of energy management in CEA, including optimal energy scheduling, interaction with microgrids, and planning issues, are reviewed. Future research directions, such as multi-time-scale dynamic modeling, uncertainty modeling, and demand response (DR) modeling under market-oriented mechanisms, are also discussed.

1. Introduction

Against the backdrop of urbanization and shrinking arable land, it is estimated that the global population will reach approximately 10 billion by 2050 [1], and global food demand will increase by 60%. However, the per capita land decreased by 20% during the period from 2000 to 2017 [2]. Traditional agriculture is confronted with rigid constraints of land, water, and environmental capacity. Also, traditional agriculture is an important source of greenhouse gas (GHG) emissions. A total of 11% of GHG emissions come from agricultural activities, among which non-CO₂ gases account for as high as 56%. CEA, sometimes referred to as plant factory (PF), is a modern agricultural production method based on precise environmental regulation. Through the optimized management of key parameters such as light, temperature, humidity, CO₂ concentration, water, and fertilizer, efficient and stable crop production is achieved. Compared with traditional agriculture, the water use efficiency of CEA can reach 40 to 50 times than that of traditional farmland [3]. The utilization rate of nitrogen fertilizer has increased from 30–40% in traditional agriculture to 85–92% in CEA [4]. An increase of 10 to 20 times in yield per unit area is reached, which is equivalent to saving 86% to 92% cultivated land [5]. Amidst the exacerbation of global climate change and the resource limitations encountered by conventional agriculture [6], controlled environment agriculture (CEA) has emerged as a crucial technological avenue for the advancement of sustainable agricultural practices [7], particularly with respect to plant factory with artificial light (PFAL) [8].

CEA can be classified into PFAL and PF with solar. PFAL adopts an opaque and well-insulated structure and is completely dependent on artificial light (AL) with a high yield and space utilization rate [9]. PFs with solar are often called greenhouses (GHs). Their enclosure structures are transparent, allowing for more obvious heat exchange with the environment. The characteristics of PFs are shown in

Table 1. Characteristics of different CEAs.

Type		Characteristics
PFAL	Vertical farming (VF)	Vertical planting layers can maximize space utilization and significantly increase the yield per unit area [10].
	Container PF	Modular design for easy deployment; it has high flexibility and can be used directly outdoors [11].
	Underground PF	Reducing energy consumption by taking advantage of the constant temperature characteristics in the underground space [12].
GH	Closed GH	The growth of crops mainly relies on sunlight, and AL is only turned on when necessary. It is not restricted by external climatic conditions and can effectively avoid the impact of natural disasters on crops [13].
	Open ventilated GH	Smooth circulation with the outside air is conducive to regulating the temperature, humidity and CO2 concentration in the GH. The structure is relatively simple. Therefore, the construction and maintenance expenses are relatively low. It is greatly influenced by the natural environment [13].

.

However, the high energy consumption problem of CEA seriously restricts its promotion. The energy consumption intensity of PFAL per kilogram of lettuce (17 kWh/kg) is approximately more than five times that of summer greenhouses [13], and AL accounts for 60–80% of the total energy consumption [14]. Therefore, energy management is the core challenge for the sustainable development of CEA. Dynamic regulation of multiple environmental parameters such as light, temperature, water, and CO₂ requires the coordination of equipment such as heating, ventilation, and air conditioning (HVAC) and AL, resulting in complex multi-energy flow coupling problems.

This paper will offer a thorough examination of the key models and problems that are receiving focused research attention, concentrating on the energy optimization of CEA. The remainder of this paper is organized as follows. Section 2 describes the environment model in CEA. Section 3 provides multi-disciplinary coupling points in energy management. Section 4 provides main applications. Section 5 identifies some potential research areas. Section 6 concludes this paper.

2. Environment Model in CEA

Light, temperature, water, and CO₂ can affect plant growth, which are dynamically controlled in CEA through electrified equipment [15]. Key environmental factors and equipment in CEA are shown in Figure 1. The interaction of various environmental factors significantly affects energy consumption. Therefore, establishing an accurate environmental model is not only the key to analyzing the operation mechanism of CEA but also the basis for achieving optimal energy scheduling [16].

2.1. Irradiation

Light is the energy source of photosynthesis. Sufficient sunlight ensures the accumulation of organic matter in the crops themselves, promoting their growth and increasing dry weight [17]. Also, light is an important factor affecting energy consumption. AL accounts for approximately 80% of total energy consumption [18]. Heat generated by AL or the sun will affect the temperature in CEA. Appropriate lighting helps improve energy utilization efficiency. The irradiation and heat in a GH are shown in Figure 2.

(1) PFAL

The PFAL has a sealed structure, and light is provided by AL. Indoor illumination can be expressed as:

$$I_{indoor}^{PF}={\displaystyle \frac{I_{AL}}{c_{irr} }}$$

(1)

(2) GH

The GH has a transparent structure. The sun will shine into the greenhouse and reach the canopy by direct or diffuse reflection. Total solar radiation inside a GH can be expressed as:

$$I_{indoor,solar}^1=I_{direct}{\delta }_{direct}+I_{diffuse}{\delta }_{diffuse}$$

(2)

In Formula (2), the first and second items represent the sunlight that directly shines and reflects onto the canopy, respectively. ${\delta }_{direct}$ is related to the solar incident angle. Some literatures set it as a constant, but there are many scholars conducting detailed studies in GHs. A modified formula was adopted in Ref. [19] to calculate total photosynthetic active radiation, which includes both solar and electric lighting. Refs. [20,21] established models of the solar incident angle, the angle of the GH roof, the latitude, and the time, thereby accurately calculating the solar irradiance.

Some GHs are equipped with photovoltaic (PV) panels to provide electricity and reduce energy costs. However, PV can create shades, reducing the amount of sunlight in the GH. Total solar radiation inside a GH with PV can be expressed as:

$$I_{indoor,solar}^2=I_{direct}{\delta }_{direct}\left(1-C_{PV}\right)+I_{diffuse}{\delta }_{diffuse}\left(1-C_{diff}{C}_{PV}\right)$$

(3)

AL is installed in the GH to supplement the light, so the total light inside the GH can be expressed as:

$$I_{indoor,solar}=\left\{\begin{array}{cc}{I}_{indoor,solar}^1,& I_{indoor,solar}^2\end{array}\right\}$$

(4)

$$I_{indoor}^{GH}=I_{indoor,solar}+{\displaystyle \frac{I_{AL}}{c_{irr}}}$$

(5)

PV generates electricity by absorbing sunlight and heat. Therefore, it is necessary to calculate the amount of light that reaches the PV panels, which can be expressed as:

$$I_{PV}=I_{dirrect}{C}_{PV}\mathit{cos}\gamma +I_{PV,diffuse}$$

(6)

In Formula (6), the first and second terms represent the intensity of light directly reaching or reflected on the PV panel from the sun, respectively. Ref. [22] presents the calculation of $\cos \gamma$ under different PV arrangements, and the diffuse reflection intensity is obtained experimentally. In Ref. [23], the intensity of diffuse reflection is refined into the reflection of the sun and the ground. The PV power on the roof of a greenhouse can provide shade inside the greenhouse. Ref. [24] studied the impact of PV shading on the growth of plants.

PV creates shade in the GH, affecting the sunlight inside. Therefore, AL is needed for supplementary lighting. Different PV coverage rates and the required amount of supplementary lighting [23] are shown in

Table 2. Different PV coverage ratio and supplementary light intensity.

PV coverage ratio (%)	25	50	60	100
Supplementary light intensity suggested ($\mathsf{\mu }\mathrm{m}\mathrm{o}\mathrm{l}/\left(\mathrm{s}·{\mathrm{m}}^2\right)$)	51	90.68	150.4	229

.

2.2. Temperature and Heat

Temperature has the greatest impact on plant growth.

Table 3. Optimum temperature and suitable range for three crop climate preferences.

Preferred Climate	$\mathbf{Optimum} \mathbf{Temperature} \mathbf{(}\mathbf{°}\mathbf{C}\mathbf{)}$	$\mathbf{Suitable} \mathbf{Temperature} \mathbf{Range} \mathbf{in} \mathbf{the} \mathbf{Light} \mathbf{Time} \mathbf{(}\mathbf{°}\mathbf{C}\mathbf{)}$	$\mathbf{Suitable} \mathbf{Temperature} \mathbf{Range} \mathbf{in} \mathbf{the} \mathbf{Dark} \mathbf{Time} \mathbf{(}°\mathbf{C}\mathbf{)}$
Mild (basket)	22.1	15.6~28	10.1~18.1
Warm	27	20.6~32.5	15~23
Cold	16	10.5~21.2	4~12

gives the optimum temperature and the suitable range for three crop climate preferences [13]. If the temperature is not within the suitable range, plants will grow more slowly.

Temperature is also an environmental factor that is relatively easy to control [25]. Therefore, it is extremely important to establish the temperature and heat model in CEA. The heat flow is shown in Figure 2.

(1) Heat generated by light

Photosynthetically active radiation (PAR) indicates the portion of light absorbed by plants, which can be expressed as:

$$R_n=\left\{\begin{array}{cc}{\displaystyle \sum _i}{R}_{n,i}^{PF},& R_n^{GH}\end{array}\right\}$$

(7)

$$R_{n,i}^{PF}=c_{irr}{I}_{indoor}^{PF}CAC\left(1-e^{-k_s{LAI}_i}\right)\prod _1^{i-1}{e}^{-k_s{\sum }_1^{i-1}{LAI}_j}$$

(8)

$${LAI}_i={DIS}_i·LAI$$

(9)

$$R_n^{GH}=c_{irr}{I}_{indoor}^{GH}CAC\left(1-e^{-k_{s}LAI}\right)$$

(10)

Formula (8) represents the PAR of the PFAL, and Formula (10) represents the PAR of the GH. Apart from the light absorbed by photosynthesis, other light will generate heat in CEA, which can be expressed as:

$$Q_{PAR}=\left(I_{indoor}^{GH}-R_n/c_{irr}\right)A{k}_{crop}$$

(11)

For PFAL, since there will be some energy loss from AL, the heat generated by the loss part can be expressed as:

$$Q_{AL,heat}=p_{AL}-\left(I_{AL}/c_{irr}\right)A{k}_{crop}$$

(12)

Therefore, the heat related to light in CEA can be expressed as:

$$Q_{rad}=Q_{PAR}+Q_{AL,heat}$$

(13)

(2) Heat loss by transpiration

Up to 99% of water in plants is lost through transpiration. The Penman–Monteith equation is usually adopted for transpiration.

$$Q_{trans}=g_{e}L·VCD$$

Model-specific constants are provided in Ref. [26]. The $VCD$ calculation is provided in Ref. [20]. Ref. [27] holds that the transpiration rates of crops are different during the day and at night. Based on Baille’s model [28], two transpiration models for the day and night were established.

(3) Heat loss from the envelope structure

The heat loss of the envelope structure is usually calculated by the heat conduction formula.

$$Q_{envelope}=\sum _v{C}_v{A}_v\left(T_{air}-T_o\right)$$

(14)

(4) Others

There is ground heat dissipation and ventilation heat dissipation in the GH, which can be respectively expressed as:

$$Q_{ventilation}={\rho }_a{N}_{ven}{C}_{pi}V\left(T_{air}-T_o\right)$$

(15)

$$Q_{gound}=C_{g}A\left(T_{air}-T_o\right)$$

(16)

Ref. [29] analyzed the heat at each layer of the cultivation shelf. In Ref. [20], thermal balance equations were established at three microscopic levels: crop leaves, crop root soil, and greenhouse air. Not only was the heat lost through transpiration considered, but also the solar incident angle was calculated based on different periods of the year and the geographical location of the GH, thereby calculating the light transmittance of the roof. In Ref. [30], the GH contains sunshade curtains and a pad cooling system for regulating the indoor temperature. In Ref. [31], a numerical simulation was conducted on the dynamic heat transfer problem between underground PFs and surrounding rock layers. Ref. [32] established a thermodynamic model of the GH, combining the equivalent heat capacity and thermal resistance of each component of the GH into a circuit, and using the resistance–capacitance model to describe the thermal behavior of the GH.

2.3. Humidity and Water

It is necessary to model humidity and water in CEA. Appropriate humidity can maintain ideal conditions for plants, prevent diseases, and optimize plant transpiration and nutrient absorption. Under conditions of high humidity, condensation water on the roof and plant leaves may cause fungal diseases. Under conditions of low humidity, the process of photosynthesis slows or halts, resulting in slow plant growth [33].

(1) Relative humidity

Relative humidity can be expressed as [34]:

$${RH}_{air}={\displaystyle \frac{H_{air}}{H_{air,sat}}}$$

(17)

$${\displaystyle \frac{d{H}_{air}}{dt}}={\displaystyle \frac{1}{h}}\left\{g_{e}VCD-g_v\left(H_{air}-H_{out}\right)-H_{cov}\right\}$$

(18)

$$H_{cov}=g_c\left[c_{cov,1} e^{c_{cov,2} T_{air}}\left(T_{air}-T_{out}\right)-\left(H_{air,sat}-H_{air}\right)\right]$$

(19)

The calculation of $H_{air,sat}$ can be found in Ref. [30]. The first, second, and third terms on the right side of Equation (18) indicate the water vapor generated through plant transpiration, the water vapor movement caused by ventilation, and the water vapor condensation on the cover, respectively. The calculation of $g_c$ can be found in Ref. [35].

(2) Irrigation

The most commonly used equation for transpiration is the Penman–Monteith equation [36], as follows.

$$ET=k_c{\displaystyle \frac{c_{ET,1}{R}_n∆+\mu \frac{c_{ET,2}}{T_{crop} + c_{ET,3}}\left(e_s-e_a\right)}{∆+c_{ET,4}}}$$

(20)

Ref. [37] conducted correlation modeling of temperature and humidity for each sub-device of air-conditioning. However, in the Penman–Monteith equation, the parameters of surface resistance and air resistance are too complex to be calculated [38], so this model is not practical. Refs. [39,40] proposed the bi-crop coefficient model. Refs. [23,41,42] adopted the improved Penman–Monteith equation formula and established the power load model of irrigation equipment. Ref. [43] holds that the transpiration process in open environments such as fields or GHs is greatly influenced by environmental factors. The Penman–Monteith equation is suitable for use. However, in PFAL, the influence of environmental parameters is reduced. Therefore, this literature simplifies the Penman–Monteith equation.

Due to the loss of some water by transpiration, irrigation is needed to maintain the water balance. The irrigation model can be expressed as Equation (21).

Table 4. Irrigation water demand.

Crop	Water Demand (mm)
	Chengdu	Haikou	Jinan
Lettuce	3.07	3.83	3.01
Cabbage	2.95	3.69	2.90
Tomato	3.41	4.26	3.34
Sweet pepper	3.18	3.97	3.12
Cucumber	3.07	3.83	3.01

provides the water requirements for different crops [39].

$$I_{irr}=ET$$

(21)

For the irrigation model, Ref. [44] considered water resource scheduling in the GH and established a two-stage stochastic optimization model considering uncertainties such as renewable energy generation, load demand, precipitation, and reservoir inflow. In Ref. [32], multiple GHs share one reservoir, and a water balance equation between water pumps and one reservoir is established.

2.4. Carbon Dioxide

CEA plays a significant role in carbon emission management. CO₂ cycling systems not only participate in the physiological processes of plants (such as photosynthesis and respiration) but also can serve as flexible regulatory units in energy scheduling, participating in the carbon emission management of the energy system.

2.4.1. Carbon Sink

The carbon sink refers to the amount of carbon absorbed. It is achieved by means of afforestation and grass planting, absorbing CO₂ in the atmosphere and fixing it into trees, vegetation, or soil, thereby reducing the CO₂ concentration in the atmosphere.

(1) Photosynthesis

The model of CO₂ in photosynthesis was established as [45]:

$$E_{crop}=LAI·q_{pr}A$$

(22)

Multiple factors, such as leaf temperature, total resistance of the leaf blade, and light density, were considered in Ref. [41]. Reasonable parameters can be adopted according to the crop variety, stage, and area. An exponential model related to solar irradiation and AL heat was adopted in Ref. [35]. Ref. [46] adopted exponential models related to indoor area, indoor temperature, and CO₂ concentration.

(2) Other

The carbon sink in CEA also includes the CO₂ loss through exchange with external air and the carbon absorbed by the soil. The CO₂ absorbed by the soil can be expressed as:

$$E_{soil}=3^{{\displaystyle \frac{T_{soil}}{10}}}{p}_{s0}A$$

(23)

The amount of CO₂ exchange with the air can be expressed as:

$$E_{ventilation}={\displaystyle \frac{1}{c_T}}{N}_{ven}V\left(c_{in}-c_o\right)$$

(24)

2.4.2. Carbon Source

Carbon sources refer to carbon emissions, which are the processes, activities, or mechanisms that release carbon into the atmosphere. Carbon sources in CEA include carbon produced by crop respiration, carbon emissions from power generation activities, and carbon released by CO₂ fertilization devices.

(1) Respiration

The CO₂ produced by crop respiration can be expressed as [47]:

$$E_{respiration}=c_{resp,1}{X}_d{2}^{\left(c_{resp,2}{T}_{air}-c_{resp,3}\right)}$$

(25)

(2) Power supply

An important carbon source for CEA is the carbon emissions generated by power supply. Ref. [41] precisely modeled the CO₂ produced by biogas and gas boiler power generation. The carbon produced by biogas power generation includes the CO₂ leaked from methane, the carbon produced by biogas combustion, and the carbon existing in biogas itself. Most PFs need to purchase electricity from the power grid. The carbon emissions generated by the purchased electricity can be calculated by methods such as the grid baseline emission factor [41], carbon flow [48,49], and marginal carbon intensity [50,51]. The CO₂ emissions can be expressed as:

$$E_{elec}=\sum _k{c}_k{p}_k$$

(26)

The power grid is included in $p_k$. When the power supply is photovoltaic, wind turbines (WTs), or other power sources without CO₂ emissions, $c_k$ is taken as 0.

2.5. Other Environmental Models

2.5.1. Time Scale

The control strategy of CEA is usually a short-term control of 15 min, which describes the environmental dynamic properties [52]. In Ref. [53], a fluid dynamics model was developed to predict the distribution of radiation, leaf temperature, air flow velocity, and relative humidity within the canopy. The measurement data were sampled at intervals of 15 min to verify the boundary conditions of the CFD model (Fluent, Ver. 2021 R2; ANSYS Inc., Canonsburg, PA, USA).

Model predictive control (MPC) effectively controls the microclimate of the GH by generating the optimal control trajectory at each time step, and can effectively handle nonlinearities [54]. Ref. [32], taking 15 min as the sampling intervals, established the differential equations of temperature, humidity, and CO₂ concentration based on mass and energy equilibrium. Ref. [55] developed a discrete MPC algorithm using the state space model to maintain the temperature in CEA. Ref. [56] developed a control strategy based on hierarchical MPC, which reduced the operating cost by 72.07% in South Africa.

The time scale of CEA varies from seconds to days. The power schedule and HVAC planning are usually continuous, at the minute or hour level, while irrigation and fertilization in CEA is discrete, calculated by hours or days, and plant growth is usually measured by days. Many studies optimize the energy scheduling of PFs at multiple time scales. In Ref. [57], a bi-level GH model with multi-energy power supply based on combined heat and power (CHP) generators, gas boilers, and thermal energy storage (ES) was established. The first layer aims to minimize economic efficiency and conducts static optimization of electrical energy. The second layer considers multi-physical dynamics of CHP, boilers, etc. Based on artificial neural networks (ANNs) [58], the refined dynamic modeling of the energy control system was carried out. Ref. [59] proposed a multi-time-scale energy management scheme considering uncertainties of renewable energy. The fast and slow time scales are used to simulate the rapidly changing power process and the thermal simulation process, respectively. The two processes are coupled through the Markov decision process, considering the interaction between the electrical and thermal processes.

2.5.2. Integration of Artificial Intelligence (AI)

Modeling the effects of the environment on crop growth is a primary obstacle restricting interdisciplinary research in agriculture [60]. Due to the mutual influence of environmental factors such as temperature, light, water, and CO₂, how to quantitatively measure the impact of environmental control measures on plants is a very difficult problem [61]. The effect of energy management for PFs usually depends on the accuracy of the models. Generally, the differences in geographical location, facility environment, and climate of PFs make it very difficult for us to obtain accurate data models [47].

Based on the limitations of CEA modeling, some scholars have begun to adopt model-free methods, namely AI technology. AI can implicitly learn and adjust complex variables such as light, temperature, water, air, and fertilizer, and can be flexibly applied to PFs in different situations without detailed models. Ref. [62] uses the multilayer perceptron model to control the temperature of semi-enclosed GHs. Ref. [63] developed an MPC strategy based on output feedback for controlling the microclimate in GHs for strawberry production. The results showed that the root mean square error of MPC and the conventional control was 2.45 °C and 3.01 °C, respectively. In response to the uncertainty of weather, Ref. [64] compared the results based on the analytical method of mass and energy balance and an artificial neural network (ANN). The results showed that the ANN model had higher prediction accuracy. Based on the optimal sequential decision-making ability, Ref. [65] adopted deep reinforcement learning (DRL) for energy management of CO₂, lighting, and HVAC systems in PFs, without the need for detailed information on plant photosynthesis, respiration, and transpiration rates. A total of 30% of energy was saved. Ref. [66] promoted a DR strategy that reduced the load demand of GHs by 28%. Ref. [67] combined the photosynthesis and respiration models with deep learning, and adopted physics-informed deep learning technology to optimize the energy use and crop production of PFs.

Despite the significant promise of AI in CEA, limitations emerge as well. AI models trained on data from one specific CEA setup often fail to generalize effectively to other environments with different layouts, equipment, cultivars, or climate conditions. Model generalization and adaptability pose a challenge. Heterogeneous CEA environments are complex, nonlinear systems with numerous interacting variables and significant uncertainties. Current AI models often struggle to fully capture these complex dynamics. Compared to traditional agriculture, the construction and operational costs of CEA are inherently higher. The integration of AI in CEA environments is likely to further increase these expenses and presents financial challenges.

3. Multi-Disciplinary Coupling Points in Energy Management

As a complex multi-disciplinary coupled system, the energy management of CEA requires a comprehensive analysis of the interactions among fields such as plant physiology, environmental engineering, low-carbon economy, and energy scheduling. The coupling relationships between plant physiological activities and environmental control, facility environment and energy systems, and energy consumption and carbon emissions are particularly crucial, forming a multi-dimensional complex coupling network.

3.1. Coupling of Plant Physiological Activities with Environmental Control

The physiological activities of plants are directly influenced by environmental conditions. For example, as the carbon source for photosynthesis, CO₂ will significantly alter the photosynthetic rate, thereby affecting the growth, quality, and final yield. The physiological activities of plants also have a feedback effect on the surrounding microenvironment. For instance, the transpiration of plants releases a large amount of water vapor, increasing the humidity of the air. At the same time, it lowers the temperature due to the heat absorption during water evaporation. There is a bidirectional dynamic coupling relationship between plant physiological activities and environmental factors.

3.1.1. Environment Constraints

The environmental parameters for plant growth need to be strictly limited within an appropriate range. Take CO₂ as an example. Although it is an essential substrate for photosynthesis, excessively high concentrations can inhibit the stomatal conductance of leaves, weaken transpiration, and lead to nutrient deficiency and premature leaf senescence in plants.

Target daily light integral (DLI) can reflect both the light intensity and the duration simultaneously.

Table 5. Crop ideal DLI.

Crop	Lettuce	Cabbage	Tomato	Sweet pepper	Cucumber
DLI	14.51	17.35	28	15	17.5

shows the ideal DLI for different crops [39,42].

DLI can be expressed as follows.

$$DLI=\sum _{N_{Light}}{R}_n{c}_T/{10}^6$$

(27)

In Formula (27), ${10}^6$ represents μ.

According to the temperature integration theory, the growth of crops over a period is mainly related to the average temperature [68]. Therefore, the average temperature in CEA within a day can be limited as follows.

$$T_{Light,ave}={\displaystyle \frac{1}{N_{Light}}}\sum _{N_{Light}}{T}_{air,t}$$

(28)

$$T_{Night,ave}={\displaystyle \frac{1}{N_{night}}}\sum _{N_{Night}}{T}_{air,t}$$

(29)

The energy consumption and crop yield in a CEA are influenced by the temperature range settings. Specifically, when a broad temperature range is set, the energy consumption of the plant factory is relatively low. However, this may lead to a decrease in crop yield. Conversely, when a narrower temperature range is set, the energy consumption of the plant factory increases, but this is accompanied by an increase in crop yield. Table 3 and

Table 6. Suitable temperature range for four crops.

Crop	$\mathbf{Suitable} \mathbf{Temperature} \mathbf{Range} \mathbf{in} \mathbf{the} \mathbf{Light} \mathbf{Time} \mathbf{(}\mathbf{°}\mathbf{C}\mathbf{)}$	$\mathbf{Suitable} \mathbf{Temperature} \mathbf{Range} \mathbf{in} \mathbf{the} \mathbf{Dark} \mathbf{Time} \mathbf{(}\mathbf{°}\mathbf{C}\mathbf{)}$
Tomatoes	22~25	17~20
Lettuce	22~25	18~20
Cucumbers	25~30	20~22
Bell peppers	22~30	15~20

gives the suitable temperature range [64].

The control of the environment of a plant factory can be expressed as:

$$X_{min}\le X\le X_{max}$$

(30)

$$X={\left[I_{indoor}^{PF}/I_{indoor}^{GH},T_{air},{RH}_{air},R_n,DLI,ET,T_{Light,ave},T_{Night,ave}\right]}^T$$

(31)

3.1.2. Growth Indicators

A variety of growth indicators are proposed to quantify the regulatory effect of the environment on the physiological activities of plants. By optimizing these indicators, environmental parameters can be indirectly regulated, thereby achieving precise management of the growth status of plants.

(1) Photosynthetic rate

The photosynthetic rate of crops is related to the light intensity of the plant canopy. The photosynthetic rate for GHs and each layer of planting racks in PFALs can be expressed as [69]:

$$F^{PF}=c_{pho}\sum _i\left\{e^{-{\displaystyle \frac{a}{c_{in}}}}\left[b-c{\left(T_{air}-d\right)}^2\right]e^{-{\displaystyle \frac{e}{R_{n,i}^{PF}}}}+f\right\}$$

(32)

$$F^{GH}=c_{pho}{e}^{-{\displaystyle \frac{a}{c_{in}}}}\left[b-c{\left(T_{air}-d\right)}^2\right]e^{-{\displaystyle \frac{e}{R_n^{GH}}}}+f$$

(33)

Ref. [42] adopted an exponential model with a reference photosynthetic rate. Ref. [47] provided the formulas of photosynthetic rate related to light intensity, temperature, dry weight, and CO₂. Ref. [70] used the photosynthetic rate index to measure the plant growth situation, thereby controlling the indoor temperature and CO₂ concentration to prevent the energy scheduling of CEA from affecting the crop growth.

(2) Daily dry matter accumulation (DMA)

The photosynthetic rate is not an intuitive and physical indicator. DMA is a more direct indicator reflecting the growth of plants, and its formula is:

$$F=\left\{\begin{array}{cc}{F}^{PF}& F^{GH}\end{array}\right\}$$

(34)

$$U_{DMA}={\displaystyle \frac{{\xi }_{cc}{\xi }_{cm}F}{1-c_{mineral}}}$$

(35)

(3) Crop growth and development rate

Since temperature has a significant impact on plants, a model of temperature versus plant growth can be established, as shown below.

$$R_{gd}=\left\{\begin{array}{cc}0& T_{air}\le T_{min},T_{air}\ge T_{max}\\ {\displaystyle \frac{T_{air}-T_{min}}{T_{opt}-T_{min}}}& T_{min}\le T_{air}\le T_{opt}\\ {\displaystyle \frac{T_{max}-T_{air}}{T_{max}-T_{opt}}}& T_{opt}\le T_{air}\le T_{max}\end{array}\right.$$

(36)

$$GDD=\left(T_{opt}-T_{min}\right)\sum _{N_{Light}+N_{Night}}{R}_{gd}$$

(37)

(4) Plant weight model during the cultivation period

This indicator describes the relationship between light and the growth of plants during the cultivation period. Ref. [43] experimentally fitted the relationship between extraction light and the quality of lettuce as:

$$m_{plant,t}=c_{plant,1}\left(c_{plant,2}+c_{plant,3}{e}^{c_{plant,4}t}\right)c_{plant,5}{I_{AL}}^{c_{plant,6}}{u}_t-c_{plant,7}$$

(38)

$u_t$ is an integer variable, and 0 and 1 indicate that AL is closed and open.

(5) Daily dry matter accumulation (TDRW)

TDRW represents the agricultural production tasks to be completed within one day.

$$TDRW={\displaystyle \frac{{\pi }_{cc}{\pi }_{cm}F}{1-c_{mineral}}}$$

(39)

(6) Annual crop yield

For VFs, all the lighting is provided by AL. Energy consumption is much higher than that of traditional agriculture and GHs. However, VFs are not affected by the external environment and can cultivate many times a year. Therefore, it is unfair for vertical farms to use the indicators of plant growth in one day or the growth indicators of one planting cycle. Thus, the annual crop yield is adopted as the indicator to measure the growth of plants in VFs [71].

$$Y=Y_1{Y}_2{Y}_{ref}{N}_{cycle}S$$

(40)

$$Y_1={\displaystyle \frac{T_{max}-T_{air}}{T_{max}-T_{opt}}}{\left({\displaystyle \frac{T_{air}}{T_{opt}}}\right)}^{{\displaystyle \frac{T_{opt}}{T_{max}-T_{opt}}}}$$

(41)

$$Y_2=c_{yield}\left({\displaystyle \frac{{PPFD}_{actual}}{{PPFD}_{target}}}-1\right)+1$$

(42)

$Y_1$ and $Y_2$ allow for the consideration of the yield modification occurring if photosynthetic photon flux density (PPFD) and leaf temperature differ from the target. For lettuce, if one growth cycle is calculated as 29 days, it will be planted 12 times a year.

(7) Others

Ref. [72] adopted an aquaponics system to achieve the recycling of water resources. Through experiments on fertilizer application and irrigation methods, the growth of lettuce was measured by taking the length of roots and leaves as indicators. Ref. [73] defined the linear relationship between plant weight and LAI. Ref. [74] proposed multiple growth physiological indicators such as disease index by optimizing light intensity and air flow velocity to improve the growth quality and reduce the occurrence of leaf tip blight.

All these indicators can be set as inequality constraints, like in Formula (30). They can also be used as an optimization objective reflecting the crop growth status.

3.2. Coupling of Facility Environment and Energy

The environmental regulation of CEA is highly dependent on electrically driven equipment, which leads to a tight coupling between the facility environment and the energy system, especially electrical and thermal energy.

3.2.1. Electricity

The power consumption of CEA mainly comes from AL, HVAC, integrated water and fertilizer systems, pest and disease control equipment, and monitoring systems. The traditional distribution network has difficulty meeting the demands of modern agriculture for power quality and cleanliness. Therefore, CEA is gradually integrating distributed energy sources, such as rooftop PV, biogas power generation, biomass energy, CHP, and heat pumps to form a new energy supply model, featuring multi-energy coupling of electricity, gas, heat, and agriculture.

(1) Lighting load

The relationship between the power consumption of AL and the radiation amount can be expressed as:

$$N_{AL}={\displaystyle \frac{I_{AL}{\eta }_{AL}A{k}_{crop}}{I_{lamp}}}$$

(43)

$$p_{AL}=N_{AL}{p}_{lamp}$$

(44)

(2) Irrigation load

Once the daily water demand of CEA is modeled, it is necessary to link the water demand with the electricity consumption, which is shown as follows:

$$p_{irrigation}=I_{irr}\times H\times {\displaystyle \frac{{\rho }_{w}g}{c_T}}\times {\displaystyle \frac{1}{{\eta }_{irrigation}}}$$

(45)

(3) PV power supply

PV panels are usually installed on the roof of GHs. PV power generation can be expressed as:

$$p_{PV}=I_{PV}{\eta }_{PV}\left[1+k\left(T_{PV}-T_{ref}\right)\right]$$

(46)

$$T_{PV}=T_o+c_{PV,1}{I}_{PV}$$

(47)

The different angles and layouts of PV will affect the radiation, thereby influencing the generation. Ref. [23] added the influence of the layouts in the PV generation model and conducted a more detailed modeling of $T_{PV}$. To provide sufficient light for crops, Ref. [35] stipulates that PV will only provide shading when the solar radiation inside GH exceeds the lower limit.

(4) Other loads and power sources

Ref. [41] provides a complete model of electric agricultural equipment in PFs, including AL, HVAC, integrated water and fertilizer systems, ventilation, electric pest control, crop pest and disease prevention, water treatment, air humidification, water temperature regulation, and control and monitoring systems. In Ref. [44], a dispatch model of an irrigation system when multiple PFs share a reservoir was established. Ref. [35] established the models of lighting, heating, cooling, and PV under time-of-use electricity prices.

If the energy system of CEA includes CHP and heat storage devices, the heat balance equation should take into account, as well as the natural gas network constraints [69]. Biomass fermentation is a very important feature of CEA and rural power grids [42]. Ref. [44] analyzed the biomass fermentation system, used the anaerobic biomass fermentation model to capture the dynamic mass transfer process, and established a correlation model between heat release and temperature during biomass fermentation.

(5) Electrical energy balance

The power balance equation in CEA can be expressed as:

$$p_{PV}+\sum _k{p}_k=p_{irrigation}+p_{AL}$$

(48)

3.2.2. Heat

CEA needs to construct a heat conservation model to coordinate the relationship between the heat demand for plant growth and the energy consumption for environmental temperature control. The specific formula is:

$${\displaystyle \frac{d{T}_{air}}{dt}}=Q_{rad}-Q_{trans}-Q_{envelope}-Q_{ventilation}-Q_{gound}-Q_{HVAC}$$

(49)

CEA needs to maintain air temperature at a suitable level for plant growth. Usually, the temperature is set at a constant value. Therefore, there are:

$${\displaystyle \frac{d{T}_{air}}{dt}}=0$$

(50)

Substituting Formula (49) into Equation (50):

$$Q_{rad}-Q_{trans}-Q_{envelope}-Q_{ventilation}-Q_{gound}-Q_{HVAC}=0$$

(51)

3.3. Coupling of Plant Physiological Activities, Energy Consumption, and Carbon Emissions

There is a significant interaction among plant growth, energy consumption, and carbon emissions. For example, the photosynthetic efficiency is jointly affected by CO₂ concentration and light intensity. Under conditions with high CO₂ concentration, the intensity of AL required to maintain the same growth rate can be significantly reduced, thereby reducing lighting energy consumption and emissions [75].

CO₂ balance within the CEA system can be expressed as:

$$V{\displaystyle \frac{d{c}_{in}}{dt}}=-E_{crop}-E_{soil}-E_{ventilation}+E_{respiration}+E_{supply}$$

(52)

In order to maintain a relatively high growth rate, CO₂ in the PF is usually fixed at a constant value, namely:

$${\displaystyle \frac{d{c}_{in}}{dt}}=0$$

(53)

Substituting Equation (52) into Equation (53), the CO₂ equilibrium equation can be obtained, which is expressed as:

$$-E_{crop}-E_{soil}-E_{ventilation}+E_{respiration}+E_{supply}=0$$

(54)

It is worth noting that the CO₂ balance formula does not include generation emissions. Whether the electricity is purchased or supplied by the CEA system itself, the CO₂ produced will eventually be emitted into the atmosphere and will not affect the CO₂ concentration inside the PF. However, in response to the call for low-carbon emission reduction, many countries usually set prices for carbon emissions, which can be calculated by $E_{elec}$.

The energy optimization model of CEA is shown in Figure 3.

4. Application

4.1. Optimal Energy Scheduling of CEA

The optimal scheduling of CEA involves seeking a compromise between crop yield and energy consumption. Existing studies have shown that with a reasonable environment, the crop yield can be increased while reducing energy cost [76]. Refs. [11,13,39,47,77,78] constructed energy consumption optimization models by regulating the environment, such as temperature and light, while Ref. [79] adjusted the quantity of crops on different shelves.

Integrating renewable energy resources (RESs) into CEA requires coordinating the spatio-temporal matching problem between the production demands of crops and the characteristics of renewable energies [80]. Ref. [81] evaluated the land requirements for renewable energy needed by CEA growing four crops under both current and future technological advancements. Refs. [59,82] considered various RESs in the CEA energy management system.

Detailed information can be seen in

Table 7. Summary of optimal energy scheduling.

References	Type	Objectives or Evaluation Indicators	Method	Characteristics or Results	Location	Energy Consumption per Lettuce Fresh Weight
[11]	Container PF	Data regression evaluated by the mean absolute percentage error	Data-driven random forest method	Heat transfer coefficient, the COP value of the air conditioning and the efficacy of LED have the highest contribution to the total energy consumption.	Shanghai	4.76 kWh/kg
[13]	Container PF and GH	Unit energy consumption per hour	GRG non-linear engine	The energy efficiency of PFALs and GHs under different climatic conditions was compared.	Many locations around the world, taking Stockholm in winter as an example	3.5 kWh/kg for PFAL 2.0 kWh/kg for closed GH 1.0 kWh/kg for open ventilated GH
[39]	Open ventilated GH	Minimize the total cost of power purchased from the external grid	Mixed-integer liner programming (MILP)	The load model of irrigation equipment was established based on the transpiration of crops.	Three cities in China, taking Sichuan as an example
[47]	Closed GH	Revenue composed of the lettuce profit and the energy cost	The MATLAB function “fmincon” [83]	Adapts and calibrates a lettuce growth model and optimizes LED light intensity and CO2 supply to maximize profit	Beijing	7.42 kWh/kg (fresh lettuce price of 34.5 RMB kg[fw]−1)
[77]	Open ventilated GH	The weighted minimum of temperature deviation and cost	Exhaustion approach	A temperature control system based on MPC was developed by coordinating the execution strategies of the heater and the ventilation window.	China
[78]	VF	Global warming potential, acidification potential, freshwater ecotoxicity, net present value, net present value per unit, capital expenditure, total annual cost	“Farm-to-fork” life cycle assessment and techno-economic analysis	GHG reduction and energy efficiency improvement can be achieved simultaneously through the optimization of operational parameters.	Five cities in the United States	21.21 kWh/kg
[79]	VF	Maximizing the demand met, minimizing the number of times shelf configurations change, minimizing the number of times crops move between shelves, minimizing the number of shelves required to meet a given demand	MILP	Adjusting the quantity of crops on different shelves to improve economy and efficiency
[84]	VF	Maximizing biomass accumulation and resource efficiency	A hybrid approach combining chained Support Vector Regression, Multi-Objective Differential Evolution, and Data Envelopment Analysis	Determine optimal light intensity and nitrogen content in nutrient solution
[59]	Open ventilated GH	Minimizing the total cost of the fast and slow scheduling cycles	An approximation method	A multi-time-scale energy management scheme considering the randomness of renewable energy is proposed.	Alberta
[82]	Open ventilated GH	The differences between temperature, humidity, CO2, light, and water and the expected values are the smallest.	Model predictive control	The operation of the storage system and the reservoir around the reference value is taken into account to minimize the exchange with the main power grid, aiming to increase the use of local renewable energy production.

. The energy consumption per lettuce fresh weight varies in different references, which may be due to differences in climates, location, shape of CEA systems, and enclosure structures.

4.2. Interaction Between CEA and Microgrids

In modern energy systems, demand-side management has become a key means to balancing load demand within high-proportion renewable energy grids [85]. As a typical flexible load, CEA has significant potential for DR. The periods with high electricity prices can be set as the dark period, and the periods with low electricity prices can be set as the light period. Environmental parameters such as temperature and humidity can be adjusted to within a certain range with delay without affecting the physiological activities of the crops.

The potential of PFs as DR was analyzed in Ref. [86]. WT capacities ranging from 8 to 12 megawatts can meet almost all of the energy demands of local PFs. Large-scale deployment of PFs can significantly reduce CO₂ emissions in urban environments, and investors will recover their investments within eight years. In Ref. [87], the cost of AL was verified to be reduced by 16% to 26% in all months of the year by adjusting the light exposure time of plants. Refs. [34,35,45,66,87,88,89,90,91] established DR management model for CEA to reduce the operating cost and analyzed the contribution of DR management to the flexibility of the power system. Refs. [32,92] studied energy management in greenhouse clusters.

When CEA interacts with microgrids, numerous uncertainties must be taken into account. On one hand, there is uncertainty within the CEA environmental models, such as the variability of crop coefficients. While these coefficients are typically determined through empirical testing and considered constant values, some applications dynamically adjust them by incorporating sensor data [30]. This method ensures that the models are adaptable to real-time conditions and fluctuations in crop behavior. Moreover, AI is increasingly being used for predictive purposes [64]. On the other hand, microgrids contain various sources of uncertainty, including environmental factors, electricity pricing, and renewable energy generation. To manage these uncertainties, microgrid systems employ a range of techniques, such as stochastic scenario-based methods [44], fuzzy modeling, and robust optimization. Ref. [89] tackles uncertainties in thermal loads and renewable energy output by developing a robust model predictive control framework. This framework uses fluctuation ranges as constraints to generate feasible solutions under the most adverse scenarios. The results demonstrate that greenhouse temperatures can still meet the necessary standards with a manageable increase in costs, even with parameter deviations of up to ±20%.

Detailed information can be seen in

Table 8. Summary of interaction between CEA and microgrids.

References	Type	Uncertainty	Objective of PF	Objective of Microgrid	Method
[35]	Open ventilated GH	×	Minimizing the total energy consumption of the greenhouse; minimizing energy cost minimization	Self-consumption maximization (the ratio of energy consumed within the system, sourced from PV generation and battery storage, to the total energy consumption); total cost minimization	Split into two sub-problems
[34]	Open ventilated GH	Electricity price, weather	Minimization of costs of energy consumption and peak demand charges	×	MILP
[45]	Closed GH	×	Minimizing the operating costs of the PF, such as the cost of purchasing electricity and the cost of load transfer	×	MILP
[66]	Open ventilated GH	×	Minimizing the total energy consumption of heating/cooling, ventilation, and irrigation systems	Maximizing the ratio of energy consumed within the system, sourced from PV generation and battery storage, to the total energy consumption; minimizing the energy cost	MILP
[87]	VF	×	Energy demand cost	×	A limited energy demand method
[88]	Not explicitly pointed out	RES	×	Minimizing operating costs of the power system	MILP
[89]	Open ventilated GH	RES, load	In grid-connected mode: minimizing the cost of power purchase and the cost of CHP In island mode: minimizing the penalty value for the out-of-bounds environmental parameter	×	Robust optimization
[90]	VF	×	The total electricity bill of the PF	×	Linear optimization
[91]	Closed GH	Price of electricity and carbon emissions	Minimizing energy procurement costs and emissions	×	MILP
[32]	Open ventilated GH	×	Minimizing the electricity purchased from the microgrid; minimizing the deviations in temperature, CO2, light, and water in the PF	Minimizing the exchange power between the PF, the reservoir, and the microgrid	Alternating direction method of multipliers
[92]	Open ventilated GH	×	Minimizing environmental deviation and power exchange deviation between microgrids and ES states	×	MPC-based algorithm

.

4.3. Planning Issues

Planning issues mainly refer to providing capacities or sites for one or more components when building a PF. Ref. [93] established a dynamic thermal model of the greenhouse to predict the air temperature inside the greenhouse, and planned and designed the angle, width, and height of the greenhouse with the goal of minimizing the temperature bias.

In the combined system of CEA and PV, installing PV panels on the roof of a GH will create a shading effect inside the GH [94,95]. Therefore, Ref. [96] used a regression model [97] to estimate the shading effect of different GH orientations and different PV coverings, thereby calculating the maximum ratio of PV covering without affecting plant growth. Ref. [98] proposed an independent integrated energy network structure for facility agriculture, established a PV capacity planning model, and analyzed the capacity allocation differences of the energy network in different seasons. Ref. [42] considered the light demand at different cycles in crops and proposed an RES planning model, which optimizes the economic and environmental benefits of the rural energy system while meeting the demands of agricultural production. Ref. [99] aimed at maximizing revenue in grid-connected mode and minimizing costs in island-isolated mode, and adopted the scenario-based robust optimization approach to plan the quantities of RESs in GHs.

In PFs powered by RESs, solar and wind are intermittent energy sources [100]. ES devices will enhance the utilization of RESs. Seasonal thermal storage is a very promising solution [101] that can store summer heat for use in winter [102]. Ref. [103] studies how to meet the heating requirements of CEAs by designing a solar energy system with heat storage. In response to the need for heating in northern China during winter, Ref. [21] utilized the heat transfer between GHs and designed a dual-source heat pump system to collect the residual air heat in GHs for heating multi-span GHs. The capacities of heat pumps, heat storage tanks, and coolers were planned.

5. Future Research Directions

(1)

Multi-time-scale dynamic modeling of plant physiology and environment. At present, environment models of PFs mostly adopt static equations. Empirical formulas in Ref. [43] or simplified equations such as the improved Penman–Monteith equation in Ref. [23] are used to describe the physiological processes of crops, which cannot accurately reflect the dynamic impact of the environment on energy consumption. Multi-time-scale coordinated strategies considering second-level power regulation and daily growth cycle have not been fully resolved. Refs. [57,59] have considered the multi-time-scale coupling of electricity and heat, but they lack a multi-time-scale analysis of plant growth conditions. Future research can focus on the deep coupling model of environment, crop growth, and energy systems.

(2)

Uncertainty modeling of complex systems. In PFs, there exist exogenous uncertainties (such as random fluctuations in light intensity, changes in electricity prices, and deviations in the output of WT and PV power) and endogenous uncertainties (such as deviations in plant growth rates and errors in load demand forecasting). Most of the existing studies adopt deterministic optimization within the CEA environmental models (such as Ref. [23]) or only consider a single uncertainty factor (such as Ref. [88]). Refs. [34,89,91] adequately addressed the uncertainties within microgrids. Future research can focus on the sufficient modeling of various randomness involved in PFs.

(3)

DR modeling under market-oriented mechanisms. As one of the highly controllable loads, the potential of PFs in demand-side ancillary services (such as frequency regulation and reserve capacity) and the improvement in power grid resilience has not been fully tapped. Refs. [34,86] are limited to basic DR strategies, lacking a collaborative optimization model for green certificate trading, carbon tax policies, and the coupling mechanism of the long-term, medium-term, and day-ahead electricity markets. There is an urgent need to develop multi-objective energy optimization scheduling and management for PF clusters under a diversified market mechanism.

6. Conclusions

CEA represents a promising solution to address the escalating global food demand amidst urbanization and diminishing arable land. This paper has offered a comprehensive review of the energy management models within CEA, highlighting the intricate interplay between plant physiological activities, environmental control, and energy consumption. While significant advancements have been made in optimizing energy use and enhancing crop yield through sophisticated environmental models and multi-disciplinary coupling, challenges remain. The dynamic nature of plant growth and the complexity of environmental interactions necessitate further research into multi-time-scale modeling and uncertainty management. Additionally, the integration of market-oriented mechanisms in energy management holds potential for future advancements. As CEA continues to evolve, its role in sustainable agriculture will become increasingly vital, contributing to food security and environmental sustainability.