Synthesis and Optimisation of an Integrated Renewable Energy and Greenhouse Network

Abstract

This paper presents a study on the synthesis and optimisation of a renewable energy and resource supply chain network (SCN) to satisfy agricultural greenhouse resource and energy demands. This is motivated by the high costs and emissions to run greenhouses due to the resources and energy required for optimal growth conditions. The investigation aims to contribute to the growing area of research on circular practices in the agricultural sector. The SCN includes biomass from agricultural waste transported to a utility hub, consisting of water and carbon dioxide (CO₂) as resource supplies, as well as a boiler and steam turbine-generator and solar photovoltaic (PV), as energy conversion technologies. The resources and energy are distributed to greenhouses. The objectives are to minimise both the total annualised costs (TAC) and environmental impact (EI), calculated as CO₂ emissions of the integrated network. Multi-periodicity accounts for the monthly and daily variation in constraints on the system, such as feedstock and solar radiation availability and energy limitations. The model is applied to a case study of an agro-industrial zone in Kwa-Zulu Natal (KZN) province, South Africa. The network meets greenhouse demands at a minimum TAC and EI of 8.052 $\times {10}^{6}$ R/y and 14,370 tCO₂e/y, respectively. The biomass supply chain (BSC) contributes most significantly to the TAC at 43.7% while biomass combustion makes up 99.8% of the EI. Additional key results include bagasse and corn stover being selected as the only feedstocks and rail as the transport mode. The 26,560 MWh/y of electricity supplied to the greenhouses is made up by 71.4% from the boiler and turbine-generator with the remainder from solar PV. The potential of solar PV as a clean and low-cost energy source is demonstrated by the model selection at its full capacity. The study confirms that holistic modelling and optimisation of renewable energy SCNs for greenhouses is necessary to meet a trade-off between the network costs and CO₂ emissions.

Introduction

Greenhouses for food production play an increasingly important role in food security and sustainability in the global agricultural sector. The controlled environment in greenhouses improves crop yields, allows for more efficient use of resources, and crop resilience against the impact of climate change. However, maintaining optimal conditions is energy- and resource-intensive, propelling research into improving greenhouse operations to minimise waste, energy consumption, and emissions in the food-value chain. The current global energy and climate challenges further incentivise moving away from carbon-intensive fossil fuels. In Southern Africa, the favourable climate for solar energy generation and robust agricultural sector provide a unique opportunity to promote the transition to using these cleaner and renewable energy sources.

To use agricultural waste as a feedstock for greenhouse energy, it is necessary to establish a supply-chain network (SCN) to facilitate the collection, transportation, conversion, and distribution of the biomass-derived energy product. This, in combination with solar power, can provide the energy required to operate a greenhouse in the form of electricity or heat. These networks, however, have associated costs and environmental concerns. A SCN must therefore be designed to meet greenhouse demands using these sources while minimising negative environmental and economic impacts. Achieving this requires the development of a model that incorporates a biomass SCN, a renewable-energy conversion system, and an energy and resource distribution network integrated with greenhouse demands.

Literature Review

Climate change-related issues such as the global energy and food crises are receiving increased attention due to their escalating effect on economic, social, and environmental sustainability (Ren et al. 2022). Agriculture is a key concern in this sustainability, due to the energy and resources consumed to ensure food security for a growing population. The traditional mode of open-field cultivation is becoming unsustainable due to increased food demands, a reduction in the availability of arable land, and highly variable and more extreme weather patterns and events. This necessitates the development of innovative, climate-smart agricultural practices such as using greenhouses to improve yields and efficiency in food production.

Greenhouse Crop-Cultivation

Greenhouse crop-cultivation is estimated to be significantly more efficient (up to 10–20 times) than open-field agricultural cultivation, owing to its ability to enable off-season cultivation, protect crops from pests, and maintain optimal growth conditions by controlling temperature, humidity, CO₂ concentration, and irrigation levels (Su et al. 2021). However, achieving these tightly controlled climatic conditions requires a high consumption of energy and resources (Su et al. 2021), with approximately 78% of the crop-production cost in greenhouses being attributed to energy consumption and 65–85% of this energy being required for heating or cooling (Runkle 2011). The costs and greenhouse-gas GHG emissions associated with high energy demands are driving extensive research into the modelling, optimisation, and control of greenhouse operations, to meet economic objectives while minimising environmental footprints (Ouammi 2021).

Renewable Energy in Greenhouses

The decarbonisation of energy systems is taking greenhouse research further, to include renewable energy sources. Existing literature on renewable energy systems in greenhouses primarily focuses on the utilisation of sources such as solar-photovoltaic and thermal, geothermal, and biomass energy (Lee et al. 2021). Taki et al. (2018) conducted a comparative analysis on fossil fuel and renewable energy in greenhouses and found that the use of renewable sources can reduce emissions and waste products in these operations by up to 52%. The most common of these is the use of solar power as a source of electricity or heat. However, the intermittent nature of sunlight presents a limitation in relying solely on a supply of solar power to prevent crop losses (Mosey and Supple, 2021). Consequently, a system of distributed energy resources (DER), which uses a network of various renewable energy sources, is typically recommended (Akorede et al. 2010). An effective way to do this while improving resource efficiency is through Industrial Symbiosis (IS)—a concept in which waste from one process is valorised into useful raw materials for another (Zhao et al. 2020). This is shown to directly reduce carbon emissions, waste to landfills, and energy and raw material consumption, while increasing economic benefits through resource-sharing (Neves et al. 2019). In Agricultural Industrial Symbiosis (AIS), biomass waste in the agricultural sector is used as a raw material feedstock for renewable-energy production such as power, heat, or fuel (Murat Yazan et al. 2020). This use of biomass waste is recognised as a key concept to facilitate the transition to more circular and sustainable agricultural practices (Murat Yazan et al. 2020).

Biomass for Energy in Greenhouses

Biomass waste as an energy source provides approximately 80% of the renewable energy obtained globally and is expected to increase by 300% by 2050 (Immerzeel et al. 2014). The combustion of biomass releases heat, which is used to generate steam for driving turbine that can produce useful energy in the form of electricity and heat (Akorede et al. 2010). However, harvesting crops for the purpose of energy generation, otherwise known as “bio-energy crop production”, presents environmental, social, and economic concerns (Immerzeel et al. 2014). This practice can lead to reduced biodiversity and soil erosion, as well as a reduction in land available for food production, which is particularly concerning given the current food shortages in Africa (Mutenure et al. 2018). As a result, using crop and livestock waste is preferable to ensure the benefits of a renewable-energy supply chain are not offset by worsening food security (Mutenure et al. 2018).

Supply-Chain Network Mathematical Modelling

There are economic and environmental challenges associated with renewable energy- and resource-supply networks which must be considered when assessing the benefits of these SCNs (Ghaffariyan et al. 2017). Furthermore, there are concerns related to the benefits for various stakeholders involved, which present issues for implementation of such networks. As a result, there has been extensive research in the field of renewable-energy supply chains, focusing on using mathematical models to optimise the benefits while minimising any negative externalities. This holistic optimisation process considers the entire system, rather than individual parts, to achieve the best economic and environmental outcomes (Ahmad Fadzil et al. 2022).

Mathematical modelling and computer programming can be powerful tools for optimising supply networks in various industries (Szkutnik-Rogoż et al. 2021). The structure of a supply-chain model typically involves suppliers, manufacturers, and consumers (Szkutnik-Rogoż et al. 2021). In the context of renewable energy supply networks, this involves feedstock supply centres or farms, conversion technologies, and demand facilities as shown in Fig. 1 (Mutenure et al. 2018). To achieve an optimal network configuration, the modelling approach is to decompose the problem into multiple layers, which are integrated into a superstructure network (Mutenure et al. 2018). The result is a set of mathematical expressions forming a linear (LP), mixed-integer linear (MILP), or mixed-integer non-linear programme (MINLP) to be solved using an appropriate modelling software.

Fig. 1

General biomass supply-chain network (Mutenure et al. 2018)

In literature, the primary function, design, and complexity of renewable energy SCNs vary. Typically, the objective of each network is related to economics, with single-objective optimisation (SOO) focusing on indicators such as total annualised cost (TAC), profit after tax or net present value (NPV). Multi-objective optimisation (MOO) includes additional indicators, such as environmental factors like CO₂ emissions, or social impact indicators such as job creation.

Cowen et al. (2019) constructed a SOO model for the TAC of a renewable-energy supply chain designed to satisfy the hot utility demand in heat-exchange networks (HENs) at various co-located process plants. The model simultaneously optimises both the SCN and an HEN. A key feature of this work highlights the advantage of network-wide simultaneous optimisation over sequential optimisation of individual HENs (Cowen et al. 2019). Furthermore, the model considers the multi-period heat demand of each HEN, ensuring optimal operation despite time-variation in utility demand (Cowen et al. 2019). Similarly, Isafiade and Short (2022) modelled a biomass SCN to satisfy the utility demands of a single process-plant HEN. This is a three-layered network, including a central energy hub. Multi-objective optimisation is carried out using the weighted-sum method with the environmental impact indicator as CO₂ emissions due to combustion in a boiler (Isafiade and Short 2022).

Mutenure et al. (2018) developed a five-layer superstructure for a supply chain converting sugarcane and sugarcane bagasse to sugar, biofuel, and electricity which included intermediate pre-treatment steps for milling, crushing, and storage. This highlights another common function of renewable-energy supply chains in literature as for producing biogas for electricity. The Biogas Supply Optimisation Model (BIOSOM) developed by Egieya et al. (2019) is the most comprehensive example of this work. BIOSOM was developed to produce biogas from manure and agricultural and lignocellulosic crops. The primary objective was to maximise profit generated by production of electricity, excess heat and digestate from anaerobic digestion, while minimising the cost of feedstocks, transport, and conversion (Egieya et al. 2019). This was expanded by Egieya et al. (2020) to incorporate environmental and social indicators in a MOO problem. The environmental indicator was the GHG emissions, which were determined using a Life Cycle Assessment (LCA) to quantify the CO₂ emissions of the network. The social impact indicator was defined as the sustainability profit which encompasses factors that affect society, such as promoting employment and the improvement of livelihoods (Egieya et al. 2020). The most comprehensive applications of an LCA on GHG emissions in renewable energy SCNs were conducted by You and Wang (2011). The study developed a model for converting biomass to liquid transportation fuel and included TAC and life-cycle GHG emissions as objectives (You & Wang 2011). The LCA used in this work considers emissions due to cultivation, growth, intermediate transport, upgrading facilities, and biofuel product usage in vehicles (You and Wang 2011).

Application of the Literature to the Proposed Investigation

Review of existing literature reveals that considerable work has been done on modelling and optimisation of greenhouses, with a growing emphasis on the use of renewable energy. Furthermore, there have been extensive studies on modelling and optimising renewable-energy supply chains to deliver heat, electricity, fuel, and resources to a range of industrial processes. To the knowledge of the authors, there is no existing research that combines these two concepts by modelling a renewable-energy supply chain integrated with greenhouse operations. The research presented in this paper is unique in that the supply chain’s demand node comprises a set of co-located greenhouses, each with its own crops having specific time-dependent energy and resource demands.

Problem Description and Statement

Problem Description

The proposed SCN superstructure (Fig. 2) has three layers consisting of: (1) biomass feedstocks at known sites; (2) a central utility hub with electricity generating systems as a boiler with a steam turbine-generator and a solar PV installation as well as water and CO₂ supplies; (3) greenhouses growing crops with varied demands for the utilities. The feedstocks in known locations (Layer 1) are transported to the utility hub (Layer 2) either by rail or truck in a biomass supply chain (BSC) network. At the utility hub, electricity is generated using the biomass to produce steam for a turbine-generator and solar radiation for solar PV. This is delivered with water and CO₂ to the greenhouses (Layer 3) of fixed sizes and in known locations, each growing a food crop with specific requirements. The selection and distribution of biomass feedstocks, transport modes, electricity for heating and cooling, as well as water and CO₂, for a minimum total annualised cost (TAC) and environmental impact (EI) on a yearly basis, must be determined.

Fig. 2

Proposed supply chain, energy, and resource distribution superstructure

Problem Statement

The problem description is used to formulate a mathematical problem statement to inform the model development. Given the following sets corresponding to Fig. 3:

• Biomass feedstocks, $F$, in known locations relative to a central utility hub.

• Transportation modes, $T$, to deliver feedstocks from each supply point.

• Energy generation technologies, $I$, to produce electricity.

• Additional resources, $R$, to promote crop growth.

• Co-located greenhouses, $G$, with known locations, floor areas, and containing crops with resource and electricity demands.

• Periods, $M$, for monthly variation in feedstock supply and greenhouse demand.

• Periods, $D$, for daily variation in energy availability and demand.

Fig. 3

Mathematical representation of the proposed network

The objective of the investigation is to perform the synthesis of an economically and environmentally optimal energy and resource SCN by minimising the TAC and CO₂e emissions.

Mathematical Model

The mathematical model developed to address the problem statement must determine the network specifications for a range of inputs in the multi-objective optimisation problem. Modelling involves formulating the objective function which is to be optimised within constraints on supply and demand of various system components. The network is represented as a linear programme (LP) with each layer modelled and integrated with the next before optimisation is performed for the entire integrated network.

Periods are introduced, as sets $M$ and $D$ (indices $m$ and $d$), to account for monthly and daily time variations. These sets are required as the greenhouse demands for heating and cooling vary both monthly and daily due to fluctuations in the outside ambient temperature. Feedstock supply also varies monthly due to harvesting seasons of the crops from which these are obtained. For the set $M$ these are denoted as $m1$ to $m12$ corresponding to the months January to December and in the set $D$, $d1$ and $d2$ correspond to day- and night-time.

Layer 1: Biomass Supply Chain (BSC) Network

The cost of each existing feedstock and transport link in the biomass supply chain (BSC) (Layer 1) during each period is modelled using an adapted method of that described in Cowen et al. (2019). The cost to purchase the feedstocks each month and operational costs for transport such as for fuel and maintenance are included (Eq. 1):

$$\begin{array}{c}{C^{BSC}}_{f,t,m}=\left(\frac{x_{f,t,m}}{\frac{{LHV}_f}n}\right)\left(T_t^{VC}.\tau_t.D_f^F.r_t+C_{f,m}^F\right)\\\begin{array}{ccccc}\forall\;f\;\epsilon\;F;&&t\;\epsilon\;T;&&m\;\epsilon\;M\end{array}\end{array}$$

(1)

In Eq. 1, the variable cost factor, ${\mathrm{T}}_{t}^{\mathrm{VC}}$(R/kg.km), accounts for transport costs based on the supply of each feedstock type, $f,$ by each transport mode, $t,$ during each month, $m$, denoted as ${x}_{f,t,m}$ (kW). The factor includes variables such as fuel, wages, maintenance, and loading or unloading capacities, as a function of both the distance (km) and amount of feedstock to be transported (ton). This is converted into an annual mass flow using the LHV of each feedstock, ${\mathrm{LHV}}_{f}$ (kWh/kg), and annual operating hours, $n$ (h/y). The straight-line distance travelled from each supply point to the energy hub, ${D}_{f}^{F}$ (km), is modified using tortuosity, ${\tau }_{r}$, and return trip, $r$, factors. The tortuosity factor accounts for the actual distance travelled and the return trip factor for return to feedstock supply points. The last term, ${\mathrm{C}}_{f,m}^{\mathrm{F}}$(R/kg), adjusts the feedstock quantity to give the cost to purchase the feedstock.

The energy demands must be met while ensuring that the amount of feedstock transported monthly does not exceed the supply capacity (Eq. 2).

$$\begin{array}{cc}\sum\limits_{t\epsilon T}x_{f,t,m}\leq{Cap}_{f,m}^F.\frac{{LHV}_f}{n.m^{Frac}}&\;\;\;\;\;\;\;\forall\;f\;\epsilon\;F;\;\;\;m\;\epsilon\;M\end{array}$$

(2)

Equation 2 ensures that the quantity of feedstock in each month for any transportation mode does not exceed supply capacity, ${\mathrm{Cap}}_{f,m}^{\mathrm{F}}$ (kg/y). The quantity supplied, ${x}_{f,t,m}$ (kW), is summed over all transportation modes, while the annual capacity is transformed to the correct units (kW) using each LHV, ${\mathrm{LHV}}_{f}$ (kWh/kg), annual operating hours, $\mathrm{n}$ (h/y), and the fraction of a month in the year, ${m}^{\mathrm{Frac}}$.

Integration with Layer 2

The supply of each feedstock during each month in Layer 1 is integrated with Layer 2 by the feedstock demand (Eq. 3):

$$\begin{array}{cc}\begin{array}{c}\sum\limits_{t\epsilon T}x_{f,t,m}\geq{bb}_{f,m}\end{array}&\;\;\;\;\;\;\forall\;f\;\epsilon\;F;\;\;\;m\;\epsilon\;M\end{array}$$

(3)

Equation 3 constrains the feedstock supply over each transportation mode as equal to or greater than the demand of each feedstock, ${bb}_{f,m}$ (kW), in each month in Layer 2. This total energy input will be required to satisfy the energy demands on the boiler and turbine-generator system, determined by the greenhouse demands and the electricity available from solar PV.

Layer 2: Utility Hub

The utility hub in Layer 2 includes a boiler and turbine-generator system and an installation of solar PV panels as the energy conversion technologies to deliver electricity, denoted by the index $i$ in the set $I$. The hub also contains irrigation water and CO₂ supplies with the index $r$ in the set $R$.

Boiler-Turbogenerator System

Modelling of the boiler, turbine, and generator system is based on the Rankine cycle in which steam is cycled through various states, in the process generating shaft work to run an electrical generator. A flow diagram of this process (Fig. 4) (El-Halwagi 2017) shows saturated liquid, the working fluid, being fed into a boiler which transforms the liquid to high pressure steam (HPS) by burning the biomass feedstock. The HPS expands and cools in the turbine, generating the shaft work required to run a generator which produces electricity. This is shown as power out of the turbine in Fig. 4. The working fluid (steam) exits the turbine at a lower pressure and temperature, in the low-pressure steam (LPS) state. The LPS is condensed using a heat sink such as cooling water and pumped back to the boiler to begin the cycle again.

Fig. 4

Steam boiler and turbine Rankine cycle system

The electrical power generated in the turbine-generator system, ${P}_{m,d}^{T}$ (kW), during each month and daily period is calculated by an energy balance over the unit (Eq. 4):

$$\begin{array}{ccc}P_{m,d}^T={\eta^{is}(\widehat H}^{HPS}{\dot m^{HPS}}_{m,d}-{\widehat H^{LPS}\dot m^{LPS}}_{m,d})&\;\;\;\forall\;m\;\epsilon\;M;&d\;\epsilon\;D\end{array}$$

(4)

Equation 4 shows an energy balance using the inlet HPS enthalpy, ${\widehat{H}}^{HPS}$ (kJ/kg), and mass flowrate, ${{\dot{m}}^{HPS}}_{m,d}$ (kg/s) in each monthly and daily period, and that of the LPS, ${\widehat{H}}^{LPS}$ (kJ/kg) and ${{\dot{m}}^{LPS}}_{m,d}$ (kg/s). The isentropic efficiency, ${\eta }^{\mathrm{is}}$, adjusts the output for energy losses during isentropic expansion of a non-ideal gas (El-Halwagi 2017). Included in the energy balance is the power generated, ${P}_{m,d}^{T}$ (kW), during this expansion.

The output power must fall within the limits of operation for the size of the system using the maximum, ${P}^{T,\mathrm{max}}$, and minimum, ${P}^{T,\mathrm{min}}$, capacity (Eq. 5):

$$\begin{array}{cc}P^{T,max}{\geq P}_{m,d}^T\geq P^{T,min}&\;\;\;\forall\;m\;\epsilon\;M;\;\;\;\;d\;\epsilon\;D\end{array}$$

(5)

A mass balance over the turbine constrains the flowrates of HPS in and LPS out as the only streams into and out of the unit (Eq. 6):

$$\begin{array}{cc}{\dot m^{HPS}}_{m,d}={\dot m^{LPS}}_{m,d}&\;\;\;\forall\;m\;\epsilon\;M;\;\;d\;\epsilon\;D\end{array}$$

(6)

The heat required to generate HPS from saturated liquid by boiling, ${Q}_{m,d}^{B}$ (kW), is based on an energy balance over the boiler (Eq. 7).

$$\begin{array}{ccc}Q_{m,d}^B={\dot m^{HPS}}_{m,d}\left(\widehat H^{HPS}-\widehat H^{Cond}\right)&\;\;\;\;\;\;\forall\;m\;\epsilon\;M;&d\;\epsilon\;D\end{array}$$

(7)

Equation 7 accounts for the change in enthalpy from that of the condensate liquid feed, ${\widehat{H}}^{Cond}$ (kJ/kg), to high pressure steam, ${\widehat{H}}^{HPS}$ (kJ/kg). The LPS, condensate, and HPS have a constant flowrate, assuming no losses in the continuous circulation.

Condensing the LPS requires a heat exchange with a cold sink such as cooling water, with the heat transferred, ${Q}_{m,d}^{Cond}$ (kW), calculated by an energy balance using the relevant enthalpies (Eq. 8):

$$\begin{array}{ccc}Q_{m,d}^{Cond}={\dot m^{HPS}}_{m,d}\left(\widehat H^{LPS}-\widehat H^{Cond}\right)&\;\;\;\;\;\;\;\forall\;m\;\epsilon\;M;&d\;\epsilon\;D\end{array}$$

(8)

Solar Photovoltaic System

The electricity obtained from solar power is estimated using Eq. 9 (McFadyen 2013) as an approximate value for solar PV output.

$$\begin{array}{ccc}P_{m,d}^S=A^SR\varepsilon^S{Sr}_{m,d}^s&\;\;\;\;\;\forall\;m\;\epsilon\;M;&d\;\epsilon\;D\end{array}$$

(9)

The electricity output, ${P}_{m,d}^{S}$(kW), is based on the panel performance ratio, $\mathrm{R}$ (%), yield or efficiency, ${\varepsilon }^{S}$ (%), total panel area, ${A}^{S}$ (m²), and daily solar radiation ${\mathrm{Sr}}_{m,d}^{\mathrm{s}}$ (kJ/m².day). Unit conversions are required to transform ${\mathrm{Sr}}_{m,d}^{\mathrm{s}}$ into a kW measurement for integration across layers.

A constraint is introduced to limit the solar PV installation to the maximum area available (Eq. 10):

$${A}^{S}\le {A}^{S,Max}$$

(10)

The total solar panelling area, ${A}^{S}$ (m²), is the number of solar panels and the area per panel with spacing, and this is a decision variable to be determined by the model. The maximum area available for the installation, ${A}^{S,\mathrm{Max}}$ (m²), is a model input to be selected by the user from a range of 20–50%.

Integration with Layer 1

The energy available from the feedstocks in Layer 2, ${\Delta H}_{f,m}$ (kW), is transferred from Layer 1 by a constraint on feedstock demand, ${bb}_{f,m}$ (kW) (Eq. 11):

$$\begin{array}{ccc}{\Delta H}_{f,m}={bb}_{f,m}&\;\;\;\;\;\forall\;f\;\epsilon\;F;&m\;\epsilon\;M\end{array}$$

(11)

The total energy from the feedstocks during each month must meet the boiler fuel requirements, ${Q}_{m,d}^{B}$(kW), which correspond to the turbine output power by the mass and energy balances (Eq. 12):

$$\begin{array}{cc}\sum\limits_{f\epsilon F}{\Delta H}_{f,m}=\sum\limits_{d\epsilon D}\frac{Q_{m,d}^B}{\eta^B}&\;\;\;\forall\;m\;\epsilon\;M\end{array}$$

(12)

In Eq. 12, the sum of all available feedstocks from the supply chain, ${\Delta H}_{f,m}$ (kW), on a monthly basis, must be equal to the demand of the boiler, ${Q}_{m}^{B}$ (kW), summed over each day to give the monthly amount. The combustion efficiency of the boiler, ${\eta }^{\mathrm{B}}$ (%), accounts for energy losses.

Layer 3: Greenhouses

Layer 3 consists of a set of greenhouses having demands for energy, water, and CO₂ along with associated costs. These are all dependent on the total greenhouse floor area.

Heating and Cooling Demands

The heating and cooling demands in the greenhouses are determined using known greenhouse areas and heating (Eq. 13) and cooling requirements (Eq. 14):

$$\begin{array}{ccc}{He}_{g,m}^G={dem}_{g,m}^{he}.A_g^G&\;\;\;\;\;\forall\;g\;\epsilon\;G;&\;m\;\epsilon\;M\end{array}$$

(13)

$$\begin{array}{ccc}{Co}_{g,m}^G={dem}_{g,m}^{co}.A_g^G&\;\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M\end{array}$$

(14)

In Eqs. 13 and 14, the demands for either heating, ${dem}_{g,m}^{he}$ (kWh/m²), or cooling, ${dem}_{g,m}^{co}$(kWh/m²), are based on known monthly energy demands for each crop. This is multiplied by the area of each corresponding greenhouse, ${A}_{g}^{G}$ (m²), to obtain total heating, ${He}_{g,m}^{G}$ (kWh), or cooling, ${Co}_{g,m}^{G}$ (kWh), in each month.

To account for the daily variation in energy demands, a percentage of the known heating and cooling requirements are allocated to either the day (sunlight hours) or night (non-sunlight hours). Generally, heating is required in cooler months when the temperature drops, and cooling required in summer when the temperature increases beyond greenhouse setpoint temperature. In the cooler months, a greater portion of the heating demand is required at night when the ambient temperature drops further below the setpoint. While in the hotter months, a greater portion of cooling demands are required in the day when the ambient temperature is higher. The energy demand for each 24-h day is allocated to the daytime (represented by index $d1$ in Eq. 15) and night-time (represented by index $d2$ in Eq. 16) periods:

$$\begin{array}{ccc}{He}_{g,m,d=d1}^G=h_{d1}^{frac}{He}_{g,m}^G&\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M\end{array}$$

(15)

$$\begin{array}{ccc}{He}_{g,m,d=d2}^G=\left(1-h_{d1}^{frac}\right){He}_{g,m}^G&\;\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M\end{array}$$

(16)

Equations 15 and 16 require a fraction of heating allocated to the day, ${h}_{d1}^{\mathrm{frac}}$, with ${He}_{g,m, d=d1}^{G}$ and ${He}_{g,m, d=d2}^{G}$ the corresponding demands in either the day ($d1$) or night ($d2$).

A similar approach is used to determine the daily cooling demands, ${Co}_{g,m, d}^{G}$ (kWh). This is based on a fraction, ${\mathrm{co}}_{d1}^{\mathrm{frac}}$, to allocate the varying monthly demands, ${Co}_{g,m}^{G}$, to the day and night (Eqs. 17 and 18).

$$\begin{array}{ccc}{Co}_{g,m,d=d1}^G={co}_{d1}^{frac}{Co}_{g,m}^G&\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M\end{array}$$

(17)

$$\begin{array}{ccc}{Co}_{g,m,d=d2}^G={{(1-co}_{d1}^{frac}{)Co}}_{g,m}^G&\;\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M\end{array}$$

(18)

As energy demands are satisfied using electricity, the total demand for the greenhouses is calculated for heating and cooling (Eq. 19):

$$\begin{array}{cc}\begin{array}{ccc}P_{m,d}^G=\sum\limits_{g\epsilon G}\frac{{He}_{g,m,d}^G+{Co}_{g,m,d}^G}{\varepsilon^e}&\;\;\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M;\end{array}&d\;\epsilon\;D\end{array}$$

(19)

The power demand for all greenhouses, ${P}_{m,d}^{G}$ (kW), during each month and day is the sum for heating and cooling across all greenhouses. The additional electricity for control systems and lighting are accounted for by a factor of the total demands, ${\varepsilon }^{e}$.

Water Demand

The irrigation water is pumped to each greenhouse from a groundwater source (Eq. 20):

$$\begin{array}{cc}\begin{array}{ccc}w_{g,m,d=D1}^G=\rho_g^p.w_g^p.A_g^G&\;\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M;\end{array}&d\;\epsilon\;D\end{array}$$

(20)

The water required, ${w}_{g,m,d}^{G}$ (L/h), is based on the specific plant growth density in the greenhouse, ${\uprho }_{g}^{\mathrm{p}}$ (plants/m²), crop water consumption, ${\mathrm{w}}_{g}^{\mathrm{p}}$ (L/plant.day), and greenhouse area, ${\mathrm{A}}_{g}^{\mathrm{G}}$ (m²). The demands are allocated to the day-time period ($d1$) based on the assumption that irrigation only takes place during the day-time period.

The power to pump water to each greenhouse is calculated using a heuristic from Ludwig’s Rules of Thumb (Coker 2007) (Eq. 21):

$$\begin{array}{cc}\begin{array}{ccc}{PP}_{g,m,d}^w=\frac{1.67w_{g,m,d}^G\Delta PD_g^G}{\varepsilon^m}&\;\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M;\end{array}&d\;\epsilon\;D\end{array}$$

(21)

The pump power, ${PP}_{g,m,d}^{w}$ (kW), is based on the water consumption, ${w}_{g,m,d}^{G}$ (L/H), converted to m³/min for use in the correlation, total pressure drop, $\Delta P$ (bar/km), distance from the source to the greenhouses, ${\mathrm{D}}_{g}^{\mathrm{G}}$ (km) and the pump motor efficiency, ${\varepsilon }^{m}$ (%).

The total power for pumping water is calculated as the sum across all greenhouses (Eq. 22):

$$\begin{array}{ccc}P_{m,d}^w=\sum\limits_{g\epsilon G}{PP}_{g,m,d}^w&\forall\;m\;\epsilon\;M;&d\;\epsilon\;D\end{array}$$

(22)

Carbon Dioxide Demand

The CO₂ demand in each greenhouse is similarly dependent on specific crop requirements (Eq. 23):

$$\begin{array}{cc}\begin{array}{ccc}{{CO}_2dem}_{g,m,d=d1}^G={CO}_{2_{g,m,d}}^G.A_g^G&\;\;\;\;\forall\;g\;\epsilon\;G;&m\;\epsilon\;M;\end{array}&d\;\epsilon\;D\end{array}$$

(23)

The total demand, ${{CO}_{2}dem}_{g,m,d}^{G}$ (kgCO₂/h), uses the greenhouse area, ${A}_{g}^{G}$ (m²), and a crop requirement factor, ${{\mathrm{CO}}_{2}}_{g,m,d}^{\mathrm{G}}$ (kgCO₂/m².h). The demand is allocated to the daytime, D1, when photosynthesis is taking place, with none assumed to be taking place at night. It should be noted that the source of CO₂ used for enrichment in the integrated network was not included in the model, rather only the quantity consumed in each greenhouse was considered.

Integration with Layer 2

The power supply and demand are used to integrate Layers 2 and 3 (Eq. 24):

$$\begin{array}{ccc}(P_{m,d}^T+P_{m,d}^S)\geq(P_{m,d}^G+P_{m,d}^w)&\;\;\;\;\forall\;m\;\epsilon\;M;&d\;\epsilon\;D\end{array}$$

(24)

The total electrical power output from the turbine, ${P}_{m,d}^{T}$ (kW) and solar PV, ${P}_{m,d}^{S}$ (kW), during each month and day must be equal to or greater than the energy demand in all greenhouses, ${P}_{m,d}^{G}$ (kW), and that for pumping water, ${P}_{m,d}^{w}$ (kW), monthly and daily.

Total Annualised Cost

Layer 1: Biomass Supply Chain (BSC) Network

The TAC of the BSC, ${C}^{BSC}$(R/y), is calculated by summation over each feedstock, transportation mode and month (Eq. 25).

$${C}^{BSC}=\sum_{f\epsilon F}\sum_{t\epsilon T}\sum_{m\epsilon M}{C}_{f,t,m}^{BSC}{m}^{Frac}$$

(25)

In Eq. 25, the cost of each feedstock and transport link, ${C}_{f,t,m}^{BSC}$ (R/y), is multiplied by the fraction of each month in the year, ${\mathrm{m}}^{\mathrm{Frac}}$, to ensure that the total of the monthly flows (kg/y) results in the costs for one year.

Layer 2: Utility Hub

The cost of the utility hub is based on the capital cost for the boiler and turbogenerator and the solar PV installation. The annual cost for the BSC (Layer 1) above accounts for the cost of feedstock, as the fuel source, to generate steam in the boiler.

The capital cost of the combined heat and power (CHP) unit as the boiler-turbine system is based on the maximum operating capacity (Eq. 26):

$${C}^{BT}={FC}^{T}{P}^{T,OpMax}$$

(26)

The capital investment, ${C}^{BT}$ (R), is calculated by a fixed cost factor, ${\mathrm{FC}}^{\mathrm{BT}}$ (R/kW) which accounts for capital expenditure on the boiler and turbine, and the maximum power to be generated in the turbine, ${P}^{T,OpMax}$ (kW) which must be greater than the highest turbine output during any month and daily period.

The cost for the solar PV installation is based on the number of panels installed (Eq. 27):

$${C}^{S}={FC}^{S}{n}^{S}$$

(27)

The total capital cost for the solar PV installation, ${C}^{S}$ (R), is based on a fixed investment factor, ${\mathrm{FC}}^{\mathrm{S}}$ (R/panel), and the number of solar panels, ${n}^{S}$. The number of panels (Eq. 28) is based on the total installed area.

$${n}^{S}=\frac{{A}^{S}}{{A}^{SP}}$$

(28)

In Eq. 28, the number of solar panels required is for the total area of the installation, ${A}^{S}$ (m²), and the area per panel including spacing, ${A}^{SP}$ (m²).

Layer 3: Greenhouses

Greenhouse TAC is a capital cost accounting for the greenhouse structure and ancillary equipment using a cost factor (Eq. 29):

$${C}^{G}=\sum_{G}{FC}_{g}^{G}{A}_{g}^{G}$$

(29)

The total greenhouse capital cost, ${C}^{G}$ (R), is based on a fixed cost factor, ${\mathrm{FC}}_{g}^{\mathrm{G}}$ (R/m²) and the greenhouse area, ${\mathrm{A}}_{g}^{\mathrm{G}}$. Each crop requires equipment of varying levels of complexity and size and resulting in varied cost factors.

Additional capital is for the piping and transmission cables to deliver utilities to the greenhouses. The cost is similarly based on fixed investment factors which are a function of either distance or electrical capacity (Eq. 30):

$${C}^{u}=\sum_{g\epsilon G}{D}_{g}^{w}{FC}^{w}+\sum_{g\epsilon G}{P}_{g}^{G,max}{FC}^{El}$$

(30)

The total fixed cost to supply utilities, ${C}^{u}$ (R), uses fixed cost factors for water piping, ${\mathrm{FC}}^{\mathrm{w}}$ (R/km), and the length of pipe required, ${\mathrm{D}}_{g}^{\mathrm{w}}$ (km). A fixed cost factor, ${\mathrm{FC}}^{\mathrm{El}}$ (R/kW), and the maximum electrical capacity required, ${P}^{G,max}$ (kW), in each greenhouse is used to calculate cost of transmission cables.

The economic objective to be minimised is the TAC for the entire network (Eq. 31) using the TAC expressions in Eqs. 25, 26, 27, 29, and 30:

$$min{TAC}^{Tot}=\sum_{f\epsilon F}\sum_{t\epsilon T}\sum_{m\epsilon M}{C}_{f,t,m}^{BSC}{m}^{Frac}+AF({FC}^{S}{n}^{S}+{FC}^{T}{P}^{T,OpMax}+\sum_{G}{FC}_{g}^{G}{A}_{g}^{G}+\sum_{g\epsilon G}({D}_{g}^{w}{FC}^{w}+{P}_{g}^{G,max}{FC}^{El}))$$

(31)

In Eq. 31, the TAC, (${TAC}^{Tot}$) is the sum of the BSC, CHP and solar PV, and greenhouse and utility infrastructure. An annualisation factor ($\mathrm{AF}$) is included to account for annualisation of the capital costs for the utility hub and greenhouses.

Environmental Impact

The environmental impact (EI) considers both direct and indirect CO₂ emissions due to combustion of biomass in the boiler and transportation to the utility hub, respectively.

The CO₂ emissions due to transport are calculated as the emissions of each existing feedstock transport link in each month (Eq. 32):

$$\begin{array}{cc}{EI}_{f,t,m}^{BSC}={CEF}_t{.D}_f^F.\tau_t.r\left[\frac{x_{f,t,m}}{\frac{{LHV}_f}n}\right]&\begin{array}{ccc}\;\;\;\forall\;f\;\epsilon\;F;&t\;\epsilon\;T;&m\;\epsilon\;M\end{array}\end{array}$$

(32)

In Eq. 32, the monthly emissions from transport in the BSC, ${EI}_{f,t,m}^{BSC}$ (kgCO₂/y), are based on a CO₂e emissions factor, ${\mathrm{CEF}}_{t}$ (kgCO₂e/kg.km), for each transport mode. This is multiplied by the distance travelled, ${\mathrm{D}}_{f}^{\mathrm{F}}$ (km), to supply a quantity of feedstock, ${x}_{f,t,m}$ (kW), transformed to annual kilograms by the LHV, ${\mathrm{LHV}}_{f}$, and number of operating hours, $\mathrm{n}$ (h/y). The tortuosity, ${\uptau }_{t}$, and return trip factor, ${\mathrm{r}}_{t}$, are included. Emissions factors are generally given as CO₂ equivalent (CO₂e) emissions to account for other GHG pollutants.

The emissions from biomass combustion are calculated using the method outlined by Isafiade and Short (2022) and adapted from Shenoy (1995) (Eq. 33):

$$\begin{array}{cc}\begin{array}{ccc}{EI}_{f,t,m}^{EH}=\frac{x_{f,t,m}}{{LHV}_f}.{CUA}_m.\frac{M^{CO2}}{M^C}.n&\;\;\;\forall\;f\;\epsilon\;F;&t\;\epsilon\;T;\end{array}&m\;\epsilon\;M\end{array}$$

(33)

The EI from combustion of each feedstock in each transport link, ${EI}_{f,t,m}^{EH}$ (kgCO₂/y), is calculated by the amount of feedstock, ${x}_{f,t,m}$ (kW), converted to an annual mass flow (kg/y) using the LHV and annual operating hours $\mathrm{n}$ (h/y).The mass percentage of non-oxidised carbon in each feedstock, ${\mathrm{CUA}}_{f}$ (%), and the ratio of the molecular mass of CO₂, ${\mathrm{M}}^{\mathrm{CO}2}$ (kg/kmol), and molar mass of carbon, ${M}^{\mathrm{C}}$(kg/kmol), are used to determine the corresponding CO₂ emissions.

The objective function to be minimised is the total environmental impact (Eq. 34):

$$min{EI}^{Tot}=\sum_{f\epsilon F}\sum_{t\epsilon T}\sum_{m\epsilon M}{EI}_{f,t,m}^{BSC}.{m}^{Frac}+\sum_{f\epsilon F}\sum_{t\epsilon T}\sum_{m\epsilon M}{EI}_{f,t,m}^{EH}.{m}^{Frac}$$

(34)

In Eq. 34, the total EI, ${EI}^{Tot}$ (kgCO₂e/y), is the sum of the annual BSC, ${EI}^{BSC}$, and energy hub, ${EI}^{EH}$, emissions. These are summed for all months, transport modes and feedstocks. The fraction of a month, ${m}^{Frac}$, in the year is used to ensure that the yearly flows remain in these units.

Multi-objective Function Formulation

The model is transformed into a multi-objective optimisation problem using TAC and EI objective functions in the weighted sum method described by Gxavu and Smaill (2012) (Eq. 35):

$$minZ=W\left(\frac{{TAC}^{Tot}}{{TAC}_{Min}^{Tot}}\right)+\left(1-W\right)\left(\frac{{EI}^{Tot}}{{EI}_{Min}^{Tot}}\right)$$

(35)

The weighted sum method adds the multiple objectives, which in this work comprises TAC and EI, to obtain a single objective termed Z in Eq. 35. A weighting factor, $W$, which sums to 1, accounts for the importance of each objective relative to the overall objective function Z. This is an input based on the selected importance of the environmental and economic objectives. Since TAC and EI have different units, the approach adopted in this work follows that of Gxavu and Smaill (2012). The approach involves first finding the minimum of both TAC, termed ${TAC}_{Min}^{Tot}$ (R/y) in Eq. 35, and EI, termed ${EI}_{Min}^{Tot}$ (kgCO₂/y) in Eq. 35, using the single objective equations (Eqs. 31 and 34). These are then used as inputs to Eq. 35 to eliminate the units for TAC, ${TAC}^{Tot}$, and EI, ${EI}^{Tot}$. Equation 35 is used to simultaneously minimise TAC and EI by minimising the overall objective function (Z). It is worth stating that the weighting factor selected, which may be based on expert knowledge or some other preference criteria, has the tendency to bias the multi-objective solution in favour of one or more objectives in the multi-objective optimisation problem. However, a Pareto curve can be generated from Eq. 35 by varying the weighting factor from 0 to 1.

Case Study

The Dube TradePort AgriZone (Dube Trade Port, 2022), an agricultural- and trading centre in the Kwa-Zulu Natal (KZN) province of South Africa is used as case study to demonstrate the model capabilities. Feedstock, greenhouse crop, and transport types are based on current activity in this region. The investment into renewable and clean energy infrastructure and the existing rail and road routes to and from the trading centre make implementing the proposed network possible. A Google map of the agrizone is shown in Fig. 5 (AfriGIS(Pty)Ltd, 2023).

Fig. 5

Google map of Dube TradePort AgriZone (AfriGIS(Pty)Ltd, 2023)

The selected feedstocks for the BSC in Layer 1 are the wastes from farming activities in the region such as cow manure, sugarcane bagasse, and corn stover. The straight-line distances of the feedstock supply points to the utility hub, lower heating values (LHVs), and carbon content of each feedstock are shown in Appendix Table A4 with Appendix Table A5 showing the supply capacity and cost based on harvesting season of each food-crop from which the biomass wastes are obtained. The transport cost and associated CO₂e emission parameters are shown in Appendix Table A6 with return trip factors of 2 to account for a direct trip back to the supply points. Appendix Table A7 shows the conditions and efficiencies of the boiler, turbine, and condenser for electricity generation from steam which are based on an operation of a similar capacity adapted from El-Halwagi (2017). The energy available from solar radiation required to determine solar PV electricity output is based on average daily radiation at a location near the AgriZone (Appendix Table A8). Three greenhouses are selected to grow tomato, cucumber, and peppers, each having specific energy demands and costing factors (Appendix Table A9). The crop resource requirements and plant growth densities as well as greenhouse costs in Appendix Table A10 are estimates for each crop in similar sub-tropical climates and conditions. The greenhouse areas and distances from the utility hub are selected within a reasonable range. Additional parameters as inputs to the model are shown in Appendix Table A11 such as minimum and maximum capacities of the energy technologies, efficiencies, and cost factors. Key assumptions are on the maximum solar panel area on greenhouse roofing which is taken to be 30% of the total floor area. The day-time greenhouse cooling and heating fractions during summer and winter are taken to be 70% and 30%, respectively. This assumes that most of the cooling or heating will be required when the outside ambient temperatures are highest or lowest for summer and winter, respectively. The selected annualisation factor of 0.1 is for a 10-year period and the weighting factor of 40:60 for TAC:EI (Appendix Table A11) places slightly more importance on the environmental than the economic objective. Distances in Appendix Table A4 were obtained from Google maps (2022).

The model is set up in the General Algebraic Modelling System (GAMS) (GAMS Development Corporation 2014), version 24.4.6, as a suitable mathematical optimisation environment for linear programming (LP) models. The result, a network TAC of 8.051 $\times { 10}^{6}$ R/y and EI of 14,370 tCO₂e/y, was obtained in 11.83 s using the CPLEX solver on an Intel® Core™ i7-1185 Central Processing Unit (CPU) at 3.00 GHz. A breakdown of the TAC and EI results for single- and multi-objective optimisation (Table 1) demonstrates that minimising only TAC gives a suboptimal EI, 15,120 tCO₂e/y, while the converse is true for minimising EI with an increased TAC at 8.559 $\times {10}^{6}$ R/y. The multi-objective result meets a trade-off between the two, with each of these higher than the respective minimums but lower than the sub-optimal single-objective solutions. A breakdown of the TAC and EI is shown in Tables 2 and 3, respectively. These are used to determine the network components which have the most significant effect on the results. Figure 6 shows the network specifications on a yearly basis for the multi-objective optimisation.

Table 1 Single and multi-objective optimisation results

Table 2 Breakdown of overall TAC

Table 3 Breakdown of overall EI

Fig. 6

Multi-objective optimisation network specifications using weighting factor of 60:40 for TAC:EI

Table 2 shows that the BSC in Layer 1 is the single highest contributor to the TAC at 43.7%, with the boiler and turbine-generator system contributing the next largest at 32.5%. The greenhouses and solar PV make up the remaining 15.5% and 8.4% of the TAC, respectively. The relatively high BSC costs can be attributed to the purchase and transporting of biomass which make up 81.2% and 18.8% of this cost, respectively. This is due to the BSC replacing the cost of a conventional fuel source which is significantly higher than the capital expenses as these are annualised over a 10-year period. The capital cost before annualisation amounts to R48.9 $\times {10}^{6}$, highlighting that these are significant, and the yearly expense would increase if stakeholders required a shorter annualisation period.

The breakdown of emissions (Table 3) shows that biomass combustion contributes 99.8% of CO₂e emissions, with the remainder from transport. The transport contribution is relatively low due to the short distances and low emissions factors associated with transport of biomass compared to the carbon content within it. Therefore, although the same amounts of biomass are transported that are burned, emissions are much higher for burning as this is proportional to the carbon content which is significantly higher than the transport emissions factors used in the conversion to emissions. Biomass is sometimes considered as a carbon–neutral fuel source, due to the absorption of carbon by growing of the crop from which the biomass is obtained. It remains important, however, to minimise these emissions as the CO₂ emitted is not in the same location or environment as that in which it was absorbed, making this burning not a natural part of the carbon balance.

The integrated network (Fig. 6) is successfully specified for the multi-objective optimisation case. Figure 6 shows that bagasse and corn stovers are the only feedstocks selected, with manure not being selected at all. This indicates that the high emissions associated with manure due to its high carbon content offset the benefits obtained from the low purchase cost of this feedstock. Bagasse is neither the cheapest nor lowest emission feedstock and is located furthest from the utility hub. It makes up majority of the feedstock supply as this is preferrable to the extremes of high costs and emissions for corn stover and manure respectively. This further demonstrates the model meeting a trade-off between costs and emissions. A detailed distribution of the feedstock selection in each month of the year is shown in Fig. 7.

Fig. 7

Feedstock selection for multi-objective optimised case

Rail is shown to be the only selected mode of transport to the utility hub, with transport by truck on roads excluded (Fig. 6). This is as rail has a lower emissions factor and operational costs, making it optimal for meeting both environmental and economic objectives. Importantly, these costs do not include investment into rail infrastructure, assuming rather that existing systems are to be used. If railway systems were not already in place, capital expenditure could make this transport mode significantly more expensive than using existing road systems.

At the utility hub, a total of 18,960 MWh/y electricity is provided to the greenhouses, 31.6 MWh/y to pump 6220 kL/y irrigation water as well as 4.44 kt/y CO₂ injected. Of this electricity, 62.1% is for cooling, 22.9% for heating and the remaining 15.0% to run ancillary equipment. A total of 71.4% of this electricity is provided by the boiler and turbine-generator system, in the process releasing 14.4 ktCO₂/y as flue gas from the boiler and 40,400 kW/y excess heat in the heat sink for condensation of LPS out of the turbine. This significant quantity of excess heat informs recommendations into utilising this as process heat such as for greenhouse heating or other operations at the site. Furthermore, the large quantity of flue-gas provides an area of investigation into carbon capture and storage and as a supply of the CO₂ required in the greenhouses to promote crop growth. The remaining electricity is from solar PV, which is selected to be installed at the maximum available area of 3000 m². This selection is a result of the reduced capital costs for electricity from solar PV at R1.066/kW compared to R1.653/kW for the boiler and turbine-generator system. These reduced costs and the emission-free operation of solar PV make it suitable for minimising both TAC and CO₂ emissions. This is an expected result as the decreasing cost and absence of emissions currently make solar PV a competitive renewable energy technology. This is, however, limited by the availability of solar radiation and the area available for the installation, highlighting the importance of a distributed energy supply system such as in the proposed network. A detailed distribution of energy supplied from solar PV and the boiler and turbine-generator systems is shown in Fig. 8.

Fig. 8

Distribution of monthly energy supplied from solar PV and boiler turbine-generator

The feedstock supply and greenhouse demand distributions across the months of the year (Figs. 7 and 8) demonstrate the model capability to vary selection monthly as variables such as cost, capacity, and demand change. The feedstock selection (Fig. 7) is influenced by several parameters such as the biomass purchase price, supply capacity, energy intensity (LHV), carbon content, and supply point distance from the utility hub. This shows that corn stover is the only feedstock selected during May and September and makes up 87.9% of the supply in August, with the rest from bagasse. During these months corn stover is the most expensive feedstock, at R430–450/ton, while bagasse remains cheaper at R300–330/ton. This highlights the model selection to consider both objectives, as corn stover has the lowest carbon content, at 43.0% compared to 47.5% for bagasse, and is closest to the utility hub. The distribution seen in Fig. 6 is a result of this trade-off, as despite there being sufficient supply of bagasse, corn stover is selected to meet the environmental objective.

The distribution of electricity from the boiler turbine-generator and solar PV systems (Fig. 8) further highlights the model’s capability to vary energy supply based on the capacities of the two technologies and demands in the greenhouse. This supports the discussion on the capabilities of solar PV as a source of electricity in this network. Solar PV is only available during the day and varies monthly due to decreased solar radiation in the winter months. Therefore, a maximum of 102.8 kW is obtained from solar PV in January (summer), compared to the maximum in June at 46.87 kW (winter). This is directly proportional to the input of solar radiation available in the region and highlights this intermittent supply. Therefore, in almost all months most of the electricity is provided by the boiler turbine-generator system due to the limited capacity of solar PV to meet the total energy demands. For example, the maximum power output of the turbine at 218 kW, is more than double the maximum of solar PV at 102 kW. This capacity is also influenced by the solar PV installation area selected by the model, in this case at the maximum of 3000 m². During the winter months, the boiler turbine-generator system operates at the minimum electricity output of 50 kW. This is due to reduced demands for heating in these months as the Kwa-Zulu Natal is a warm region, often requiring little heating in winter. This means in these months approximately 50–60% of the supply can be provided by solar PV. The result of operating the boiler and turbine-generator system at the minimum capacity is an excess of electricity produced in the winter months. When compared with demand, in the colder months from May to October, an average of 24% excess electricity is produced. This is important to note for the possibility of utilising or selling excess electricity to the grid.

Sensitivity Analysis

Boiler Efficiency

Variations in the biomass feedstock LHV are influenced by factors such as the source and moisture content of the feedstock. This has a direct impact on boiler efficiency during combustion, with the sensitivity of the EI to a boiler efficiency in the range of 65–85% as shown in Fig. 9. A sensitivity analysis on the boiler efficiency from 75% in the base case to 85% decreases both the TAC and the EI by 4.5% and 11.8%, respectively. Alternatively, decreasing efficiency from 75 to 65% increases TAC and EI by 5.94% and 15.4%, respectively. This highlights the importance of feedstocks being in the predicted conditions to achieve efficient combustion in the boiler and, therefore, correctly estimated minimum costs and emissions.

Fig. 9

Effect of boiler efficiency on emissions

Transport Costs

The variability of transport costs due to fluctuations in the market fuel prices is another important factor to consider for its effect on TAC. A 50% increase in the transport cost factors (Fig. 10) shows that the TAC increases by 5.02% without significant effect on the EI. These changes in the network outputs highlight the importance of securing favourable prices. The reason for the insignificant increase in TAC despite large increment in transport cost can be attributed to the relatively low contribution of transport cost to the TAC since the TAC is influenced more by the cost of feedstocks which comprises 81.2% of the BSC costs. The result for EI, when transport cost is increased by 50%, also shows a relatively low reduction from 11.68 to 11.56 ktCO₂e/y. Again, this is because transport cost does not have a significant impact on EI. The slight reduction in EI is due to the slightly varied selection of feedstocks since the solver attempts to simultaneously minimise TAC and EI. It is also worth noting that in Fig. 10, the profile of the increment in TAC due to transport cost price increase is not consistent due to the solver switching from one energy source and transport mode to another, including other parameters that contribute to the TAC, to obtain the optimum solution for TAC and EI. For each increment in transport cost, the impact on TAC due to switching from one energy source to another for the feedstocks is dependent on parameters such as feedstock type and purchase price, shipping distance, available capacity at supply point per season amongst others. Fluctuations of the feedstock purchase prices are not considered; however, this may be useful to investigate as waste biomass becomes more competitive in the market.

Fig. 10

Effect of transport operational cost on total annualised cost

Conclusions

This paper presents a synthesised and optimised model for an integrated renewable energy and resource SCN to satisfy greenhouse demands. This was done by developing a novel GAMS model, represented as an LP, to determine specifications for a minimum TAC and EI for the entire network. The model successfully selected the optimal quantities and types of feedstocks and transportation modes monthly. The distribution of electricity from the energy technologies to greenhouses and that for pumping water was determined, including the selection of the optimal solar PV area to install for electricity contribution to the power supply. The requirements on CO₂ and irrigation water supplies were also determined. Including three feedstocks, two transportation modes, two energy conversion technologies, and three greenhouses of different crop types provides flexibility in the application of the model to a range of greenhouse SCN scenarios and scales of operation.

The results demonstrated the model behaviour in meeting a trade-off between TAC and EI. Comparing single-objective optimisation cases indicates that the economic and environmental objectives cannot be minimised simultaneously without performing multi-objective optimisation. This also highlights the need to include an environmental objective, as minimising only cost results in significantly higher emissions. The feedstock selection of majority bagasse due to the moderate costs and emissions compared to extremes of high and low for manure and corn-stover is an example of this trade-off. A trade-off is not required in transport selection as rail has lower factors for both operational costs and CO₂e emissions. The selection of solar PV to its maximum capacity demonstrated the capabilities of this renewable energy technology for its low costs and emissions. The distribution of supply from this and the boiler turbine-generator which provides most of the electricity supports the need for distributed energy systems due to the intermittent supply of solar radiation. Furthermore, the maximum capacity of solar PV area indicates that increasing the available area, such as on the roofing of other buildings, should be considered for its ability to further reduce costs and emissions.

The sensitivity of results to the boiler combustion efficiency and the transport cost factors was determined as the variables expected to fluctuate the most due to changes in feedstock condition and market prices for fuel. The TAC and EI results are sensitive to both variables, and these findings underscore the dependence of the case study results on the input parameters to the model.

In conclusion, the findings highlight the significance of utilising modelling and optimisation techniques of renewable energy SCNs in greenhouse operations, to minimise both emissions and costs. This approach is valuable for all stakeholders in implementing more cost-efficient and sustainable systems. The trade-off between environmental impact and cost highlights the significance of holistic, network-wide optimisation.

Recommendations

The investigation provides insights into areas of further research and expansions to the model. The potential of solar power could be further investigated by considering a solar thermal or solar photovoltaic and thermal (PVT) hybrid system which could both heat and cool greenhouses and surrounding facilities. This could increase solar power energy output and thus reduce costs and emissions. Using solar thermal means, heat could be provided at night when there is no solar radiation. Furthermore, the cooling effect of placing solar panels on greenhouse roofing could be included for its ability to reduce cooling required in the hotter months. There is also opportunity to reduce costs and emissions through more efficient use of energy and resources from the boiler and turbine-generator system. The boiler flue gas and waste heat from the turbine are two unutilised streams which could be captured and used for CO₂ enrichment and greenhouse heating, respectively. Such systems involve additional costs and complexity and therefore investigation into feasibility is recommended. Future work could also include a detailed economic analysis, as it would provide more accurate outcomes in terms of the economic feasibility of the network for the stakeholders involved. Further research is needed to assess this and the complete environmental consequences of the SCN. This is necessary to account for the indirect CO₂ emissions from the harvesting of biomass wastes or the production of solar PV panels, known to be both resource- and energy-intensive.

Appendix

Table 4 Feedstock parameters for combustion energy and emissions

Table 5 Feedstock seasonal periods, capacities, and costs based on harvesting seasons

Table 6 Transport costing and emissions parameters

Table 7 Boiler and turbine operation parameters (El-Halwagi 2017)

Table 8 Daily solar radiation available for the region investigated at KwaZulu Natal (Kibirige 2018)

Table 9 Greenhouse energy demand and costing factors by crop-type

Table 10 Additional greenhouse parameters by crop-type

Table 11 Additional parameters as inputs to the model