Aquaponic systems require energy in different forms, heat, solar radiation, electricity etc. Typical actuator components of an aquaponic system include pumps, aerators, heaters, coolers, feeders, propagators, lights, etc., which need electrical energy to operate. Hybrid Energy Systems (HES) can help in improving the economic and environmental sustainability of aquaponic systems with respect to energy aspects. Energy management is one of the key issues in operating the HES, which needs to be optimized with respect to the current and future change in generation, demand, and market price, etc. In this paper, a Decision Support System (DSS) for optimal energy management of an aquaponic system that integrates different energy sources and storage mechanisms according to priorities will be presented. The integrated model consists of photovoltaic and solar thermal modules, wind turbine, hydropower, biomass plant, CHP, gas boiler, energy and heat storage systems and access to the power grid and district heating. The results show that the proposed method can significantly increase the utilization of HES and reduce the exchange with the power grid and district heating and consequently reduce running costs.
Global warming and climatic shift has become a major concern nowadays. Because of this, most of the countries have begun to turn their attention towards the clean green renewable energy sources. The design of hybrid solar-wind power systems has received considerable attention in the last decade [
Due to the complexity of hybrid systems, their design and operation is very difficult. Therefore, many approaches have been proposed for the optimization of these systems [
This paper presents a method based on a network flow problem formulation to determine the optimal energy supply mix for aquaponic systems under consideration of the daily profiles for electricity, heat and water pumping demand. The objective is to minimize demand deficit, while maximizing the utilization of renewables at low exchange with the power grid. Hence, a basic understanding of aquaponics is vital and required. Aquaponics can be described as an energy efficient method of producing food particularly in comparison to conventional hydroponics and aquaculture systems. This is predominately because the combination of the two techniques allows the energy costs to be shared. Aquaponic systems on the whole operate within a controlled environment for year round production and this requires an energy input of some kind particularly in temperate climates. Essential components such as the pump and aerators may be mechanically powered via a non-electrical means e.g. via foot or gravity. This may not be possible however in larger systems or where a high level of automation is required and so in most aquaponic systems it is strived to integrate renewable energy technologies within the systems wherever possible. The novelty of the model lies in the prioritization of renewable energy source for allocation based on the produced-energy form and requested-energy form, i.e., why use electrical energy produced by PV for heating if there direct is heat energy from biomass of flat plate solar collector. Therefore, many different priority constraints are included in the network flow optimization problem formulation.
The paper is organized as follows: In Section 2, a detailed problem description will be presented. The proposed methodology will be given in Section 3. An analysis of the current situation and the implementation of the proposed methodology as well as the obtained results for a case study will be given in Section 4. Sensitivity analysis of the main influencing variables is shown in Section 4.2. Finally, in Section 5 the main conclusions are drawn.
The ideal hybrid energy generation system for an aquaponic system is shown in
For a generic system, it is important to have a well-defined and standardized procedure taken for the management of the hybrid system based power generation for aquaponics. The procedure is as follows:
1) Demand side assessment: Assess the energy users in the aquaponic system [
2) Energy resources assessment: Resource assessment can be done by calculating potential available renewable energy resources using meteorological data (wind solar irradiation) or primary source data (e.g. gas in case of CHP) available.
3) Constraints: annual electricity and heat demand, reliability, net present cost, environmental factors etc.
4) Once the system configuration is selected, optimization is performed with suitable optimization technique as will be described in the following sections.
This is a discrete-time energy flow allocation problem, demanding to strictly satisfy all the physical constraints of the system, handling all the operational targets according to a predefined priority series and minimize the total energy conveyance cost and system’s losses. At the same time the deviations between the actual and the desired releases have to be minimized. Following
The SoC and the thermal storage varies dynamically in the system. Therefore, these variables are used to represent the overall state of the system. The energy allocation problem is formulated as a discrete-time optimal control problem as in [
min u k , k = 1 , ⋯ , K { F ( x K ) + ∑ k = 0 K − 1 f 0 k ( x k , u k , z k ) } (1)
subject to
x 0 = x ( t 0 ) (2)
g K ( x K ) ≤ 0 (3)
x k + 1 = f k ( x k , u k , z k ) (4)
h k ( x k , u k , z k ) = 0 (5)
g k ( x k , u k , z k ) ≤ 0 (6)
where x 0 is the initial states vector; h k is a vector of m equality constraints (e. g. balance of non-storage nodes); g k ≤ 0 is a vector of k inequality constraints (e. g. minimum (maximum) battery storage level); F N is the terminal cost function; f 0 k is a strictly convex scalar objective function for time k given in terms of the vectors x k , u k and z k and all discrete variables in x are finite.
As in [
The equality and inequality constraints of the full discrete-time optimal control problem are composed of the constraints of the individual network elements (nodes and connections). The node-link representation enable node specific definition of the objective function, e.g. for a demand node the demand fulfillment need to be defined. The overall objective function is the weighted sum of all objectives defined in the network elements. In the node-link HES network, a node represents a physical component of interest such as energy source, storage,
Variables | Description |
---|---|
EXh | Heating energy provided by the system [kWh] X ∈ [ W T , P V , S H P , C H P , F P C , B , N e t ] |
EXe | Electrical energy provided by the system [kWh] X ∈ [ W T , P V , S H P , C H P , N e t ] |
EXp | Pumping energy from the system [kWh] X ∈ [ W T , P V , S H P , C H P , N e t ] |
EXb | Energy produced and sent to the battery [kWh] X ∈ [ W T , P V , S H P , C H P ] |
CHe | Energy provided from the battery for electricity [kWh] |
CHh | Energy provided from the battery for heating [kWh] |
CHp | Energy provided from the battery for pumping [kWh] |
SoC(t) | the level of battery charge [kWh] at time instant t |
HS(t) | the level of heat storage [kWh] at time instant t |
aggregate energy demand site. A link represents an energy flow between two different nodes, but can also stand for energy losses.
The Mainly, there are six types of network elements for nodes: Source/Supply nodes (S), Generation nodes (SG), Distributor nodes (DT), Storage nodes (R), Consumer nodes (D) and Supply/Consumer nodes (SD).
As in [
∑ i ∈ E ( j ) Q i k = 0 (7)
where i ∈ E ( j ) is the adjacency set of node j.
For example in
E h ( t ) = ∑ X E X h ( t ) | X ∈ [ W T , P V , S H P , F P C , B , N e t , C H , C H P ] (8)
E e ( t ) = ∑ X E X e ( t ) | X ∈ [ W T , P V , S H P , N e t , C H , C H P ] (9)
Q w ( t ) is proportional to the energy used for pumping water, i.e.
Q w ( t ) = E p ( t ) η p s / ( ρ w g H ) (10)
where ρ is the water density [kg・m−3], g is the gravity constant acceleration [m−2]; η p s is the pumping system efficiency, H is the height of pumping and E p ( t ) is represented by node 13 and is the hourly energy that can be used in the time interval t for pumping water.
E p ( t ) = ∑ X E X p ( t ) | X ∈ [ W T , P V , S H P , N e t , C H , C H P ] (11)
For node 20, the energy that is sent to the network E n e t i n ( t ) is composed of the surplus energy produced by the WT, PV and SHP, i.e.
E n e t i n ( t ) = ∑ X E X n e t ( t ) | X ∈ [ W T , P V , S H P ] (12)
E X n e t ( t ) , for X ∈ [ W T , P V , S H P ] and Y ∈ [ h , e , p , b ] , are known because they are the surplus of electrical energy. That is,
E X n e t ( t ) = max ( 0 , E X ( t ) − ∑ Y E X Y ( t ) ) (13)
For node 12, if there is deficit in energy supply, energy is taken from the network for different purposes Y ∈ [ h , e , p ] , as follows:
E n e t o u t ( t ) = ∑ Y E n e t Y ( t ) (14)
For supply nodes, the supply model describes a node to which energy is supplied to the network at a predefined rate, e.g., node 15 in
∑ i ∈ E ( j ) Q i k + Q s u p , j k = 0 (15)
The storage model describes a storage based on a discrete-time energy balance equation expressed in Equation (16) with stored volumes as state variables. Control variable is the energy outflow ( C H Y ). The model includes time-varying constraints for the storage volume as well as an objective term to penalize deviations from a predefined reference trajectory for the storage content.
S j k + 1 = ( 1 − α ) S j k + Δ t k η d ( ∑ i ∈ E ( j ) ( Q i k − θ i ) ) − Δ t k η c ( ∑ i ∈ E ( j ) ( C H Y , i k − θ i ) ) (16)
The storage volume is denoted by S, the self-discharge of the storage by α, the power inflow is denoted by Q and discrete time step is denoted by t. C H Y denotes the discharged power, θ the time delay, η c the storage charging efficiency and η d the storage discharging efficiency. The volume of the storage can be scaled to enhance convergence properties of the optimization algorithm. Equation (16) is subjected to the following constraints,
S j , min k ≤ S j k ≤ S j , max k (17)
S j 0 = S j ( t 0 ) (18)
Specifically for node 10, the battery works as an inventory for the surplus electrical energy that can, in this way, be stored. Specifically, a state equation for the battery storage can be formalized as the actual state of Charge of the battery
plus the excess energy from the supply X ∈ [ W T , P V , H P ] and the energy utilized from the battery by the different users Y ∈ [ h , e , p ] . That is,
S o C ( t ) = ( 1 − α b ) S o C ( t ) + η c ∑ X E X b ( t ) − ∑ Y C H Y ( t ) η d (19)
Every battery has a maximum capacity S o C max . Therefore, this restriction in battery capacity is also considered as a constraint of the system as follows:
S o C ( t ) ≤ S o C max (20)
The same principle can be applied to express the heat storage state Equation node 11,
S ( t ) = ( 1 − α h ) S ( t − 1 ) + η c , h Δ t k P c , h ( t ) − Δ t k n d , h P h o u t ( t ) (21)
S min ≤ S ( t ) ≤ S max (22)
where α h is the self-discharge of the heat storage, P c , h ( t ) is heat power charged to heat storage at time t, S max the maximum heat storage, S min the minimum heat storage, P h o u t ( t ) heat power discharged from heat storage and η d , h is the heat storage discharging efficiency.
Energy demand is modeled as a set of diversion and instream flow targets for consumer nodes, the demand model describes a node from which energy is extracted by a customer Q d e m , j . The governing flow balance equation is described by Equation (23) as follows:
∑ i ∈ E ( j ) Q i k − Q d e m , j k = 0 (23)
subject to the constraint: Q min , j k ≤ Q d e m , j k ≤ Q max , j k = Q r e f , j k
According to the management goal several objective functions can be defined for the demand model which penalizes the demand deficit of the consumer node j, e.g., a quadratic penalty term:
J 0 ( Q j k ) = ρ j k Δ t k ( Q d e m , j k − Q r e f , j k ) 2 (24)
A power generation node is governed by some primary energy source, e.g. solar radiation, wind, flow and the generation efficiency. The power generation by WT, PV, and SHP are governed by the following equations, respectively:
E w t ( t ) = f ( v w ( t ) ) (25)
E p v ( t ) = f ( G ( t ) ) (26)
E h p ( t ) = f ( H ( t ) , Q ( t ) ) (27)
For the BP, FPC plant and CHP, the following restrictions apply, the BP, FPC and CHP may not be in operation e.g., in summer heating is not necessary, and water for heating passing through the plate collector may be stopped. This implies the following relations:
E b h ( t ) ≤ E b = f ( μ ( t ) ) (28)
E f p c h ( t ) ≤ E f p c = f ( G ( t ) ) (29)
P c h p ( t ) ≤ P c h p , max (30)
The Equations (25)-(30) for energy generation by renewable energy source have been discussed in several journal papers and we therefore refer to [
electric and 1.6 kW thermal. The electrical power P c h p , e is calculated depending on the load as in the following equation:
P c h p , e ( t ) = P c h p , e , n f e ( P c h p , L ) P c h p , L (31)
where P c h p , L takes values between 0 and 1. f e ( P c h p , L ) is the ratio electrical
power efficiency at a given load to the electrical power efficiency at nominal load as expressed in Equation (32)
f e ( P c h p , L ) = η c h p , e , L η c h p , e , L , n = P c h p , e , L / Q c h p P c h p , e , L , n / Q c h p , p , n (32)
where Q c h p , p is the primary power and Q c h p , p , n is the nominal primary power. The theoretical thermal power is calculated analogously to the electrical power with f t h ( P c h p , L ) .
The primary power is calculated according to the following expression:
Q c h p , p , L = Q c h p , t h P c h p , e , L η t h , n = Q c h p , p , n P c h p , e , L (33)
where η t h , n is the thermal power efficiency.
Each arc/connection in
on Q i j . The requirement for lower and upper bounds results in the term capacitated flow network.
The basic model for connections defines a time-varying lower and upper bound for the discharge along the connection and is subjected to the following constraints:
Q i , min k ≤ Q i k ≤ Q i , max k (34)
The basic model can be extended to a model which defines a time-varying lower and upper bound for the discharge along the connection as well as an objective term to attenuate discharge variations. The objective function can be expressed as in Equation (35)
J ( Q i k ) = ρ i Δ t k ∑ w = 1 W ( Q i k − Q i k − w ) 2 (35)
Please note that the objective term is associated with the introduction of auxiliary optimization variables according to the number of steps for considering the discharge variation penalty term. Therefore, only a few time steps should be considered in this term. In most cases one step will be enough for a sufficient attenuation of the discharge variation.
This is a special optimization problem, because the solution we are looking for should give priorities to some decision variables compared to the others. Precisely this means if PV alone can generate enough power then the other variables like the grid are kept at their minimum. If PV alone cannot generate enough then WT will follow and so on according to their priority. There are some solvers, e.g., CPLEX which can solve this problem by issuing priority orders.
In order to reach a more adequate level of adherence to the physical system more detailed models are resolved by taking into account nonlinearities in the objective function and constraints, which request a nonlinear programming solver [
To test the feasibility of the proposed methodology, it was applied to one demonstration project setting, which is built to supply power for an aquaponic system [
Combined heat and power (CHP) at the site is used to generate both electricity and heat. This has an electrical output of 16 kW and a thermal output of 34.5 kW. The gas driven CHP plant has an electrical efficiency of 31.0% and a thermal efficiency of 66.9%, which means that the overall efficiency is 97.9% [
There are 48 PV modules from Heckert NeMo P60―with an area of 80.16 m2. Together, the modules have a total output of 12.48 kWp. According to the system simulation of the manufacturer, the yield of the system is approx. 12,500 kWh/a [
A boiler (gas heating) is used as a redundant device for heat generation in the event of a failure of the CHP. It also runs on days with very high heat requirements. There is no more detailed information on gas heating from the site. For this reason, with the help of invoices, approximate values for gas consumption were determined.
The energy consumption of the plant is divided into the consumption of the aquaculture, the greenhouse and the cooling system and the gas requirement of the CHP and boiler. The electricity consumption is read off every month by the electricity meters in the system. An air/water heat pump of the type Zeta Rev HE LN from the company Bluebox is used for cooling. It has a cooling capacity of 49.2 kW and is responsible for various functions. The main task is to cool the room temperature in the greenhouse in the summer months to constant 19˚C. The system also produces cooling water for the cooling fins, which is used to produce condensation.
In the balance-sheet period of 12 months (August 2016 to July 2017), the high energy consumption of the cooling system (3000 to 4300 kWh/month) can be seen in the warm summer months―May to September (
The heat required by the greenhouse can be easily calculated according to the scheme of the KTBL (Board of Trustees for Engineering and Construction in agriculture). According to the scheme, the Thermal transmittance U of the
respective building components, the surfaces to be heated A and the temperature difference ΔT (between temperature in the greenhouse and the outside temperature) flows into the calculation as follows:
Q t o t a l = Q r o o f + Q S t G + Q S t A = 28041.00 W (39)
where the parameters are defined as in
To calculate the maximum heat requirement of the plant, the standard temperature of minus 12˚C is used. The internal temperature remains constant at 19˚C. Thus, the design temperature difference is ∆T = 31 K and this results in a heat demand of 90.818 W for the aquaponics plant.
An assumed annual heating load curve of the aquaponics plant can be seen
In percentage terms, the components of aquaculture (pumps, filters, mixing tanks, etc.) consume about 18,624 kWh/a in a continuous production process. The usage is between 1500 and 2000 kWh/month. Despite the production stop in the winter months of December and January, the components of the greenhouse (pumps, measuring and control systems, condensate traps etc.) consume about the same amount of electricity (18,810 kWh/a). Over the entire year, the power consumption in both zones is 30% for each of them. The current required for cooling is 24,876 kW/a, which accounts for a total of 40%, although the cooling system is not used during the production stop of the greenhouse. In total, the plant consumes 45,876 kWh of electricity in one year. A primary disadvantage of RAS technology is that water must be moved from the culture tank to the different unit processes that restore used water to acceptable levels of quality for fish growth. Therefore, pumping is required. Pumping energy is estimated based upon the amount of lift required (how high the water must be elevated above the culture tank free water surface) and the flow rate required to support fish growth. Thus, it can be seen that the energy requirements for pumping are proportional to the pumping pressure (total dynamic head (TDH) the pump works against), the Feed to gain ratio (FCR) and the required flow per kg of feed fed per day.
Parameter | Design value |
---|---|
Thermal transmittance roof surface (UCSroof) | 4.6 W/(m2×K) |
Thermal transmittance walls Greenhouse (UStG) | 1.27 W/(m2×K) |
Thermal transmittance walls aquaculture (UCStA) | 0.284 W/(m2×K) |
Greenhouse floor area (AG) | 360.30 m2 |
Envelope factor (F) | 0.35 m−1 |
Rated temperature difference Ti ? Ta (∆T) | 9.5˚C = 9.5 K |
Inside temperature greenhouse TiG | 19˚C = 292 K |
Inside temperature aquaculture TiA | 27˚C = 300 K |
Average annual temperature Ta | 9.5˚C = 282.5 K |
Glass wall area greenhouse | 265.07 m2 |
Greenhouse roof area | 393.90 m2 |
Area of aquaculture | 95.87 m2 |
Greenhouse heat transmission envelope area | 754.84 m2 |
The aquaponics plant uses natural gas for the CHP and boiler. Natural gas does not always have the same calorific value, it depends on the exact gas composition. The natural gas, provided by the Municipal Works GmbH, has an average calorific value of 11.23 kWh/m3. The fuel consumption of the CHP and the boiler is calculated based on the known total gas consumption of the plant of 428,087 kWh/a. On the basis of the generation data of the CHP which is read from the electricity meter of 96,010 kWh/a and the electrical power of the CHP taken from the data sheet of the company Smartblock of 16 kW, the operating hours (OH) of the CHP can be calculated first as follows:
OH = ( electrical generation ) / a electrical power = 96010 kWh / a 16 kW = 6000.63 h / a (40)
With the calculated operating hours and the given fuel consumption of the CHP ( CHP fc ) from the data sheet of smartblock, the natural gas consumption of the CHP ( CHP gas ) can be calculated as follows:
CHP gas / a = OH / a ∗ CHP fc = 6000.63 h / a ∗ 51.6 kW = 309623.51 kWh / a (41)
By specifying the total and now known natural gas consumption of the CHP, the next step is to determine the natural gas, which is necessary for the boiler ( Boiler gas ).
Boiler gas / a = Gas total / a − CHP gas / a = 428087 kWh / a − 309623.51 kWh / a = 118761.49 kWh / a (42)
Cost analysis
The costs of the CHP, the photovoltaic system and the grid are listed in order to obtain a power cost value over an accounting period of twelve months. In German, a CHP ordered before the year 2016 falls under the KWKG (Cogeneration Law) 2012 and is remunerated at 5.41 cents/kWh. The prerequisite for this is own use and kWel ≤ 50 kW, which is given in this aquaponics plant. Since 2017, however, the electricity consumed by the company itself has been subject to a levy of up to 40% for the EEG (renewable energy law) levy, i.e., 2.5 cents/kWh. Similarly, taxes for the electricity own use of the photovoltaic system amounts to 2.54 cents/kWh, must also be paid. The electricity from the grid results in costs of 16.8 cents/kWh. Therefore, the overview of Electricity costs of the aquaponics plant (August 2016-July 2017) are listed in
Energy source | Energy | Cost | Sum |
---|---|---|---|
Gas | 428.087 kWh | 0,043 ?kWh | −18.40774 ?a |
Production CHP | 96.010 kWh/a | 0.0541 ?kWh | +5.19414 ?a |
BHKW-Levy EEG 2017 | 56.442 kWh/a | 0.025 ?kWh | −1.41105 ?a |
PV Own use | 10.787 kWh/a | 0.0254 ?kWh | −273.99 ?a |
From Grid 2016 | 6.990 kWh | 0.1680 ?kWh | −1.17432 ?a |
From Grid 2017 | 13.590 kWh | 0.1680 ?kWh | −2.88312 ?a |
Total electricity Cost | −548.34 ?a | ||
Total energy cost | −18.95608?a |
Due to the demand of the CHP for natural gas, the operator of the aquaponics system requested to conduct a feasibility study to utilize only renewable energy sources and design an hourly operational strategy for the only RES system. In the following, the intention is to initiate and evaluate possibilities for optimization using the methodology described in this paper by conducting a feasibility analysis on RES for sustainable and efficient methods of energy production by tapping the natural resources of wind and photovoltaic solar energy, biomass, FPC, and micro-hydro. The dimensions of the proposed system components are listed in
The meteorological input data used for the study was taken from HydroMet/AgriMet. At the measured site, the wind speed [m/s] and the solar radiation [W/m2] for the selected month August, 2015 are as plotted in
Source | Parameter | Description | Value | Units |
---|---|---|---|---|
FPC | η f p c | Efficiency of the FPC | 0.437 | |
A f p c | Area | 4.0 | m2 | |
WT | ρ a | air density | 1.23 | |
A w | Area swept by the blades in m2 | pi*33 | ||
C p | Betz Coefficient | 16/27 | ||
V n | Rated wind speed | 11 | m/s | |
V c | cut-in wind | 3.5 | m/s | |
V s | cut-out wind | 25 | m/s | |
P n | Rated electrical power | 35 | kW | |
H h u b | Hub height | 30.5 | m | |
H m | Height of measurement | 10 | m | |
z 0 | Surface roughness length | 0.03 | m | |
SHP | ρ H 2 O | 1000 | kg/(m3) | |
η turbine | Turbine efficiency | 0.8 | ||
g | acceleration of gravity | 9.81 | ||
Biomass | η b h | plant efficiency | 0.11 | |
LHV | lower heating value | 18.6 | MJ kg−1 | |
VM | Biomass volumetric mass | 82 | kgm−3 |
The network flow optimization formulation described in 3 was implemented C++ and solved using the IPOPT Solver to find an hourly operation strategy for the hybrid management system for the aquaponics. The results will be discussed in the next section.
The results illustrated in
The variability of the energy generated by the wind turbine can be seen in
After finding the optimal solution using the mean meteorological conditions scenario (mean wind and solar irradiation in
impact on the cost analysis of the system as the efficiency of the renewable components of the hybrid system hugely depends upon these parameters. The system will become more feasible if the wind speed is higher, amount of solar radiation is higher and primary energy price is lower and vice versa. Sensitivity analysis is the study of the sensitivity of the system when these parameters change their values.
A decision support system for real time HES management was presented in this paper to define the optimal energy flows in an aquaponic facility. Firstly the current HES was analyzed both on supply and demand sides to find potential improvements. The potential HES system in consideration is characterized by a mix of renewable resources (SHP, solar plate collector, PV, biomass and wind supplemented by storage systems, the power grid and district heating) to satisfy sustainably different energy and heat demands. The methodology was applied to a typical aquaponic system with all types of energy needs, heating, pumping and electricity. A typical August day scenario was created and the optimal results to satisfy all the energy demands were found. Further, sensitivity analysis of the optimal solution using other meteorological scenarios was performed to check the robustness of the solution. It could be shown that the strategy can be applied to an aquaponic facility to manage its energy system sustainably while allocating renewable energy sources to the maximum extent according to demand and availability and limiting the energy exchange with the power grid or district heating.
The research leading to these results has received funding from the European Union’s Seventh Framework Programme FP7-ENV-2013-WATER-INNO-DEMO under Grant agreement No. 619137. We thank the anonymous reviewers and the editors for their valuable comments which are helpful to greatly improve the quality of this manuscript.
Karimanzira, D. and Rauschenbach, T. (2018) Optimal Utilization of Renewable Energy in Aquaponic Systems. Energy and Power Engineering, 10, 279-300. https://doi.org/10.4236/epe.2018.106018