Sizing Optimization and Experimental Verification of a Hybrid Generation Water Pumping System in a Greenhouse

In remote agricultural areas, electrical energy is usually deficient for pumping water into greenhouses. Photovoltaic (PV) panels and wind generators are considered suitable options for power supply. )e reliability of hybrid generation water pumping depends primarily on the number of system components, which should be adapted to the local climatic conditions and crop irrigation schedule. In this study, a universal size optimization model is established to optimize the configuration of a hybrid PVwind-battery (PWB) generation system. )e climatic conditions and crop irrigation schedule are parameterized in the model. Minimization of the annual cost of the hybrid PWB system is the objective function. )e constraints include the battery state of charge (SOC) and the power supply reliability, which consists of the loss of power supply (δLPS) and the excess energy (δEX). )e numbers of PV panels and batteries, as well as the rated power of the wind generator, are the decision variables. )e optimization model of the PWB generation system is solved using a particle swarm optimization (PSO) algorithm based on penalty function. )e model is then applied to determine the optimal configuration of a water pumping system for a greenhouse used to grow tomatoes. Measured climatic data are used in the optimization process, which is conducted in the month of maximum irrigation water requirement (August). )e optimal results for this greenhouse are two PV panels and two batteries, and the rated power of the wind generator is 375W. Furthermore, field experiments are performed to validate the optimization model. )e field experiment results show that the total output power of the PV panels and wind generator during 15 d are 41.478 kW and 6.235 kW, respectively.)e total load power of the pump is 36.965 kW.)e field experiments demonstrate that the optimal results are able to meet the power requirements of the water pumping system and the sizing optimization model is appropriate.


Introduction
In remote agricultural areas, limited electricity is one of the most crucial issues and it is common to use diesel generators to supply electricity for water pumping systems [1,2]. However, due to the instability of fuel prices, the use of renewable energy has become an important option that could solve the energy shortage crisis and ensure sustainable development [3]. Photovoltaic (PV) and wind energy are often abundant in remote areas [4,5] and have been widely used in agricultural applications [6][7][8]. In addition, renewable energy sources have many advantages, namely, low generation costs, availability, and environmental friendly [9][10][11]. However, there are issues associated with the instability and intermittent nature of solar and wind energy, and the high initial investment, as well as the low conversion efficiency of PV panels and wind generators [12][13][14]. It is difficult to ensure reliable electricity supply and minimize the cost of the hybrid PV-wind-battery (PWB) generation system. e devices in the system have to be sized appropriately [15,16]. erefore, the optimization of hybrid PWB generation system is crucial to ensure reliable water pumping performance at low cost.
Various methods have been developed to establish the optimization model of the PWB system [17][18][19]. For example, Muhsen et al. [19] proposed sizing algorithms based on the minimization of cost functions using the loss of load probability concept. Shrestha and Goel [20] focused on developing analytical methods based on a simple calculation of the PV modules' surface and the battery's capacity using the energetic balance method. Zhang et al. [21] focused on the cost versus reliability issue by determining the optimal size of the system elements from an economic point of view. Tégani et al. [22] proposed a methodology for an optimal sizing design and strategy control based on a differential flatness approach, which was applied to a hybrid stand-alone PV-wind system. A multiobjective techno-economic optimization approach based on the LINGO software was used to ensure the optimum configuration between two conflicting objectives such as the system reliability and cost optimizations [23].
Moreover, many conventional optimization methods have been used for hybrid PWB systems. e linear programming model, mixed-integer linear programming, and iterative techniques are examples of classical algorithms that have been widely used for optimizing hybrid PWB systems [24]. In addition, Maleki [25] employed the improved bee algorithm and harmony search algorithm to optimize the design of six grid-independent hybrid renewable energy systems. e results demonstrated that the improved bee algorithm showed significant promise. Zhang et al. [26] presented an efficient method based on a heuristic procedure for the optimization of an independent off-grid hybrid system. e simulation results showed that the heuristic procedure was more promising than the harmony search and annealing methods. A new hybrid optimization algorithm based on three algorithms was proposed for the optimal configuration of a stand-alone off-grid hybrid PV and wind energy system. e simulation results demonstrated the advantages of the hybrid optimization algorithm for a stand-alone hybrid renewable energy system [27]. Maleki [28] applied an optimization approach based on evolutionary programming to evaluate the operational and performance cost of a grid-connected hybrid system. An offgrid PV/wind turbine (WT)/fuel cell (FC)/diesel hybrid system with different fuel prices was used to provide electricity in a remote area, and the model was optimized using a discrete simulated annealing algorithm. e simulation results indicated that the PV/diesel/FC hybrid system was the most cost-effective system for power generation [29]. According to the literature, previous studies have made excellent progress in size optimization of the hybrid system. However, some systems may result in an oversized system for one location and an undersized one for another one [30].
e oversized system not only increases the reliability but also increases financial cost, while the undersized sacrifices reliability for system economics. us, the system size must be carefully selected for each specific application and location. Previous studies have mainly concentrated on the off-grid and grid-connected hybrid systems. Few studies have focused on sizing optimization of hybrid generation systems for agricultural irrigation, especially for different crop irrigation schedule and climatic conditions. erefore, it is necessary to establish a universal size optimization model for hybrid generation systems for the agricultural irrigation system. In addition, the traditional model-solving algorithms have drawbacks, such as rigid iterations, low flexibility, and long computation times [31]. e particle swarm optimization (PSO) algorithm has been widely used because of their efficient global search solutions, strong robustness, and anti-interference ability [32][33][34][35]. Furthermore, it uses a small number of parameters for adjustment, and similar parameters can be used for different applications, making PSO appealing for the optimization of nonlinear functions [36,37].
Consequently, this work proposes a universal sizing optimization model of a hybrid PWB system to minimize the annual cost of the system. Excess energy and the loss of power supply are used as constrains, and the numbers of PV panels and batteries, as well as the rated power of the wind generator, are the decision variables. e model is solved by the PSO algorithm based on the penalty function. e solar radiation, ambient temperature, wind speed, irrigation duration, and other variables are parameterized in the model. e optimal configurations of the hybrid PWB generation system can be obtained for specific irrigation systems by considering the local climatic conditions and crop irrigation schedule. Field experiments are conducted to validate the optimization model. Figure 1 shows the structure of the hybrid PWB powered drip irrigation system, which comprises an irrigation system and a power supply system. e irrigation system consists of a water pump, pipe networks, and emitters. e power supply system consists of PV panels, batteries, and a hybrid PV-wind controller. Wind and solar sources provide the electrical energy for the water pump to raise water for crop irrigation. Figure 2 shows the algorithm block diagram for size optimization of large-scale systems. e input parameters include meteorological parameters, load parameters, and the economic and technical specifications of the system. e optimal combinations of the hybrid power system are obtained with the objectives to ensure system reliability and minimize the cost.

Water Pump Power Requirement Model.
e reference evapotranspiration of the greenhouse crop is calculated using the following equation [38]: where ET 0 is the reference evapotranspiration (mm h −1 ), Δ is the saturation slope of the vapor pressure curve at temperature T m (kPa°C −1 ), R n is the monthly average daily net radiation at the grass surface (MJ m −2 h −1 ), G is the monthly average daily soil heat flux density (MJ m −2 day −1 ), c is the psychrometric constant (kPa°C −1 ), e a is the saturation vapor pressure (kPa), e d is the monthly average actual daily vapor pressure (kPa), and T m is the monthly average daily air temperature (°C). e amount of irrigation required by the greenhouse crops is determined by the following equation: where I is the amount of irrigation (mm), K c is the crop coefficient, and ΔW is the change in soil moisture in the crop root zone (mm). e flow rate of the water pump is determined by the daily irrigation amount, the irrigation area, and the irrigation duration, as expressed by the following equation: where Q is the flow rate of the water pump (m 3 h −1 ), M is the daily irrigation amount (mm), A is the irrigation area (m 2 ), t c is the irrigation duration (h), and η i is the irrigation efficiency (%). e water pump power is obtained using the following equation: where P pump is the water pump power (W), ρ is the water density (kg m −3 ), g is the acceleration of gravity (m s −2 ), H is the water pump head (m), and η p is the water pump efficiency (%).

Wind Generator Output Power
Model. For a wind generator, the output power is related to the wind speed. If the wind speed exceeds the cut-out value, the wind generator stops working to protect the generator. e output power of the wind generator is described in terms of the wind speed using the following equation [7,10,39]: where P w is the output power of the wind generator (W), P w,rate is the rated power of the wind generator (W), v w is the current wind speed (m s −1 ), v ci is the cut-in value for the wind generator (m s −1 ), v r is the rated wind speed of the wind generator (m s −1 ), and v co is the cut-out value for the wind generator (m s −1 ).

PV Panel Output Power
Model. e power generated by the PV panels is calculated using the following equation: where P pv is the generated power of the PV panels (W), N pv is the number of PV panels, η pv is the yield from the PV panels (%), A pv is the area of a single PV panel (m 2 ), and G ir is the solar radiation (W·m −2 ). e yield model is convenient to use and adaptable to the site characteristics and PV panel technology. In this work, the yield model is chosen to model the PV panels, as defined in the following equation [1,2,40]: where η r is the PV panel efficiency under the reference conditions (%), β is the temperature coefficient of the PV panel, T c is the PV panel temperature (°C), and T cref is the reference cell temperature (°C). e cell temperature T c , which depends on the ambient temperature T a and the solar radiation G ir , is calculated using the following equation [1,2,40]: where T a is the ambient temperature (°C) and NOCT is the nominal operation cell temperature (°C).

Battery Model.
Batteries are widely used in hybrid generation systems to store surplus electrical energy and to supply load demand in the case of a deficit of output power from the wind generator and PV panels. Owing to the random nature of power generation by the PV panels and wind generator, the battery capacity constantly changes in hybrid generation systems. erefore, to describe the charge and discharge process of the battery, the state of charge (S OC ) (the ratio between the remaining capacity and the rated capacity of the battery at a certain point in time) is used to describe the remaining capacity of the battery. e battery capacity at time t is calculated by equations (9) and (10): where S OC (t − Δt) is the capacity of the battery at time t − Δt (%), ΔE store is the theoretical charge or discharge capacity of the battery (Wh), η in is the charge efficiency (%), η out is the discharge efficiency (%), N b is the number of batteries, and E rate is the rated capacity of a single battery (Wh). e battery capacity of the hybrid generation system should maintain the balance. us, when the power generated by the PV panels and the wind generator is lower than the power requirements of the water pump, the battery will discharge to balance the requirements of the pump. e discharge capacity of the battery during the period Δt is calculated by Similarly, when the power generated by the PV panels and wind generator is higher than the power requirements of the water pump, the battery will be charged. e charge capacity of the battery during Δt is calculated by using the following equation:

Objective Function.
e objective of the model is to minimize the total annual cost of the hybrid generation system while satisfying the load power requirements and ensuring reliability of the power supply. is objective can be achieved by optimizing the number of PV panels, batteries, and the rated power of the wind generator. e total annual cost includes the initial capital cost, installation cost, and the costs of operation and maintenance [41]. Hence, the objective function is calculated by using the following equation: where C T is the total annual cost of the system (RMB), C acap is the annual initial capital cost (RMB), C ains is the annual installation cost (RMB), and C aom is the annual operation and maintenance cost (RMB). e annual initial capital cost of the system is calculated by using the following equation: (14) where C RF is the capital recovery factor, C pv is the unit cost of the PV panel (RMB), C w is the cost of the wind generator (RMB W −1 ), C b is the unit cost of the battery (RMB), and C con is the unit cost of the hybrid PV-wind controller (RMB).
It should be noted that the capital recovery factor is used to convert the total capital cost into the annual capital cost and is calculated by using the following equation [6,42]: where d is the real interest rate (%) and n l is the project lifetime (years).
In general, the lifetime of a battery is 5 years and the lifetime of a hybrid PV-wind controller is 10 years. us, the unit cost of the battery and controller can be calculated using equations (16) and (17): where P b is the battery price (RMB), P con is the controller price (RMB), S FF is the sinking fund factor, and f is the inflation rate (%). e sinking fund factor is the ratio used to calculate the future value of a series of equal annual cash flows, and it is calculated by using the following equation [10,43]: where l is the lifetime of the battery or solar controller (years). e annual installation cost, which includes the cost of workmanship, transportation, wiring, and other miscellaneous expenses, is assumed to be 10% of the annual initial capital cost [43]. e annual operation and maintenance cost, which mainly includes the repair cost of the system, is planned to repeat annually and is assumed to be 2% of the annual initial capital cost [43,44].

Constraints.
To ensure system reliability, the loss of power supply (δ LPS ) and excess energy (δ EX ) are used as the reliability indexes of the hybrid PWB generation system. δ LPS is defined as the energy deficit in relation to the total power requirements of the water pump. During the period considered, it is defined using the following equation [45,46]: 4 Mathematical Problems in Engineering where P discharge (t) is the actual discharge power of the battery at time t (W). Correspondingly, the δ EX is defined as the excess energy, which is determined by using the following equation [47]: where P charge (t) is the actual charging power of the battery at time t (W). In addition, the battery S oc must meet the following constraints to avoid overcharging or overdischarging, which adversely affects the lifetime of the battery [23,46]: where S OC max is the maximum allowable S oc of the battery (%), while S OC min is the minimum allowable S oc of the battery (%). During the charging or discharging process, when S OC (t + Δt) < S OC min at time t + Δt, the actual discharge capacity of the batteries during Δt is expressed by using the following equation: When S OC (t + Δt) > S OC max at time t + Δt, the actual charged capacity of the batteries during Δt is described by using the following equation: e improved PSO algorithm-based Son penalty function is used to obtain the optimal results. e numbers of PV panels and batteries and the rated power of the wind generator are used as the decision variables. e objective function is then minimized by searching the optimal combination of N pv , N b , and P w,rate . e auxiliary function is expressed using the following equation: where M p is the penalty factor and N is the number of constraints; this then gives

Improved Particle Swarm Optimization Algorithm.
e PSO algorithm is based on populations called swarms that are formed of particles, with each particle representing a potential approach to the problem. Particles move around in a multidimensional search space during flight. Each particle adjusts its position depending on its experience and that of adjoining particles. However, finding the optimal solution using the PSO requires significant effort due to the constantly moving particles and the need to evaluate the fitness at each new position [47]. To be more precise, the position of a particle i at moment k can be regarded as xk i and the velocity as vk i. e position and velocity vectors are then stored during the processing of the algorithm at time k to update the population at time k + 1. e PSO also utilizes the best position information, which is obtained from the particle, to update the current particle swarm at a particular time defined by pk i, and the best position is the particle location at a time defined by pk g. In the next iteration, the velocity and position of each particle are determined using the current velocity and position as expressed by equations (26) and (27): where ω is the inertia weight parameter, c 1 is the cognitive coefficient, c 2 is the social coefficient, and r 1 and r 2 are both random numbers between 0 and 1 [47,48]. As the inertia weight particle inherits the previous flight velocity, the adjustment of the inertia weight value can be found between the global and local searching balance. e inertia weight parameter is improved by the linear weighting method [49]. e inertia weight parameter is defined in the following equation [37,50]: where ω max is the maximum inertia weight and ω min is the minimum inertia weight.

Mathematical Problems in Engineering
Normally, the parameter ω ranges from 0.4 to 0.9 [49], k is the number of current iterations, and K is the maximum number of iterations.

Simulation Process.
e simulations are developed in MATLAB R2014a. e flowchart of the optimization model is shown in Figure 3. e strategy block diagram is used to determine which hybrid system to run. When the wind power is equal to zero, the PV/battery system operates. When the PV power is equal to zero, the wind/battery system operates. If both the wind power and PV power are not equal to zero, the PV/wind/battery system comes into operation.
e specific calculation process is as follows.
First, the parameters such as solar radiation, ambient temperature, wind speed, and other parameters are fed into the optimization model. en, determine whether P pv + P w ≥ P pump . If P pv + P w ≥ P pump , the excess power is charged to the battery and the capacity of the battery is calculated using equation (12). Alternatively, the battery will discharge to balance the requirements of the load, and the discharge capacity is calculated using equation (11). Next, the battery S OC (t) is calculated using equations (9) and (10). If S OCmin ≤ S OC (t) ≤ S OCmax , it follows that the battery is charging or discharging normally. If S OC (t) < S OCmin , there is an energy deficit in the system. If S OC (t) > S OCmax , there is an energy surplus. Next, the load loss and energy surplus are calculated for the period T. Finally, δ LPS and δ EX are obtained from equations (19) and (20). Second, the auxiliary function is evaluated and the optimal results are obtained.

Results and Discussion
e model applications are performed in Weinan, Shaanxi, China (34°95′N, 109°58′E). Tomatoes are irrigated in a greenhouse, and the growing period is from August to December. e water consumption intensity of the tomato is 4.4, 2.7, 1.2, 0.92, and 1.0 mm d −1 for each month in the growing period. e maximum water requirement occurs in August. us, the system components are optimized for the month of August. In addition, based on the local irrigation schedule and irrigation demand of tomatoes, the water pump has to operate for 10 h/day. e detailed technical specifications of the components are provided in Table 1.
e hourly solar radiation on the horizontal surface (Figure 4(a)) and the ambient temperature (Figure 4(b)) are measured using an AV6592 PV cell tester, as shown in Figure 4. e hourly wind speed is obtained from a meteorological station. e data are recorded every ten minutes, and the mean hourly value is used in this study, as shown in Figure 5. e input parameters for the optimization model are shown in Table 2, and Table 3 shows the parameters of the PSO algorithm. e cognitive coefficient and social coefficient are equal to 2.05 based on experience. Presimulations have showed that the fitness function value kept steady after about 37 iterations. e maximum of iterations is determined by the fitness function value. If the fitness function value does not change any longer during iteration, the iteration can be terminated. erefore, the maximum of iterations is set as 200 to avoid wasting too much simulation time. A high particle velocity may prevent finding the optimal solution of the model and a low particle velocity will affect the convergence speed of the model; therefore, the particle velocity range is set as −3-3. Because the optimization problem in this study is relatively simple, the number of particles is set as 20 and the population is set as 1-70, respectively.

Optimization Results.
e convergence curve of the PSO algorithm is shown in Figure 6. e annual cost does not present any variations from iteration 37 onwards.
e optimization simulation results are two PV panels and two batteries, and the rated power of the wind generator is 375 W. e annual cost of this configuration is 1281.6 RMB.

Field Experiment Results
. Field experiment is conducted on 1-15 August, 2017, in the greenhouse growing tomatoes located at the Agricultural Science Research Institute, Weinan, Shaanxi, China. As shown in Figure 7, the hybrid PV-wind controller is used to measure the power generated by the PV panels and wind generator, as well as the hourly power required by the water pumping system. e hourly performance of the hybrid system based on the optimized configuration is illustrated in Figure 8.
While the water pump is working, the S OC decreases at first and then increases. e reason is that the PV and wind power generation capacity is not sufficient to meet the load power requirements at the beginning. At this time, the battery needs to provide electricity for part of the load power requirements, and thus the battery S OC decreases gradually. However, after the S OC reaches its minimum value, the battery S OC begins to increase. is is because the PV and wind power generation capacity goes up gradually and is able to meet the load power requirements. With the increase in PV and wind power generation, their sum begins to exceed the load power requirements. In consequence, the battery S OC rises gradually before reaching its maximum value. ese results show that the battery switches between charging and discharging states continuously. It is evident that the optimal configuration of the PV panels, wind generator, and batteries can ensure 10 h working time per day for the device providing good conditions. e total output power of the PV panels and wind generator during 15 d are 41.478 kW (Figure 8(a)) and 6.235 kW (Figure 8(b)), respectively. e total load power of the pump is 36.965 kW (Figure 8(c)). e optimal configuration of the PV panels, wind generator, and batteries ensures the drip irrigation system remains fully functional. e S OC of the battery is often greater than 50% during the 15 d (Figure 8(d)).

Discussion.
is work focuses on establishing an optimization model to minimize the annual cost of a PWB generation system while ensuring the reliability of the system. Also, the climatic conditions and crop irrigation Start Input data: economic and technical specifications of PV panels and batteries. Hourly solar radiation, ambient temperature, wind speed, etc.
Generation of number of PV panels, batteries and rated power of wind generator by PSO Battery discharge capacity by function (9) Battery charge capacity by function (10) S OC (t) by function (11) (12) S OCmin ≤ S OC (t) ≥ S OCmax S OC (t) > S OCmax Actual charge capacity by function (23) Actual discharge capacity by function (22)    schedule are parameterized in the model. is study differs from that of Yahyaoui et al. [1,2], who used the principle of energy supply and demand balance to determine the optimal components of system. In addition, in the present model, the annual cost is calculated using a dynamic approach, which consists of not only the initial capital cost but also the replacement cost, installation cost, and the costs of operation and maintenance. e constraints of the present model are the loss of power supply (δ LPS ) and excess energy (δ EX ). Compared with the work of Bakelli et al. [46], Olcan [23], and Aziz et al. [51], the present work also uses δ EX to obtain more accurate optimization results. Furthermore, this study employs the penalty function to transform the constrained optimization problem into an unconstrained problem, which is consistent with a previous study that focused on a hybrid diesel-organic Rankine cycle (ORC)/PV system [47]. Moreover, the results of the field experiment demonstrate the applicability of the proposed model to a PWB generation system to determine the optimal components and achieve reliability. e optimization model is applied to a water pumping system in a greenhouse in Weinan for   0  160  240  320  400  480  560  640  720  80 Time ( Figure 4(a) Ambient temperature (°C) Figure 4   irrigating tomatoes. However, the model is equally applicable to other locations and other irrigated crops. Because the climatic conditions (e.g., solar radiation, ambient temperature, and wind speed) and irrigation schedule of crops (e.g., irrigation amount and irrigation duration) are parametric design in the model. In addition, the loss of power supply affects the system components and annual costs. e optimal configuration of the PWB system depends on the water requirements and the type and moisture sensitivity of the crops during the critical period. Since the model considers the operating conditions such as the number of cloudy days, the model that reduces the loss of power supply can be used to ensure design redundancy to meet the agricultural production requirements.

Conclusions
A universal sizing optimization model for a hybrid PWB generation system was established, and the climatic conditions and crop irrigation schedule were parameterized in the model. Minimization of the annual cost was the objective function. e constraints include the battery S OC and the power supply reliability, which is composed of the loss of power supply (δ LPS ) and excess energy (δ EX ). e numbers of PV panels and batteries, as well as the rated power of the wind generator, were the decision variables. Measured climatic data and the water requirement for irrigated tomatoes were used in the optimization model. e optimal configuration of the proposed hybrid PWB generation system was obtained. Finally, the performance of the system was tested in a greenhouse in Weinan for 15 d. e field results showed that the total output power of the PV panels and wind generator were 41.478 kW and 6.235 kW, respectively. e total load power of the pump was 36.965 kW. e results demonstrated that the optimized system was able to meet the power requirements of the water pumping system, thereby validating the size optimization model.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare no conflicts of interest.