Optimal Power Dispatch and Reliability Analysis of Hybrid CHP-PV-Wind Systems in Farming Applications

Abstract

Renewable energy sources (RES) are seen as potential alternative energy sources for rural communities to meet energy demand where electricity supply is inaccessible. Wind and Photo-Voltaic (PV) power is seen as mature and sustainable alternatives for rural electrification. This paper discusses the optimal power dispatch for hybrid combined heat and power (CHP), wind, PV and battery systems with a view to determining the operation of the hybrid system for farming applications. This is accomplished by considering the basic power system probability concepts to assess the performance of the reliability indices. The proposed mathematical model seeks to minimize the system operation costs from CHP. The developed model was validated on five case studies with the same load profile, solar radiation, wind speed and CHP generating unit parameters and solved using a CPLEX solver embedded in Algebraic Modelling Language. The sensitivity analysis performed indicates that the hybrid system achieved a higher reliability as compared to other case studies. The result shows 48% of energy cost reduction is achievable when considering the proposed hybrid CHP, wind, PV and battery system as compared to energy supply via CHP.

1. Introduction

In an agricultural system, electricity is a crucial resource for food production. The farming activities involved include an irrigation system, a livestock rearing operation, household activities, the drying of agricultural products, a hydroponics system and operating farming machinery. However, most of the farming activities occur in rural areas and are faced with acute problem of electricity supply and access to other necessary amenities. The technical and economical constraints of the unavailability of grid connection are due to the remoteness of these regions and lack of financial support for grid extensions to benefit small populations [1]. Therefore, for farming applications, most farmers are engaged with the possibilities of generating electricity onsite. Diesel generators are the most preferable source of energy generation, owing to their simplicity. However, due to the need to produce thermal and electrical energy simultaneously, combined heat and power (CHP), also known as cogeneration or distributed generation, plays a vital role in power industry. The CHP efficiency is high compared to normal generators, owing to its double energy generation and resulting in significant energy savings for an optimized system [2]. This advantage renders CHP systems attractive for farming applications meeting both heating and electrical loads. CHP can also be incorporated with the available renewable energy sources (RES), making the combination suitable for power generation in remote areas. The deployment of RES into electricity production for farm settlement serves as a means of ensuring energy cost savings, enhancing energy security, reducing CO₂ emissions and increasing availability and reliability of power supply [3,4].

Hybrid systems with CHP, PV, wind and battery storage present a solution to the intermittency of solar radiance and wind speed, owing to their ability to serve the required load subject to the availability of climate and weather conditions, which would otherwise cause a serious problem to the system. In order to guarantee steady power supply, battery backup is mostly employed due to the variation in the solar radiation and wind speed. In this setting, the hybrid systems are deployed with a backup battery system to enhance the power system reliability and efficiency as well as to reduce the cost incurred by farmers to produce electricity [5]. Recently, in the literature, there has been keen interest in evaluating the impacts of RES for sustainable electrification in rural areas. Murugaperumal [6] focuses on designing and technical and economic analysis of hybrid RES for arid areas electrification. Solar, wind and biomass technologies were considered to expand the electricity performance in Korkadu village, and HOMER software was used for the performance evaluation. Elkadeem [7] presents a comprehensive investigation of hybrid RES for the sustainable electrification of an irrigation system. Several hybridizations of the RES were considered with a view to obtaining a more feasible solution with low operating cost. Patel [8] presents an optimal components selection for cost reduction in a grid-isolated renewable energy system. Rezk [9] designed an isolated PV and battery storage system for an irrigation system. HOMER software was employed for the optimization process, and the economic performance was evaluated using annualized cost of the system. Abedini [10] presents an optimal management approach to diesel-PV-wind systems for microgrids. A new optimization algorithm was proposed to improve the speed of computation and accuracy.

Analyzing the reliability of hybrid CHP-wind-PV and battery systems is crucial for performance indicators of the system because it aids in assessing the impact of RES on the system adequacy. This is an important factor for effective scheduling and operation of the proposed hybrid system [11]. There are two techniques for evaluating the reliability of power systems. Monte Carlo Simulation (MCS) is an approach for computing the reliability indices of the hybrid system. This method makes use of statistical components derived from failure and repair information for handling stochastic models. MCS is a good approach for obtaining an approximation solution to power system problems, though it is computationally exhaustive and lacks easy implementation in a large network [12]. The analytical technique is the other method of assessing the system reliability, which make use of mathematical expression in computing the reliability indices. Here, an accurate solution is guaranteed with less computational burden [13]. There is some recent literature that considered the importance of reliability to power systems and renewable energy sources. Li [14] proposed an algorithm for reliability assessment considering energy management in a Microgrids system. Rathore [15] investigates comparison between analytical and MCS methods for evaluating loss of load expectation (LOLE) and expected energy not served (EENS) for a pumped hydro storage and renewable energy systems. Adefarati [16] presents an overview for evaluating the distribution system reliability with integration of RES. Yu [17] investigates the impact of loss of load expectation as a determining factor for meeting the customer load demand. MCS was used in computing the reliability indices for Taiwan’s power system.

Based on the aforementioned reviews, this research focuses on the optimal power scheduling of a hybrid CHP-wind-PV and battery system for minimizing the operation cost for farming applications. The objective is to explore hybrid RES in reducing the electricity costs, enhancing reliability of the hybrid system and also minimizing the cost associated with energy not served. A reliability framework for assessing the performance indicators of the system was proposed. A multi-state Markov model was proposed to analyze the availability of the stochastic nature of wind, PV and battery storage. The reliability indices such as LOLP, LOLE, EENS and CENS were computed to determine the influence of RES on the reliability of hybrid systems.

This paper is arranged as follows: Section 2 introduces the proposed model system architecture, describing the combined heat and power, Photovoltaic, wind energy and battery storage system. The optimization model consisting of the problem formulation and its model constraints are described in Section 3. Section 4 presents the reliability analysis of the proposed hybrid CHP-wind-PV and battery system. The methodology and test case studies are presented in Section 5 and the simulation results are discussed in Section 6, while the research work is concluded in Section 7.

2. System Architecture

The proposed hybrid system is presented in Figure 1, which consists of energy sources and the load. The energy sources include CHP generators, wind turbines, PV and battery systems. The load demands for the farming applications include an irrigation system, a livestock rearing operation, household activities, the drying of agricultural products, a hydroponics system and operating farming machinery. The RES is structured in a way to support farming applications load based on the availability of these resources. The heat required for the farming activities are solely supply from the CHP generators. The hybrid CHP-wind-PV and battery system has been proposed for powering the farming applications due to the following reasons: The model can operate in a standalone mode, serve as a means to support constant supply of electricity at a least operating costs and also enhance the reliability of the power systems. The supply is close to the consumers, thereby eradicating the costs associated with grid extension to the region. The components of the hybrid systems are described below.

2.1. Combined Heat and Power

Combined heat and power, also known as cogeneration or distributed generation, plays a significant role in the energy sector. CHP involves generating both electricity and heat simultaneously through a single technological process such as natural gas [2,18]. The double energy generation renders CHP more energy efficient as compared to normal generators, leading to significant energy savings. CHP is a source of greenhouse gas emissions, although these are minimal when compared to a diesel generator. The production of heat depends solely on the power generation, and this introduces a complication to the system [19]. The fuel cost of CHP is a function of both power and heat, and it is given as:

$$C_{\_chp}(P_{chp,t},H_{chp,t})=\underset{electrical}{\underbrace{a_{chp}+b_{chp}{P}_{chp,t}+c_{chp}{(P_{chp,t})}^2}}+\underset{heat}{\underbrace{{\alpha }_{chp}{H}_{chp,t}+{\beta }_{chp}{(H_{chp,t})}^2+{\delta }_{chp}(H_{chp,t}{P}_{chp,t})}}$$

(1)

where $C_{\_chp}(P_{chp,t},H_{chp,t})$ is the fuel cost of CHP generating units to generate both electrical energy $P_{chp,t}$ and heat energy $H_{chp,t}$ at time t. $a_{chp}$, $b_{chp}$, $c_{chp}$, ${\alpha }_{chp}$, ${\beta }_{chp}$ and ${\delta }_{chp}$ are the cost coefficients for CHP generating units.

2.2. Photovoltaic System

The solar PV system consists of many solar cells that are interconnected in solar panels to give the required voltage and current. Electricity produced is from solar radiation via conversion of sunlight [20]. The hourly PV power output can be computed as [21]:

$$S_t=A_{pv}{\eta }_{pv}{R}_{pv}^t$$

(2)

where $S_t$ represents the hourly power output of the PV, $A_{pv}$ is the area of the PV generator in m², ${\eta }_{pv}$ is the efficiency of the PV generator and $R_{pv}^t$ is the hourly solar irradiation on the PV system in kWh/m².

2.3. Wind Energy

The wind turbine utilizes its rotating blades to convert the kinetic energy to electrical energy. The output power of the wind turbine is determined by the availability of wind speed and the characteristics and efficiency of the wind turbine. The hourly output power of the wind generator is expressed as [22]:

$$W_t=\frac{1}{2}\rho {\lambda }_{w}A{\eta }_w{V}^3$$

(3)

where $W_t$ is the hourly output power of the wind generator, $\rho$ is the air density, ${\lambda }_w$ is the coefficient of wind turbine, $A$ is the swept area of the wind turbine, ${\eta }_w$ is the efficiency of the wind generator and $V$ is the wind velocity.

2.4. Battery System

In a standalone system, battery storage can be deployed as system backup owing to the uncertain nature of PV and wind systems. A lithium-ion battery (Li-Ion) is always used with renewable energy systems. The performance of battery is determined by its state of charge, ambient temperature and rate of charging and discharging. The charging and discharging of a battery depend on the output power from the PV and the battery at any given point in time. The battery state of charge is given as [23]:

$$B_{soc}(t)=B_{soc(0)}-\sigma {\displaystyle \sum _{\gamma =1}^t{P}_B(\gamma )} \text{for} 1\le \gamma \le t$$

(4)

where $B_{soc(0)}$ is the initial battery state of charge, $B_{soc}(t)$ is the state of charge at time t, $P_B(\gamma )$ is given as the rate of charging and discharging of the battery at time t and $\sigma$ is the efficiency of the battery. The capacity of the battery must be within the given allowable limits and this is expressed as:

$$B_{soc}^{\min }\le B_{soc(0)}-\partial {\displaystyle \sum _{\gamma =1}^k{P}_B(\gamma )}\le B_{soc}^{\max }$$

(5)

$$B_{soc}^{\min }=(1-dod)B_{soc}^{\max }$$

(6)

where $B_{soc}^{\min }$ and $B_{soc}^{\max }$ are the minimum and maximum allowable capacity, respectively, and $dod$ represents the depth of discharge.

3. Optimization Model of Hybrid System

To obtain an optimal value for the hybrid system, an optimization modeling was performed. Therefore, this paper introduces a proposed optimization model that seeks to minimize the daily operation costs of producing both electrical and heat energy for farming applications. The RES is designed in such a way as to supply the farming loads based on the availability of PV and wind resources. The battery storage is solely charged by the PV, and the PV can also be used to supply the load as shown in Figure 1. The CHP is majorly responsible for the heat loads and subsequently for electrical loads when there is insufficient energy from renewable energy sources.

3.1. Objective Function

The main objective of this research is to minimize the fuel cost of CHP whilst satisfying all the necessary constraints. The CHP has a convex cost function in relation to the heat and power, and the problem formulation is expressed as:

$$Min\left[{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{chp=1}^{CHP}\left(\left\{a_{chp}+b_{chp}{P}_{chp,t}+c_{chp}{(P_{chp,t})}^2\right\}+\left\{{\alpha }_{chp}{H}_{chp,t}+{\beta }_{chp}{(H_{chp,t})}^2+{\delta }_{chp}(H_{chp,t}{P}_{chp,t})\right\}\right)}}\right]$$

(7)

3.2. Model Constraints

For this optimization process, the objective function is bounded by the operational constraints:

$${\displaystyle \sum _{chp}{P}_{chp,t}+P_{w,t}+P_{i,t}=d_t}$$

(8)

$${\displaystyle \sum _{chp}{H}_{chp,t}=d_t^H}$$

(9)

$$P_{i,t}+P_{B,t}\le P_{s,t}$$

(10)

$$P_{chp}^{\min }\left(H_{chp,t}\right)\le P_{chp,t}\le P_{chp}^{\max }\left(H_{chp,t}\right)$$

(11)

$$H_{chp,t}^{\min }\left(P_{chp,t}\right)\le H_{chp,t}\le H_{chp,t}^{\max }\left(P_{chp,t}\right)$$

(12)

$$0\le P_{w,t}\le W_t$$

(13)

$$0\le P_{s,t}\le S_t$$

(14)

$$B_{soc}^{\min }\le B_{soc(0)}-\partial {\displaystyle \sum _{\gamma =1}^n{P}_B(\gamma )}\le B_{soc}^{\max }$$

(15)

where

• $P_{chp,t}$ is the optimal power from CHP generating units at time t;
• $H_{chp,t}$ is the optimal heat from CHP generating units at time t;
• $P_{i,t}$ is the power flow from the PV and battery at time t;
• $P_{s,t}$ is the PV output power at time t;
• $P_{w,t}$ is the wind turbine output power;
• $P_{B,t}$ is the charging and discharging power of the battery at time t;
• $d_t$ and $d_t^H$ are the hourly electrical and heat demands for the farming activities;
• $H_{chp,t}^{\min }$ and $H_{chp,t}^{\max }$ are the lower and upper heat capacities of the CHP generating units;
• $P_{chp,t}^{\min }$ and $P_{chp,t}^{\max }$ are the lower and upper power capacities of the CHP generating units.

The constraints can be briefly described as follows:

• Constraint (8) is the supply-demand equation for electrical energy, and it states that any time t, the power produced by CHP generating units, PV and wind generating units equals the total electrical loads.
• Constraint (9) is the supply-demand equation for heat energy, and it states that at any time, the sum total of heat generated from CHP equals the system heat demand.
• Constraint (10) ensures that the sum of charging and discharging of battery power and power fed into the load must be less or equal to the total forecasted PV.
• Constraints (11) and (12) are the CHP capacity limits for both the power and heat, respectively, and must be within limits.
• Constraints (13) and (14) are wind and PV energy limits, respectively; they enforce that the optimal values must be within forecasted values [24].
• Constraint (15) is the battery state of charge limit, and it states that the available battery capacity must be within allowable capacity.

4. Reliability Analysis of the Proposed Hybrid Model

The reliability of power systems is aimed at estimating the impact of customer load interruptions. This theory has been identified by academics and the power sector for its effective planning and decision making on matters such as long-term maintenance scheduling, operation dispatch and expansion planning [25]. The reliability analysis approaches are responsible for quantifying the contribution of RES on the power system reliability by evaluating their impact to return the interrupted supply [26,27]. This theory is recognized as suitable for studying uncertainty factors; therefore, assessment of the proposed model with the wind-PV-battery system will be carried out in order to estimate the system reliability with varying levels of renewable energy sources integration.

4.1. Multi-State Model of the Wind-PV-Battery System

Recently, reliability theory plays an important role in the operational phase when considering power system integration of renewable energy sources owing to its stochastic characteristics. The reliability and availability of the proposed hybrid system is influenced by the performance of PV, wind and battery. Reliability analysis of the three components is important in order to determine the operation or failure of the system. In this study, the system is depicted by either an ON state representing the operational condition of each component or an OFF state representing the failed condition of each component. Figure 2 presents a multi-state Markov model for the PV, wind and battery system, where 1 and 0 stand for ON and OFF states, respectively.

$$P_{ON}=\frac{\mu }{\mu +\lambda }$$

(16)

$$P_{OFF}=\frac{\lambda }{\lambda +\mu }$$

(17)

The state transitions and a clear description of the eight states are well illustrated in Figure 2. In the state space transitional probability of the wind-PV-battery system, the system will be in operation when the wind, PV and battery are functional, as shown in state 1; otherwise the system will be in non-functional states, as evidenced in state 2 to state 8. The failure and repair rate of wind, PV and battery systems are represented as ${\lambda }_{WT}$,${\lambda }_{PV}$,${\lambda }_B$ and ${\mu }_{WT}$,${\mu }_{PV}$,${\mu }_B$, respectively, and this determined the direction of transition in the system. The failure state of the system is expressed in term of absorbing state, and it depicted in matrix form.

$$T=(I-{\lambda }_R-{\lambda }_L-{\lambda }_I)$$

(18)

The Mean Time to Failure (MTTF) of the PV-wind-battery system is expressed in relation to the identity matrix as given in Equations (19) and (20).

$$MTTF=\left[I\right]-{\left[T\right]}^{-1}$$

(19)

$$MTTF={\left[1+{\lambda }_R+{\lambda }_L+{\lambda }_I\right]}^{-1}$$

(20)

The equivalent total failure and repair rate of the wind, PV and battery system are expressed as:

$${\lambda }_{WT\_PV\_B}={\lambda }_{WT}+{\lambda }_{PV}+{\lambda }_B$$

(21)

$${\mu }_{WT\_PV\_B}=\frac{{\lambda }_{WT}+{\lambda }_{PV}+{\lambda }_B}{\left[\left(1+\frac{{\lambda }_{WT}}{{\mu }_{WT}}\right)\left(1+\frac{{\lambda }_{PV}}{{\mu }_{PV}}\right)\left(1+\frac{{\lambda }_B}{{\mu }_B}\right)-1\right]}$$

(22)

4.2. Reliability Indices

The reliability assessment focuses on evaluating how the system supplies are interrupted by uncertainties caused by renewable energy sources [28]. The application of reliability indices gives a better analysis of renewable energy sources utilization in a power system by providing relevant information about the system performance and capacity. In this study, the key indicators for analyzing the system reliability are discussed below:

• Loss of load probability: LOLP is the probability of a power system experiencing load shedding during a specific time period. This is employed as a measure by utilities to assess the total number of days in a year that the generators’ capacity was unable to meet the daily peak load. The loss of load probability can be expressed as:

  $$LOLP={\displaystyle \sum _{j=1}^J{p}_j{\ell }_j}$$

  (23)

  where $j$ is the capacity outage state, $p_j$ is the state probability of the capacity outage state j, and ${\ell }_j$ is the outage duration of the capacity outage state j.
• Loss of load expectation: This is a metrics that measure the number of days (hourly) in a year when the peak load is more than the generated power. This is mostly used by utilities to assess the security of power supply, and it can be expressed mathematically as:

  $$LOLE={\displaystyle \sum _{j=1}^J\phi \left(p_j{\ell }_j\right)}$$

  (24)

  where $\phi$ is the number of days in a year.
• Cost of energy not served: This is a measure used by utilities to monetize the effects of power interruption caused by insufficient generating capacity. This is a reliability metric that furnished the customers with relevant information on the costs incurred at the time that peak load was not met. In this study, $5.5/kWh is used as the standard value for cost of load loss in South African power systems. The cost of energy not served can be expressed as:

  $$CENS={\displaystyle \sum _{j=1}^J{C}_{\_ENS}{{\rm E}}_{\_ENS}}$$

  (25)

5. Description of Study Cases

Figure 1 gives a description of the proposed farming system. The load demand in the considered farming activities includes an irrigation system, a livestock rearing operation, household activities, the drying of agricultural products, a hydroponics system and operating farming machinery. The data for the hourly load demand for power and heat energy in the system are found in [21]. The technical and reliability specifications used for the hybrid system are presented in

Table 1. Technical and reliability specification of the proposed hybrid system.

Components	Capacity (kW)	Failure Rate	Repair Rate
Wind turbine generator (WTG)	12	0.05	20.6
PV	15	0.04	18.25
Battery	10	0.0312	51.96
CHP	50	0.032	21.89

.

The following reliability indices are considered to properly evaluate the influence of renewable energy sources on the power system: loss of load probability (LOLP), loss of load expectation (LOLE), expected energy not served (EENS) and cost of energy not served (CENS). Different combinations of renewable energy system units are used to verify their respective effects on the power system reliability, and this is performed on the following case studies:

• Case I: Farming system powered with CHP;
• Case II: Farming system powered with CHP and PV;
• Case III: Farming system powered with CHP and wind turbines;
• Case IV: Farming system powered with CHP, PV and battery storage system; and
• Case V: Farming system powered with CHP, wind turbines, PV and battery storage system.

For all case studies, the five generating systems consist of two CHP generating units of 30 kW and 20 kW, respectively, a 12 kW wind turbine generating unit, a 15 kW PV system and a 10 kW battery system, as shown in Table 1. The developed optimization model is solved using CPLEX 12.8 solver programmed in Algebraic Modelling Language (AML) [29,30]. AML are used for solving optimization problems.

6. Results and Analysis

The study results of the hybrid system for farming applications are evaluated to determine the impacts of power scheduling and reliability assessment on the optimal operation of the proposed hybrid model. The developed optimization model is analyzed, and the obtained results from the five case studies of the proposed model are discussed based on the power dispatch and economic and reliability performance, and they are described as follows:

Case I: In this case study, the two CHP generating units supplied all the farming loads since no other alternative sources are available. Figure 3, Figure 4 and Figure 5 show the configuration pattern, and the results obtained in

Table A1. Optimal hourly parameters for case I.

Time (h)	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MW}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MWth}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MWth}\right)$
1	20.96	10.87	10.18	13.82
2	20.72	10.68	10.44	14.56
3	20.59	10.58	10.7	15.3
4	20.49	10.51	10.96	16.04
5	20.59	10.58	11.49	17.51
6	21.11	10.99	11.75	18.25
7	21.59	11.38	11.75	18.25
8	22.22	11.88	11.88	18.62
9	24.14	13.39	12.01	18.99
10	24.58	13.75	12.01	18.99
11	25.53	14.5	12.27	19.73
12	26.17	15	12.54	20.46
13	25.33	14.34	12.27	19.73
14	26.46	15.24	12.01	18.99
15	26.68	15.42	11.75	18.25
16	26.44	15.23	11.75	18.25
17	25.9	14.8	10.96	16.04
18	25.55	14.52	11.36	17.14
19	24.75	13.88	11.62	17.88
20	23.51	12.89	11.75	18.25
21	22.22	11.88	11.62	17.88
22	21.5	11.3	11.36	17.14
23	21.33	11.17	10.44	14.56
24	21.05	10.95	10.44	14.56

reveals that the power and heat demand by the farm loads depends on the two CHP generators since RES are not available to complement it. The reliability assessment of this case study shows the following results: LOLP is 0.043, EENS is 4.8 MWh/year, LOLE is 15.66 day/year and the CENS is $26,400 per year. From the sensitivity analysis given in Table A1, it can be observed that the reliability of the power systems is enhanced with the incorporation of renewable energy sources as proposed for the farming applications.

Case II: In this case study, the two CHP generators and PV are used to meet the farm demand. The integration of PV in the proposed model has improved the reliability performance of the system when compared with case I, as presented in

Table A2. Optimal hourly parameters for case II.

Time (h)	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MW}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MWth}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MWth}\right)$	${\mathit{P}}_{\mathit{w}} \left(\mathbf{MW}\right)$
1	16.74	7.53	10.18	13.82	7.56
2	16.53	7.37	10.44	14.56	7.5
3	15.99	6.93	10.7	15.3	8.25
4	15.76	6.76	10.96	16.04	8.48
5	15.86	6.83	11.49	17.51	8.48
6	15.85	6.83	11.75	18.25	9.42
7	16.12	7.03	11.75	18.25	9.82
8	16.45	7.3	11.88	18.62	10.35
9	18.07	8.58	12.01	18.99	10.88
10	18.44	8.88	12.01	18.99	11.01
11	19.43	9.66	12.27	19.73	10.94
12	20.21	10.28	12.54	20.46	10.68
13	19.52	9.73	12.27	19.73	10.42
14	20.8	10.75	12.01	18.99	10.15
15	21.29	11.14	11.75	18.25	9.67
16	21.44	11.25	11.75	18.25	8.98
17	21.24	11.09	10.96	16.04	8.37
18	21.31	11.15	11.36	17.14	7.61
19	21.01	10.92	11.62	17.88	6.7
20	20.32	10.36	11.75	18.25	5.72
21	18.2	8.69	11.62	17.88	7.21
22	17.18	7.87	11.36	17.14	7.75
23	16.94	7.68	10.44	14.56	7.88
24	16.76	7.55	10.44	14.56	7.69

. The reliability assessment of this case study shows the following results: LOLP is 0.031, LOLE is 11.23 day/year, EENS is 4.5 MWh/year and the CENS is $24,750 per year as shown in

Table 2. Sensitivity analysis for CHP-wind-PV and battery system.

Reliability Metrics	Case I	Case II	Case III	Case IV	Case V
LOLP	0.043	0.031	0.028	0.026	0.02
LOLE (day/year)	15.66	11.23	10.19	9.47	7.25
EENS (MWh/year)	4.8	4.5	3.88	3.55	3.3
CENS ($/year)	26,400	24,750	21,340	19,525	18,150

. The CHP units and the wind turbines are utilized simultaneously to supply the electrical loads of the farming system. The performance of the operating parameters is presented in Figure 3, Figure 4, Figure 5 and Figure 6 showing the hourly optimal power scheduling of the CHP units and PV system. It can be observed that during the night and in the early morning the loads are solely fed by the CHP generating units.

Case III: The third case study utilizes the CHP generators and wind turbines; it is designed to power the farm loads. Figure 3, Figure 4, Figure 5 and Figure 7 give the representation of power and heat flows from CHP unit 1, CHP unit 2 and wind turbines, respectively. It can be seen that the wind turbines power was exhausted before considering the CHP units as shown in

Table A3. Optimal hourly parameters for case III.

Time (h)	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MW}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MWth}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MWth}\right)$	${\mathit{P}}_{\mathit{s}} \left(\mathbf{MW}\right)$
1	20.96	10.87	10.18	13.82	0
2	20.72	10.68	10.44	14.56	0
3	20.59	10.58	10.7	15.3	0
4	20.49	10.51	10.96	16.04	0
5	20.59	10.58	11.49	17.51	0
6	21.11	10.99	11.75	18.25	0
7	21.59	11.38	11.75	18.25	0
8	17.77	8.34	11.88	18.62	7.99
9	18.25	8.72	12.01	18.99	10.56
10	16.99	7.73	12.01	18.99	13.61
11	17.18	7.88	12.27	19.73	14.97
12	17.8	8.37	12.54	20.46	15
13	17.09	7.8	12.27	19.73	14.78
14	18.32	8.79	12.01	18.99	14.59
15	19.12	9.42	11.75	18.25	13.56
16	19.85	9.99	11.75	18.25	11.83
17	20.23	10.3	10.96	16.04	10.17
18	21.28	11.13	11.36	17.14	7.66
19	24.75	13.88	11.62	17.88	0
20	23.51	12.89	11.75	18.25	0
21	22.22	11.88	11.62	17.88	0
22	21.5	11.3	11.36	17.14	0
23	21.33	11.17	10.44	14.56	0
24	21.05	10.95	10.44	14.56	0

; this is a major contribution to system cost reduction. In addition, the reliability assessment of this case study shows CENS is $21,340 per year, EENS is 3.88 MWh/year, LOLE is 10.19 day/year and LOLP is 0.028, and this depicted in graphical representation in Figure 8. Here, the results show a better optimal power dispatch and improved reliability as compared to case II because of the hourly availability of the wind turbines.

Case IV: The configuration pattern and optimal power and heat flows are presented in Figure 3, Figure 4, Figure 5 and Figure 9. This case study utilizes CHP generating units, PV and battery storage system. The battery storage serves as a backup for the PV making this case study an improved version of case II. Figure 8 gives the graphical view of the combined PV and battery power. The PV is responsible for charging the battery, and the battery supplied the load together with CHP generating units when the PV was unavailable, especially during the night and early hours of the day. The reliability assessment of this study shows CENS is $19,525 per year, EENS is 3.55 MWh/year, LOLE is 9.47 day/year and LOLP is 0.026. It is observed that the simulated results have demonstrated that PV and battery storage system integration can improve the reliability of the proposed system and minimize electricity production costs as shown

Table A4. Optimal hourly parameters for case IV.

Time (h)	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MW}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MWth}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MWth}\right)$	${\mathit{B}}_{\mathit{s}\mathit{o}\mathit{c}}$	${\mathit{P}}_{\mathit{B}} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{i}} \left(\mathbf{MW}\right)$
1	18.65	9.04	10.18	13.82	3.71	−4.14	4.14
2	18.41	8.85	10.44	14.56	6.49	−3.71	3.71
3	18.52	8.94	10.7	15.3	9.1	−3.48	3.48
4	18.55	8.97	10.96	16.04	11.58	−3.31	3.31
5	18.75	9.11	11.49	17.51	14.19	−3.48	3.48
6	19.17	9.45	11.75	18.25	17.5	−4.41	4.41
7	19.13	9.43	11.75	18.25	21.46	−5.28	5.28
8	14.83	6	11.88	18.62	20.27	3.58	6.41
9	19.13	9.42	12.01	18.99	19.73	2.72	9.84
10	17.39	8.05	12.01	18.99	17.51	4.97	10.64
11	18.84	9.19	12.27	19.73	15.53	3.63	12.34
12	19.27	9.53	12.54	20.46	14.4	2.52	13.48
13	17.94	8.47	12.27	19.73	12.3	4.8	11.98
14	19.88	10.03	12.01	18.99	11.86	2.58	14.01
15	19.45	9.67	11.75	18.25	12.5	−0.85	14.41
16	19.38	9.61	11.75	18.25	14.11	−2.15	13.98
17	19.03	9.35	10.96	16.04	16.24	−2.84	13.01
18	19.7	9.87	11.36	17.14	19.78	−4.72	12.38
19	22.12	11.79	11.62	17.88	27.99	−7.94	7.94
20	17.41	8.05	11.75	18.25	34.52	−6.71	6.71
21	17.36	8.03	11.62	17.88	39.33	−6.05	6.05
22	17.93	8.46	11.36	17.14	43.16	−5.11	5.11
23	18.48	8.91	10.44	14.56	46.77	−4.81	4.81
24	18.37	8.82	10.44	14.56	50	−4.31	4.31

.

Case V: In this case study, the power produced by the CHP generating units has significantly reduced with the integration of PV, wind turbines and the battery storage system, as displayed in Figure 3, Figure 4 and Figure 5. This indicates a substantial reduction of electricity production costs for the farming loads due to increase utilization of PV, wind and battery in the proposed hybrid systems as displayed in the optimal power flows diagrams in Figure 6, Figure 7 and Figure 8. The incorporation of PV, wind and battery storage into the model enhanced the system reliability with the following figures: LOLP is 0.02, LOLE is 7.25 day/year, EENS is 3.3 MWh/year and the CENS is $18,150 per year, as shown in

Table A5. Optimal hourly parameters for case V.

Time (h)	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MW}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_1} \left(\mathbf{MWth}\right)$	${\mathit{H}}_{\mathit{c}\mathit{h}{\mathit{p}}_2} \left(\mathbf{MWth}\right)$	${\mathit{B}}_{\mathit{s}\mathit{o}\mathit{c}}$	${\mathit{P}}_{\mathit{B}} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{i}} \left(\mathbf{MW}\right)$	${\mathit{P}}_{\mathit{w}} \left(\mathbf{MW}\right)$
1	13.73	5.14	10.18	13.82	4.65	−5.39	5.39	7.56
2	13.52	4.98	10.44	14.56	8.41	−5.02	5.02	7.5
3	13.19	4.7	10.7	15.3	11.45	−4.04	4.04	8.25
4	13.5	4.97	10.96	16.04	14.18	−3.64	3.64	8.48
5	13.83	5.21	11.49	17.51	17.04	−3.81	3.81	8.48
6	13.72	5.14	11.75	18.25	19.89	−3.8	3.8	9.42
7	14	5.34	11.75	18.25	23.1	−4.27	4.27	9.82
8	14.06	5.41	11.88	18.62	20.76	5.12	4.87	10.35
9	15.35	6.42	12.01	18.99	18.67	4.79	7.77	10.88
10	14.1	5.44	12.01	18.99	14.79	8.17	8.44	11.01
11	14.72	5.92	12.27	19.73	11.23	6.76	10.21	10.94
12	14.51	5.76	12.54	20.46	8.69	8.39	11.61	10.68
13	13.04	4.59	12.27	19.73	5.38	5.41	10.37	10.42
14	15.01	6.16	12.01	18.99	3.95	3.92	12.67	10.15
15	14.22	5.53	11.75	18.25	3.94	2.01	13.55	9.67
16	13.88	5.25	11.75	18.25	5.43	−1.98	13.81	8.98
17	13.53	4.98	10.96	16.04	7.89	−3.28	13.45	8.37
18	13.8	5.2	11.36	17.14	12.33	−5.92	13.58	7.61
19	13.43	4.91	11.62	17.88	22.12	−10	10.05	6.7
20	13.04	4.58	11.75	18.25	30.98	−8.8	8.8	5.72
21	11.61	3.47	11.62	17.88	36.99	−7.01	7.01	7.21
22	12.71	4.32	11.36	17.14	41.62	−6.17	6.17	7.75
23	13.49	4.95	10.44	14.56	45.92	−5.74	5.74	7.88
24	13.55	5.01	10.44	14.56	50	−5.43	5.43	7.69

and Figure 9.

7. Conclusions

In this paper, an optimal power operation and reliability evaluation of hybrid CHP, PV, wind and battery systems for farming applications was developed. The objective is to minimize the operation costs of producing electricity for farm loads whilst maximizing the effective utilization of RES as well as improving the reliability of the proposed hybrid system. This is achieved by considering the basic operating indicators to assess the reliability of the proposed hybrid system. The optimization model developed was solved using the CPLEX solver embedded in Algebraic Modelling Language and validated on five case studies. The proposed method implemented can be employed to measure the impacts of integrating RES to ensure energy cost reduction and also to enhance the system reliability.

The results obtained show that the power generated by CHP generating units is substantially reduced owing to an increase in utilization of power from PV, wind and battery systems. It is observed that there is substantial reduction in cost of electricity generation and cost associated with load loss due to increased integration of RES in the hybrid system. It is therefore necessary to encourage farmers or power investors to incorporate RES with conventional power sources in order to minimize power shortages and also to improve power system efficiency and performance.