Cost and availability optimization of wind energy with distributed energy resources of a microgrid

Abstract

A microgrid, an emerging technology in the electric power systems, has various benefits due to the implementation of distributed energy sources along with the loads. A microgrid utilizing the wind energy, solar energy, combined heat and power, natural gas generator, diesel generator, and battery storage is considered in an islanded mode of operation. The economic dispatch optimization is implemented using a reduced gradient algorithm to optimize the Operation and Maintenance cost in the islanded mode of the microgrid. The cost of each energy source is evaluated for every hour of the day using MATLAB code. Then, the availability of each energy source in the microgrid is evaluated. The results obtained are validated by comparing the Operation and Maintenance cost and the availability of each energy source in the microgrid. The optimal solution is achieved by considering the change in wind forecast and battery energy storage profiles.

Keywords

Wind energy microgrid Operation and Maintenance cost economic dispatch optimization availability

Introduction

The increase in the need for the electrical power led to the demand for the microgrid development (Basak et al., 2011; Islam and Gabbar, 2012; Sortomme and El-Sharkawi, 2009). The development in the forthcoming power systems is mainly effected by the energy savings, environment effects, and economic scenarios. A microgrid is implemented by combining the renewable energy sources with a generator so that the distributed energy resources (DERs) can be employed with the utmost benefits (Lasseter et al, 2003; Ramabhotla, 2015). Renewable energy like wind energy is the greatest source of electricity in the entire world. The incorporation of renewable energy source like wind energy has numerous advantages such as the clean energy, lower effect of global warming, and carbon dioxide minimization in comparison with several non-renewable energy sources.

The microgrid operates at a low voltage with generators, energy storages, and loads in both grid-connected and islanded modes, and the loads can be both critical and non-critical loads (Islam and Gabbar, 2012). The change from the grid connected to the islanded mode happens with the occurrence of faults on the grid (Chamana and Bayne, 2011). The unpredictability, higher installation costs, and varying output power are major disadvantages of solar and wind energies, and due to the intermittent nature of weather, they are often considered negative loads. Recent research in the microgrid is performed with DERs, diesel generator, and a battery energy storage and is considered to supply reliable power to the customers in the remote area (Dufo-López and Bernal-Agustín, 2008; Ma et al., 2014). Modeling, design, and optimization of microgrid in islanded mode of operation have been done by several researchers (Celli et al., 2005; Ma et al., 2014; Ramabhotla, 2015; Ramabhotla et al., 2016).

The objective of this article is to achieve the energy management in microgrid by optimizing Operation and Maintenance (O&M) cost with respect to the availability of wind energy with all the energy sources in the microgrid (Katiraei et al., 2008). This can be achieved by applying the economic dispatch optimization technique to obtain the optimal O&M cost of the microgrid (Ramabhotla et al., 2014; Zhang and Giannakis, 2014).

O&M cost optimization of microgrid using economic dispatch optimization

Economic dispatch optimization is defined as an effective method to obtain the least cost of the system while supplying the power to the load by dispatching the generation sources. The generation sources’ constraints should be satisfied. The economic dispatch formulation is given as follows (Ramabhotla et al., 2014)

M i n (F) = \sum_{i = 1}^{N G} F_{i} P_{i}

(1)

Subject to: real power balance

\sum_{i = 1}^{N G} P_{i} = D

(2)

The unit generation capacity limits are given as follows

P_{i}^{\min} ⩽ P_{i} ⩽ P_{i}^{\max}

(3)

where $P_{i}^{\min}, P_{i}^{\max}$ are the minimum and maximum output power of source i; NG is the number of sources; $P_{i}$ is the MW generation of source i; D is the total system load; F_i is the total production cost of source i.

Cost functions

The cost function of each energy source consists of O&M cost. The O&M cost contains the O&M cost of each energy generated by energy source and also the O&M cost of the purchased energy from the utility. The combined heat and power (CHP), diesel generator, and natural gas generator cost functions are achieved using a second-order Lagrangian function as follows (Ramabhotla et al., 2014)

F_{i} (P_{i}) = \propto_{i} + β_{i} P_{i} + γ_{i} P_{i}^{2}

(4)

where i is the generating source; P_i is the electrical power output of a source i; F is the operating cost of source i in US$/h; α, β, γ are the cost coefficients of each energy source in US$/h, US$/MWh, US$/MW²h.

Table 1 shows the cost coefficients of CHP and two generators (Georgia Tech, 2007). The solar energy (F_solar), wind energy (F_wind), and battery energy storage (F_battery) cost functions are shown as follows (Augustine et al., 2012)

Table 1.

Cost coefficients of the CHP and generators.

	CHP (P_CHP)	Generator 1 (P_Gen₁)	Generator 2 (P_Gen₂)
α (US$/h)	0.035	0.02	0.02
β (US$/MWh)	0.035	0.02	0.02
γ (US$/MW²h)	0.035	0.02	0.02

Source: American Public Power Association (n.d.); Pipattanasomporn and Willingham (n.d.).

CHP: combined heat and power.

F (P_{i}) = a I^{p} P_{i} + G^{E} P_{i}

(5)

a = \frac{r}{[1 - [{(1 + r)}^{- N}]}

(6)

where P_i is the energy source generation (kW), a is the annuitization coefficient, r is the interest rate (0.09 for base case), N is the investment lifetime (20 years), I^p is the investment cost per unit installed power (US$/kW), and G^E is the O&M cost (US$/kW).

Solar generation

The 24-h generation data of solar energy are shown in Figure 1. The output power peak is shown at the 13th hour of the day. The cost function of solar energy (F_solar) is calculated as follows

F (P_{s o l a r}) = 0.0165 * P_{s o l a r}

(7)

where $G^{E}$ of solar energy is 1.6 cents/kW.

Figure 1.

Solar power generation.

Wind generation

Wind energy is a very prominent renewable energy source with low cost and provides sustainable energy. The wind energy is integrated with other energy resources in the microgrid and optimal cost and availability are attained. The 24-h generation data of wind energy are shown in Figure 2. The cost function of wind energy (F_wind) is calculated as follows (Augustine et al., 2012)

F_{w i n d} = 0.0165 * P_{w i n d}

(8)

where $G^{E}$ of the wind energy is considered as 1.6 cents/kW. Various profiles of wind energy are obtained as shown in Figures 3 to 6.

Figure 2.

Wind energy generation.

Figure 3.

Wind profile changed—1.

Figure 4.

Wind profile changed—2.

Figure 5.

Wind profile changed—3.

Figure 6.

Wind profile changed—4.

The wind energy source forecast is first obtained from the real-time data in United States as shown in Figure 2. Then, the forecast data are modified in various profiles as shown in Figures 3 to 6. Obtaining the varying profiles helps to figure out the optimization of the availability with respect to cost (total and O&M). For testing purposes, the performance of the wind energy source is assumed at various intervals.

Loads

A critical load of 2.5 MW of power rating is considered in the microgrid. The critical load demand must always be met by the energy sources in the islanded mode of microgrid. Table 2 shows the critical load demand for 24 h of a day.

Table 2.

Critical load demand for 24 h.

Time (h)	Load (MW)	Time (h)	Load (MW)	Time (h)	Load (MW)
1	2.1	9	2.4	17	2.3
2	2.1	10	2.45	18	2.25
3	2.2	11	2.5	19	2.2
4	2.25	12	2.5	20	2.15
5	2.3	13	2.5	21	2.14
6	2.35	14	2.4	22	2.1
7	2.35	15	2.4	23	2.1
8	2.4	16	2.3	24	2

Energy storage

A lithium-ion battery energy storage of 500 kW is included in the microgrid due to the advantages such as high useable capacity, extended cycle life, and fast and efficient charging. A charging and discharging rate of C/2 and C/3 is considered. Thus, it charges for every 2 h and discharges for every 3 h. While in the charging mode, the battery acts as a load and the total load becomes 3 MW. The battery State of Charge (SoC) must always lie in the range of 10% and 90%. The battery $G^{E}$ is considered as 1.6 cents/kW and the cost function is as follows

F_{b a t t e r y} = 0.0165 * P_{b a t t e r y}

(9)

Various profiles of battery are obtained as shown in Figures 7 and 8 and considered for cost optimization. The battery energy storage profile is first obtained and then the data are modified in various profiles as shown in Figures 7 and 8. Obtaining the varying profiles helps to figure out the optimization of the availability with respect to cost (total and O&M). For testing purposes, the performance of the battery energy storage is assumed at various intervals.

Figure 7.

Changed Battery profile 1.

Figure 8.

Changed Battery profile 2.

In the islanded mode of the microgrid, the selling/buying of power from/to the utility grid is not considered. The constraints of all energy sources are shown in Table 3.

Table 3.

Constraints of energy sources.

Wind energy: 0 ⩽ P_wind ⩽ 500 kW	CHP: $0 ⩽ P_{C H P} ⩽ 1.5 MW$	Generator 1: $0 ⩽ P_{G e n 1} ⩽ 1 MW$
Generator 2: $0 ⩽ P_{G e n 2} ⩽ 1 MW$	Solar energy: 0 ⩽ P_solar ⩽ 500 kW	Battery: 100 ⩽ P_battery ⩽ 400 kW

Reduced gradient algorithm

The reduced gradient method is applied to achieve the least cost of the microgrid in the islanded mode of operation. The generation source cost is obtained by applying the MATLAB code for every hour of a day. The algorithm for the reduced gradient method is given as follows:

A microgrid with a CHP (P_CHP), two generators (P_Gen₁ and P_Gen₂), battery (P_battery), solar (P_solar), and wind (P_wind) energy is considered.

Initial power of P_CHP, P_Gen₁, and P_Gen₂ is considered.

P_Gen₂ is always considered as dependent and is expressed as follows

P_{G e n 2} = P_{l o a d} - P_{C H P} - P_{G e n 1}

where P_load is the load demand.

Then, the total cost which is to be minimized is as follows

C O S T = F_{C H P} (P_{C H P}) + F_{G e n 1} (P_{G e n 1}) + F_{G e n 2} (P_{l o a d} - P_{G e n 1} - P_{G e n 2})

where F_CHP, F_Gen₁, and F_Gen₂ are the cost functions of P_CHP, P_Gen₁, and P_Gen₂, respectively.

Find $\nabla C O S T = [(d (C O S T) / d P_{C H P}) / (d (C O S T) / d P_{G e n 1})]$

$X_{1} = X_{0} - C O S T * δ$ where X₁ is the power generated after each iteration and $X 1 = [P_{C H P} / P_{G e n 1}]$ ; δ is the experimental value of the acceleration factor, taken as δ = 10 (taken as a base value); and X₀ is the initial power generated.

$X 0 = [P_{C H P_i n i t i a l} / P_{G e n 1_i n i t i a l}]$

The iterations are completed when the incremental cost at generator 2 is equal to that at CHP and generator 1; the above gradient becomes 0.

If the gradient is not equal to 0, then step 6 is repeated.

End.

Availability

Availability, A(t) is defined as “the ability of an entity to be in a state to perform a required function under given conditions at a given instant of time” (Weibull.com, n.d.). It can be well defined as the ratio of uptime to the total time and the total time is the summation of uptime and downtime. The failure rate of the system is determined by the downtime and failure rate of a component while figuring the system configuration (Oggerino, 2001; Weibull.com, n.d.). An electrical power system combines the series and parallel components. In a series system, the failure rates of all components are combined to find the failure rate of the system. In the parallel system, failure rate must be analyzed to determine it.

The microgrid energy sources that are connected in parallel are considered in this research. This will enhance the chances of microgrid availability because if one of the components fails, the other component operates individually without any failure. This is the advantage of connecting the components in parallel for the availability optimization. Figure 9 with the equation explains the same concept of availability. When a failure in wind energy source occurs, the other energy sources operate and supply power supply to the loads. If the solar energy source is not available, the battery energy source generates power supply and supplies power to the critical load.

Figure 9.

Parallel component.

A microgrid consists of all sources in parallel. Figure 9 represents the connection for the parallel components in a system. So, the availability of the microgrid can be determined as follows (Oggerino, 2001; Ramabhotla, 2015)

Availability, A_{p a r a l l e l} = 1 - [(1 - A_{1}) (1 - A_{2})]

(10)

where A₁ is the availability of component 1; A₂ is the availability of component 2.

A microgrid, which is considered as a repairable and operational system, can operate continuously without fail. Thus, a microgrid possesses higher availability when compared to other power grids (Song et al., 2012). The controllable energy sources play a vital role in improving the availability of the microgrid. The integration of renewable energy sources like wind energy along with the battery energy storage achieves the maximum availability. The battery charging and discharging operation and the varied availability will cause difficulty in calculating the availability of the microgrid.

Availability versus O&M cost optimization of microgrid

The objective of this article is to achieve the optimal solution by comparing the availability with respect to the O&M cost of the microgrid in the islanded mode of the microgrid. The microgrid availability is determined for all profiles. The optimized microgrid availability with O&M cost is developed by considering all generating profiles of the sources.

All the energy sources supply power to the critical load in the islanded mode of the microgrid. The battery energy storage is charged and discharged for every 2 and 3 h, respectively.

Profile 1: all sources included

When all the energy sources like solar, wind, two generators, and CHP along with a battery energy storage are considered, the generation profiles are obtained as shown in Figure 10. Each curve represents the generated power of each energy source. Figure 11 shows the availability and the O&M cost curves plotted for 24 h of a day.

Figure 10.

Profiles of all sources included.

Figure 11.

Availability and cost curve of the microgrid with all the sources included.

Profile 2: all sources included except wind

Figure 12 shows the graphs for O&M cost of each energy source except for wind energy. Figure 13 shows the availability and O&M cost curve for all the energy sources, except for wind energy, which are plotted for every hour of a day. For Figures 12 and 13, the wind energy profile is not considered.

Figure 12.

All sources included except wind.

Figure 13.

Availability and cost curve of the microgrid without the wind.

Profile 3: all sources included except wind and solar

Figure 14 shows the graphs for O&M cost of each energy source except for wind and solar energy sources. Figure 15 shows the availability and O&M cost curves for all the energy sources, except for the wind and solar energy. These graphs are plotted for every hour of a day.

Figure 14.

All sources included except wind and solar.

Figure 15.

Availability and cost curve of the microgrid without the solar and wind.

Profile 4: all sources included except solar

Figure 16 shows the graphs for O&M cost of each energy source except for the solar energy. Figure 17 shows the availability and O&M cost curves for all the energy sources, except for the solar energy. These graphs are plotted for every hour of a day.

Figure 16.

All sources included except solar.

Figure 17.

Availability and cost curve of the microgrid without the solar.

Profile 5: all sources included with wind and battery profiles—1 changed

From Figures 18 to 25, all energy sources including wind energy, solar energy, two generators, and CHP along with battery energy storage are considered. The forecasts for wind energy profiles are obtained from Figures 3 to 6 and included for optimization. Then, the change in the profile of battery energy storage is acquired from Figures 7 and 8 and considered for the optimization of O&M cost and availability in the microgrid (Ramabhotla, 2015).

Figure 18.

All sources included with wind and battery profile changed - Profile 1.

Figure 19.

Availability and cost curve of the microgrid with the changed wind and battery profiles - 1.

Figure 20.

All sources included with wind and battery profile changed - Profile 2.

Figure 21.

Availability and cost curve of the microgrid with the changed wind and battery profiles - 2.

Figure 22.

All sources included with wind and battery profile changed - Profile 3.

Figure 23.

Availability and cost curve of the microgrid with the changed wind and battery profiles - 3.

Figure 24.

All sources included with wind and battery profile changed - Profile 4.

Figure 25.

Availability and cost curve of the microgrid with the changed wind and battery profiles - 4.

Figure 18 represents the O&M cost of all energy sources along with wind change profile as shown in Figure 3. Figure 19 shows the availability and O&M cost curves for all the energy sources for 24 h of a day.

Profile 6: all sources included with wind and battery profiles—2 changed

Figure 20 represents the O&M cost of all energy sources along with wind change profile as shown in Figure 4. Figure 21 shows the availability and O&M cost curves for all the energy sources for 24 h of a day.

Profile 7: all sources included with wind and battery profiles—3 changed

Figure 22 represents the O&M cost of all energy sources along with wind change profile as shown in Figure 5. Figure 23 shows the availability and O&M cost curves for all the energy sources for 24 h of a day.

Profile 8: all sources included with wind and battery profiles—4 changed

Figure 24 represents the O&M cost of all energy sources along with wind change profile as shown in Figure 6. Figure 25 shows the availability and O&M cost curves for all the energy sources for 24 h of a day.

In Profile 1, the O&M cost is high when all the sources are included as shown in Figure 10. Output power of each source is obtained, and all the energy sources are compared in this profile. Due to the high O&M cost obtained, more profiles are acquired and evaluated (Ramabhotla, 2015).

In Profile 2, wind energy is not considered, and the O&M cost is still high as shown in Figure 12. This is due to the high investment cost of solar energy. The availability is high and can vary depending on the generating power from each source.

In Profile 3, both wind and solar energies are not included. Both the wind and solar energy sources are intermittent in nature. From Figure 14, the output power from each source can be understood. The availability of each source is shown in Figure 15. The availability, when compared to Profiles 1 and 2, is less.

From Profile 4, the solar energy is not included, thus the O&M cost is decreased. The wind energy is included, and with the high investment cost to include wind energy, the O&M cost is increased. When compared to Profile 3, the system performance is high since the wind energy is integrated into the microgrid. This also increases the system’s availability.

Profiles 5–8 represent the profiles of the microgrid with all the energy sources along with the change in the profiles of wind and battery energy storage. The wind energy and battery energy storage vary depending on their profile changes. In Profile 5, the change in the wind profile and battery profile is included. The O&M cost of the system is high especially during peak energy use hours of the day. Regardless of the wind power generation, the availability varies. From Profile 6, the O&M cost and the availability are high due to the high wind generation. In Profiles 7 and 8, the O&M costs of the microgrid will increase with respect to the increase in the power generation of the wind energy. The availability of the system will also increase due to the integration of the wind energy into the system.

The comparison of Profiles 1–4 shows that the minimal O&M cost of the microgrid cannot be obtained due to the above-mentioned reasons. The comparison of Profiles 5–8 depicts that the optimal O&M cost of the microgrid is obtained from the Profiles 6 and 7. The higher availability is also obtained in these profiles. The battery energy storage integration into the microgrid makes the system stronger. Thus, Profiles 6 and 7 give the best solutions with regard to the optimized availability and O&M cost of the microgrid in the islanded mode of operation.

Hence, by comparing all the profiles mentioned above, the profiles with change in wind and battery energy storage will provide the optimal O&M cost and availability in the islanded mode of the microgrid (Ramabhotla, 2015).

Conclusion

This article studies the availability and the minimal cost optimization in the islanded mode of the microgrid. The O&M cost optimization is implemented using the economic dispatch method in islanded mode of optimization. To optimize the O&M cost, all energy sources are considered by evaluating wind energy with various generating profiles. Renewable energy like wind energy meets the demand for the electricity supply and also reduces the challenges due to the fossil fuel depletion. The profiles with wind forecast change and battery energy storage provide the best solution. The wind energy integration with other energy sources achieves the highest availability in each profile ranging from 94% to 100%. Therefore, wind energy played a vital role in enhancing the availability and cost reduction of the microgrid. Thus, the optimal solution for the O&M cost along with the availability is obtained by integrating the wind energy with other DERs in the islanded mode of microgrid.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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