# Compressed Air Energy Storage System Control and Performance Assessment Using Energy Harvested Index

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Brief Survey of Typical Energy Storage Systems

**Figure 1.**Energy storage systems with different storage capacity [9].

_{exchanged}= ∫ Idt

_{kinetic}= 0.5 m

_{f}V

^{2}

_{f}is the rotating mass of the flywheel in kg and V is the circular velocity of the flywheel in m/s.

_{P}

^{3}, g is acceleration due to gravity in m/s

^{2}, Q is discharge through the turbines in m

^{3}/s, H is effective head in m and η

_{P}is efficiency of the pump. The delivered energy of a pumped hydro storage system can be determined by the product of the output power obtained in Equation (4) and the time duration.

_{1}V

_{1}[(P

_{2}/P

_{1})

^{(n-1/n)}− 1]

_{p}/c

_{v}), P

_{1}and P

_{2}are the atmospheric and the tank pressure in a compression cycle respectively.

## 3. Proposed Criterion for Energy Storage Capability and Control Performance Assessment

_{s}is the total sample time, E

_{storted}(t

_{i}) is the amount of stored energy at the time t

_{i}and the E

_{excess}(t

_{i}) is the amount of available excess energy. This new index has been introduced in consideration of the limited capacity of storage systems because of their physical limitation in energy conversion and storage. For example, a battery cannot store more energy when it reaches its nominal voltage, nor can a hydro storage system when the reservoir is full. On the other hand, in a CAES system air can be compressed to higher pressures during high excess energy regimes. This concept will be more attractive in locations that have non-uniform excess energy distribution during a given time scale (e.g., an hour time scale). In a non-uniform excess energy profile, the frequency of the high wind speed regimes is higher in a specific time duration, while this frequency is low during the rest of the time. In this case the excess energy is available only for a short duration of the time, and the storage system capability to capture this opportunity is critical in order to achieve a high wind penetration.

## 4. Proposed Hybrid Power System (HPS) Description

_{wind Turbine}= 0.5 C

_{p}(V

_{w}) ρ A

_{r}V

_{w}

^{3}

_{p}is the wind power coefficient, A

_{r}is the cross section area swept by rotor and V

_{w}is the wind speed. The air density ρ can be taken as 1.225 kg/m

^{3}. In this study, the Bergey Excel-S 10 kW wind turbine is chosen, based on the available average wind speed and demand. Considering the power curve provided by the manufacturer, the C

_{p}value can be considered as a function of wind speed, and it can be obtained using a Gaussian Equation in the following form:

_{w}is the wind speed and other parameters are provided in Table 1.

Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|

ɑ_{1} | 0.2 | b_{1} | 5.963 | c_{1} | 2.218 |

ɑ _{2} | 0.1555 | b_{2} | 3.825 | c_{2} | 1.228 |

ɑ _{3} | 0.2439 | b_{3} | 10.06 | c_{3} | 4.004 |

ɑ _{4} | 0.1056 | b_{4} | 15.59 | c_{4} | 5.769 |

_{p}value as a function of wind speed variation was applied to Equation (7), and the obtained power curve is shown in Figure 4, where it has been compared to the Bergey Excel-S 10 kW wind turbine power curve from its manufacturer’s datasheet. The resulting power curve is almost identical to its catalog values for wind speeds lower than 16 m/s. This approximation is sufficient for wind farms located in sites where the wind speed average value is less than 16 m/s, which is valid for the objective site of this case study (Ramea, NL, Canada).

^{3}can be expressed by the following equation:

_{a}is the atmospheric pressure and P

_{f}is the final pressure. Figure 6 shows the variation of the pneumatic CAES storage energy density with changes in the number of energy conversion stages and working pressure. It can be observed that it is essential to increase the maximum pressure in the tank in order to increase the energy density of the storage system. In addition, increasing the number of stages can improve the energy density characteristics of the storage system. However, the effect of increasing the number of stages on the energy density will be decreased in all pressure ratios, especially after five stages. This result should be considered in general design of a CAES system in order to define the optimum number of stages and its working pressure.

## 5. Using the Harvested Energy Index in CAES Systems

_{compressor}= (n/n − 1) P

_{1}Q [PR

^{(n-1/n)}− 1]

_{1}). Assuming a polytropic process for both compression and expansion, the polytropic exponent of air for the compression process can be considered 1.45 for compression and 1.36 for expansion [14]. The pressure of the tank will increase depending on the amount of the entered air mass to the reservoir based on Equation (11), where the change in air mass can be calculated using Equation (12):

^{n}= mRT

- 1-
- The charging cycle: This condition happens when the output power of the wind turbine is more than the load, and the storage system has available storage capacity. In this condition, the excess power is applied to the compressor and the output flow rate of the compressor is calculated using Equation (10). The total air mass entered to the high pressure tank can be obtained using Equation (12) and the tank pressure can be obtained using Equation (11). The tank pressure will continue to increase as long as the excess power is available and the tank pressure is lower than its nominal value.
- 2-
- The rejection cycle: In this cycle, the energy storage is charged to its maximum capacity and any additional power cannot be stored. Considering the fixed blade configuration for the wind turbine, this rejected power will be consumed by the dump load in order to maintain the system stability.
- 3-
- The discharge cycle: The storage system starts to deliver power to the load, when the output power of the wind turbine is not sufficient to meet the demand. This cycle will be terminated when the storage system is fully discharged or the wind speed increases and the wind turbine output power is sufficient for the load.
- 4-
- The shortage cycle: Diesel generator will operate in this mode in order to compensate the wind turbine output power. In this situation, the total power of the wind turbine and storage system is less than the required power for the load. The fuel consumption of the diesel can be calculated by using its power-fuel consumption equation.

_{DG}is the diesel generator power in W and FC

_{DG}is the diesel generator fuel consumption in L/h.

^{3}in order to store 5 kWhr in 16 bar working pressure. This value was chosen, based on the obtained HEI for different energy storage capacities shown in Figure 8. As seen in this Figure, the system with the 5 kWhr capacity is the first storage system which can reach 100 percent HEI, and has a capacity close to the maximum load. The working pressure of the 16 bar was chosen for the base working pressure of the system by considering four-stage compression with reasonable energy density (Figure 6) and efficiency (Figure 7). It was assumed that the compressor unit has the ability to change its configuration to reach required flow rate and the working pressure. This assumption was made in order to assess the impact of the working pressure on the performance of the HPS. In practice, a system with working pressure of 3, 9, 27, and 81 can be obtained using four-stage compression and compression ratio of 3 for each stage to reach higher energy densities. The assumed parameters were chosen based on the available data for the wind and demand in order to show the impact of the proposed HEI on increasing the captured energy. The impact of the developed control strategy on the fuel consumption of the diesel generator will be compared with other control strategies.

**Figure 10.**Change in average HEI in a day time scale considering only constant working pressure for compressor.

Control method | Fixed 10 bar | Fixed 26 bar | HEI in 25 stages | HEI in 4 stages |
---|---|---|---|---|

Shortage Duration | 326 [min] | 225 [min] | 163 [min] | 192 [min] |

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

SedighNejad, H.; Iqbal, T.; Quaicoe, J.
Compressed Air Energy Storage System Control and Performance Assessment Using Energy Harvested Index. *Electronics* **2014**, *3*, 1-21.
https://doi.org/10.3390/electronics3010001

**AMA Style**

SedighNejad H, Iqbal T, Quaicoe J.
Compressed Air Energy Storage System Control and Performance Assessment Using Energy Harvested Index. *Electronics*. 2014; 3(1):1-21.
https://doi.org/10.3390/electronics3010001

**Chicago/Turabian Style**

SedighNejad, Hanif, Tariq Iqbal, and John Quaicoe.
2014. "Compressed Air Energy Storage System Control and Performance Assessment Using Energy Harvested Index" *Electronics* 3, no. 1: 1-21.
https://doi.org/10.3390/electronics3010001