WSEAS TRANSACTIONS on SYSTEMS

Jianhui He, Guoqiang Ao, Jinsheng Guo, Ziqiang Chen, Lin Yang

voltage of FESS can be defined as a fix value^{U }

,

## Where

k_{1 }

and

k_{2 }

denote

separately

the

I (t ) input or output current can be defined as

and the efficiency of FESS is ^{η }. Then the ideal energy change of FESS is given as follow

coefficient of air resistance and rotary resistance According to the equations (1), (2), (6), (7), (8), the energy characteristics of FESS can be expressed as:

( equation: ) d t t I U E ∫ = Δ η

（4）

Rotary speed of flywheel varies linearly with time, so the energy transmission between FESS and exterior system is a gradual process. Motor or generator absorbs or releases power through the accelerating or decelerating torque that is forced on flywheel. Under the effect of angular acceleration, the actual variety of energy will have phenomenon of delay at certain extent. Define the accelerating or decelerating torque at

t i m e ( t ) a s

T (t)_{, then }

T (t ) Δω =

J

⋅Δt =

η UI (t ) Jω (t )

Δt

(5)

( ) ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ = t d λ dω(t ) =

4 ∫ ( ) ( ) ( ) ( ) ] ( ) ( 4 ) ( ) ( ) ( ) ( ) ] ( ) ( ) − + − − − + − ∫ t r R l d t t k t k t U I r R l d t t k t k t U I ω π ρ ω ω η ω ω π ρ ω ω η 4 4 2 2 1 2 m i n 2 m a x 4 2 2 1 4

（9）

When there is no energy transmission, the rotary speed of flywheel will be reduced slowly to its minimal value under the effect of resistant power. At this moment, the friction resistance of flywheel approaches gradually to zero and then the rotary speed will be hardly reduced anymore. According to the equation (9), under situations of charging or discharging with maximal power, the change of energy storage state of FESS and the rotary speed of flywheel can be obtained

The actual change of energy is inferred as follows:

ΔE =

1 2

J(ω(t)+ Δω)^{2 }−

1 2

J = ∫ 2 η ω

U I (t )d t

−

⎜ ⎜ ∫

ηUI(t)⎞^{2 }ω(t) ⎠

dt 8J ⋅t t

with initial conditions of

, λ = 0 ω = 1350rpm

and

, λ = 1 ω = 18000rpm

. Fig.3 presents the

（6） The hybrid system uses high-speed flywheel

system with working speed ^{ω > }^{103 rpm }, so

the negative item of equation (6) is a high-order infinitely small item. Then the actual change of energy is expressed as follows:

^{ΔE ≈ }∫^{ηUI(t)dt ≈ ΔE }

（7）

energy characteristics of FESS.

Charging time of FESS is relative short. With maximal charging power, it needs less than an hour to change the energy storage state from

0

to l. Discharging time is about half that of

charging and the FESS can operate continuously for nearly half an hour with its maximal output power after full charging.

Thus the actual energy characteristics of FESS are very close to its ideal value. High lose of energy is a factor that cannot be neglected. The energy loss of FESS is similar to the internal resistance of chemical battery. It is mainly caused by air friction and rotary friction and exists all the time during the running process of FESS. The energy loss is given as follows:

( ) ( ) ( ) ∫ ⋅ + = d t t k t k E ω ω 2 2 1 l o s （8） s

Fig.3 Energy characteristics of flywheel system

### ISSN: 1109-2777

641

Issue 5, Volume 8, May 2009