J. D. DUAN, J. X. HUANG 1501

be parts of V- curve falling in the unsteady region; In

Figure 10, the intersection of P- and Pmax- curve may

be zero or one. If the proportion of constant impedance

and dynamic load is 2:1, P- and Pmax- curve don’t in-

tersect, the system has always been in power balance.

Nevertheless, with increase of proportion of dynamic

load, P- curve moves up, the scr increases, and the value

of maximum power increases, P- and Pmax- curve will

get an intersection, thus, there will be parts of P- curve

falling in the unsteady region.

7. Instability Mechanism Analysis

7.1. Instability Causes by the Slip

The node voltage drops along with increase of the slip.

And the system stay in the edge of voltage stability until

V- and Vcr- curve intersect. If the slip continues in-

creasing, the system will be instable, the voltage start

recovery until the slip reach s .At this moment if s is

lower, there will be enough space for voltage to recover,

it won’t cause voltage collapse. Conversely, if s is larger,

voltage can’t return to the critical voltage, because the

slip can’t increase again. And finally, it will be voltage

collapse.

The node power increases along with increase of the

slip. And the system stay in the edge of power stability

until P- and Pmax- curve intersect. If the slip continues

increasing, the power will be unbalance. Th e node power

is the same to the node voltag e which has recovery char-

acteristic. In scr< s< 1, with increase of the slip, the node

power decrease, however if the power system transfer

limits can’t increases, the system will always be in power

unbalance state.

7.2. Instability Causes by the Proportion of

Dynamic Load and Constant Impedance

Load

Along with increase of the proportion of dynamic load,

V- curve moves down, s increases, and then the more

curve will fall in unstable region. However the increase

of s means the voltage recovery space is reduced, the

decrease of the voltage minimum corresponding to s

means there is bigger distance between the value of vol-

tage instability and the value of critical voltage. It’s un-

favorable to voltage recovery, thereby, the system volt-

age stability weakens. On the contrary, the increase of

proportion of constant impedance load will enhance the

system voltage stability. Further more, if the proportion

of constant impedance load increases to an extent, V-

and Vcr- curve won’t intersect, load characteristic which

changes along with the slip has no effect on voltage sta-

bility.

With increase of proportion of dynamic load, P-

curve moves upward, scr increases, the node power

maximum corresponding to scr increases, and the more

curve will fall in unstable region. Conversely, with in-

crease of proportion of constant impedance load, P-j

move downward, scr decreases, and the more curve will

fall in unstable region, but the node power maximum

corresponding to scr decreases. Here the amount of scr

means the positional closeness of Pmax- curve and the

node power maximum. Due to the change of load pro-

portion, P- may be intersect with Pmax- before scr, or

may be intersect with Pmax- after scr. However, if they

get intersection before scr, the more transmission power

will be transferred under the power balance conditions.

Further more, with regard to heavy load line, we hope

that it can reduce transmission power under the power

balance conditions, so the proportion of dynamic load

should be increased. With regard to heavy load line, we

hope that it can transfer more power under power balance

conditions, so the proportion of constant impedance load

should be increased. But the overlarge proportion of con-

stant impedance load is unfavorable to transfer more

power, and the overlarge proportion of dynamic load is

unfavorable to power balance. Hence, a reasonable load

proportion should be taken, and then a reasonable power

will be transferred under power balance conditions,

which benefits to avoiding power unbalance and enhance

transmission efficiency.

8. Conclusions

This paper takes the equivalent impedance load model to

analyze load characteristic and study the mechanism of

voltage instability considering load characteristics based

on static voltage stability region. The following conclu-

sion will be obtained through the above analysis:

1) The change of th e slip result in the change of power

factor and module of impedance, consequently, causes

the change of load characteristic. And the system stabil-

ity worsens along with increase of th e slip.

2) The different proportions of constant impedance

load and dynamic load result in different comprehensive

load characteristics which generate different impacts on

static voltage stability. The amount of s determines the

strength of system voltage stability. The amount of scr

determines the maximum of power transmission.

3) The increase of proportion of Constant impedance

load is helpful to voltag e stability, however if the pro por-

tion is overlarge, it’s not conducive to power transfer.

Therefore, a reasonable load proportion could avoid

power unbalance and enhance transmission efficiency.

REFERENCES

[1] P. W. Sauer, B. C. Lesieutre and M. A. Pai, “Maximum

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