In which two states the positive reactivity overcomes the temperature coefficient of reactivity (aT):

Increasing the power and temperature of reactor core might decrease concentration of boric acid. Accordingly this event might cause to inject positive reactivity.

In addition for the reactors which apply fuels including Pu, because of having a resonance for Pu in thermal neutrons range so through increasing core’s temperature the related resonance is broadened and absorbs more neutrons and because of Pu is fissionable therefore fissionable absorption occurs and is caused excess reactivity.

Also either accident or unfavorable issues as a feedback can be considered. Accidents of a nuclear reactor are totally classified based on following:

1. Over power accident.

2. Under cooling accident.

Each mentioned issues are divided to other sub issues. Over power accident is due factors such as:

1. Control rod withdrawal including uncontrolled rod withdrawal at sub critical power and uncontrolled rod withdrawal at power that will cause power excursion.

2. Control rod ejection.

3. Spent fuel handling.

4. Stem line break.

5. External events such as earthquake, enemy attack and etc.

In each mentioned issues the positive reactivity to nuclear reactor core can be injected. But there is another important accident that is: under cooling accident. Under cooling accident is classified to three sub accident among: LOCA (loss of coolant accident), LOHA (loss of heat sink accident) and LOFA (loss of flow accident).

LOCA accident from loosing coolant is derived. This event in PWR reactor can occur through breaking in primary loop of reactor either hot leg or cold leg.

In this state the existent water in the primary loop along with steam are strongly leaked that blow down event occurs. But when the lost water of primary loop through RHRS (Residual and Heat Removal System) including HPIS (High Pressure Injection System), LPIS (Low Pressure Injection System) and Accumulator (passive system) are filled this process is entitled Refill. When the primary is filled and all the lost water in it is compensated then the reactor sets in the normal status.

In the blow down status the raised steam is due loss of pressure in primary loop and moving the situation of reactor’s primary loop from single phase to two phase flow.

LOHA accident from loosing heat sink in reactor is derived. Heat sink is as steam generator in nuclear reactor. This event when occurs heat exchanging between primary and secondary loops are not done.

This event might occur through lacking water circulation in the secondary loop of reactor. Not circulating the water might occur through closing either block valve (which sets after demineralizer tank) or other existent valves in the secondary loop.

LOFA accident from disabling and loosing the pumps in either primary loop or secondary is derived. In case either primary loop’s pump or secondary encounter with problems LOFA accident might occur.

In the secondary loop the main feed water pump has duty of circulation of feed water to steam generator and sets after condenser pump.

In view of dynamically stability of a nuclear reactor, there is a stable system so that an excess reactivity is injected to it and it able to be stabled again in shortest time. The stability of linear systems in the field of complex numbers by defining the polarity of closed loop transfer’s function is determined.

In case all the polarities are in the left side of imagine page then system will be stabled. In the time field the stability definition means system’s response to each input will be definitive. In the matrix form all the Eigen values of system have real negative part.