## Criticality of a Power Reactor – Power Defect

**For power reactors** at power conditions the reactor can behave **differently** as a result of the **presence of reactivity feedbacks**. Power reactors are initially started up from **hot standby mode** (subcritical state at 0% of rated power) to **power operation mode** (100% of rated power) by withdrawing control rods and by boron dilution from the primary coolant. During the reactor startup and up to about 1% of rated power, the reactor kinetics is **exponential** as in zero power reactor. This is due to the fact all temperature reactivity effects are minimal.

On the other hand, during further power increase from about 1% up to 100% of rated power, **the temperature reactivity effects play very important role**. As the neutron population increases, the fuel and the moderator increase its **temperature**, which results in **decrease in reactivity** of the reactor (almost all reactors are designed to have the **temperature coefficients negative**).

See also: Operational factors that affect the multiplication in PWRs

**The negative reactivity coefficient** acts against the initial positive reactivity insertion and this positive reactivity is **offset** by negative reactivity from **temperature feedbacks**. In order to keep the power to be increasing, **positive reactivity must be continuously inserted** (via control rods or chemical shim). After each reactivity insertion, the reactor power stabilize itself on the power level proportionately to the reactivity inserted. The **total amount of feedback reactivity** that must be offset by control rod withdrawal or boron dilution during the power increase is known as **the power defect**. **The power defects** for PWRs, graphite-moderated reactors, and sodium-cooled fast reactors are:

- about
**2500pcm**for PWRs, - about
**800pcm**for graphite-moderated reactors - about
**500pcm**for sodium-cooled fast reactors

**The power defects** slightly depend on the fuel burnup, because they are determined by the **power coefficient** which depends on the fuel burnup. **The power coefficient** combines the **Doppler**, **moderator temperature**, and** void coefficients**. It is expressed as a change in reactivity per change in percent power, **Δρ/Δ% power**. The value of the power coefficient is always negative in core life but is more negative at the end of the cycle primarily due to the **decrease in the moderator temperature coefficient**.

It is logical, as power defects act against power increase, they act also **against power decrease**. When reactor power is decreased **quickly**, as in the case of **reactor trip**, power defect causes a positive reactivity insertion, and the initial rod insertion must be sufficient to make the reactor **safe subcritical**. It is obvious, if the power defect for **PWRs** is about **2500pcm** (about 6 βeff), the control rods must weigh **more than 2500pcm** to achieve the **subcritical condition**. To ensure the **safe subcritical condition**, the control rods must weigh more than 2500pcm plus value of **SDM** (SHUTDOWN MARGIN). The total weigh of control rods is design specific, but, for example, it may reach about 6000pcm. To ensure that the control rods can **safe shut down the reactor**, they must be maintained above a minimum rod height (rods insertion limits) specified in the technical specifications.