Patent ID: 12191044

DETAILED DESCRIPTION

FIG.1shows schematically a flow chart of a method according to an embodiment for a pressurized water nuclear reactor. The nuclear reactor3includes a reactor pressure vessel which includes fuel rods in a reactor core. The nuclear reactor3, in particular the reactor pressure vessel, is connected to one or more primary cooling fluid circuit(s)5or primary circuit(s)5, in which the cooling fluid is driven by a main coolant pump7. The one or more primary circuit(s)5transports with the cooling fluid the heat generated by the nuclear fission of the nuclear fuel in the fuel rods to one or more heat exchanger(s)9. The pressure in the one or more primary circuit5is so high that an evaporation of the water or cooling fluid circulating in the primary circuit is avoided.

The one or more heat exchanger(s) or steam generator(s)9generate(s) steam, for example from water or a secondary cooling fluid circulating in one or more secondary circuit(s). The steam is then transported via the one or more secondary circuit(s)11to one or more steam turbine(s), where the steam generated from the secondary cooling fluid expands and generates a rotation which is used by one or more electric machine for generating electrical energy. The secondary cooling fluid is condensed and provided back to the heat exchanger9.

The nuclear reactor3includes a plurality of rods that are adapted to be driven between the fuel rods for controlling the power generated by the nuclear reactor3. For example, the nuclear reactor includes so called L-rods14and D-rods16. The L-rods14are provided mainly to control the local power density within the reactor core or the axial power distribution. The D-rods or control rods16are provided to control the absolute power of the reactor core. The control rods16absorb neutrons and depending on the insertion depth, the power production of the nuclear reactor can be controlled, for example because the influence the neutron flux within the reactor. Therefore, by using the control rods16, the power of the nuclear reactor3can be quickly adapted. The control rods16are organized in sets (or banks) of control rods16. For example, a nuclear reactor3may include a plurality of sets of control rods16, each including between 3 and 8 control rods16.

A movement of the control rods16or set of D-rods is possible between the position of the L-rods, in particular the free end of the L-rods14, for example where the free end of the control rods16corresponds to the free end of the L-rods14, and the fully inserted end position or lower end position for the control rods16. The free end of the L-rods14and the control rods16corresponds to the lower end, if the rods are inserted from the top of the nuclear reactor3. In an embodiment, the fully inserted end position of the control rods16ends is nearly the bottom of the reactor core of the nuclear reactor3. For example, lower end position is about at 300 cm insertion of the control rods16. The insertion depth of the control rods16and the L-rods14is determined based on the free end extending into the reactor core. In the present example, it is considered that the control rods16and L-rods14are inserted from the top into the nuclear reactor3. Other types of nuclear reactors may have control rods16and L-rods14which are inserted from the bottom. Then, the fully inserted end position is an upper end position for the control rods16.

For example, a typical PWR (pressurized water reactor) with German design with about 1500 MW electrical power has 4 moving sets (or banks) of control rods16with 4 control rods each to control the reactor power. Such a reactor may have a set of L-rods with about 45 L-rods.

For monitoring and controlling of the nuclear reactor3there are provided a plurality detectors for continuous detecting the neutron flux density, where according to an embodiment eight times six detectors are provided in a so called SPND (self powered neutron detector) lance18.

How to control the axial power distribution and the corresponding axial Xenon oscillation with the L-rods, is, according to embodiments, part of a standard reactor control58as it is used with the “adaptive Power Distribution control” in PWR with German design. This “adaptive Power Distribution control” is triggered by an “axial 2-point-Xenon-calculation” module (one point for the upper and the other point for the lower core half; input is given by the SPND lances18). The dynamic of the “adaptive Power Distribution control” is adapted in that way that the needed L-rod position change is made in parallel to the load change. Therefore, this adaptive Power Distribution control substantially needs no injections of boric acid and deionized water to compensate the change of the position of the L-rod which is used to control the axial Power Distribution PD at part load. In other words the position changes of the L-rods to control the axial power distribution is, regarding the reactivity, compensated by the reactivity effect due to the change of the reactor power.

According to embodiments, the sets of control rods16can be inserted one after the other. The sets of control rods or the control rods16have only a slight influence to the axial power distribution. The power of the nuclear reactor is controlled and thus the movement of the control rods16depending on the measuring of the average coolant temperature—ACT.

The minimization of BODE-injections (boric acid and/or deionized water injections) is made according to the present disclosure and is given by the means of an entire reactivity control, which is adapted to the several grid related control modes.

Further, the nuclear reactor includes sensors20for detecting the power of the nuclear reactor3, for example via the neutron flux.

According to embodiments, the power of the nuclear reactor3is controlled via the power regulated at a generator level. The control rods16and L-rods14are then moved in order to adapt the power of the nuclear reactor3to the power required by the generator. When the power of the nuclear reactor3is adapted, also the temperature of the primary cooling fluid is changed. A higher power results in a higher temperature of the primary cooling fluid. The temperature of the cooling fluid has also an effect on the reactivity of the nuclear reactor3.

Long term modification of the reactivity, in particular due to Xenon and fuel consumption is controlled by amending the concentration of boric acid and/or deionized water. These addition of one of these two fluids could be also called BODE addition or injection in the present disclosure. The boric acid within the primary circuit5acts as a neutron absorber. Thus with a higher concentration of boric acid the power or the reactivity is reduced. To increase the reactivity deionized water is added to the primary circuit5in order to reduce the concentration of boric acid and thus to increase the reactivity. There are separate pumps22,23to inject deionized water24and/or boric acid26into the primary circuit5. The pump22is provided to inject deionized water24and the pump23is provided to inject boric acid26into the primary circuit5. The amount of deionized water24and/or boric acid26can be controlled using valves28,30and/or the pumps22,23. The pumps22,23are operated, only in the case of a required BODE-injection.

The control of a nuclear reactor is rendered complicated due to the complex time dependent function of the Xenon-135 (called Xenon or Xe herebelow) concentration in the reactor core. Xenon acts as neutron poison or neutron absorber. The Xenon values change within hours. The Xenon is created due to the fission chain of the nuclear fuel and disappears when absorbing neutrons and by Xenon decay. However, the creation and the neutron absorption appears with a time delay, so that for the actual and future power of the nuclear reactor, the actual, past and future values of the Xenon must be taken into account, in particular for optimal controlling of the position of the control rods16via the concentration of the boric acid (by BODE-injection). When a nuclear power plant operates a long time at a constant power, the Xenon concentration reaches an equilibrium or steady state. The Xenon reactivity is a linear function of the Xenon concentration.

FIG.2shows two examples of a nuclear reactor operating for a specific time at a partial power.

InFIG.2(a)the power PRis first at 100% (i.e. the full power of the nuclear reactor) and then reduced to 30% of the full power. The partial power of 30% of the full power is then maintained for about 2 h before the power is ramped up, at point A, to 98% of the full power. During partial power, the Xenon concentration increases and therefore also the Xenon reactivity. At point B, the nuclear reactor reaches the target power of 98% of the full power. As it can be seen, the Xenon reactivity, on ramp up, i.e. between points A and B, is reduced as the reactor burns off the Xenon-135, which begins to absorb more neutrons and reduces the reactivity shortly after the point A. As it can be seen fromFIG.2(a), the reduction of the xenon reactivity between point A and point B due to the burn off of Xenon is about 100 pcm, which corresponds to the movement of about 20% of a length a set of D-rods or control rods.

InFIG.2(b)the power PRis first at 100% (i.e. the full power of the nuclear reactor) and then reduced to 30% of the full power. The partial power of 30% of the full power is then maintained for about 6 h before the power is ramped up, at point A, to 98% of the full power. At point B, the nuclear reactor reaches the target power of 98% of the full power. As it can be seen, the Xenon reactivity, on ramp up, i.e. between points A and B, is reduced as the reactor burns off the Xenon-135, which begins to absorb more neutrons and reduces the reactivity shortly after the point A. As it can be seen fromFIG.2(b), the reduction of the xenon reactivity between point A and point B due to the burn off of Xenon is about 500 pcm, which corresponds to the movement of about 100% of a set of D-rods or control rods.

Thus, it can be seen that the Xenon concentration, and therefore the reactivity based on the Xenon depends largely on the waiting period and the previous operation of the nuclear reactor3.

A nuclear power plant can be operated in several operating modes related to the needs of the electrical grid.

In a primary control mode providing immediate power within seconds to support the network frequency, wherein the additional power is provided between 0 and 15 minutes (normally within seconds) for stabilizing the grid frequency. The primary control is deducted from the grid frequency deviation to the standard frequency.

In a secondary control mode providing the required power from the power plant latest after 15 minutes. This is also named load follow operation. In the secondary control mode for which a request for additional energy is remotely commanded via the generator target power, which can be changed stepwise. The additional electric energy has to be provided latest within 15 minutes. Only the maximal power gradient dPG/dt and the power range are known in advance. The partial power operating time may be several hours. The power changes are requested in a stochastic manner. In the secondary control, the PRtarget power must be achieved at any moment, so that the control rods16must have a specific predefined or predetermined position.

The tertiary control mode provides middle and long-term modification of the power. In the tertiary control, the duration and the required power is determined between the grid operator and the reactor operator.

The primary control can be applied in parallel to the secondary and the tertiary control.

In the tertiary control, a power ramp up will be carried out after a waiting time according to the agreement between the reactor operator and the operator of the power grid. The power ramp up depends on the actual reactor power PR, the PRtarget power and the power ramp up, called also power gradient dPG/dt. As stated above, the power request is provided by the generator control to the nuclear reactor. Thus, also the power gradient dPG/dt, which has to be provided to the power grid is provided by the generator control. In the tertiary control mode this corresponds to the value which is used and in the secondary control mode this corresponds to the maximal power gradient.

InFIG.1, the flow chart includes several input values, in particular the actual reactor power PR, which is measured using the sensors20, the PRtarget power32, which is for example provided by the reactor operator, the waiting period34, for example provided by the reactor operator, until the ramp up of the power to the PRtarget power32, the grid secondary control36, which can be for example activated or deactivated by a button36, the grid primary control38, which can be for example activated or deactivated by a button38, the reactivity coefficients40, which are automatically determined, and a control set value predictor impact42to activate or deactivate the control rod sets setpoint adjustment based on a total reactivity balance.

The actual reactor power PRcan be also determined using other means, for example by determining the power of the electric generator.

The reactivity coefficients40are provided by core design calculation, which is done for each fuel element cycle. These coefficients are variables in the software of the reactor control and they are dependent of the equilibrium boron concentration of the reactor core, which decreases during the entire fuel element cycle to compensate the fuel burn up. In other words, the reactivity coefficients are calculated based on the equilibrium boron concentration of the reactor core. These variables are set via a service unit during fuel element change respectively outage. In other words, a characteristic curve is used to determine each reactivity coefficient based on the equilibrium boron concentration of the nuclear reactor3. The reactivity coefficients40slowly change during the fuel element cycle. The equilibrium boron concentration of the reactor core is the concentration of boric acid which is used during an operation of the nuclear reactor3at a steady or constant power over a long period of time, in particular when the Xenon concentration reaches a steady value at full power. A plurality of reactivity coefficients, which are used, will be explained withFIG.10here-below. As the reactivity coefficients40change very slowly they can be considered constant for the calculation of the reactivity balance. In other words, the reactivity coefficients are variables, which are dependent of the “full load days” in the actual fuel element cycle (for example 1 year) or a related parameter (as a reference boron concentration in full load equilibrium conditions) and can be set as a characteristic via an interface or service unit of the reactor control during fuel element change according to the core design of the next core.

The flow chart inFIG.1includes an actual value calculation module44in which the actual concentration values of Xenon and Iodine in the nuclear reactor3, in particular in the reactor core of the nuclear reactor3, are calculated based on the actual and past power PRof the nuclear reactor3. The actual Xenon value is also designated Xe-value inFIG.1and the actual Iodine value is designated J-value. In other embodiments, as shown inFIG.4, the Xenon reactivity ρXeis provided instead of the Xenon concentration.

FIG.4shows the calculation of the actual concentration values of Xenon and Iodine based on the actual and past power PRof the nuclear reactor. The calculation is adapted to the type of the nuclear reactor3and the charging with nuclear fuel. The input value is the actual power PRof the nuclear reactor. The boxes marked with ΓXe, λJ, λXe, BXE, AJ, AXE are linear functions using known parameters. The boxes with a cross are multipliers. The past values of the power PRof the nuclear reactor3is taken into account by the integrator45awith regard to the iodine concentration. In other words, the integrator obtains via the integration of the difference between the Iodine production and the Iodine decay the actual Iodine concentration value. The Xenon decay and the Xenon loss due to neutron absorption is subtracted from the sum of the direct Xenon production and the Xenon from Iodine decay. The integrator45bcalculates from the Xenon concentration gradient the Xenon concentration actual value. In the embodiment shown inFIG.4, using ΓXethe calculation gets the actual Xenon reactivity value ρXe. For example, the reactivity value of the Xenon is provided in the unit pcm—percent mille.

The flow chart inFIG.1further includes a predictor module46. The predictor module performs a cyclical prediction of the concentration of Xenon, and in particular Iodine, in the nuclear reactor3, in particular the nuclear core of the nuclear reactor3.

The predictor module46predicts the concentration of Xenon for the waiting period, in particular for the end of the remaining waiting period and the end of the ramp up period. For that purpose, the predictor module obtains the actual Xenon and Iodine concentration values from the actual value calculation module44, the time needed for ramp up Δtramp upand the set values for the reactor power PRfor the waiting period and the ramp up period from a control module48.

The control module48provides all needed values for the Xenon prediction based on the input value of the PRtarget power, whether the nuclear reactor3should work in a secondary control mode (obtained from block36), the remaining waiting period and the actual power PRof the nuclear reactor3.

The functioning of the predictor module46is explained with respect toFIGS.3and5. The predictor module46calculates in an iteractive manner the Xenon concentration and thus the Xenon reactivity. In an embodiment, in addition the Iodine concentration values are also calculated. The boxes marked with ΓXe, λJ, λXe, BXE, AJ, AXE are linear functions using known parameters. The boxes with a cross are multipliers. To take into account the time dependency of the Iodine concentration the integrator48ais used. In other words, the integrator obtains via the integration of the difference between the Iodine production and the Iodine decay the Iodine concentration value. The Xenon decay and the Xenon loss due to neutron absorption is subtracted from the sum of the direct Xenon production and the Xenon from Iodine decay. The integrator48bcalculates from the Xenon concentration gradient dXe/dt the Xenon reactivity actual concentration value ρXe. For starting the prediction, the actual Xenon concentration value and the actual Iodine concentration values are read once at the beginning of the predictor operation. The box48ctriggers each calculation steps with specific time increments, as it will be explained below. Using ΓXethe calculation gets the predicted Xenon reactivity values ρXefor the end of the waiting period or the end of the ramp up, as it also will be explained below. According to embodiments, the end of the waiting period corresponds to the start of the power ramp up.

The (remaining) waiting period and ramp up period is divided for the purpose of calculation into a predefined number of steps. According to an example, between 50 and 500 steps are used, in particular between 100 and 300. In the embodiment shown 200 steps are respectively calculated for the waiting period and the ramp up. This means that for the waiting period and the ramp up period, the time distance Delta T or Δtincrementbetween two subsequent calculation steps may be different, as for example the ramp up period may be substantial shorter than the waiting period. For example, as the Xenon concentration and/or Xenon reactivity during the waiting period, after reaching its maximum, always tend to reach an equilibrium state, a fixed number of calculation steps can be used despite the lengths of the waiting period of for example 40 hours or 100 hours or more.

If the waiting period is zero, for example when the nuclear reactor3is operated in the secondary mode, see below, only the prediction for the ramp up period is calculated. For the purpose of calculation, the predictor module46stores the calculated predicted Xenon concentration, Xenon reactivity values and/or Iodine concentration values in a respective memory. In an example, the Xenon concentration value and/or the Xenon reactivity ρXeis stored for the end of the waiting period (see point A inFIG.3) and after the ramp up period (see point B) inFIG.3. ΔtincrementinFIG.5correspond to Δtramp upand Δtwaiting periodinFIG.1.

It should be noted that the prediction for the waiting period is only performed, in case the nuclear reactor should work in the tertiary control mode and not the secondary control mode (or load follow operation marked with N-SR in the drawings).

The actual Iodine concentration and the actual Xenon concentration or reactivity values are read respectively for the beginning of the waiting period for the calculation, if a waiting period exists, or for the beginning of the ramp up (in case of no waiting period or when the waiting period has lapsed).

It should be noted that the waiting period decreases with the time progress, i.e. the beginning for the purpose of the calculation progresses for each time the prediction module46starts again with the complete calculation of the Xenon concentration, the Xenon reactivity and/or the Iodine concentration values.

Based on the set value of the reactor power PRfor the waiting period and the ramp up period, the Xenon reactivity ρXeor the Xenon concentration in particular after the waiting period (point A inFIGS.3and5) and after the ramp up period (point B inFIGS.3and5) is stored.

The Xenon concentration or the Xenon reactivity ρXeafter the ramp up period (Point B) and the Xenon concentration or the Xenon reactivity before the ramp up period or start of the power ramp up (Point A; either at the end of the waiting period for the tertiary control mode or the actual Xenon concentration for the secondary control mode) are used to determine, by the predictor46, the Xenon concentration change and/or the Xenon reactivity change ΔρXeduring the ramp up period.

According to embodiments, the predictor module46calculates also the Iodine concentration for the waiting period and/or the ramp up period, in particular at the end of the waiting period.

The actual value calculation module44and the predictor module46and the control module48are forming together a tandem module50which is running automatically and in real time in a digital reactor control system. For example, each actual value calculation module44and the predictor module46respectively calculate the predicted Xenon reactivity and/or concentration values every 50 milliseconds. The new prediction of the predictor module46is based on respectively updated actual Xenon and Iodine concentration values. The time for calculation of the Xenon reactivity for each which means for the waiting period and for the ramp up period requires respectively about 10 seconds based on200calculation steps. That means 20 seconds totally related to tertiary control and only 10 seconds related to the stochastic secondary control, where quicker calculation results are desired. The accuracy of this method is discussed later on.

The prediction values enable to calculate the support of the Xenon reactivity ρXeduring the ramp up phase. It should be noted that the Xenon reactivity and/or Xenon concentration only depends on the power and its time dependent change of the nuclear reactor. This Xenon reactivity or concentration prediction is only a part of an entire reactivity balance which is needed to determine the optimal control rod16position before the next ramp up.

The predicted Xenon reactivity change ΔρXeduring ramp up from the prediction module46is provided to a reactivity balance module52, which additionally considers that part of the total reactivity balance which is based on reactivity coefficients provided by the reactivity coefficient module40. In detail one or more of the following reactivity effects—besides Xenon—are also considered for calculating a predetermined control rod setpoint for the start of power ramp up or at the beginning of the ramp up and/or the total reactivity balance. In particular accordingFIG.10the reactivity balance is visualized for a reactor operator.

The (total) reactivity balance is adapted to determine, based on the reactivity values, the optimal control rod16position, such that the nuclear reactor can reach the PRtarget power at any moment or after the waiting period using the control rods16. This optimal control rod position may be also called predetermined control rod setpoint for the start of power ramp up in the present application.

The control rod position may be then provided to the control rods set setpoint adjustment54. In theFIG.10, the PRtarget power is set to 100% of full load, which is the maximal allowed power of the nuclear reactor3. For that purpose, the total reactivity (ρρ inFIG.10) taking into account also the predicted Xenon reactivity change ΔρXeduring ramp up should be in the optimal case zero.

The potential reactivity ρD(possible reactivity increase due to the raising of the D-rods or control rods16(ΔD). The reactivity potential can be calculated based on the effectivity ΓDM, of the control rods, which is a reactivity coefficient provided by the reactivity coefficient module40, and their actual insertion depth (ΔD) below the lower end of the L-rods; the effectivity ΓDMis averaged with the respect to varying efficiency depending on the insertion depth. The reactivity potential ρDis calculated by multiplying the effectivity ΓDMwith the actual insertion depth (ΔD) and corresponds to the reactivity potential by raising the control rods or D-rods until the lower end of the L-rods.

The control rods or D-rods shall be raised until their stationary full power (of the nuclear reactor) setpoint (here approximately 45 cm below L-rods as control margin), which is indicated inFIG.10as VFA value. This will lower the possible reactivity increase by the reactivity value ρVFA. The stationary full power setpoint is optionally used to provide even under full power a possibility for raising the control rods in order to regulate small power variations. The reactivity ρVFAof the maneuvering margin of the control rods at full load is considered separately with the reactivity coefficient at that insertion depth ΓD. The reactivity potential ρVFAis calculated by multiplying the effectivity ΓDwith the full load setpoint distance to the set of L-rods, in particular the lower end of the L-rods. Here, the effectivity ΓD, which is a reactivity coefficient, is provided by the reactivity coefficient module40.

A further potential reactivity value may be the reactivity ρLof the L-rods due to the actual insertion depth of the L-rods (ΔL) below their stationary full power setpoint. The corresponding reactivity coefficient (ΓL), which corresponds to the effectivity of the L-rods, is provided by the reactivity coefficient module40. The movement of the L-rods is principally needed to counter the peak top tendency of the axial power distribution at part load. The reactivity potential ρLis calculated by multiplying the effectivity ΓLwith the actual insertion depth ΔL.

Another value is the reactivity ρPdue to the future ramp up of the reactor power to PRtarget power (ΔP) with its reactivity coefficient (ΓP), which is provided by the reactivity coefficient module40.

The reactivity ρACTdue to difference of the Average Coolant Temperature (ACT) of the primary circuit5to the reference temperature at full load (ΔACT; in the present example approximately 310° C. at full load) with its reactivity coefficient ΓT, which is provided by the reactivity coefficient module40.

According to an embodiment, the reactivity balance may also take into account the reactivity impact ρCVCScaused by deadtime effects of BODE-injections via the Chemical Volume Control System CVCS being determined by a dead time simulation combined with the relevant reactivity coefficient of the boron concentration ΓC. In this example, also the reactivity coefficient of the boron concentration ΓCis provided by the reactivity coefficient module40.

To be capable to ramp up to the PRtarget power, using in particular the control rods or D-rods16, the reactivity sum Σρ=ρVFA+ρD+ρL+ρP+ρACT+ρXe+ρCVCSof all considered reactivity values should be zero. There may be even more or less reactivity values for calculating the reactivity sum, the reactivity balance, the optimal control rod position and/or the predetermined control rod setpoint for the start of power ramp up. At the PRtarget power, i.e after ramp up, it also should be zero. Thus, the optimal position of the control rods16for the ramp up is determined and used for the calculation of the reactivity balance. Thus, according to embodiments, the optimal control rod positon or the predetermined control rod setpoint for the start of power ramp up is calculated based on the total (predicted) reactivity.

If there is any deviation, for example as shown inFIG.10with Σρ=56 pcm, when the control rods are not in the optimal position for the ramp up and being, in particular provided to the control rod set setpoint adjustment54, the amount of needed BODE injection is calculated based on the reactivity coefficient of the boron concentration ΓCand linearized (simplified) mixture equations (see below) in relation to the sum of mass of primary circuit together with CVCS to determine the amount of BODE in kg and or kg/s (as the operator prefers). As input data for the boric acid relevant mixture equation the boron concentration in the boric acid storage tanks cBis needed. The mixture equations are as follows:

QB=M·ln⁡(1+Δ⁢ccB-c)≈M·Δ⁢ccB-c(1)Δ⁢c=(cB-c)·(eQBM-1)≈QBM·(cB-c)(2)QD=M·ln⁡(c-cD(c-cD)-Δ⁢c)≈M·Δ⁢cc(3)-Δ⁢c=(c-cD)·(1-e-QDM)≈c·QDM,(4)wherein QBis the amount injected boric acid mass, QDis the amount deionized water mass, c the concentration of the boric acid in the primary cooling fluid, Δc the change of the boric acid concentration in the primary cooling fluid, cBis the boric acid concentration in the injected boric acid, cDis the boric acid concentration in the injected deionized water, and M is the mass of the primary cooling fluid together with the Chemical Volume Control System CVCS. For example the boric acid concentration in the injected boric acid is about 7000 ppm and the boric acid concentration in the injected deionized water is below 1000 ppm (parts per million). For example, the mass M is about 300 t at 310° C.

Generally, the reactivity coefficients of the reactivity coefficient module40have no time delay effects or are strongly time dependent. The reactivity coefficients in the reactivity coefficient module40do not include coefficients for the Xenon reactivity coefficient.

According to embodiments, when the nuclear reactor is operated in the tertiary control mode, derived from the above considerations and coefficients a time criteria is calculated, in particular by the reactivity balance module52, which determines the time before ramp up which is needed to bring the control rods16to the predetermined control rod setpoint for the start of power ramp up, which is needed to ramp up to the target power value, for example by using boric acid or deionized water injections. For example, for that purpose not only the predetermined control rod setpoint for the start of power ramp up, but also the actual control rod position and the mixture of the primary cooling fluid based on one or more of the above equations (1) to (4) is taken into account for the calculation of the time to reach the predetermined control rod setpoint for the start of power ramp up. If the time criteria is reached, the reactivity balance module52is adapted to inform the Floating/ELPO module56that the floating or ELPO modes should be terminated, which are called second and third submode here-below. The time criteria depends in particular on the reactivity coefficients provided by the reactivity coefficient module40and/or the actual setting of the control rods16. In some embodiments, some additional time is added in order to have a security margin.

Considering the selected grid operating modes the following strategies and adaptions are automatically used:

If the secondary control mode is selected, for example if the button36is activated, which means that the waiting time should be zero, (N-SR is ON; waiting time is zero), the nuclear reactor has to reach a PRtarget power at any moment, which cannot be predicted. For that purpose, the control rods16must be adjusted in such a way that the PRtarget power can be reached through control rod16movement at any moment. This is done predicting the Xenon reactivity during the ramp up of power, in particular at the beginning and the end during the ramp up of power, in order to know the portion of the Xenon reactivity supports the ramp up of the power with the maximal selected power gradient dPG/dt.

In the secondary control mode, the reaching of the target power is preponderance compared to the minimizing of the addition of boric acid and/or deionized water. E.g. the Xenon build up to Xenon-Maximum at part load has to be compensated by deionized water injection, after boric acid injection is needed as shown inFIG.6. The boric acid injection and deionized water injection is performed, in particular automatically by the standard reactor control58, which keeps the control rods16at the adjusted setpoints or positions provided by the control rods set setpoint adjustment module54, which is provided by the reactivity balance module52. In other words, the optimal control rod position or predetermined control rod setpoint for the start of power ramp up is directly used as setpoint by the control rods setpoint adjustment module54. In the secondary control mode, it is not necessary to calculate a prediction of the Xenon reactivity for the waiting period. InFIG.6, graphs for the secondary mode and a first submode of the tertiary mode are shown. With respect to the deionized water injection and the control rod16position, the secondary mode is shown with the continuous thick lines60a,60b. The other curves or graphs are equal in this special case for the secondary mode and the first submode of the tertiary mode discussed below. The graph60bshows the setpoint of the control rods16and their actual value. InFIG.6, due to the scaling the setpoint and the actual value of the position of the control rods or D-rods16cannot be distinguished.

Typically, the control rods16(D-bank or set of D-rods), after being lowered in order to reduce the power of the nuclear reactor3, are continuously raised a bit during the waiting period till the Xenon maximum according to the calculated setpoint via the reactivity balance module52, because the Xenon reactivity support for the ramp increases by the increased burn up effect of the Xenon.

According to embodiments, the tertiary control mode is detected by the entering of a waiting period in which the nuclear reactor is operated at partial load, so that for example a further minimization of BODE-injections can be possible.

Depending on the waiting period, the nuclear reactor can be controlled in one or more, in particular three different submodes. The beginning of the waiting period is defined as the time at which the power is reduced to a partial power. For example, the partial power may be between 30% and 90% of the maximal power of the nuclear reactor. In the following, these three different modes are detailed.

When the power is reduced, the Floating/ELPO module56stores automatically dependent on the adjusted waiting time, which submode is used.

According to embodiments, the control of the setpoints during floating mode or ELPO have preponderance over the control of the setpoint given by the reactivity balance52. For example, if the Floating/ELPO module56provides information to the control rods set setpoint adjustment module54, whether a floating mode or an ELPO mode is used this overrules the setpoints provided by the reactivity balance module52. In other words, depending on the adjusted waiting time, the Floating/ELPO module56provides information to the control rods set setpoint adjustment module54, whether a floating mode or an ELPO mode is used. Then, the control rods set setpoint adjustment module ignores the setpoints provided by the reactivity balance module52.

For example in case of a waiting period tPL, which corresponds to a part load time or duration of the part load phase, at partial load being less than a first predetermined time, a first submode is used. The first predetermined time is related to the time to reach the maximum Xenon concentration. That means, that it can be expected, that there is only a reactivity loss by Xenon in this time period of approximately 8 hours. In some embodiments, the first predetermined time is for example 2 h after the Xenon maximum or 30% of the waiting time until the Xenon maximum after the Xenon maximum. According to an embodiment, which is shown inFIG.6, the control rods setpoints61(thin line) are determined such that the PRtarget power can be reached after the waiting time. Here the setpoint61acorresponds to the predicted position of the control rods that enable to reach the target power after power ramp up. The reactivity reduction due to the Xenon concentration is compensated by the addition of deionized water via the reactor control58as in the secondary control mode. The first line and second line show the phases where boric acid and deionized water is added to the primary circuit. Compared to the secondary mode, the injection of deionized water starts a bit later as in the above mentioned example of the secondary control mode, see thin line63a, because the control rods16(set of D-rods) have to be withdrawn—compensating the Xenon-build up—to reach their setpoint for power ramp up, see dashed line63bwhich reaches the control rods setpoint61a. The boric acid injection is blocked by signalization of Xenon-build up in the standard reactor control58. Considering the waiting period this setpoint for the control rods16hereby considers the Xenon reactivity support for ramp up in the Xenon maximum due to the increased burn up effect from the beginning of the waiting period. The remaining curves of the first submode of the tertiary control mode corresponds to the curves of the secondary control mode inFIG.2, i.e. during reducing of the power, the actual control rod position corresponds to the thick line.

The amount of boric acid and deionized water is determined by the standard reactor control58, which keeps control rods16at the adjusted setpoints provided by the control rod set setpoint adjustment module54, which is provided by the reactivity balance module52. As stated above, the Floating/ELPO module56does not provide setpoints to the control rod set setpoint adjustment module54. The predetermined control rod setpoint for the start of power ramp up provided by the reactivity balance module52is used.

The third line shows the Xenon concentration over the time, the fourth line the position of the control rods16(their insertion into the reactor core in centimeters) and the fifth line the power of the nuclear reactor3over the time. This control submode functions similar to the secondary control mode. Only the waiting time is considered in the Xe-Prediction in this case. Hereby the visualization of the reactivity balance, for example as shown inFIG.10, in the ramp up phase for the reactor operator is more precise even at the beginning of the waiting time.

According to this example, a control rod setpoint61afor/at the end of the waiting period is shown, which is based on the entire reactivity balance including the predicted Xenon reactivity to support ramping up the nuclear reactor3in the Xenon maximum. In other words, it is the predicted control rod setpoint for the start of power ramp up. When entering the partial power mode, the control rods or D-rods16are lowered in order to reduce the power of the nuclear reactor3, here to about 75% of the full power. As it can be seen fromFIG.6, the Xenon concentration raises during the waiting period. This is compensated by adding deionized water to the primary circuit3after reaching the predicted setpoint61aby the control rods16. Latest until the end of waiting period (here, the waiting period is about 6 h), the control rods16reach the control rod setpoint61aat a position for the start of power ramp up. During the ramp up, the Xenon concentration is reduced due to the effects already described above (i.e. the Xenon-135 burns off). After reaching the PRtarget power, the Xenon concentration still reduces, so that boric acid is added to the primary circuit in order to decrease the reactivity, which is due to the decreased Xenon concentration.

InFIG.7, the waiting period tPLat partial load is between the first predetermined time, for example 8 hours, and a second predetermined time, for example about 30 hours. That means that it can be expected that there is after the reactivity loss by Xenon a reactivity win and this can be compensated by moving the control rods16to minimize BODE-injections extremely. For this purpose, a second submode is used, the so called floating mode. The second predetermined period (here about 30 hours) correspond to a time where different aspects, in particular regarding ELPO, have to be considered during long term part load operation, in particular that the D-sets or control rods shall be in their “full load position” to have an optimized fuel burn up and an optimal conditioned core regarding pellet cladding interaction (PCI).

In the second submode, the Floating/ELPO module56informs the control rod set setpoint adjustment module54that the second submode or floating mode should be used. According to embodiments, the module54, upon reception of the information that the second submode or floating mode should be used, commands the standard reactor control58to inhibit BODE injections to compensate the Xenon concentration change, in particular within the upper control limit (UCL) and lower control limit of the control rods16. Thus, in case of constant power of the nuclear reactor3, the Xenon concentration is compensated by the movement of the control rods16by the standard reactor control58, for example indirectly via the ACT control. In other words, the module54ignores the setpoints provided by the reactivity balance module52.

The second submode or floating mode will be explained in detail with the help ofFIG.7. The first line and second line show the phases where boric acid and deionized water is added to the primary circuit. The amount of boric acid and deionized water is extremely minimized compared with the cases before, because the normal control rod D-set control is deactivated regarding activation of BODE-injections and the D-set or control rods moves to compensate the Xenon reactivity change (e.g. via the ACT controller within the reactor control58). According to embodiments, the control rods16are moved between regulating limit values within the standard reactor control (for example UCL=“upper control limit” to ensure a minimal distance to the lower end of the set of L-rods). Thus it is ensured that the control rods16will not be inserted too little. The third line shows the Xenon concentration over the time, the fourth line the position of the control rods16(their insertion into the reactor core or nuclear core in centimeters) and the fifth line the power of the nuclear reactor3over the time.

In this second submode, the increase of the Xenon concentration is compensated by the control rods16. In other words, the control rods16are moved out of the reactor core until they reach their upper control limit UCL. If still further compensation of the increase of the Xenon concentration is needed, some deionized water is added to the primary circuit, see the maximum of the Xenon concentration graph, between approximately 6 h and 8 h. When the Xenon concentration decreases after its maximum, the total reactivity increases so that the control rods are moved down in the reactor core until a depth of approximately 300 cm, which they reach at approximately 15 h. In this special case the rods reach at approximately 15 h the predetermined position for ramping up the power to the PRtarget power.

When the power should be increased to the PRtarget power, here 100% of the power of the nuclear reactor3, the control rods16are raised up. At the same time, the Xenon concentration decreases, so that after reaching the target power, the further reduction of the Xenon concentration is compensated by the addition of boric acid. After the minimum Xenon concentration, the Xenon concentration raises to an equilibrium state after about 30 h. The creation of Xenon corresponds in the equilibrium state to the burn off of Xenon due to neutron absorption and Xenon decay. During the raise, again deionized water is added to compensate the change of concentration of the Xenon.

As it can be seen fromFIG.7, which shows with the hatched regions the comparison with a reactor control, where the control rods remain inserted for the later ramp up. The example inFIG.7shows the maximal boric acid and deionized water reduction compared to a standard regulation without considering the waiting time. It should be noted that the reduction of boric acid and deionized water increases when the end of the cycle approaches, i.e. before the fuel rods have to be exchanged to new ones, as the deionized water additions increase extremely. For example, to have the same effect, the deionized water addition is at the end of the cycle exponentially higher (in the last 20% of the fuel element cycle more than 10 times higher) compared to the beginning of the cycle. Thus, the costs for treating or recycling of the cooling water of the primary circuit5increases or otherwise the load flexibility will be decreased.

If the waiting time would be shorter than in this example inFIG.7(e.g. 11 hours) the control rods would not reach the predetermined control rod setpoint for the power ramp up or the control rod setpoint for the start of power ramp up by simply compensating the decrease of the Xenon concentration, the Floating/ELPO module56receives a signal from the reactivity balance module52, for example a termination signal “time criteria reached”, to terminate the floating mode. Hereby the control is handed over to the standard reactor control58, which is adapted to control the valve28in order to add further deionized water to the primary circuit5so that the control rods16can reach the predetermined control rod setpoint for the start of power ramp up, provided by reactivity balance module52, till the end of the waiting period for ramping up the power. In other words, the predetermined control rod setpoint for the start of power ramp up is provided by the control rod set value adjustment54according to the result of the reactivity balance52and with calculated waiting time in the Xenon prediction module46.

If the waiting time would be longer than in this example inFIG.7(e.g. 20 hours) the control rods would exceed the predetermined control rod setpoint for the start of power ramp up, the predetermined control rod setpoint being determined by the reactivity balance module52, by simply compensating the further decrease of the Xenon concentration, the Floating/ELPO module56, for example by receiving a signal from the reactivity balance module52, terminates the second “floating” submode and the control is handed over to the standard reactor control58. This is important in order to be able to further insert the control rods16into the reactor core in case of an emergency shut down (ensure shut down reactivity). In other words, the control rods16are not lowered further because the standard reactor control starts the boric acid injection according to the control deviation, which is given by the actual control rod position compared to their predicted setpoint provided by the control rods set setpoint adjustment54.

InFIG.8, when the waiting period tPLat partial load is greater than the second predetermined time, for example approx. 30 hours, a third submode is used. The third submode may be also called Extended Low Power Operation (ELPO) mode.

This second predetermined period (here approximately 30 h but it can be much longer e.g. 60 h) corresponds to a time where different aspects regarding ELPO have to be considered: during long term part load operation the D-sets shall be in their “full load position” to have an optimized fuel burn up and an optimal conditioned core regarding pellet cladding interaction (PCI). For example, the second predetermined period is at least 30 h.

The third submode will be explained with the help ofFIG.8. The first line and second line show the phases where boric acid and deionized water is added to the primary circuit. The amount of boric acid and deionized water is in this case also minimized because the Xenon build up (after reaching part load) is used to withdraw the D-set to “full load position”. In other words, the reactor core is nearly control rod free. The third line shows the Xenon concentration over the time, the fourth line the position of the control rods16(their insertion into the reactor core in centimeters) and the fifth line the power of the nuclear reactor3over the time.

In the third tertiary submode the Floating/ELPO module56has precedence with respect to the control rod set value adjustment module54compared to the predicted setpoint of the reactivity balance module52. In the third submode, the Floating/ELPO module56informs the control rod set setpoint adjustment module54that the third submode or ELPO mode should be used. According to embodiments, the module54, upon reception of the information that the third submode or ELPO should be used, commands that the set values for the control rods16should be the “full load position” (nearly control rod free or full power position). Thus, in case of constant power of the nuclear reactor3, after the control rods have reached the full load position, the Xenon concentration is compensated by BODE injections by the standard reactor control58, for example indirectly via the ACT control. In other words, the module54ignores the setpoints provided by the reactivity balance module52.

In a first step, the control rods are lowered or inserted into the reactor core in order to reduce the power of the nuclear reactor3. In the example ofFIG.8, the power is reduced to 75% of full power. Then, the Xenon concentration increases and the control rods16are withdrawn out of the reactor core in order to compensate the reactivity loss due to the increase of the Xenon concentration. The control rods16are moved out of the reactor core until they reach their “full load position” (nearly control rod free) or, in parallel, the upper control limit UCL. If still further compensation of the increase of the Xenon concentration is needed some deionized water is added to the primary circuit, see the maximum of the Xenon concentration graph, between 6 h and 8 h, see reference sign62. When the Xenon concentration decreases after its maximum, the total reactivity increases and boric acid is added into the primary circuit5by the standard reactor control58, which is given by the setpoint “full load position” of the control rods set setpoint adjustment module54and the actual control rod16position. According to embodiments, the boric acid is added in a discontinuous manner. The boric acid is added, until an equilibrium of the Xenon concentration is reached, i.e. that the Xenon gradient is nearly zero, inFIG.8during the period with the reference sign64.

Before the end of the waiting period, the control rods16have to be moved to the predetermined control rod setpoint for power ramp up. Thus, in due time before the end of the waiting period, the third submode or ELPO mode is terminated in the Floating/ELPO submodule56, by receiving the termination signal “time criteria reached” from the reactivity balance module52. Then, the reactivity balance module52provides the set points for the control rods16to the control rods set setpoint adjustment module54, which corresponds to the predetermined control rod position or setpoint before ramp up, and the standard reactor control58injects deionized water, which moves the control rods16to the predetermined control rod setpoint for the start of power ramp up provided by the control rod set value adjustment54. Deionized water is added, see reference sign66, to the primary circuit5during the movement of the control rods16to the predetermined control rod set value.

In this third submode, the control rods are moved out of the reactor core in order to have the fuel rods burn off homogenously and due to pellet clad interaction (PCI).

The third submode or ELPO submode is terminated between 1 h and 3 h before the waiting time ends, according to the generation of the signal “time criteria reached” provided by the reactivity balance module52based on the reactivity and mixture balance of the primary cooling fluid. It should be noted that the control rods16do not exceed a lower regulation limit LRL, in particular in each of the tertiary control submodes. The lower regulation limit LRL depends on the actual power PRof the nuclear reactor. The higher the actual power, the higher lower regulation limit in order to enable the nuclear reactor to be shut down at any moment using the control rods16.

According to embodiments, as already discussed above, the reactivity balance module52further determines, based on the predicted Xenon reactivity and the reactivity coefficients of the reactivity coefficient module40, whether the tertiary control modes Floating or ELPO should be terminated. For this purpose, the reactivity balance module52determines, based on the actual reactivity coefficients, the predetermined control rod-setpoint, the actual control rod16position and the mixture balance (according to the simplified mixture equations (1) to (4) mentioned above) the needed injection time to bring the D-sets to the needed position for ramp up. If this needed injection time plus a tolerance becomes greater than the remaining waiting time the signal “time criteria reached” is active and terminates ELPO or Floating mode.

The reactor control58may also work without the predicted Xenon reactivity values and also works without the modules52,56and38. In this case the D-rod set setpoint has to be set manually.

The accuracy of the Xenon prediction module with200calculation steps, for each the waiting time and the ramp up time, is shown inFIG.9with an example of a part load time of 15 hours. As it can be seen fromFIG.9, which shows from the top to the bottom the Xenon concentration, the prediction error, the position of the control rods or D-rods16and the power of the reactor in an example of the tertiary control mode using the second submode (Floating mode), the prediction error decreases as the end of the waiting period approaches. This is due to the cyclically repeated calculation of the prediction of the Xenon reactivity, which works with the remaining waiting period. The error is compared to the regulating preciseness substantially low. Even at the beginning of the waiting time this calculation error is little with a value of 10 pcm. This is comparable with a control rod set deviation of approx. 8 cm, if the reactivity coefficient of the control rod set is 1.2 pcm/cm. Compared with the control threshold for the control rod set at part load of 30 cm is insignificant.

FIG.10shows a visualization for an operator of a nuclear reactor. The visualization may be provided on a screen. The visualization shows additional to in the beginning discussed reactivity balance arrow the remaining waiting period and if the grid relevant submodes ELPO or Floating mode are set. Further,FIG.10shows the PRtarget power, the ramp up rate of 2.1%/min (PG-Grad=dPG/dt), which is derived from the turbine control. “Hd. SW-Fkt.” refers to the manual setpoint for the control rod16as a proposal for the reactor operator, if the predictor influence to the reactor control should be switched of, whereas “Hd. SW Fkt. actual value” is the really effective value in the reactor control of the control rods16.

According to some embodiments, the time constants and control intensity bands may be adapted for the control of the nuclear reactor in case of the selected primary control mode.

According to embodiments, the method or algorithms for the Xenon prediction enables minimized calculation steps and is adapted to the selected grid control mode for determining the Xenon contribution in the expected ramp up phase which is needed for the implementation into a real time digital reactor control. The in the embodiments used method allows all grid relevant control modes (even unexpected transients as load rejection to inhouse load) including stochastic remote controlled load changes by the tandem Xenon calculation with one calculation of actual Xenon and Iodine value as basis for the second predictive calculation of the Xenon contribution in the ramp up phase.

In some examples of implementation, any feature of any embodiment described herein may be used in combination with any feature of any other embodiment described herein.