You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


This invention relates to a method and apparatus for operating a nuclear electric power generating plant, and more particularly a method and apparatus for controlling the nuclear electric power generating plant to follow variation of a power demand of an electric power system, that is the output of the generator by controlling the quantity of recirculating water and by the operation of control rods of a boiling water type nuclear reactor (BWR).
At present, nuclear electric power generating plants are generally operated at their rated outputs (rated power) for the purpose of improving running efficiency in view of such factors that the percentage of the electric power generated by nuclear electric power generating plants is not so high with reference to total electric power generated by all electric power generating stations, that the cost of power generation is lower than that of steam electric power generating plants, that the outputs of nuclear electric power generating plants have not yet been controlled to follow the power demand of the electric power system, and that the rate of combustion or life of nuclear fuel varies depending upon the power output. For this reason, variation in the electric power demand has been satisfied by varying the outputs of hydroelectric and or steam electric power plants without varying the outputs of the nuclear electric power generating plants.
In recent years, however, with increase in the number of nuclear electric power generating plants as well as increase in the capacity of reactor-generator unit, the percentage of power generated by nuclear electric power generating plants has increased. Moreover, the power demand during nighttime is becoming much lower than daytime power demand with the result that it is necessary to operate nuclear electric power generating plants much more flexibly to supply power economically, reliably and stably with the entire electric power generation plants. To satisfy such requirement, should the output of a nuclear plant be reduced to 75% of its rated output in response to a large decrease in the nighttime power demand, optimum result could not be obtained in view of effective life of the nuclear fuel.
For clarifying the reason why the effective use or life of the nuclear fuel is important, the outline of a BWR generating plant and its output control in response to power demand will firstly be described as follows:
Referring to FIG. 1 which diagrammatically illustrates a BWR type nuclear reactor and a steam turbine generator set operated thereby, the reactor 5 is equipped with a core flow quantity control system 101 and a control rod control system 102. In the example shown in FIG. 1, a recirculation path includes a jet pump 105 and a recirculation pump 104 connected in a recirculation pipe 103 and the number of revolutions of the pump 4 is controlled by the core flow quantity control system 101. However, it should be understood that the quantity of recirculation can also be controlled by controlling a flow control valve, not shown connected in the pipe 103 and that the pump 104 may be disposed in the reactor 5. As is well known in the art, the control rod control system 102 controls the extent of insertion of control rods 109 (only one is shown) into fuel assemblies 108 (only one is shown) of a reactor core 107 to control the thermal output of the reactor. After passing through a water-steam separator 110 and a superheater 111, the steam generated by the reactor 5 is supplied to a steam turbine 6 for driving an electric generator 8, and the condensate in a condenser 7 is returned to the reactor 5 by a feed water pump 114.
The control of the nuclear electric power generating plant to follow up variation of the power demand can be readily and rapidly performed with the control rod control system 102 and the core flow quantity control system 101 of the type described above. The control rod control system is principally used for controlling the burn up exposure of the nuclear fuel over a relatively long time and for controlling the output to a lower output and can control the output at a rate of 3% per minute.
The core flow quantity control system 101 utilizes the characteristic of the reactor that its output is substantially proportional to the flow quantity of water through the core so that this system is used to control a large output for a short time, or to quickly control the output, and can control the reactor output at a higher rate of about 30%/min. Thus, a combination of these two control systems permits stable and quick control of the output in a range covering high and low outputs.
FIG. 2 shows the relation between the core output (ordinate) and the core flow quantity (abscissa) in which a portion 201 between points B and C shows the power-flow control line effected by the control rod while the speed of the recirculation pump 104 is maintained at a constant value. For example, while the reactor is running at point B as the control rod is inserted or extracted, the reactor output decreases or increases along line 201.
A line 202 between points A and B shows a powerflow control line when the core flow quantity is varied while maintaining a pattern of the control rods (i.e., an insertion pattern thereof in the core) at a definite pattern. For example, at point A when the core flow quantity is decreased by decreasing the number of revolutions of the recirculation pump 104 the output decreases substantially in proportion thereto and vice versa.
Thus, the power control as shown by a solid line A-B-C-B'-A' shown in FIG. 3 can be realized by controlling the output along a line A-B-C-B-A shown in FIG. 2.
In FIG. 3, solid line 301 shows a reactor output curve, while a dotted line 302 shows a reactor core flow quantity curve, both representing the relation between the output and the core flow quantity which vary with time.
Where the output is varied in a relatively narrow range of from 100 to 65%, the output can be varied rapidly as above described only with the control of the flow quantity. Although it is possible to control nuclear electric power generating plants based on this principle so as to meet variations in power demand of the electric power system, for the reason described above, at present nuclear power plants are operated at a high output for sharing a base load.
One example of the output control with the core flow quantity control will be described as follows. It should be noted that in the foregoing description the interval .DELTA.t between points A and A' in FIG. 3 in which the output is varied is relatively short, for example, of the order of several to several tens minutes. Where this interval is lengthened to about several hours, it becomes necessary to control the reactor output to compensate for transient variation in the concentration of xenon (X.sub.e.sup.135) (X.sub.e.sup.135 transient) formed during the output variation. More particularly, when the interval is long, effect of xenon X.sub.e.sup.135, one of the fission products having a life time of several hours can not be neglected. Since X.sub.e.sup.135 has a large thermal neutron flux absorption cross-sectional area, it manifests a negative reactivity effect for the reactor output control so that in the output control this effect must be compensated for.
FIG. 4 shows one example of an output variation pattern where the effect of the transient variation of X.sub.e.sup.135 can not be neglected as at a week end in which a low load condition persists for about two days. In order to cause the reactor output to follow a portion 401 of the load pattern A through G, the control is effected while compensating for the negative reactivity variation of X.sub.e.sup.135 as shown by curve 403 in FIG. 4. Thus, it is necessary to control the core flow quantity according to curve 402 shown in FIG. 4 such that it gives a positive reactivity variation sufficient to cancel the negative reactivity variation of X.sub.e.sup.135 shown by curve 403.
When the variation with time of the reactor output shown by curve 401 in FIG. 4 and of the core flow quantity shown by curve 402 is represented by an out-put-flow quantity control diagram (power-flow control map) similar to that shown in FIG. 2, a graph shown in FIG. 5 can be obtained in which the reactor output varies along lines 501 through 504 in the order of points A, B, C, D, E, F and G.
With reference to FIGS. 6 and 7, items to be followed at the time of varying the reactor output to follow a load demand variation (load variation) will be described as follows.
FIG. 6 is a diagram showing a running region in which the abscissa represents the core flow quantity, while the ordinate the reactor output, and the running permissible region is represented by a rectangle bounded by lines 601 through 604. Curve 601 shows a permissible minimum core flow quantity, curve 602 a permissible maximum core flow quantity and curve 603 a rod block line, that is a curve limiting the extent of withdrawal of the control rods for the purpose of preventing damage of the nuclear fuel as well as excessive reactor output. Line 604 represents a permissible maximum output limit, while lines 605 and 606 represent loci (represented by points B.sub.1, T.sub.1, T.sub.1 ' and B.sub.1 '; and B.sub.2, T.sub.2, T.sub.2 ' and B.sub.2 ') of the reactor output and the core flow quantity at the time of following up the load variation. A solid line locus 605 shows one example that can be practiced because of its narrow width of output variation, while a broken line locus 606 shows one example difficult to practice because of its wide width of output variation. At running point B.sub.1 the output is high and the core flow quantity is the maximum whereas at running point T.sub.1, the output is high and the core flow quantity is the maximum. As will be described later, at these points, since the cooling of the nuclear fuel and the output distribution are critical it is necessary to carefully operate the reactor not to damage the fuel. It is desirable that these high output points B.sub.1 and T.sub.2 are sufficiently spaced from limit lines 602 through 603 (that is to have sufficient margine). Thus, like point B.sub.2, any running point should not lie on the outside (to the left) of the rod block line 603. Likewise, points T.sub.1 and T.sub.2 should not lie on the outside of the maximum core flow quantity line 602.
FIG. 7 is a graph showing variation of the core average output distribution in the axial direction of the nuclear fuel rods in the core where the reactor output is increased or decreased at the time of a load variation follow up running. More particularly, curve 701 represents an output distribution prior to the load variation follow up running. Thus, in the core of a BWR type reactor, a nuclear thermal hydraulic phenomenon persists, and as the water utilized as a coolant flows toward upper along the fuel rods, it is gradually heated to form steam foams (voids) whereby steam-water two phase flow flows upwardly while gradually increasing the volume ratio of the voids. For this reason, at the lower portion of the core, void volume ratio is 0% but as the steam phase increases at the upper portion of the core the void volume ratio increases to about 70%. Thus, on an average, the void volume ratio of the entire core becomes to about 40%. Where the void volume ratio of the moderator is high, as the leakage of the thermal neutron flux that sustains the nuclear fission reaction is large, the output of the fuel rods decreases. At the central portion of the core, the output is large because of high density of the neutron flux generated by the fuel rods, whereas at the upper and lower portions of the core the output lowers due to high leakage of the neutron flux. For the reason described above, the axial thermal output of the fuel rods is the highest at the central portion as shown by curve 701.
In order to prevent thermal and mechanical damages of the fuel rods, especially under a high output condition, so-called preconditioning (PC) running is adopted wherein the output is gradually increased and the output distribution at this time is called a PC envelope 702. In principle, the reactor is operated within the range of this envelope, and the operation in a range outside of the PC envelope causes damage of the fuel rods, which in turn causes dangerous hazard of radioactivity.
Under the initial distribution condition, when the core flow quantity and hence the reactor output are decreased to follow up decrease in the load, the negative reactivity of X.sub.e.sup.135 once increases and then decreases with a time constant of about 10 hours so that the reactor output decreases and then increases corresponding thereto. Accordingly, in order to maintain the reactor output at a constant value, the core flow quantity is increased and then decreased to compensate for the poisonous effect of X.sub.e.sup.135. During this process, as at point B.sub.1, there is a case wherein the output is high but the core flow quantity is small. Under this state, as the void distribution in the reactor shifts downwardly the output at the upper portion of the core decreases, whereas that at the lower portion increases correspondingly, thus manifesting an output distribution 703 B.sub.1 in which a peak appears at the lower portion which exceeds initial distribution 701, thus decreasing the margin with respect to the PC envelope 702. Of course, this condition is not advantageous for the fuel. During the normal load variation follow up running in nighttime, as a result of reduction in the reactor output, the poisonous effect of X.sub.e.sup.135 appears at about the noon of the next day when the output is returned to a high level.
Where the reactor running is returned to the high output running from the low output running during nighttime by increasing the core flow quantity to meet the large power demand during daytime, as shown by point T.sub.1 both the output and the core flow quantity become the maximum, and the output distribution of the reactor becomes so-called upper peak output distribution 704 in which an output peak appears at the upper portion of the core, the peak exceeding the initial output distribution 701 thus decreasing the margin with respect to the PC envelope 703.
Where the decrease in the power demand of the electric power system is large and persists over a long time, the locus of a characteristic showing the relation between the reactor output and the core flow quantity is shown by a curve 606 shown in FIG. 6 which drifts over a wider range than the locus 605 (T.sub.1, T.sub.1 ', B.sub.1 ' and B.sub.1). Accordingly, point B.sub.2 may lie on the outside of the rod block line 603. The output distribution in such case is shown by a curve 703 B.sub.2 shown in FIG. 7 which extends to the outside of the lower portion of the PC envelope 702, thus causing damage of the fuel rods. In addition, depending upon the load variation follow up pattern, the locus 606 might lie on the outside of limit curve 602 or 604, and its output distribution may also lie on the outside of the PC envelope 702.
As above described, when varying the reactor output to follow up load variation, it is essential to maintain the reactor output, and the core flow quantity in allowable running ranges while maintaining the output distribution below the PC envelope 702. To vary the output variation width, the output variation speed, the output decrease time, etc., corresponding to various patterns of the load variation in the power system there arises a number of strict factors that makes it difficult and complicated the load follow up running of the nuclear electric power generating plants.
The load follow up output variation pattern just described is a typical one in which under a high load during daytime, the high output is maintained, while during nighttime the low reactor output is maintained and the output is varied in the morning and evening.
Generally, a power system grid is constituted by a plurality of electric power generating stations and a plurality of grids are interconnected to constitute an extensive power network. Accordingly, where the grid or network covers a wide area the load variation during daytime and nighttime is somewhat averaged due to time difference in different districts and the load variation during day and night is alleviated due to power flow between adjacent networks or grids. However, in a small grid in a relatively small district, due to absence of a time difference, the load variation during day and night, especially near noon occurs simultaneously throughout the district. It is also necessary to compensate for the load variation caused by natural calamities or unexpected happenings and it is necessary to compensate for such load variation by controlling the outputs of the electric power generating plants in a given district. This is important because it is possible to maintain the quantity and quality (i.e., frequency) of power supply of a given grid or entire power network. Accordingly, in the following description, a medium size network is taken as an example.
In addition to the load variation during day and night, it is also necessary to take into consideration decrease of load of about 10%, based on the total load for about one to 1.5 hours during lunch time. This makes it difficult to maintain a balance between the load and the output of the power plants. To this end, it has been the practice to rapidly vary the outputs of steam and or hydroelectric power stations. Accordingly, although it is desirable to use BWR type electric power generating plants capable of rapidly varying their outputs to compensate for the load variation at the lunch time, at present, for the reason described above such requirement has not yet been realized.