DE19638853C2 - Process for determining performance and optimizing the use of power plants in a swell chain - Google Patents

Description

The invention relates to a method for determining the power of force work a swell chain, each with the help of the storage space curve and the underwater consumption curve the level curves in the storage space and from it Turbine output can be determined via head and flow.

Under the swell chain there is a closed hydrau here and below to understand the power plant chain. Compared to other hydraulic Systems such as B. storage power plants with large heads and upstream Weekly, monthly or yearly memories are one thing for swell chains Relocation of the water volume over several hours to a maximum of one day can achieve the following special features:

The inflow is subject to the influence of power plants strong fluctuation.

The dynamic hydraulic processes in the accumulators influence the Performance assessment or energy generation.

Due to the high degree of expansion, energy generation is variable Level differences depending on the individual barrages.

For these swell chain systems, there are diverse and very close links between their components, which are in a model for the computer-aided operational planning (simulation and possibly subsequent opti mation) must be taken into account. For the use of such practical tools relieves the burden on the load distribution staff Routine tasks, support with questions in normal operation, about Check the feasibility of timetables, review and analysis for already expired operating situations and increased operational safety.

The complexity of these hydraulic systems had in the past always inevitably to model club in connection with the computing power folds led. These are one reason for the rather low practical Suitability of the operational planning procedures created so far. Dynamic gush  and sunshine in the storage spaces, the strong temporal and spatial Coupling of the barrages via the head, the flow and the volumes as well as the presence of special storage spaces, such as canals and flow sections, require a detailed modeling of the hydraulic conditions in order to meet today's accuracy requirements of swell chain operators to be able to.

A storage space of a swell chain must be in the stationary state Volume V, the storage space flow rate Q, any intermediate feeder Z, described the underwater level UW and its upper water level OW.

A transition line of a natural or Oberliegerkraftwerk predetermined inflow Q t | to and set at the power plant effluent transition line Q _from ^t inevitably result in a variable upper water and lower water level stand. The basic system of differential equations for transient drains has been known since Barre de Saint Venant (1871). The exact calculation, however, requires too much data collection, data input and computing effort.

Therefore, stationary curves - the storage _volume curve V = f _V (Q, OW) and underwater _{consumption curve} UW = f _uw (Q, OW) - are determined by the electricity supply companies with the help of storage space _{plumbing in} order to be able to calculate water levels, flows or volumes. These curves describe the combination of level, flow and volume in the case of stationary conditions in the storage space.

The dependency of the water volume in the damming on the inflow and outflow and any natural intermediate feeder is generally described by the continuity equation.

V ^t = V ^t- Δ ^t + Δt. (Q t | zu + Z t | kl - Q t | ab) [1]

In standard models, the stationary volume V ^t is now used to calculate the respective level curves together with the storage volume curve and the underwater consumption curve.

However, this modeling is unsuitable for swell chains. This simple model does not take into account dynamic processes in the storage spaces. It should be noted that a change from Q t | to the underwater level UW ^t affects immediately, but the wave travel time t _{l, too, is} required to act on the upper water level OW ^t . A change in Q t | ab, on the other hand, immediately affects the headwater level OW ^t and in turn requires the wave duration t _{l, ab} to act on the underwater level UW ^t . Furthermore, this simple representation applies to a storage space only until a possible intermediate feeder changes the mirror position of a storage space too much.

Due to this known fact, some models described in the literature have now attempted to map the real reaction of the headwater level (after the wave transit time) to an inflow change by delaying the inflow Q t | zu in the continuity equation:

In this attempt to model the dynamic level movements, an error arises in relation to the total volume V ^t , since in reality the inflow Q t | zu is immediately included in the total volume and does not delay the wave propagation time. A volume share of the "correct" total volume would therefore always be missing. This modeling is therefore only permissible for storage spaces with large volumes or for flow sections. For Austrian swell chains, for example, this formulation is not sufficient due to the small volumes of the storage spaces; the error in the total volume V ^t would have too great an effect on the level curves.

The object of the present invention is to overcome the disadvantages mentioned to avoid known methods of the type mentioned and ins  in particular such a method or the underlying model improve that accuracy taking better account of the dynamic processes in the storage spaces is increased without too much data to have to operate collection, data entry and computing effort.

This object is achieved according to the present invention in that with values of the inflow Q t | zu, the outflow Q t | ab as well as a possibly existing small intermediate feeder Z t | kl, for loading calculation of the level curves of two independent, location-related volumes balance sheets for the headwater level and the underwater level are used, in which inflow and outflow changes are delayed with the fictitious Wedge volume that could come after the change must be taken into account.

The essential step for improvement is therefore according to the invention now that for the calculation of the level two additional independent dependent, location-based volume balances are modeled. The general Volume balance is not used for modeling the level, but only for that Calculation of the total volume used.

In the location-based volume balance for the headwater level, an inflow change is delayed (t _{l, closed} ), but then suddenly with the fictitious wedge volume that could come after this inflow change.

The volume balance for the underwater level is completely analogous to a change in the drainage delayed by the wave duration (t _{l, ab} ), but then suddenly again with the fictitious wedge volume that could come after this drainage change.

The location-related volumes U t | OW and U t | UW according to / 3 and / 4 differ from the total volume V ^t according to / 1 after an inflow or outflow change, but are correct in the steady state or in the steady state (here according to t _{l, zu} or t _{l, ab} ), due to the volume delay, in contrast to / 2 again with V ^t .

The small intermediate _feeder Z _kl includes all inflows and outflows of the storage space that are not assigned to the adjacent power plants and is therefore not located in the storage space according to the model. Its modeling only serves to correct the volume. In the case of high absolute values and serious changes in time of Z t | kl, it is consequently not to be expected that the level curves will be sufficiently realistic.

In a further embodiment of the method according to the invention, it is therefore provided that, in the case of larger, variable intermediate feeders Z ^t, the respective storage space is divided up into corresponding partial storage spaces.

In the case of an intermediate feeder Z ^t allgemein 0, there is generally a kink in the mirrored position of the storage space in the steady, stationary state, since there is no longer a uniform storage space flow. This fact is negligible for a small intermediate _feeder Z _kl , but it must be taken into account for large intermediate feeders Z _gr .

The easiest way to describe this kink is by looking at the storage space at the confluence of the large intermediate feeder viewed hydraulically in divides two fictional storage spaces. As a result, storage space curves and consumption curves for both storage compartments are available separately so that all four levels are functions of their local volumes and Flows can be calculated.

For Z t | gr ≠ Const, this storage space separation is taking into account the Problem, for the calculation of general steady state (requires volume distribution V t | 1 + V t | 2) is absolutely necessary.  

For each time step and level, the Invention a fictitious, stationary state of the total storage space by a Total volume V t | 1 + U t | 2 and storage space flow rates per partial storage space Q t | 1 and Q t | 2 To be defined.

According to another embodiment of the invention is advantageously seen before that the partial storage spaces are considered arithmetically connected by a compensation flow Q _A and the local volumes and flows of the partial storage spaces are otherwise determined independently of each other. As a result, the equations for the local volumes and flow rates of both partial storage spaces can be formulated completely independently of one another. The only thing that needs to be considered is which inflows and outflows are included in the volume balances immediately or with a delay. The wave _{transit times of} both partial storage spaces are identified with the assigned indices "1" or "2" (t _{l1, zu} and t _{l1, ab} or t _{l2, zu} and t _{l2, ab} ).

Which of the two fictitious partial storage spaces Z _{gr is} assigned in terms of modeling at the interface is irrelevant for the end result, since this assignment affects the equations for the local volumes and flows, but not their respective values calculated therefrom.

For a simplified description of a delayed inflow or outflow change, a volume delay function ΔV is defined, which only updates the flow rate Q ^t after the constant delay time t _v in the volume balances:

ΔV (Q, t, t _v ) = Δt. Q ^t-tv + t _v . [Q ^t-tv - Q ^t-tv- Δ ^t ]

Partial storage space 1

V

       t | UW     

= V

       t-Δt | UW     

+ Δt. [Q

       t | too     

+ Z

       t | kl1     

] - ΔV (Q _A

, t, t _{l1, ab}

)

Q t | UW = Q t | zu

V t | ZW1 = V t-Δt | ZW1 + ΔV (Q _zu , t, t _{l1, zu} ) + Δt. [Z t | kl1 - Q t | A]

Q t | ZW1 - Q t | A

Partial storage space 2

V

       t | ZW2     

= V

       t-Δt | ZW2     

+ Δt. [Q

       t | A     

+ Z

       t | gr     

+ Z

       t | kl2     

] - ΔV (Q _ab

, t, t _{l2, ab}

)

Q t | ZW2 = Q t | A + Z t | gr

V t | OW = V t-Δt | OW + ΔV (Q _A , t, t _{l2, zu} ) + ΔV (Z _gr , t, t _{l2, ab} ) + Δt. [Z t | kl2 - Q t | ab]

Q t | OW = Q t | ab

Both partial storage spaces have a different slope of the mirror position at the interface, but the levels must be identical for each time step:

ZW t | 1 (V t | ZW1, Q t | ZW1) - ZW t | 2 (V t | ZW2, Q t | ZW2) = 0

The only unknown in this equation is Q t | A. Their zeros are therefore possible solutions for Q t | A. Technical / official system data (this includes the storage space curve and the underwater consumption curve) are approximated by groups of curves that meet the mathematical criteria of strict monotony. Taking this strict monotony of the storage space curve and the underwater consumption curve into account, it follows

and therefore there can theoretically only be a maximum of one zero. Additional However, zeros can be outside of the definition range Extrapolation errors that violate the strict monotony arise.

Q t | A can theoretically and practically briefly in certain cases become negative. A quick shutdown of machines on a reject line has a water movement from the location of the power plant in the following transition state upstream. Since negative flows in the domain nor times are not included, must be extrapolated. Correlates with These extrapolations are quantitative errors, however, over time decrease exponentially very quickly.

In steady steady state applies

Q t | A = Q t | zu + Z t | kl1 = Q t | ab - Z t | gr - Z t | kl2

V t | UW = V t | ZW1 = V t | 1

V t | ZW2 = V t | OW = V t | 2

The fictitious storage compartment partition has this in part u. U. undesirable side effect that changes in the inflow or inflow to the separator wall to be reflected. However, these reflections are necessary here as they the information about the recation of the opposite partial jam return space and thereby correct V t | OW or V t | UW. Also are fictitious storage space separations are often necessary precisely where they did in reality Similar reflections occur (e.g. transition from storage space to channel).

The main advantage of this so-called module model is that justifies that the module described above "storage space with a small intermediate feeder "through equalization flows, can be networked as required.  

Each coupling offers the possibility of integrating a large intermediate feeders.

In contrast to this module model described above is in the compact model described assume that there is no one Reflections and negative balancing flows, but also none Modularity exists because the equations and volume balances are always for the whole storage space must be formulated. The compact model described first works in the originally described case with a small intermediate feeder, if there are equivalent storage space curves for both variants and Z t | gr = Z t | kl1 = Z t | kl2 = Z t | kl = 0 applies.

In a further preferred embodiment of the invention it is provided that the storage spaces are chained in such a way that for the calculation of the case height or the power in the assigned power plant the difference between the in the storage space in the upper water and in the lower storage space local based underwater level is formed, and the upper water level with the help of location-based volume balance and runoff as well as the underwater level below Relationship between the local volume balance and the inflow be determined. This is now a very simple and advantageous way enables the power values determined in this way at least as part of the Objective function of an optimization of power plant operations of the swell chain be used.

In electrical supply companies with purely thermal generation computer-aided operational planning procedures with the help of algorithms linear programming (LP), mixed-integer programming (Mixed Integer Programming, MIP) and Dynamic Programming for many Years.

The previously known operational planning methods for river power plant chains (Swell chain systems) are not very suitable for practical use net. Hydraulic systems, especially the special case of a swell chain,  are much more complex than thermal systems. The strong temporal and spatial coupling of the barrages via head, flow and volume, dynamic runtime effects in the barrages, etc. as well as highly restricted coupled sizes require great simplifications in the optimization models to ensure the calculability with the known algorithms can.

In a particularly preferred further embodiment of the invention Solution of the mentioned problems to optimize a genetic algo rithmus used in which the first generation of individuals made copies simulated on the basis of their power plant or storage space drains Starting solution is formed, with each individual from a number of Genes exist, each of which is the state of the power plant in one represented time step, and in which a number of Opera each one affects an individual and in a certain way the Power plant outflows of this individual changes, after which the for each individual Generation of the objective function value is determined and the individuals with better objective function value with a higher probability into the next one Generation. So a process was developed that works with Using a genetic algorithm the use of resources even then if these resources are complex systems with non-linear relationships represent, optimize in reasonable time. This procedure is used in hereinafter referred to as Genetic Resource Optimization (GROPT).

The new optimization process was based on known Genetic algorithms developed. GROPT is looking for an optimal solution in Solution space of the much more precise simulation model and can be based on one Source solution that, for example, with a simpler model of an LP / MIP Optimization was calculated, put on. However, a starting solution does not have to be exist.

GROPT can of course also be used for different optimization horizons,  e.g. B. Daily timetables (e.g. 24 hours with a time step width of 30 Minutes) as well as detailed timetables (e.g. 4 hours with a time step width of 5 minutes).

GROPT's tasks in creating e.g. B. of daily and fine Timetables is the change in power plant outflows to eliminate even current upper water level and / or intermediate level violations, to the full exploitation of the threshold area and for optimal setting of the switching and control points taking into account a non-linear hydraulic and electrical model of the river power plant chain (SIM).

The original solution is simulated based on its power plant outflows and copied x times. These x individuals form the first generation of GROPT.

The operators are responsible for the individual individuals of a gener ation to change, which in turn leads to the next generation is formed. Only one operator is active per individual. After Selection of an individual is made through the self-adjusting control of that Operator with a higher probability selected in the previous one past generation has had greater effectiveness. This operator changes the power plant outflows of the individual and then hands over to the Corrections.

On the basis of the power plant created by operators and corrections fluxes, the target function value is calculated for each individual of the generation net. Those individuals with a better objective function value plant themselves more likely to advance into the next generation. The algo rhythm is ended when the target function value of the best individual is over a number of generations is not improved or a total of one definable number of generations is exceeded.

To represent the variables of the optimization problem, see a simple genetic algorithm uses a coding mechanism that maps the variables to binary strings (binary coding). Every indivi  duum of a generation consists of a sequence of 0 and 1 (genes).

In GROPT, each individual is also made up of a set of genes, however, each gene the condition of the power plant in a particular Represented time step (the state of a power plant consists of the Power plant outflow, power plant output, headwater level, etc. Darge represents by a state vector). For a full view of the For example, states of ten power plants exist in one day Timetable with a half-hour grid of 480 states vectors (48 time steps. 10 power plants). Every individual therefore has over 480 genes. Each generation consists of a parameterizable number of Individuals (e.g. 11).

The use of state vectors as genes eliminates one time-consuming conversion of the coding.

In simple genetic algorithms, two individuals become parents generation and a position k within the binary string of the individuals randomly chosen. All genes of the two individuals starting with the kth gene are interchanged. There are also more complex realizations of Crossover operators who take problem-specific knowledge into account.

The following steps are carried out by the operator crossover in GROPT:

• 1. Random selection of two individuals of the old generation.
• 2. Random selection of a power plant.
• 3. Random selection of the beginning of an interval in individual 1 and individual 2. The end of the intervals is chosen so that the entire amount of water to be delivered by this power plant (delivery volume) unchanged remains (integral constraint).
• 4. Exchange of the state vectors in interval 1 with those in interval 2nd
• 5. Random selection of a second power plant. For all power plants that  topologically between the first and the second selected power plant a crossover is also carried out, the same inter valle offset by the running time of the respective power plant can be used.
• 6. Multiplicative correction of power plant outflows in the selected Intervals so that the integral constraint is met.
• 7. Copy the resulting two new individuals into the next one Generation.

The operator crossover crosses two timetables together to print to pass on a good driving style to everyone. The volumes of the Storage spaces of the power plants selected for the operator crossover change only insignificant due to this operation (integral constraint).

In simple genetic algorithms, a mutation is one with one low probability, random change in the value of a Position in the binary string.

The block mutate operator of the GROPT goes through the following steps:

• 1. Random selection of a power plant and four control times in this power plant. These determine intervals 1 and 2 .
• 2. Change in the power plant outflows of the first interval by one random value.
• 3. Change the power plant outflows of the second interval by the same Amount of water in the opposite direction, so that the integral constraint is observed.
• 4. Random selection of a second power plant. For all power plants that topologically between the first and the second selected power plant a block mutate is also carried out, the intervals being around the runtime of the respective power plant will be offset and as the end time the nearest regulation is searched for.

The further operator Rotate according to the invention is available in simple genetic algorithms are not.  

The GROPT operator Rotate goes through the following steps:

• 1. Random selection of a power plant and two times in this power plant (interval).
• 2. Shift the power plant outflows by a random amount selected number of time steps. The ones overwritten by moving Power plant outflows are reclassified at the beginning of the interval, whereby the integral constraint remains fulfilled.
• 3. Random selection of a second power plant. For all power plants that topologically between the first and the second selected power plant a rotate is also carried out, the intervals around the Runtime of the respective power plant.

The Rotate finds special driving styles faster than tipping other operators.

Every individual of a generation contains in addition to strength a success value per operator. Give these success values Information about how successful the individual operators have been in the past Generations have been applied to an individual.

The sum of the success values is always standardized to one. From these A probability of selection is determined according to standardized success values be for each operator between a maximum and a minimum value can be restricted. Through the success values become operators, which so far were successful, including to educate the next generation with a higher one Probability used.

In addition, according to the invention, the following marginal or off closing conditions are taken into account and corrections are made accordingly become.

The dispensing volume for each power plant is from the beginning and end conditions, the discharge volume of the upper bed and the natural inflow certainly. The power plant outflows integrated over the time range  each storage space are compared with this dispensing volume and the strength Factory outflows changed so that the difference becomes zero.

Forbidden areas of use are those flow areas in which the machines may not be operated for technical reasons.

Power plant outflows, the values assumed within prohibited areas are set to the closer limit. So that can not in any If a turbine is operated in a prohibited area. The one The volume correction ensures that the integral constraint is maintained accomplishes.

Depending on the violation of an upper water level limit (below the minimum or exceeding the maximum headwater level) is in the same and possibly also in the previous time step the power plant outflow decreased or increased. The amount of correction is determined from the slope of the tangent to the Storage space curve estimated.

The upper water level correction is done in cooperation with the volume correction and the prohibited area, thus competing corrections be excluded.

The change in power plant outflows is i. a. limited. To the gener Avoiding invalid timetables will only result in such power plant outflows changes that are within the specified limits.

A quiet driving style mostly desired by the power plant operators (i.e. no too frequent change in power plant outflows) can be caused by a Penalization can be achieved. How many are defined for each optimization run Regulations (including circuits, i.e. how many changes to the power plant flow) per power plant are permitted. Any further regulation will penalized.

The number of regulations going beyond the permitted number is determined by all power plants added up (dimensionless) and with a penalty factor multiplied. The resulting penalty value is taken into account in the objective function  inspects.

As a starting solution, a manually created one or one created by LP / MIP calculated timetable can be used. However, there is no starting solution be specified. In this case, GROPT itself calculates an initial solution (e.g. running water operation).

The objective function consists of the weighted work and the sum of the Penalties together. The weighted work is calculated by the generated Work per time step with a user-specified weight is copied. The weight defines the time periods in which the Energy is more valuable to the user.

The behavior of the power plant chain is used to calculate the target function simulated. This results in those values that are used in the objective function calculation flow in. Was GROPT only the power plant outflows of fewer power plants changed, it is not necessary to re-simulate the whole chain. In In this case, the simulation starts at the top power plant of the first modified power plant and ends at the lower power plant of the last geän power plant, which results in significant computing time savings.

The invention is explained in more detail below with reference to the diagrams or sketches shown in the drawings. Fig. 1 shows a schematic diagram for modeling the dynamic processes in a storage space of a Schwellkette for explaining the inventive method; Fig. 2 shows a correspondingly expanded sketch regarding a storage space with a large intermediate feeder; Fig. 3 to a particular shows another sketch of the application of the method of the invention Real-storage space; Fig. 4 shows a basic scheme for representation of the variables of the optimization problem to an embodiment of the inventive method; Fig. 5 is a sketch for explaining the operation of a Blockmutate operator in optimizing the power plant operations in accordance with an advantageous embodiment of the invention; Fig. 6 shows accordingly the effect of a Rotate-Opera tors according to an embodiment of the invention; FIG. 7 shows the operation of a crossover operator in a manner similar to FIG. 5 and FIG. 6; Fig. 8 shows a section of an example of the success values of the operators according to Fig. 5 to 7 when applied to successive individuals; Fig. 9 shows a schematic sketch for explaining the process of adapting the success values in a self-adjusting control according to an embodiment of the invention and Fig. 10 shows a schematic overview sketch of the functioning of the overall method according to the invention including its configurations.

If one considers a storage space of a swell chain according to FIG. 1, it is described in the stationary state by its volume V, the storage space flow Q, the underwater level UW of the upper bed and its upper water level OW.

The storage space content curve provides the functional stationary relationships

V = f _v (Q, OW)

and the underwater consumption curve

UW = f _UW (Q, OW).

Based on these two - in the electricity supply companies - stationary family of curves and a stationary initial state, a simple but physically justifiable description for level curves in the storage space must be developed, which subsequently determine the head and thus the generated turbine performance in the optimization. These level curves are caused by time-variable values of the inflow Q t | zu, a possibly existing intermediate feeder Z ^t and the outflow Q t | ab (power plant outflow of the underlying) (stationary: Q t | ab = Q t | zu + Z ^t ).

The continuity equation describes the dependency of the water volume in the congestion on the inflow and outflow and any natural intermediate feeder:

This stationary volume V ^t could be used to calculate the associated headwater level, together with the above two equations, and with this the underwater level for each time step.

However, this modeling is particularly unsuitable for smaller swell chains. This simple model does not take into account any transient processes in the storage spaces. It should be noted that a change from Q t | to the underwater level UW ^t affects immediately, but the wave time t _{l, too, is} required to act on the upper water level OW ^t . A change in Q t | ab, on the other hand, immediately affects the headwater level OW ^t and in turn requires the wave duration t _{l, ab} to act on the underwater level UW ^t .

Furthermore, this simple representation applies to a storage space only as long as until not a possible intermediate feeder the mirror position of a storage space changed too much.

Runtimes and retention times have a significant impact on the actual level changes in a storage space. From records of the deed neutrals level and power plant runoff can be observed that the wave duration is constant with good nutrition. This is different only depending on the direction of flow. The retention time, however, is completely of the respective flow, the respective volume and the respective depending on the upper water level. Since the retention time implicitly results from the Storage space curve results in simplifications (e.g. linearization) the same is not permitted. The same applies to the mapping of the quasi Retention time, which is implicit in the underwater consumption curve and the Storage space curve is included. Therefore, simplifications in the Underwater consumption curve not allowed.

Would be based on a simulation model that the figure neglecting the wave propagation time, so the calculated level  course - in the transition states and the non-steady instatio nary and stationary states - a physically implausible behavior demonstrate.

An incorrect level curve would result in the drop height associated with it a faulty calculation of the power plant performance and thus ultimately the objective function in the subsequent optimization of the power plant use bring oneself. Those that can be achieved through better use of the head This could nullify optimization gains.

The storage volume curve V = f _v (Q, OW) and the underwater consumption curve UW = f _UW (Q, OW) form the only references to reality. They therefore also serve as the basis for the mapping of transient processes. As described, the consideration of the wave transit time in the model is essential for a "correct" behavior in the transitional and unsteady states. As already mentioned, the continuity equation is

V ^t = V ^t-Δt + Δt. (Q t | zu + Z ^t - Q t | ab)

not suitable for this in this general form. In many models for hydraulic systems that are used in the optimization, attempts are now made to map the real reaction of the headwater level (after the wave transit time) to an inflow change by delaying the inflow Q t | zu in the continuity equation:

The problem is that this would result in an error in relation to the total volume V ^t , since in reality the inflow Q t | to immediately enters the total volume and does not delay the wave travel time. A volume share of the "correct" total volume would therefore always be missing. This modeling is therefore only permissible for storage spaces with large volumes or for flow sections. For the swell chains considered, this formulation is not sufficient due to the small volumes of the storage spaces; the error in the total volume V ^t would have too great an effect on the level curves. Therefore, the general volume balance is not used for the modeling of the levels, but only for the calculation of the total volume. For the calculation of the levels, two independent, location-based volume balances are modeled, which are used once for the calculation of the upper water level and once for the calculation of the underwater level.

An inflow change is delayed in the volume balance for the headwater level (t _{l, closed} ), but then suddenly with the fictitious wedge volume that could come after this inflow change.

The volume balance for the underwater level is completely analogous to a change in the drainage delayed by the wave duration (t _{l, ab} ), but then suddenly with the fictitious wedge volume that could come after this change in the drainage.

The location-related volumes V t | OW and V t | UW differ from the total volume V ^t after an inflow or outflow change, but they are in the steady steady state or in the steady transient state (here according to t _{l, to} and t _l, respectively) ) again match V ^t .

The small intermediate _feeder Z _kl includes all inflows and outflows of the storage space that cannot be measured, and is therefore not located in the storage space according to the model. His modeling only serves to correct the volume, which is necessary in the presence of real, not measured, small inflows in the individual storage spaces. Furthermore, this correction value results in a parameter which can be useful for fine adjustment of the model when it is placed on real process states.

With high absolute values and serious changes in time of Z t | kl, realistic level curves can no longer be expected. In this case, reference should be made to the explanations below for Fig. 2 ("storage space with large intermediate feeder").

For the headwater level, the local flow is the discharge

Q t | OW = Q t | ab

or the inflow for the underwater level.

Q t | UW = Q t | zu

Finally, the time-dependent headwater level OW ^t is that headwater level OW which, assuming a fictitious steady state with V = V t | OW and Q = Q t | OW, follows from the inverse function of the storage volume curve.

OW ^t = f _OW (V t | OW, Q t | OW)

To calculate the time-dependent underwater level UW ^t , you first need a fictitious upper water level, which is determined via V t | UW and Q t | UW. This fictitious headwater level is finally used together with Q = Q t | UW in the underwater consumption curve, with which UW ^{t can be} assigned to the fictitious steady state with V = V t | OW and Q = Q t | OW.

UW ^t = f _UW [Q t | UW, f _OW (V t | UW, Q t | UW)]

The volume balances for the calculation of the levels assume that t _{l, zu} and t _{l, ab are} constant, but not necessarily the same.

The whole can now be linked to complex chains according to FIGS. 2 and 3.

From Fig. 2, the configuration of a storage space with a large intermediate feeder Z _gr can be seen, in which there is generally a kink in the mirror position in the steady statio nary state, since there is no longer any union storage flow. This fact is negligible in the case of the small intermediate _feeders Z _kl1 and Z _kl2 which are also shown, but they must be taken into account with regard to the large intermediate _feeders Z _gr . This kink can be represented most simply as described at the beginning by hydraulically dividing the storage space at the confluence of the large intermediate feeder into two fictitious parts, with the result that storage space content curves and consumption curves must be available separately for both storage compartments, so that all four levels can be calculated as functions of their local volumes and flow rates. For a large intermediate feeder that is not constant in time (Z t | gr unequal constant), such a separation is absolutely necessary for the calculation of general steady state conditions.

The two partial storage spaces are considered connected according to FIG. 2 by a compensating flow Q _A. The equations for the local volumes and flow rates of the two storage compartments, which are thus independent of one another, and further detailed explanations are initially set out in connection with the reference to an embodiment of the method according to the invention.

In the arrangement according to FIG. 3, which serves only as an example for a real task, a total of four partial storage spaces are used between the dam for power plant 1 (KW-1) and that for power plant 2 (KW-2). The self-jammed large intermediate feeder Z _gr with storage volume V ₃ separates the main storage space at its mouth (intermediate level "Duel") into two parts. The diversion at weir M requires a further division of the total storage space. The flow path from weir M to the underwater level of KW-2 is not considered separately here.

Referring to Figs. 4 to 10 to optimize the planning of power plant operations in a Schwellkette will be described below, based on the aforementioned model, to feasible, and above all economic lichere schedules, as it can create the load distribution, with the model calculated to can. The new optimization method used for this is based on the use of known, so-called genetic algorithms. This method, called GROPT (genetic resource optimization), is looking for an optimal solution in the solution space of the described simulation model of the swell chain and can be based on an initial solution that was calculated, for example, with a simpler model of LP / MIP optimization. However, an initial solution does not have to exist and can be determined by GROPT itself in this case.

GROPT is used for different optimization horizons (daily schedules (24 hours with a time step width of 30 minutes) as well as detailed timetables (4 hours with a time step width of 5 minutes).

GROPT's task in creating daily and detailed timetables is the change in the power plant outflows to eliminate any waiters water level and / or intermediate level violations, for full use the threshold and for optimal setting of the switching and control points considering a non-linear hydraulic and elec tric model of the river power plant chain (SIM).

The original solution is simulated based on its power plant outflows and copied x times. These x individuals form the first generation of GROPT (see Fig. 4).

The operators shown in FIGS. 5 to 7 with regard to their effect have the task of changing the individual individuals of a generation, from which the next generation is subsequently formed. Only one operator is active per individual. After the selection of an individual, the operator who has had greater effectiveness in the previous generation is more likely to be selected by the self-adjusting control. This operator changes the power plant outflows of the individual and then passes them on to the corrections.

On the basis of the power plant outflows created by operators and corrections, the target function value is calculated for each individual of the generation. Those individuals with a better objective function value are more likely to reproduce into the next generation. The algorithm is terminated if the target function value of the best individual does not improve over a number of generations or if a definable number of generations is exceeded overall - see also FIGS. 9 and 10 or the associated description.

To represent the variables of the optimization problem, see a simple genetic algorithm uses a coding mechanism that maps the variables to binary strings (binary coding). Every indivi duum of a generation consists of a sequence of 0 and 1 (genes).

In GROPT, each individual also consists of a set of genes, but each gene represents the state of the power plant in a certain time step (the state of a power plant consists of the power plant outflow, the power plant output, the headwater level, etc. represented by a state vector). For a complete representation of the states of, for example, ten power plants, there are 480 state vectors (48 time steps. 10 power plants) in a daily schedule with a time step pattern of half an hour. Each individual therefore has 480 genes (see Fig. 4). Each generation consists of a configurable number of individuals.

The use of state vectors as genes eliminates one time-consuming conversion of the coding.

The operators preferably used in the present method by GROPT are shown in the sketches according to FIGS. 5 to 7 with regard to their effect on the individual individuals or schedules (power plant outflows over time).

The Blockmutate operator goes through steps shown in FIG 5, the following work.:

• 1. Random selection of a power plant and four regulation times score in this power plant. These determine intervals 1 and 2.
• 2. Change in the power plant outflows of the first interval by one  random value.
• 3. Change the power plant outflows of the second interval by the same Amount of water in the opposite direction, so that the integral constraint is observed.
• 4. Random selection of a second power plant. For all power plants that topologically between the first and the second selected power plant a block mutate is also carried out, the intervals being around the runtime of the respective power plant will be offset and as the end time the nearest regulation is searched for.

Referring to FIG. 6, the Rotate operator passes GROPT of the following working steps:

• 1. Random selection of a power plant and two times in this power plant (interval).
• 2. Shift the power plant outflows by a random amount selected number of time steps. The ones overwritten by moving Power plant outflows are reclassified at the beginning of the interval, whereby the integral constraint remains fulfilled.
• 3. Random selection of a second power plant. For all power plants that topologically between the first and the second selected power plant a rotate is also carried out, the intervals around the Runtime of the respective power plant.

This operator finds special control strategies of the swell chain, such as such as tipping, faster than other operators.

According to Fig. 7, the following steps are carried out by the crossover operator in the GROPT:

• 1. Random selection of two individuals of the old generation.
• 2. Random selection of a power plant.
• 3. Random selection of the beginning of an interval in individual 1 and individual 2. The end of the intervals is chosen so that the entire  amount of water to be delivered by this power plant (delivery volume) unchanged remains (integral constraint).
• 4. Exchange of the state vectors in interval 1 with those in interval 2nd
• 5. Random selection of a second power plant. For all power plants that topologically between the first and the second selected power plant a crossover is also carried out, the same inter valle offset by the running time of the respective power plant can be used.
• 6. Multiplicative correction of power plant outflows in the selected Intervals so that the integral constraint is met.
• 7. Copy the resulting two new individuals into the next one Generation.

The operator crossover crosses two timetables together to print to pass on a good driving style to everyone. Because of the making This operator is new driving styles by mixing old driving styles mainly responsible for a stable convergence to the global optimum. The Volumes of the storage spaces of the power plants selected for the operator crossover change only marginally as a result of this operation (integral secondary condition).

Every individual of a generation contains in addition to strength a success value per operator. Give these success values Information about how successful the individual operators have been in the past Generations have been applied to an individual.

The sum of the success values is always standardized to one. From these A probability of selection is determined according to standardized success values be for each operator between a maximum and a minimum value can be restricted. Through the success values become operators, which so far were successful, including to educate the next generation with a higher one Probability used.  

Fig. 8, the values of the success operators crossover Blockmutate and Rotate shows the individuals 1 (IND1) and 2 (IND2).

The course of the adaptation of the success values is shown in FIG. 9. To simplify matters, each generation consists of four individuals and the number of operators is two.

At the beginning, all are successful for the gene (1) initialization generation value the same. The selection now selects the individual 1 three times and once that Individual 2 based on the objective function values. From the selection probability Opportunities for the formation of the gene (2) results, for. B. a two-time call the Crossover operator and calling the Mutate operator twice. This results in the selection probabilities for the formation of the Gene (3).

Each time an individual passes through an operator, the associated success value increased by a certain value (here by 0.02). Then the success values of the individual are standardized to 1 in total.

Assuming that individual 4 of the gene (2) one after the simulation has achieved a much better objective function value than the other Indi viduen, the "Select" will now select this more often (here even 4x). This The individual emerged from the mutation from gene (1). That means that Mutate is more effective than the crossover. The mutate Operator therefore gets a higher probability of selection for education next generation gene (4).

In Fig. 10 in an overall view of the course of the process is of a Initialisierungsfahrplan via the described improved hydraulic simulation to the repeated application of the addressed operators of the genetic algorithm presented. In addition, corrective measures are indicated on the right, which allow volume corrections, level corrections, exclusion of prohibited areas of use of the machines, correction of power plant outflow gradients, schedule stabilization and the like in the manner already described. Using a new application of the improved simulation model or the use of weighted work and a sum of penalties, a target function is determined which is compared with the corresponding target functions of other generations or individuals. The optimization is expediently ended when the target function value of the best individual no longer improves over a predetermined number of generations, or when a predefinable number of generations has been reached overall.

Claims (17)

1. Method for determining the performance of power plants in a swell chain, the level curves in the reservoir and the turbine output being determined by means of the storage space content curve and the underwater consumption curve, from which the turbine output is determined by the head and flow, characterized in that Q t | zu zu zu , the discharge Q t | ab as well as a possibly small intermediate feeder Z t | kl, two independent, location-based volume balances for the headwater level and the underwater level are used for the calculation of the level curves, in which inflow and outflow changes are delayed with the fictitious wedge volume that might come behind the change are taken into account. 2. The method according to claim 1, characterized in that in the case of larger, variable intermediate feeders Z ^t, the respective storage space is divided into corresponding partial storage spaces. 3. The method according to claim 2, characterized in that for everyone Time step and level a fictitious, stationary state of the total storage space by a total volume V t | 1 + V t | 2 and storage space flows per partial storage space Q t | 1 and Q t | 2 is defined. 4. The method according to claim 2, characterized in that the partial storage spaces are considered arithmetically by a compensating flow Q _A as connected and the local volumes and flows of the partial storage spaces are otherwise determined independently of each other. 5. The method according to one or more of claims 1 to 4, characterized characterized in that the storage spaces are chained in such a way that for the Calculation of the head or the power in the assigned power plant Difference between the upper water and the lower in the storage space localized underwater level is formed, and the upper  water level with the help of the location-based volume balance and the discharge as well the underwater level, taking into account the local volume applicable there balance and the inflow can be determined. 6. The method according to claim 5, characterized in that he so averaged performance values at least as part of the objective function of an opti Power plant inserts of the swell chain can be used. 7. The method according to claim 6, characterized in that for opti a genetic algorithm is used in which the first Ge generation of individuals from copies of one based on their power plant or Storage drains post-simulated starting solution is formed, each Individual consists of a number of genes, each of which is the condition of the power plant in a certain time step, and in which from a number of operators one acts on an individual and in a certain way changes the power plant outflows of this individual, after which the target function value is determined for each individual of the generation and the individuals with better objective function value are more likely to be transferred to the next generation. 8. The method according to claim 7, characterized in that before the Determination of the target function values regarding the power plant outflows integral volume constraint, which says that given a variable Intermediate feeder, as well as start and end volume the sum of all outflows each storage space must be constant in the planning period, be corrected. 9. The method according to claim 7 or 8, characterized in that before the Determination of the target function values regarding the power plant outflows given limits, e.g. B. regarding storage volume, headwater level, discharge gradients, etc., checked and corrected if necessary. 10. The method according to any one of claims 7 to 9, characterized in that the execution of the genetic algorithm is ended when the Target function value of the best individual over a predetermined number of  Generations no longer improved, or if overall a predefinable one Number of generations is reached. 11. The method according to one or more of claims 7 to 10, characterized characterized in that for each individual of a generation in addition to the the genes representing the power plant states a success value per operator is used, which provides information about how successful the individual Operators in previous generations have been applied to an individual and according to which previously more successful operators also used to form the next most generation are preferred. 12. The method according to one or more of claims 7 to 11, characterized characterized in that as a starting solution with a simplified hydrau Model of the swell chain using a power plant deployment plan calculated using LP / MIP is used. 13. The method according to one or more of claims 7 to 12, characterized characterized in that the objective function is a combination of weighted work and a sum of penalties is used, the weighted work out the total work generated per time step by multiplying by one user-defined weight factor is determined and by means of the penalties predefined, undesirable operating conditions are disadvantaged. 14. The method according to claim 13, characterized in that when changed the power plant outflows of only a few power plants in the course of the optimization the objective function is only partially limited to the changed area is newly determined. 15. The method according to one or more of claims 7 to 14, characterized characterized in that when a block mutate operator acts on the opti randomly from the total number of power plants in the swell chain first selected and selected for this and for all downstream of the first power plant up to a randomly selected second the power plant two random time intervals are set in which then  the power plant outflows averaged and randomly past within one certain limits selected value are shifted so that the Volume balance remains unchanged. 16. The method according to one or more of claims 7 to 15, characterized characterized in that when a crossover operator acts on the opti two old generation individuals and one of the power plants Be chosen at random that in both selected individuals, the beginning of each of an interval at random and the end is determined so that the total amount of water to be delivered by this power plant remains unchanged that then the state vectors are exchanged at both intervals that a second power plant is chosen at random and for everyone between that first selected and this second lying power plants such crossover operator is used, the same inter valle are used offset by the running time of the respective power plant, and that the two new individuals thus created entered the next generation be copied. 17. The method according to one or more of claims 7 to 16, characterized characterized in that when a rotate operator acts in the optimization a first power plant and two associated ones that define an interval Times are chosen at random that the power plant outflows this Intervals then ver by a randomly selected number of time steps be pushed, with the overwritten power plant outflows at the beginning of the interval to be reclassified that a second power plant by chance selected and for everyone lying between this and the first selected Power station also uses a rotate operator, with the intervals to be offset by the duration of the respective power plant.