DE112012003487T5 - System and method for optimizing the operation of a water network - Google Patents

Abstract

A system for optimizing the operation of a water network, comprising at least one data storage unit (23) for storing a hydraulic model and at least one operating restriction of the water network (17), the hydraulic model determining the dependence of pressure levels and currents in the water network on an operating state of at least one actuating unit (20) of the water network and an expected water demand, at least one processing unit including an optimization unit (OP), wherein the optimization unit is adapted to create at least operating configuration information for the at least one actuator by minimizing an objective function of an optimization problem, the optimization problem based on the hydraulic model, at least one output interface (18) for providing the at least one operating configuration information for the at least one actuator. In order for the water network to be operated with a lowered lower water level limit of a water storage facility, the at least one processing unit also includes a scenario generation unit (SG) for creating a finite set of scenarios in the form of possible realizations of the expected water demand over time and / or operating condition and or features of the at least one actuator and / or the at least one parameter of the hydraulic model, wherein the finite set of scenarios is based on probability information about the uncertainty of those variables. The optimization unit is adapted to minimize the objective function of the optimization problem by performing stochastic optimization, the optimization problem further including the objective function of representing at least one undesirable side effect of the operation of the at least one actuator, the at least one operational constraint, and the finite set of scenarios.

Description

The invention relates to a system and a method for optimizing the operation of a water transport and / or distribution network, also referred to below as water network. The system comprises at least one data storage unit for storing a hydraulic model and at least one operating restriction of the water network, the hydraulic model representing the dependence of the pressure levels and flows in the water network on an operating state of at least one actuating unit of the water network and on an expected water requirement, at least one processing unit comprising an optimization unit wherein the optimization unit is adapted to create at least one operation configuration information for the at least one actuator by minimizing an objective function of an optimization problem, the optimization problem being based on the hydraulic model, and at least one output interface for providing the at least one operation configuration information for the at least one adjusting unit. The steps performed by the above system elements define the corresponding method.

As energy prices continue to rise, more and more water utilities are reviewing the operating strategy of their energy-intensive water transport and / or distribution networks to reduce energy and operating costs. While a water distribution network transports water from a source of water to various industrial and / or private water consumers, a water transport network transports water over long distances of several hundred kilometers, for example from a seawater desalination plant to one or more water distribution networks. When operating these water networks, there is the possibility of significant improvements in operating efficiency. The replacement or overhaul of energy-consuming actuators in the water network, z. As pumps, is a possibility that is already being implemented most often today. The other possibility is to optimize the interaction between the various actuators and the entire operating strategy of the entire network.

The upper diagram in 1a shows a method of operating a water network as it is currently underway: Water supply facilities try to adjust the network planning so that the water levels 1 in the water storage facilities, also referred to as water storage head, between the upper limits 2 and the lower limits 3 being held. The upper and lower limits are in 1a shown as dashed lines. The change of the water level 1 between these limits is controlled depending on the water consumption in the network by configuration of the pump system and by a direct connection of the water storage level with the pump control system: when the water level approaches the lower limit, pumps are automatically switched on to increase the water storage level. When the water level is high enough, pumps will shut off. The number of pumps that is switched on at the same time is in the lower diagram in 1a shown.

Thus, current operating procedures focus on maintaining water levels in reservoirs to meet customer demand at all times, but customer demand is subject to uncertainties. To cope with this uncertainty in demand, water supply facilities artificially set higher limits for reservoir pressure head limits in the reservoirs, up to 80% of the fill capacity, to maintain high water levels in the reservoirs. In this way, there is enough water in the storage facilities to meet the demand, even if there are unexpected changes in demand. However, this approach leads to an increase in operating costs due to the required higher pumping capacity.

In addition, this approach disregards possible advantages of a temporal shift of the filling operations, z. When power rates are low, or operating pumps to transport the water through the network at a reduced rate or with the highest efficiency, which can be achieved by adding water to storage devices such as storage devices. As storage tanks, is stored when it is not needed.

In general, the optimization of a water network is the determination of operating information that must be taken into account when subsequently generating the control signals for at least one of the network's actuators, the actuators typically including pumps, valves within the network, and actuators to control the flow to and / or effluent from water reservoirs and for controlling one or more source streams of the water network. The operating information for the actuators shall be determined in such a way as to minimize network operating costs such as energy consumption while respecting the water demand, minimum and / or maximum pressure or flow height in the water pipes of the network and other operational limitations of the water network.

Methods for optimizing the operation of water distribution networks are in the WO2011 / 092012 A2 and in "Combined Energy and Pressure Management in Water Distribution Systems" by P. Skworcow et al., Proc. World Environ- mental and Water Resources Congress, 2009, Great Rivers, pp. 709-718, and in "Optimization Models for Operative Planning in Drinking Water Networks" by J. Burgschweiger et al., ZIB Report 04-48, Konrad-Zuse. Center for Information Technology, Berlin (2004). These optimization methods are based on deterministic hydraulic models or specially adapted deterministic models that map the physical properties of water distribution networks. Based on these models, optimization algorithms are used to provide optimized actuator operating schedules and parameters over a particular, time horizon, e.g. 24 hours, taking into account changes in energy tariffs, time-varying demand and possible storage capacities over this time horizon. Taking the full optimization horizon into account, full utilization of storage capacity of the water network can be used to postpone pumping or energy-intensive operations in times of low energy rates and operate pumps at energy-efficient speeds, even if the demand is higher than the amount of pumped water.

Unfortunately, the operation of water networks is extremely complex and affected by many uncertainties. Uncertainties are, for example, varying water requirements over time and changing parameters, such. Pump efficiency or differences between the water network model and the real process. The uncertainties in demand make a prediction necessary for the optimal actuator schedules, e.g. As for pumps, valves, storage tanks, sources, is necessary, difficult and affect the quality of the optimization results. In fact, uncertainties can even lead to unworkability or undesirable system behavior.

The left diagram in 1b shows an example of a predicted water demand trend 5 which was forecasted at 0h00 for the next 24 hours. The predicted water demand trend 5 is the darker of the two curves with solid lines. The right diagram in 1b shows the resulting optimized water level trend 6 in a water storage device, in particular a water tank, as it is for the predicted water requirement 5 is expected when using optimized actuator schedules calculated at 0h00 for the next 24 hours. This is again the darker of the two curves with solid lines. The optimization of the actuator schedules is based in the example 1b on known deterministic optimization algorithms. In the event that the real need varies and is different from the predicted - which is very likely to happen at a time, e.g. B. due to increased outdoor temperatures or due to sporting events in which water is consumed, the lower or upper limit of the water storage tank can be under or exceeded. The lower and upper limits of the water level in the water tank are in the right diagram in 1b represented by dashed lines. In the example off 1b Optimized actuator schedules will be at 0h00 for the predicted demand curve 5 calculated and applied for the next 24 hours. The lighter of the two curves in the left diagram in 1b illustrates the need for demand realization in reality 6 , As you can see, the need is in reality 6 about 6 hours longer than the expected demand 5 , between about 6h00 and noon. Consequently, the real water level falls below 8th in the water storage facility, the acceptable lower limit. If this undershoot is too great, the pressure may be too low, at least in parts of the water network. A mechanism to avoid falling below the lower limit, eg. B. by automatically switching on a pump in the water storage device, can be integrated into the optimization algorithm, but could possibly lead to low energy savings. In the worst case, this could even lead to higher energy consumption than without optimization. In general, an undershoot under the optimization algorithm must be allowed to feasibly solve the optimization problem. To take this into account, the introduction of a relaxation of the lower limits is known. This is done by introducing slip variables. To compensate, they are penalized in the objective function to be optimized in order to avoid their use. However, it often happens that the optimal deterministic solution requires falling below the lower water level limit when considering an arbitrary demand. Most of the time, this is not controllable before, since using a deterministic model, it is not possible to predict how far below the limit will be.

To overcome this situation, existing solutions interacting with a control system or SCADA system collect real-time network operating data and recalculate optimized actuator schedules or alarm limit settings to accommodate the new network situation , The recalculation is based on a periodic schedule, eg. B. every hour, or based on events such. As the violation of lower or upper limits. In the solution formulation of the optimization algorithms, large safety margins are included in order to optimize the parameters in such a way that these problems are overcome and at any time, even with oneself changing conditions, a supply of customer needs is ensured. This again leads to a more conservative approach to how the water network is run and operated. In the case of event-based recalculations, recalculations may become necessary relatively often, resulting in frequent corrections of the actuator timings and thus significant actuator activity. Ultimately, the energy savings can be lower than in the optimization described above without any adaptation to the grid situation.

Deterministic modeling strategies have the disadvantage that they can take into account model uncertainties and operational uncertainties only very limited. This can lead to impracticability or unwanted optimization solutions when implemented in the real world.

It is an object of the present invention to provide a system and method for optimizing the operation of a water network that overcomes the conservative approaches described above to avoid the artificially high limits for water levels in the storage devices; H. in particular, to lower the lower water level while at the same time reducing the risk of the water running out.

According to the invention, the at least one processing unit further comprises a scenario creation unit for creating a finite set of scenarios in the form of possible implementations of the expected water demand over time and / or the operating state of the at least one actuator and / or the at least one parameter of the hydraulic model the finite set of scenarios is based on probability information about the uncertainty of the expected water demand, the operating state or the at least one parameter, and the optimization unit is adapted to minimize an objective function of the optimization problem by performing stochastic optimization, the optimization problem being the objective function for display at least an undesirable side effect of the operation of the at least one actuator, the at least one operational constraint and the finite set of scenarios in the form of a scenario-based optimization model.

According to the invention, the optimization problem is formulated and solved by directly taking into account describable model and operational uncertainties, thereby ensuring that defined limits and demand values are met. This also provides an overall more cost-effective solution than using a deterministic model as a basis. In particular, since it can be ensured that the lower water level limit of a water storage device is not far below, the lower water level limit can be safely set to a low value.

• • gemessene Signale, insbesondere Eingaben oder Störungen im Hydraulikmodell, wie z. B. Wasserbedarf,
• • Betriebszustand und/oder Merkmale der Stelleinheiten, wie z. B. Effizienzkurven, z. B. Pumpeneffizienzkurven, und
• • Modellparameter, z. B. Rohrrauigkeitskoeffizienten.

The uncertainties are described for one of the following:

• • measured signals, in particular inputs or faults in the hydraulic model, such as: B. water demand,
• • Operating status and / or features of the actuators, such as B. efficiency curves, z. B. pump efficiency curves, and
• • Model parameters, eg B. pipe roughness coefficients.

Further uncertainties can be defined. For example, if further input information of the optimization problem, such. Electricity tariffs or water source costs not previously known for the next optimization time horizon, which in the example described below is 24 hours, such information may also be included in the form of uncertainties rather than additional deterministic inputs to the optimization problem.

In a first embodiment of the invention, the scenario generation unit is adapted to apply a subsequent scenario reduction technique to bundle similar scenarios and thus reduce computational effort for the optimization unit during processing of the resulting scenario-based optimization models. In another embodiment, the scenario generation unit is adapted to create the finite set of scenarios by forming a top scenario and a subset that define the range of possible implementations over time for at least one of the above values or parameters that are subject to uncertainty , This is a very simple approach for cases where there is little information about uncertainties and probabilities.

In a specific embodiment, the scenario generation unit is adapted to represent the uncertainties through a stochastic process, where each stochastic process is performed on a single stochastic process underlying continuous probability space over a time horizon of limited duration, thereby generating an explicit representation of the uncertainties.

In another embodiment, the scenario generation unit is adapted to create the finite set of scenarios by deriving the uncertainties of measurement data from the water network. Alternatively, uncertainty data may be read from a memory unit or entered by an operator into the system and thus into the scenario generation unit.

The scenario builder may also be adapted to provide the finite set of scenarios in the form of a graphical tree scenario tree. The scenario tree may then be further customized by a user before being used to create the optimizer optimization problem.

In a specific embodiment, the target function reflects the resulting energy consumption and / or the water flow from a source when the at least one actuator is in operation.

In this particular embodiment, the optimization unit may be further adapted to take into account changing energy and water tariffs from the source.

In another embodiment, the optimization problem is formulated as a limited discretization of a scenario based on a stochastic two-stage programming model.

The hydraulic model may be based on a description of the topology of the water network comprising a node set and an edge set, the node set consisting of storage nodes, water demand nodes, and source nodes, and wherein the marginal set represents water pipes, pumps, and valves.

In this case, the hydraulic model is then formed by state equations representing the dependence of the time dependent state of the water network on the at least one operating configuration information of the at least one actuator and the expected water demand, and wherein the time dependent state of pressure levels in the nodes of the node set and currents at the edges the marginal amount exists.

In order to explicitly consider the change of a lower water level limit of a water storage device, the at least one processing unit may further comprise a water level setting unit adapted to adjust a dependency between lowering the lower water level limit and an extent at which the at least one side effect is reduced the at least one operational constraint is met, and to provide as further input to the optimization problem for the optimization unit.

In addition, the water level configuration unit can be adapted to a dependency between the reduction of the unwanted side effect and a risk that the water storage device reaches a critical water level, wherein the critical water level can indicate that the water storage device is about to dry out, or that they have a water level reached, which is no longer sufficient to provide sufficient pressure for the transport of water through the water pipes, estimate and provide as further input to the optimization problem for the optimization unit.

In another specific embodiment, the scenario generation unit is adapted to provide the finite set of scenarios for a decision support unit, the decision support unit adapted to estimate a corresponding impact on the water network for an identified potential cause of a defect in the water network, the finite amount of Scenarios is considered.

The invention and its embodiments will be more apparent from the following examples taken in conjunction with the accompanying drawings, in which:

1a , b are operational diagrams of water storage devices known in the art,

2 Scenario tree for a parameter P,

3 Uncertainties of a parameter M, whose model was created using three scenarios,

4 a system for optimizing the operation of a water network,

5 a comparison between an optimization without and one with uncertainties in a model,

6 Examples of outputs created by a water level adjustment unit.

As explained above, the main idea of the invention is the following: Instead of formulating only one optimization problem, as is done with deterministic model approaches, the uncertainties in the various parameters of the hydraulic model of the water network become a finite set of possible implementations of a respective parameter P in the course time, resulting in scenario-based optimization models. Each scenario represents a possible parameter realization over time, ie where at some point in the future a certain value for the respective parameter P with a specific probability ω ₁ ... ω _{r is} assumed, resulting in a so-called scenario tree as he is in 2 is shown.

Each path from the root to one of the leaves is consistent with a scenario. The nodes correspond to certain times t {0, ..., T}, at which decisions c (t) are made.

For example, the optimization problem can be solved by using two-step stochastic programming (2SSP) techniques.

In many situations, only incomplete information about the underlying probability distribution is available. Scenario creation is then usually based on the use of historical data that is applied to estimation, simulation, and sampling techniques or includes the knowledge of an experienced network operator.

The computational burden of solving scenario-based optimization models depends heavily on the number of scenarios in the model. Therefore, a tradeoff must be made between the accuracy of the approximation and the model size, which increases exponentially with the number of scenarios. The use of special scenario reduction methods helps to reduce the computation time. An embodiment of the invention is therefore based on the idea of reducing the number of nodes in the scenario tree by bundling similar scenarios. In the extreme case, the finite set of possible parameter realizations, i. H. the finite set of scenarios, for example, reduced to only two scenarios, a sub-scenario and an upper scenario, where each of the two scenarios or curves represents the one curve from the lower and upper half of all curves with the highest probability.

The consideration of uncertainties in the formulation of the optimization problem leads to more robust operation configuration information for the at least one actuator since inefficiencies can be more easily avoided. On a longer term basis, it also leads to higher cost savings as the safety margins of the upper and lower limits of the water levels that are required today due to deterministic problem formulations can be reduced.

• • ein Stellantrieb-Zeitplan in Form einer zeitlichen Abfolge von Betriebszuständen der zumindest einen Stelleinheit oder
• • eine Verweistabelle für Betriebsanweisungen für die Erzeugung eines Steuersignals für die zumindest eine Stelleinheit, wobei die Betriebsanweisungen in Abhängigkeit vom aktuellen Zeitpunkt und/oder aktuellen Zustand des Wassernetzes definiert werden, oder
• • eine Menge von Parametern, einschließlich beispielsweise Mindest- und/oder Höchstwerten für die Steuersignale, die für die zumindest eine Stelleinheit erzeugt werden sollen.

The operation configuration information for the at least one actuator may be one of the following:

• An actuator schedule in the form of a chronological sequence of operating states of the at least one actuator or
• A reference table for operating instructions for the generation of a control signal for the at least one actuating unit, wherein the operating instructions are defined as a function of the current time and / or current status of the water network, or
• A set of parameters including, for example, minimum and / or maximum values for the control signals to be generated for the at least one actuator.

An example of a stochastic approach to optimizing a water network under uncertainties will now be described in greater detail for the example of modeling the uncertainty in water demand.

The first step is to create a model of the water network structure and dynamics.

The task of water supply systems is the transport and distribution of the required amount of water in the necessary quality at the right time to particular consumers or storage or water treatment facilities. Raw water is at sources such. As groundwater or surface water such as rivers or lakes, fed into the network. If necessary, the raw water is subjected to a chemical treatment. Thereafter, the clean water is either stored in small storage facilities located directly at the sources or pumped into the network. Pumps pass the water through pipes by raising the head at certain points to overcome differences in altitude and to compensate for pressure drop in pipes caused by friction losses. The number of individual pumps that are turned on in a pumping station is described by a discrete decision variable. It can be any integer value between the lower limit zero and the upper limit defined by the maximum number of pumps in the pump station. Valves are network elements for controlling flows and pressure levels. They can be throttled to different extents to control the movement of water through pipes. Special attention must be paid to the storage devices because they are the only network elements that provide a buffer between network inflow and outflow. They decouple different sections of water network and make the system flexible, allowing various possible operating strategies to be implemented.

The topology of the water network is described by a graph G = (N, E), where N stands for a node set and E for an edge set. The node set N = N _rn ⋃ N _cn ⋃ N _dn ⋃ N _sn consists of storage node N _rn , connection node N _cn , water demand node N _dn and source node N _sn , and the margin set E = E _pi ⋃ E _pu ⋃ E _va includes or represents water pipes (E _pi ), pumps (E _pu ) and valves (E _va ) is.

The physical, dependent on the time t state y (t) of the network consists of pressure levels in the nodes and currents at the edges. The state y (t) satisfies a system of differential algebraic equations (DAEs) comprising Kirchhoff-type conservation laws, non-linear pressure-altitude flow relationships of pumps, valves and pipes, and the rate of change of water storage heights in the storage devices due to currents ,

The differential algebraic equations are affected by the control and decision variables c (t), some of which are integral and which represent the network operating configuration for the pumps, the valves and the source current, i. H. the operating configuration information for the actuators, in particular the actuator schedules. In addition, the water demand ξ (t) determines the outflow from the system.

Formally, the equations of state F, ie the system of DAEs, can be considered as F (c (t), y (t), ý (t), ξ (t)) = 0, ∀t ∈ [0, T] (1) where ý (t) is the first time derivative of the network state y (t).

The formulation of the optimization problem includes the objective function Φ, the equations of state F, and the operational constraints G, some of which are simple limits.

The objective function Φ = (Φ _pu + Φ _sn ), which is to be minimized, consists of operating costs, such. Pump energy costs Φ _pu and source current costs Φ _sn occurring during the time horizon T.

The restrictions G limit the state of the system to its practical operating range, for example the requirement that the pumps operate in the physical range of a positive pressure increase.

wobei gilt: F(c(t), y(t), ý(t), ξ(t)) = 0, ∀t ∈ [0, T] Zustandsgleichung (3) und G(c(t), y(t)) ≤ 0, ∀t ∈ [0, T] Einschränkungen (4). The operational planning problem and thus the optimization problem is then

where: F (c (t), y (t), ý (t), ξ (t)) = 0, ∀t ∈ [0, T] Equation of state (3) and G (c (t), y (t)) ≤0, ∀t ∈ [0, T] Restrictions (4).

The optimal solution for the decision variable c (t) is the answer that the user, i. H. the water supply company, in the real technical system must implement.

In general, the DAE system is discretized on a fixed time scale, and the control and decision variables c (t) are chosen to be piecewise constant, turning the optimization problem into a dynamic mixed integer nonlinear programming (MINLP) problem.

The mixed-integer component is due to the coexistence of continuous and discrete pump variables. The nonlinear part includes the objective function and the pressure head-flow relationships. Depending on the numerical solver and the underlying algorithm, smooth functions are highly desirable, especially when using derivative-based optimization techniques.

The current practice of water network operations planning is to solve the fixed-demand optimization problem ξ (t), usually the expected demand, which makes the optimization deterministic.

According to the invention, a stochastic optimization is instead used, which makes it possible to take into account model and demand uncertainties. In general, a common practice for correcting random disturbances in dynamic processes is the application of a so-called moving horizon. Provided probability information about the uncertainty data is available, stochastic models go one step further by explicitly including this stochastic information in future events. The decision making process becomes predictable rather than just reacting to past water demand realizations. Therefore, a stochastic process is required that describes the random water demand events as they occur within their likelihood. The stochastic process for the random water demand ξ = ξ _t with t ∈ [0, T] is defined on a certain underlying continuous probability range, which is inter alia a function of the set of equations of state F and a probability distribution P described above Duration of the time horizon is.

Of course, the explicit representation of an uncertainty through a stochastic process leads to the extraction of information over time. This additional model information increases the complexity of the optimization model, resulting in large stochastic programs. Most solution methods for such comprehensive programs are based on the approximation by a time-discrete stochastic process, where ξ _{t takes} values in R ^s (for t ∈ {0, ... T}), where s: = | N _dn | stands for the number of demand nodes. The stochastic variables ξ _t are observed directly before time t, and ξ ₀ is assumed to be t = 0. Thus, the time-discrete stochastic process is a collection of random variables ξ = (ξ ₀ , ..., ξ _T ) in R ^sT .

auf, unter der Annahme, dass eines der Szenarien in der Realität stattfinden wird.In order to obtain a numerically easy-to-implement optimization problem, uncertainty regarding water demand is modeled as a finite set of possible demand realizations over time, resulting in scenario-based optimization models. This means that a discrete approximation of the underlying probability distribution is considered, which is given by a finite probability domain, which among other things is a function of special scenarios ω _j with j = 1, ..., r. Each scenario represents a possible water demand realization of the future and occurs with a probability of π _wj ≥ 0. Overall, the model scenarios show

on, assuming that one of the scenarios will take place in reality.

All scenarios of the model Ω = {ω ₁ ,..., Ω _r } can be represented in the form of a scenario tree as shown in 2 is shown. Each path from the root to one of the leaves is consistent with a scenario. The nodes correspond to particular times t ∈ {0, ..., T}, at which decisions c (t) are made, ie when certain actuator actions are performed. The margins show the uncertain water demand variables. The scenario tree branches for every requirement realization of the model at every t ∈ {0, ..., T}. In order to comply with the notation of the stochastic process ε, each scenario ω _j ∈ Ω marks a possible water demand _realization ξ _ωj = (ξ _ωj1 , ξ _ωjT ), where ξ _{ωjk stands} for the jth scenario for the period k.

Since the results of the real underlying problem are of great interest, creating such a scenario tree is an important task. The main goal is to properly represent the underlying probability distribution of ξ because the optimal and optimal solutions depend on the scenarios selected. For many applications, incomplete information about the underlying probability distribution is available. Scenario creation is then usually based on the use of historical data that is applied to estimation, simulation, and sampling techniques or includes the knowledge of an experienced network operator.

In general, four different approximation modes for the real probability distribution P can be distinguished by a finite set of scenarios in terms of the level of information available: full knowledge of P, known parameter family, sample information and low level of information. If only a small amount of information is available based on observational data, the creation of a top and a bottom scenario shows typical samples as found in 3 are shown. The upper scenario 10 and the sub-scenario 11 then define the range of possible demand realizations and provide limits to the optimal value of the optimization problem. In addition, an expected value scenario, with 9 be created, which may be the scenario with the highest probability currently.

The computational burden of solving scenario-based optimization models depends heavily on the number of scenarios in the model. Therefore, a tradeoff must be made between the accuracy of the approximation and the model size, which increases exponentially with the number of scenarios. Frequently, special scenario reduction techniques are used while still providing appropriate approximations. These methods are based on the application of a subsequent scenario reduction.

The goal is to reduce the number of nodes in the scenario tree by bundling similar scenarios. The reduced trees and the original tree are then compared by a certain probability distance metric. New probabilities are then assigned to the reduced tree so that the new probability measure is closest to the initial distribution according to a metric of the natural distance.

Another important fact is based on the robustness of the optimal target value and the optimal solution with regard to the scenarios used. Robustness is desired, d. H. Small perturbations of the scenarios and the corresponding probabilities should lead to very small changes in the optimal target value and the optimal solution.

As described above, it is envisioned that probability information on the uncertainty of water demand will be available and that stochastic optimization techniques may be used to exploit it. The stochastic optimization problem then serves to minimize an objective function which, in particular, accounts for expected operating costs, subject to the minimization of the requirement that the obtained operating configuration information for the actuators be available for all water demand implementations.

As discussed above, the uncertainty in water demand is modeled as a finite set of possible demand realizations, resulting in so-called scenario-based optimization models to obtain a numerically easy to implement optimization problem.

In addition to considering the uncertain demand structure as described above, a two-step programming (2SSP) method takes advantage of the fact that only a portion of the decisions that are the here-and-now decisions x are so-called first-stage decisions , must be taken before the need can be observed. This is known as non-anticipatory.

The remaining tax variables, the relief actions z, so-called decisions of the second stage, need to be fixed at a later date, if a part of the needs has already been observed.

In general, this leads to stochastic multi-stage programming. Here we restrict attention to the more optimistic two-step approach, where the choice of remedies z is based on full knowledge of demand realization ξ.

wobei gilt: F(x(t), z(t, ξ_t(ω_j))) = 0, ∀t ∈ [0, T], ∀ω_j ∈ Ω Modellgleichheiten (6), G(x(t), z(t, ξ_t(ω_j))) ≤ 0, ∀t ∈ [0, T], ∀ω_j ∈ Ω Modellungleichheiten (7), a ≤ (x(t), z(t, ξ_t(ω_j))) ≤ A, ∀t ∈ [0, T], ∀ω_j ∈ Ω variable Grenzen (8), wobei

Φ_2SSP

die zu minimierende Zielfunktion ist,

Φ_pu

die Energieverbrauchskosten in der Pumpenstation pu sind und

Φ_sn

die Quellstromkosten sind.

In the following, we will denote the variables of the 1st and 2nd stages with x (t) and z (t, ξ _t (ω)). A scenario-based optimization problem in the form of a 2SSP model formulation, in which the auxiliary action is defined from the time t ~ ∈ (0, T), is as follows:

where: F (x (t), z (t, ξ _t (ω _j ))) = 0, ∀t ∈ [0, T], ∀ω _j ∈ Ω model equations (6), G (x (t), z (t, ξ _t (ω _j ))) ≤ 0, ∀t ∈ [0, T], ∀ω _j ∈ Ω model inequalities (7), a ≤ (x (t), z (t, ξ _t (ω _j ))) ≤ A, ∀t ∈ [0, T], ∀ω _j ∈ Ω variable boundaries (8), in which

Φ _2SSP

the objective function to be minimized is

Φ _pu

the energy consumption costs in the pump station are pu and

Φ _sn

the source electricity costs are.

The energy consumption costs Φ _pu take into account, among other things, the pump efficiency. The pumps convert electrical energy into mechanical energy of water. Pump efficiency, called wire-to-water efficiency, describes the efficiency of this conversion. It increases with the flow rate through the pump to some point, called peak efficiency, and then decreases with increasing flow rate.

The source electricity costs Φ _sn reflect the cost of providing water from the water sources, e.g. B. water treatment facilities, desalination plants or water reservoirs.

Other costs which can be taken into account in the objective function Φ _2SSP are so-called penalty costs for violations of the boundary conditions in the water reservoirs.

The term cost is not just monetary, but is also used to generally represent the level of undesirable side effects that should be minimized. These undesirable side effects are generally related to the operation of the actuators as each actuation action results in at least one of the generation of too much noise or carbon dioxide, the use of too much electrical energy, the increase in the amount of expensive water flowing from a reservoir in the network is pumped, or the achievement of an undesirable frequency and / or amplitude of the control operation itself leads. All of these and other undesirable side effects can be modeled in the objective function and thus in the optimization problem and are then avoided as much as possible due to the minimization of this objective function.

Due to the finite discretization of the underlying stochastic process, equations (5) to (8) take the form of a deterministic optimization model. Therefore, it is also called the corresponding deterministic equivalent of the 2SSP problem. The advantages of the deterministic equivalent are better numerical handling by avoiding probability integrals.

Based on the example of a water network 17 as it is in 4 As shown, 2SSP leads to more cost-effective and robust water supply while providing security of water supply. The water network off 4 consists of water pipes which connect the following operating elements: Sources S, from which water flows into the network, Consumption Units C, where the water leaves the network, pumps 20 to increase the head at certain positions, to level differences to overcome and pressure drop decreases in the pipes, water storage facilities, such. B. water reservoirs or tanks 21 to balance to provide a buffer between network inflow and outflow and to decouple different water network sections, and different types of valves, as by the remaining elements in the network 17 to control the movement of water through the tubes to control flows and pressure levels by throttling the valves to varying degrees.

To determine the potential benefit of solving a stochastic problem over solving a corresponding deterministic problem in which the expected demand replaces the unsafe need, the value of the stochastic solution (VSS) is used. The VSS is a fitting feature because it indicates how well the optimal solution of a 2SSP model works in comparison to the optimal deterministic solution embedded in a framework with uncertain needs.

The structure of 2SSP models ensures that the first-level decisions are only viable if there is a feasible remedial action for each demand scenario presented. This means that the variables of the first level are calculated in order to make the model feasible in the long term, so that the optimal water storage water levels lie between the predefined limits. This keeps the water levels in 2SSP under control.

This is from the right side of the 5 can be seen which the expected water storage level 14 and the resulting real water storage level 15 for the stochastic optimization of the 2SSP model of the water network described above. Both the expected and the resulting real water storage level 12 and 13 lie between the upper and lower water level limits, which are shown as dashed lines. Further random assertion attempts confirmed the feasibility of 2SSP, allowing for lower water storage levels in the storage facilities. As a result, fewer pumps are required, resulting in additional cost savings.

On the other hand, the corresponding model, which is based on an expected and not an uncertain demand value, is unworkable, indicating that an optimal deterministic schedule for an expected demand for real needs is not necessarily optimal or even feasible. In order to make the water nets feasible, slippage variables had to be introduced, and in response to a sudden increase in water demand, even falling below the lower water level had to be accepted, such as the expected water storage level 12 and the resulting real water storage level 13 on the left in 5 is apparent.

In general, it has been determined that the optimum target values Φ _2SSP Φ _EEV , which further _{substantiates} the significance of stochastic optimization for water mains operation.

Another important aspect of the stochastic approach is the computational effort. The model size of the 2SSP models increases linearly with the number of scenarios, and the calculation time shows quadratic growth in terms of the number of scenarios. But even a rough approximation of the underlying probability distribution with few scenarios yields good results compared to deterministic optimization, with moderate increase in computational complexity. In addition, additional small perturbations of the demand scenarios in the model lead to a marginal difference in the optimal target values or in the optimal solution of the stochastic programs.

4 shows an example of a system 16 for the stochastic optimization of the operation of a water network. The system 16 includes an optimization unit OP for performing the above-described minimization of the objective function to generate at least one operation configuration information, in particular at least one actuator schedule, which is then output to a control system CS at the desired at least one actuator of the water network 17 via an output interface 18 to be applied. The actuators of the water network 17 are the pumps 20 to increase the pressure level at certain points within the network, the pumps and the valves of the water storage device 21 and the different types of valves within the network.

The system 16 also includes a scenario creation unit SG. The scenario generation unit SG is arranged to generate future water demand scenarios ω _j from water supply uncertainties derived from real data of the water network, ie historical measurement data MD comprising water demand measurement data. The measured data MD are in a memory unit 23 saved to the system 16 belongs. The storage unit 23 can either be a volatile data storage, for. B. a RAM, or a permanent data storage.

The scenarios are assumptions about future water demand, with expected water demand varying with time of day, day of the week or season. Accordingly, day-night fluctuations, higher water demands in the hot and sunny months of the year or due to mass events by the scenario creation unit SG can be taken into account. In addition, the scenario generation unit SG can take into account further information that implicitly influences the water demand, for example information about electricity tariffs ET and / or water source costs WSC stored in the storage unit 23 stored in memory or can be entered directly into the system by an operator. Other such additional information may include outdoor temperatures, weather forecasts, and mass public event information. For example, in addition to modeling water demand scenarios, the scenario generation unit SG may also create scenarios for the fluctuation of the efficiency of the water pump water networks. For this purpose, pump efficiency features may be present in the memory unit 23 stored and used by the scenario generation unit along with measurement data on the operation of the water pumps to include the future uncertainty in the water pump efficiency in the model.

The finite set of scenarios for the future water demand created by the scenario creation unit SG is then provided to the optimization unit OP where it is input to the optimization problem. The optimization problem also takes into account a hydraulic model F of the water network 17 (see equations (3) and (6)), at least one operational constraint G (see equations (4) and (7)) and at least one objective function Φ to represent an undesirable side effect U of the operation of the at least one. Actuator, which are included as example in the model as energy consumption costs Φ _pu and source electricity costs Φ _sn . Further, the optimization problem may even take into account variations in parameters on which at least one undesirable side effect depends, such as variations in electricity tariffs ET affecting energy consumption costs Φ _pu , and fluctuations in water source cost WSC tariffs that affect the source electricity costs Φ _sn . Accordingly, the optimization unit OP is adapted to the respective variations of the parameters from the memory unit 23 to obtain.

The scenarios can also be presented via a man-machine interface to an operator who can adapt them according to his experience.

In particular embodiments, the scenario generation unit SG is arranged to derive upper and lower scenarios and, if necessary, one or more further expected value scenarios. The scenario generation unit SG may be adapted to provide the water demand scenarios of a graphical display, for example in the form of a tree, as in FIG 2 , or in the form of a time-dependent graph showing the upper and lower scenarios as well as the expected value scenario, as in 3 , Shows, or to make visible in other suitable graphical form.

The system 16 Also includes a water level setting unit LA adapted to determine a dependency between a decrease in the lower water level limit of a water storage device and an extent to which the at least one undesirable side effect U is reduced while simultaneously maintaining the at least one operating restriction G Optimization unit OP as an updated operation constraint G for the optimization problem to provide a new value for the lower water level limit. An example of such a dependency is in 6 where energy savings are presented over a varying lower limit. The energy savings are actually a reversed unwanted effect U in the sense that the undesirable effect is the financial energy costs. The higher the energy costs, the lower the energy savings. The hatched area indicates a range in which none of the at least one operational constraint G is broken.

The water level setting unit LA may also be adapted to determine the new value for the lower water level by further taking into account the dependency between the unwanted side effect reduction U and a risk for the water storage device to reach a critical water level. An example of such a dependency is in 7 represented as a level of risk over energy savings. The higher the energy savings, the higher the risk of reaching the critical water level. Based on such a relationship, an optimum can be found at a level of risk that the operator of the water network is willing to carry.

The above dependencies can be determined in terms of functional relationships or tables or rule-based relationships.

Another element in the system 16 may be included is a decision support unit DS. The decision support unit DS receives the finite set of scenarios from the scenario creation unit SG and uses them as input to assess a corresponding impact of an identified potential cause of a defect in the water network 17 on the water network 17 ,

• a) Empfangen einer Defektbenachrichtigung, die auf ein Problem im Wassernetz 17 hinweist;
• b) Bestimmen einer Reihe von möglichen Ursachen für den gemeldeten Defekt aus der Defektbenachrichtigung;
• c) Bestimmen einer geschätzten Auswirkung für jede mögliche Ursache;
• d) Sammeln der geschätzten Auswirkungen für jede mögliche Ursache, um eine wichtige Angabe bezüglich des gemeldeten Defekts abzuleiten.

A method performed by the decision support unit may include the following steps:

• a) Receiving a defect notification that indicates a problem in the water network 17 points;
• b) determining a number of possible causes of the reported defect from the defect notification;
• c) determining an estimated impact for each possible cause;
• d) Collect the estimated effects for each possible cause to derive an important indication of the reported defect.

In this method, the step of determining an estimated impact for each possible cause includes a risk scenario with initial grid conditions and assumed future grid conditions of the water network, wherein the finite set of scenarios is used to represent the future grid conditions.

The output of the decision support unit DS, d. H. the indication of importance may then be used by the control system CS to determine how quickly to respond to the defect and / or to establish a priority or order in which to respond to a reported defect.

Claims (15)

System for optimizing the operation of a water network, comprising: at least one data storage unit ( 23 ) for storing a hydraulic model (F) and at least one operating restriction (G) of the water network, wherein the hydraulic model (F) the dependence of the pressure levels and currents in the water network ( 17 ) of an operating state of at least one actuating unit ( 20 ) of the water network ( 17 and at least one processing unit including an optimization unit (OP), wherein the optimization unit (OP) is adapted to provide at least one operation configuration information (c (t)) for the at least one Actuator ( 20 ) by minimizing an objective function (Φ) of an optimization problem, the optimization problem being based on the hydraulic model (F), at least one output interface ( 18 ) for providing the at least one operating configuration information (c (t)) for the at least one actuating unit ( 20 ), characterized in that • the at least one processing unit also includes a scenario generation unit (SG) for creating a finite set of scenarios (Ω) in the form of possible implementations of the expected water demand (ξ (t)) over time and / or operating condition and / or features of the at least one actuator and / or the at least one parameter of the hydraulic model (F), wherein the finite set of scenarios (Ω) relates to probability information about the uncertainty of the expected water demand, operating condition and / or characteristics of the at least one The optimization unit (OP) is adapted to minimize the objective function (Φ) of the optimization problem by performing stochastic optimization, the optimization problem also being the objective function (Φ) for representing at least one undesired one Side effect (U) of operation s of the at least one actuating unit which takes into account at least one operational restriction (G) and the finite set of scenarios (Ω). The system of claim 1, wherein the scenario generation unit (SG) is adapted to apply a subsequent scenario reduction technique to cluster similar scenarios (ω _j ). The system according to one of claims 1 or 2, wherein the scenario generation unit (SG) is adapted to calculate the finite set of scenarios (Ω) by forming an upper scenario ( 10 ) and a sub-scenario ( 11 ) that define the range of possible implementations over time. A system according to any one of the preceding claims, wherein the scenario generation unit (SG) is adapted to represent the uncertainties through a stochastic process (ξ _t ), each one stochastic process is defined on an underlying continuous probability space over a time horizon of limited duration. System according to one of the preceding claims, wherein the scenario creation unit (SG) is adapted to calculate the finite set of scenarios (Ω) by deriving the uncertainties of measured data (MD) from the water network ( 17 ) to create. System according to one of the preceding claims, wherein the scenario creation unit (SG) is adapted to calculate the finite set of scenarios (Ω) in the form of a scenario tree ( 22 ) for a graphical representation. A system according to any one of the preceding claims, wherein the objective function (Φ) is the. resulting energy consumption (Φ _pu ) and / or the flow of water from a source (Φ _sn ) reflected when the at least one actuator ( 20 ) is in operation. The system of claim 7, wherein the optimization unit (OP) is adapted to take into account changing energy (ET) and source (WSC) tariffs. A system according to any one of the preceding claims, wherein the objective function (Φ _2SSP ) is _formulated as a limited discretization of a scenario based on a stochastic two-stage programming model. System according to one of the preceding claims, wherein the hydraulic model (F) is based on a description of the topology of the water network ( 17 ), comprising a node set (N) and an edge set (E), the set of nodes consisting of storage nodes (N _rn ), connection nodes (N _cn ), water demand nodes (N _dn ), and source nodes (N _sn ), and wherein the marginal amount of water pipes ( E _pi ), pumps (E _pu ) and valves (E _va ) represents. The system according to claim 10, wherein the hydraulic model (F) is formed by equations of state which determine the dependence of the time-dependent state (y (t)) of the water network ( 17 ) of the operating state of the at least one actuating unit ( 20 ) and the expected water demand (ξ (t)) and where the time-dependent state consists of pressure levels in the nodes of the node set (N) and flows at the edges of the edge set (E). A system according to any one of the preceding claims, wherein the at least one processing unit further comprises a water level adjustment unit (LA) adapted to adjust a dependency between lowering a lower water level limit (LA). 3 ) a water storage device ( 21 ) and an extent to which the at least one undesired side effect (U) is reduced while at the same time maintaining the at least one operation restriction (G), and the optimization unit (OP) has a new value for the lower one as the updated operation restriction for the optimization problem Water level limit ( 3 ). The system of claim 12, wherein the water level adjustment unit (LA) is adapted to adjust the new value for the lower water level limit (LA). 3 ) by further determining a dependency between the reduction in the unwanted side effect (U) and a risk for the water storage device ( 21 ), to reach a critical water level. The system of any one of the preceding claims, wherein the scenario generation unit (SG) is adapted to provide the finite set of scenarios (Ω) to a decision support unit (DSU), wherein the decision support unit (DSU) is adapted to identify an identified potential cause of a defect in the water network ( 17 ) to assess a corresponding impact on the water network, taking into account the finite set of scenarios (Ω). Method for optimizing the operation of a water network, comprising the following steps: • storing a hydraulic model (F) and at least one operating restriction (G) of the water network ( 17 ), whereby the hydraulic model (F) shows the dependence of pressure levels and currents in the water network ( 17 ) of an operating state and / or features of at least one actuating unit ( 20 ) of the water network and an expected water demand (ξ (t)), Generating at least one operating configuration information item (c (t)) for the at least one setting unit ( 20 ) by minimizing an objective function (Φ) of an optimization problem, the optimization problem being based on the hydraulic model (F), providing the at least one operating configuration information (c (t)) for the at least one actuator ( 20 ), characterized by the following steps: • creating a finite set of scenarios (Ω) in the form of possible implementations of the expected water demand (ξ (t)) over time and / or operating condition and / or features of the at least one actuator and / or the at least one parameter of the hydraulic model (F), wherein the finite set of scenarios (Ω) on probability information on the uncertainty of the expected water demand, the operating state and / or features of the at least one actuator or the at least one parameter of the hydraulic model • minimizing the objective function (Φ) by performing a stochastic optimization, the optimization problem further comprising the objective function (Φ) for representing at least one undesirable side effect (U) of the operation of the at least one actuator ( 20 ), which takes into account at least one operational constraint (G) and the finite set of scenarios (Ω).

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