DE102004041661A1 - Pump stations and pumps control method in pipeline, involves total energy consumption of all pumps minimised at predetermined total flow and height - Google Patents

Abstract

The method is for the control of pump stations and pumps in a pipeline and involves the total energy consumption of all pumps minimised at a predetermined total flow and height. The pipeline has a pump station PS1 with one pump (1), a pump station (PS2) with three pumps (2,3,4) and a pump stastion (PS3) with two pumps (5,6). The first pump station is in flow direction connected via a pipeline segment (S12) with the second pump station, the second pump station is connected with the third pump station via a pipeline segment (S23) and the first pump station is connected via a pipeline segment (S1) with a first user (V1), which in turn is connected via a further pipeline segment (S2) with a further user (V2). The pump stations generally have several possible different pumps, producing via the users a regular and specific fluid quantity. Control is effected by the adjustment of the speed of the individual pumps and the pressure heights of the individual pump stations to be produced. An independent claim is also included for a computer program product.

Description

The The invention relates to a method for controlling a tree-like Arrangement with over Pipeline segments connected pumping stations with it Pumps, for example, through the pipeline, water, oil or a other liquid or another liquid mixture is pumped.

The The object underlying the invention is now a method to control pumping stations and pumps in such a pipeline specify such that thereby the total energy consumption of all pumps minimized at a given total flow and given heights becomes.

These The object is achieved by the features of claim 1 according to the invention. The further claims relate to advantageous embodiments of the method according to the invention and a corresponding computer program product.

The Invention consists essentially in a method for optimal Control of pumping stations and pumps in a pipeline, where the pump stations each comprise at least one pump and in the flow direction via pipeline segments each with at least one further pumping station or at least a consumer are connected in such a way that in the underlying Graphene does not create undirected circles, and control over the Setting the speeds of the individual pumps and the one to be generated pressure levels the individual pumping stations takes place, at first the energy demand of a pumping station dependent on of river and pressure altitude preferably is minimized and then the distribution of generating pressure levels on the individual pumping stations is done such that the entire energy needs all pumping stations possible becomes low.

following The invention will be explained in more detail with reference to an embodiment shown in the drawing.

In the drawing, for this purpose, a topology of a pipeline for conveying water is shown by way of example, wherein the pipeline pumping stations PS ₁ with a pump 1 , PS ₂ with pumps 2 .. 4 and PS ₃ with pumps 5 and 6 having. The pumping station PS ₁ is in the flow direction via a pipeline segment S12 with the pumping station PS ₂ , the pumping station PS ₂ via a pipeline segment S23 with the pumping station PS ₃ and the pumping station PS ₃ is in turn via a pipeline segment S1 with a first consumer V ₁ and this tapping point still connected via a further pipeline segment S2 with another consumer V ₂ . The pumping stations generally have several possibly different pumps and consumers consume a certain amount of water on a regular basis.

The Topology of the pipeline, at the node pumping stations, consumers, Feeders, branch points and edge segments are, must be one have acyclic structure.

For each Pipeline segment is given a plant characteristic that indicates how much pressure needs to be generated to allow some flow through this segment for pumping, this pressure, for example, in meters indicated is hereinafter always in connection with the pressure to be generated from the height to be produced is spoken. The plant characteristic not only takes into account the geodesic to be overcome Height but also pressure losses which for example by friction within the Pipeline arise.

• – H_p(λ,q) = die Höhe, die diese Pumpe bei Drehzahl λ und Durchfluss q produziert.
• – E_p(λ,q) = die Energie, die diese Pumpe bei der Drehzahl λ und Durchfluss q verbraucht.

A respective pump is described by the following characteristics:

• - H _p (λ, q) = the height that this pump produces at speed λ and flow q.
• - E _p (λ, q) = the energy that consumes this pump at the speed λ and flow q.

The height and energy characteristics for every pump must have certain properties, such as the indication of a minimum and a maximum speed.

For each speed λ _i with 1 ≤ i ≤ k, the characteristics are not given by a closed formula but by the values at certain nodes qi / 0, ..., qi / n, where qi / 0 / qi / n is the smallest / biggest river is that at the speed λ _i can be pumped by the pump.

are for the Pump the contour lines not falling monotonously, it becomes part of the domain of definition This pump cut off, since the calculation for each height requests that the amount the associated potential rivers is an interval.

In the method according to the invention, the existing non-linear optimization problem, within a respective pumping station, z. B. the station PS ₂ with the pumps 2 . 3 and 4 to consider for a given pair (h, q) of height h and flux q the minimum necessary energy. The solution to this partial problem is then used to calculate the optimum heights for the individual pump stations PS ₁ ..PS ₃ using an approach of the so-called "dynamic programming".

The characteristic curves are linearly interpolated between two interpolation points, that is to say for a rotational speed λ _i and a flux q ε [qi / j, qi / j + 1], the following applies:

In general, the characteristic curve for a rotational speed λ is calculated from the known characteristic curve of another rotational speed λ ₀ by means of the following transformation rule:

In order for the transformation rule to be applied, qi / 0 and qi / n must be used for the interpolation points
The following apply:

If this is not true, the definition ranges of H (λ _i , ·) and E (λ _i , ·) are reduced accordingly.

In order to achieve continuous transitions, in the case of several known characteristic curves, the characteristic curves between them should be calculated as convex combinations of the transformed characteristic curves. If, therefore, λ _i <λ <λ _{i + 1} for a possible rotational speed λ, then the altitude and energy characteristics can be specified as follows:

to Determining the minimum energy consumption of a pumping station fixed height and fixed flow, the speeds of the pumps are determined.

• • 1. Bestimmung der Energie E_i(h₀,·):[q i / min(h₀), q i / max(h₀)]→[0,∞), die die Pumpe P_i benötigt, um einen Fluss auf eine bestimmte Höhe h₀ zu pumpen.
• • 2. Aufteilen des Flusses auf die einzelnen Pumpen durch Lösen des folgenden nicht linearen Optimierungsproblems (NLP)
  
  q_i = 0 oder q i / min(h₀) ≤ q_i ≤ q i / max(h₀) für alle i = 1, ..., r.
• • 3. Berechnung der Drehzahlen für jede Pumpe.

This happens in three steps:

• 1. Determination of the energy E _i (h ₀ , ·): [qi / min (h ₀ ), qi / max (h ₀ )] → [0, ∞), which the pump P _i needs to flow up to pump a certain height h ₀ .
• 2. Splitting the flow to the individual pumps by solving the following nonlinear optimization problem (NLP)
  
  q _i = 0 or qi / min (h ₀ ) ≤q _i ≤ qi / max (h ₀ ) for all i = 1, ..., r.
• • 3. Calculation of the speeds for each pump.

Let qi / min (h ₀ ) / qi / max (h ₀ ) be the minimum / maximum flow that can be pumped from pump P _i to height (h ₀ ).

each Pump is through the four parameters height (h), flow (q), speed (λ) and Energy (q) described. There are two within each of this Borders freely selectable, the remaining Both result from the characteristics. So it can be, for example the energy in dependence of speed and flow but also depending on altitude and flow be calculated. In this embodiment Both functions are denoted by E to get too many indexes avoid. These parameters clearly show that which function is meant.

For a fixed height h ₀ and a flow q, the energy E _i (h ₀ , q) for pump P _{i is given} by resolving H _i (λ, q) = h ₀ to λ and substituting λ into E _i (λ , q).

D = –h0(λi+1 – λi). (6) Equivalence formulas yield a polynomial of degree 3 in λ: Aλ 3 + Bλ 2 + Cλ + D = 0, in which

D = -h 0 (λ i + 1 - λ i ). (6)

With the so-called Cardan formula, the three roots of this polynomial are calculable. The sought speed λ is the root which lies in [λ _i , λ _{i + 1} ]. An insertion of this speed λ in E _i [λ, q] then gives the energy demand E _i (h ₀ , q).

By calculating the respective value E _i (h ₀ , q) for different fundamental values q and by means of a suitable approximation, which will be described in more detail below, an approximation for the energy E _i (h ₀ , ·) results: [qi / min. h ₀ ), qi / max (h ₀ )] → [0, ∞).

are these functions convex, d. H. their derivatives are strictly monotone growing, then there is a precise solution to this problem.

This Result will be used below to indicate the heights to be produced to distribute the pumping stations. For this, the problem is first discretized, this means, An accuracy s is selected and then only heights considered that correspond to this accuracy. Can a pumping station So for example all heights from [30,40] produce, and is s = 0.5, so be for this Pumping station only the heights 30.0, 30.5, 31.0, 31.5, ..., 40.0.

"Dynamic Programming" is based on the principle that the optimal solutions to the overall problem are made up of optimal solutions for the subproblems, as is the case here:
Let PS ₁ , ..., PS _{k be} the pumping stations connected in series. For i = 1,..., K (h _i , q _i ) let the height-flux pair describe the pipeline segment between PS _i and PS _{i + 1} . The total height to be produced is

Dynamic Programming now exploits the following property of the pipeline:
The energy requirement of a pumping station PS _i depends only on how much height it generates and how much pre-pressure, that is, how much height is more than the required height of h ₁ +.. + H _i-1 , the previous pumping stations PS ₁ , ..., PS _i-1 generated. It does not depend on how this form was created, that is, how much pre-pressure has generated which of the pumping stations PS ₁ , ..., PS _i-1 .

als minimaler gemeinsamer Energieverbrauch der Stationen PS₁, ..., PS_i-1 definiert, wenn diese gemeinsam die Höhe H produzieren, so folgt:

Formally this means:
A pair (H ', H'') of heights is hereinafter referred to as (PS ₁ ⋃ PS _i-1 , PS _i ) called, if it is permissible and possible that the pumping stations PS ₁ , ..., PS _{i -1} together produce the height H 'and that PS _i produces the height H''. Will still

defined as the minimum common energy consumption of the stations PS ₁ , ..., PS _i-1 , if these together produce the height H, then:

• • 1. Bestimme für jede Pumpstation PS_i die Menge J_i = möglicher Höhen, die diese Pumpstation produzieren kann.
• • 2. Berechne für jede Pumpstation PS_i den Energiebedarf
  
  für jede Höhe h ∊ J_i.
• • 3. Für i = 2, ..., k (a) Bestimme die Menge J aller zulässiger und möglicher Gesamthöhen, die von PS₁, ..., PS_i erzeugt werden können. (b) Für alle H ∊ J: Berechne und speichere
  
  gemäß Gleichung (7) und speichere die optimale Verteilung von H auf die Pumpstationen PS₁ ⋃ ... ⋃ PS_i-1 und PS_i.

The further process steps for the distribution of the heights to be produced on the individual pumping stations then result as follows:

• 1. Determine for each pumping station PS _i the amount J _i = possible heights that this pumping station can produce.
• • 2. Calculate the energy requirement for each pump station PS _i
  
  for each height h ε J _i .
• • 3. For i = 2, ..., k (a) Determine the set J of all allowable and possible total heights that can be generated by PS ₁ , ..., PS _i . (b) For all H ε J: Compute and save
  
  according to equation (7) and store the optimal distribution of H on the pumping stations PS ₁ ⋃ ... ⋃ PS _i-1 and PS _i .

The Procedural steps for distribution of the heights to be produced The individual pumping stations will be described below with reference to the simple one explained in detail in the drawing embodiment.

The pump stations and consumers are here connected to each other by four pipeline segments S12, S23 and S1 and S2, on which the height to be supplied and the flow to be pumped is plotted. The height that a pumping station can provide when it is on is also recorded. The height to be achieved results in h ₁ = h ' ₁ = 30, h ₂ = h' ₂ = 30, h ₃ = h ' ₃ + h' ₄ = 40 and h _ges = 100.

• 1st step: As step length s = 1 is selected.
• 2nd step: First, the first pumping station PS, considered. This can theoretically produce all heights between 0 and 40. However, since it has to pump the river at least 30 units of length, there is only the option for this pumping station to produce a height H ₁ between 30 and 40. Therefore, J ₁ = {30, 31, ..., 40}.

If PS ₁ produces a height of H ₁ ε [30,40], PS ₂ must produce a height of at least 30 - (H ₁ - 30) ≥ 20 and at most 100 - H ₁ ≤ 70.

Therefore, for the height to be generated by PS ₂ , H ₂ ε [20,70] and thus J ₂ = {20, 21, ..., 70}.

• 3. Schritt: Nun werden für jede Pumpstation PS_i die minimalen Energieverbrauche für die möglichen Höhen aus J_i berechnet.
• 4. Schritt: Für i = 2 gilt J = J₁ = {30, 31, ..., 40} für alle Höhen aus J wird nun der Energieverbrauch von PS₁ ⋃ PS₂ gemäß Gleichung (7) bestimmt und die zugehörige optimale Aufteilung der Höhen auf PS₁ und PS₂ gespeichert.

Now consider all the total heights H ₁ + H ₂ which the first two pumping stations can generate together. These are all between 30 + 30 = 60 and 100. If PS ₁ and PS _{2 can} now produce a height of H ' ₁ ε [60,100], PS ₃ must have a height of at least 40 - (H' ₁ - 60) ≥ 0 and at most 100 - H ' ₁ ≤ 40 produce. Therefore, for the height to be generated by PS ₃ , H ₃ ε [0.40] and thus J ₃ = {0, 1, ..., 40}.

• 3rd step: Now, for each pumping station PS _i, the minimum energy consumption for the possible heights is computed from J _i .
• 4th step: For i = 2, J = J ₁ = {30, 31, ..., 40} for all heights from J, the energy consumption of PS ₁ ⋃ PS _{2 is determined} according to equation (7) and the associated optimal one Splitting the heights stored on PS ₁ and PS ₂ .

For i = 3, J = {60, 61, ..., 100}. The minimum energy consumption of PS ₁ ⋃ PS ₂ ⋃ PS ₃ for h _ges = 100 is now determined by equation (7). If, for example, it turns out that this minimum energy consumption is achieved, if PS ₁ ⋃ PS ₂ produces a height of 80 and PS ₃ a height of 20, then see how the optimum distribution of heights on PS ₁ and PS ₂ is common Height of 80 was. Was this 30 for PS ₁ and 50 for PS ₂ , so the optimum distribution of the heights on PS ₁ , PS ₂ and PS _{3 is} just given by 30,50,20.

Since the energy consumption of a pumping station is not necessarily monotonically increasing in height, it may be advantageous to produce a pressure greater than h _tot in the pipeline.

The Procedure can transfer be in the case that the pipeline contains branches, so that For example, at a pumping station several pipes out or more Lead pipes in. The condition is, however, that there are no circles at all. The case that the pipeline contains circles is much more difficult to solve.

Claims (4)

Method for optimally controlling pump stations and pumps in a pipeline, wherein the pump stations (PS ₁ , PS ₂ , PS ₃ ) each have at least one pump ( 1 .. 6 ) and in the flow direction via pipeline segments (S12, S23, S1, S2) are each connected to at least one further pumping station (PS ₁ , PS ₂ , PS ₃ ) or at least one consumer (V ₁ , V ₂ ) such that no undirected circles arise in the underlying graph, and the control over the adjustment of the rotational speeds of the individual pumps and the pressure levels to be generated of the individual pumping stations takes place, - in which the energy demand of a respective pumping station is minimized depending on the flow and pressure level as far as possible and - in which subsequently the distribution of the pressure levels to be generated on the individual pumping stations takes place in such a way that the total energy requirement of all pumping stations is minimized. Method according to Claim 1, in which, in order to minimize the energy requirement of the respective one pumping station, a height characteristic (H _i (λ, q)) of the respective one pump (i), each dependent on a pump speed (λ) and a flow (q) ( h ₀ ) and is dissolved according to a permissible pump speed and this pump speed is used in an energy characteristic (E _i (λ, q)) of the respective one pump, which is dependent on a pump speed and a flow (q), in each case for one height ( h0) to obtain the energy demand as a function of the flow, at which, for the respective pumping station and respective height, the flow is thus distributed to the pumps of the pumping station is that in total the total flow generated and the energy demand of the respective pumping station is as low as possible. Method according to Claim 1 or 2, in which the distribution of the pressure levels to be generated to the individual pumping stations takes place by dynamic programming, the minimized total energy requirement E _{1,... I} (h) of the first pumping stations in each case utilizing the already calculated minimized total energy requirement E _{1, .., i-1} (h ') of the first i-1 pumping stations and the energy demand E _i (h'') of the i-th pumping station according to E _{1, .., i} (h) = min {E _{1, .., i-1} (h ') + E _i (h'') | h '+ h''= h, discretized with a step size s} recursively calculated, where h' is a height that can be generated by the first i-1 pumping stations, and h '' is a height that can be generated by the i-th pumping station is. Computer program product for carrying out the Method according to one of the preceding claims.