DE102014214863A1 - Method for computer-aided control of power in an electric power grid - Google Patents

Abstract

The invention relates to a method for computer-aided control of the power in an electrical power network, wherein the power grid has a predetermined nominal frequency and a plurality of interconnected via power lines (PL) network nodes (N1, N2, ..., N5), wherein the network nodes (N1, N2, ..., N5) comprises one or more first network nodes (N1, N4, N5) and one or more second network nodes (N2) and one or more third network nodes (N3), wherein a respective first network node (N1 , N4, N5) is a generator node that generates power in the grid and provides primary control power (PRL) and secondary control power (SRL), wherein a respective second network node (N2) is a generator node that generates power in the power grid by means of regenerative power generation, and wherein a respective third network node (N3) is a load node that draws power from the power network (N3). In the method according to the invention, based on a modeled stationary state of the power network, a condition is predetermined to the secondary control power (SRL) generated by the first network node (s) before failure of at least a part of the second network node (N2), whereby upon fulfillment of the condition in the case of failure of at least part of the second network nodes (N2) sets a stable network state. In this case, the power generation of the second network node (N2) is limited, wherein the limit of the power generation by the secondary grid power (SRL) available in the power grid of the first network node (N1) is set such that the predetermined condition is met.

Description

The invention relates to a method for computer-aided control of the electrical power in an electrical power network and to a corresponding device. Performance is to be understood here and below as active power.

An electrical power network comprises a multiplicity of network nodes interconnected via power lines, which feed electrical power into the power grid or remove electrical power from the power grid. For stable operation of a power grid, a faster balance between the fed-in electrical power and the extracted electrical power is required.

In electric power grids, so-called primary control power or secondary control power is provided by at least part of the network nodes to compensate for power fluctuations. In power grids, where grid nodes generate electrical power partly also via regenerative power generation, it can not be guaranteed that the grid is still stable after failure of grid nodes with renewable energy. Here and in the following the term of the failure of a network node is to be understood far. The term of the failure includes in particular a shutdown in terms of equipment protection in case of a fault in the network, without the failure is caused by a defect in the disconnected network node.

The publication [1] discloses a mission planning for large power transmission networks taking into account variable power generation from wind farms. Resource planning is optimized for different, differently weighted wind production scenarios, without considering the effects of primary balancing and wind farm outages.

The object of the invention is to provide a method for computer-aided control of the power in an electrical power grid with regenerative power generation, wherein in case of failure of regenerative power generators, a stable network state can be ensured.

This object is solved by the independent claims. Further developments of the invention are defined in the dependent claims.

The inventive method is used for computer-aided control of the power in an electrical power grid, wherein the power grid has a predetermined nominal frequency of the generated alternating current or the generated alternating voltage (eg., 50 Hz or 60 Hz). The power grid includes a plurality of network nodes interconnected via power lines, the network nodes comprising one or more first network nodes and one or more second network nodes and one or more third network nodes. A respective first network node is a generator node which generates power in the power grid and provides primary control power and secondary control power in a manner known per se. A respective second network node is a generator node which generates power in the power grid by means of regenerative energy generation. Such network nodes are not suitable for the provision of primary control power or secondary control power. Furthermore, a respective third network node is a load node that draws power from the power network. Optionally, network nodes in the power network may also represent a combination of a first and / or second and / or third network node.

The above terms of the primary control power and the secondary control power as well as the terms of the primary and secondary control are familiar to those skilled in the art. The primary control power is provided by a so-called proportional control (Droop Control) as a function of the deviation of the frequency in the power grid from the nominal frequency. A corresponding proportionality factor flows in (also referred to as droop gain). In contrast to the primary control, the secondary control is not frequency-dependent, but is performed to compensate for power fluctuations via a control center in the power grid.

In the method according to the invention, in a step a), a stationary state of the power network, in which a constant frequency in the power network is established by means of the primary control power of the first network node (s), is modeled after failure of at least part of the second network node. Based on this stationary state of the power network, in step b), a condition is predetermined to the secondary control powers generated by the first network node or nodes, in particular when the power generated by the second network node or nodes increases, before the at least part of the second network node fails. The secondary control power is in this sense a negative power which describes the decrease of the generated power of the first network nodes as the power generation of the second network nodes increases.

If the predetermined condition is met, in the case of the failure of the at least one part of the second network node, the absolute deviation of the frequency in the power network from the nominal frequency is below a first threshold value. Alternatively or additionally, in the event of failure of the at least one part of the second network nodes, at least one magnitude phase difference, which occurs between the voltages of two network nodes connected via one or more power lines in the power network, is below the second threshold value. In other words, the condition is predetermined such that even after failure of the second network node, a stable network state is present. Possibly. a plurality of different second threshold values for the respective magnitude phase differences can be predetermined. In a preferred embodiment, the at least one magnitude phase difference defined above is the maximum magnitude phase difference from all the phase differences that occur between the voltages of two network nodes (directly) connected via a power line in the power grid. In this case, there is only a single second threshold.

Finally, in a step c) of the method according to the invention, the power generation of the second network node (s) is limited in the power grid, the limit of power generation being determined by the secondary control power of the first network node or nodes (ie the reserve of secondary control power) available in the power grid such that the power generation above given condition is met.

The inventive method provides a suitable prediction of the network state after the failure of nodes with regenerative power generation. Based on this, a condition is imposed on the secondary control power. By suitable definition of the reserves of the secondary control power can be ensured by a stable operation of the power grid even in case of failure of regenerative generators.

The stationary state of the power network can be modeled differently depending on the embodiment of the method according to the invention. In a particularly preferred embodiment, the stationary state is modeled based on load flow equations for the active powers occurring in the respective network nodes. Nevertheless, the stationary state of the power network can possibly also be modeled via a dynamic physical model, as described, for example, in US Pat. As described in document [2].

When using load flow equations, the condition is taken into account in a particularly preferred embodiment that the ohmic resistance on the power lines between adjacent network nodes in the power grid is negligibly small compared to the reactance on the power lines between adjacent network nodes. This simplifies the modeling of the stationary state and the calculations in the method according to the invention can be carried out more quickly.

wobei P_i die am Netzknoten i erzeugte Wirkleistung ist;
wobei θ_i bzw. θ_j die Phase der Spannung im jeweiligen Netzknoten i bzw. j ist;
wobei N_i die Menge der zu einem jeweiligen Netzknoten i benachbarten Netzknoten repräsentiert;
wobei u_i bzw. u_j die Effektivwerte der Spannungen in den jeweiligen Netzknoten i bzw. j sind;
wobei r_ij der ohmsche Widerstand und x_ij der Blindwiderstand der Stromleitung zwischen Netzknoten i und j ist.In a preferred embodiment, the load flow equation for a respective network node i is as follows:

where P _{i is} the active power generated at the network node i;
where θ _i or θ _{j is} the phase of the voltage in the respective network node i or j;
where N _{i represents} the set of network nodes adjacent to a respective network node i;
where u _i and u _{j are} the rms values of the voltages in the respective network nodes i and j, respectively;
where r _{ij is} the ohmic resistance and x _{ij is} the reactance of the power line between network nodes i and j.

In a further preferred embodiment, the predetermined condition is formulated as a set of inequalities. These inequalities are linear with respect to the secondary control powers. The predetermined condition is thus satisfied when the secondary control powers satisfy the inequality relations in the set of inequalities. With this variant, a simple formulation of the predetermined condition and thus a fast computer-aided implementation of the method according to the invention is ensured.

wobei 1 ein Einheitsvektor und II eine Einheitsmatrix ist;
wobei ΔP ein Vektor ist, der einen Eintrag für jeden Netzknoten des Stromnetzes enthält, wobei der Eintrag für einen jeweiligen ersten Netzknoten die von dem jeweiligen ersten Netzknoten bereitgestellte Sekundärregelleistung ist und wobei der Eintrag für einen jeweiligen zweiten und dritten Netzknoten Null ist;
wobei P₀ ein Vektor ist, der einen Eintrag für jeden Netzknoten des Stromnetzes enthält, wobei der Eintrag für einen jeweiligen ersten und zweiten Netzknoten der in diesem Netzknoten bei Nennfrequenz erzeugten Leistung entspricht und wobei der Eintrag für einen jeweiligen dritten Netzknoten der von diesem Netzknoten entnommenen Leistung (mit negativem Vorzeigen) entspricht;
wobei ΔP_W ein Vektor ist, der einen Eintrag für jeden Netzknoten des Stromnetzes enthält, wobei der Eintrag für einen jeweiligen zweiten Netzknoten kleiner als der zugehörige Eintrag des Vektors P₀ ist, falls der jeweilige zweite Netzknoten nicht ausgefallen ist, und bei Ausfall des jeweiligen zweiten Netzknotens der zum aktuellen Zeitpunkt im jeweiligen zweiten Netzknoten erzeugten Leistung entspricht, d. h. ΔP_W,i = P_0,i, und wobei der Eintrag für einen jeweiligen ersten und dritten Netzknoten Null ist;
wobei k_P ein Vektor ist, der einen Eintrag für jeden Netzknoten des Stromnetzes enthält, wobei der Eintrag für einen jeweiligen ersten Netzknoten einem Proportionalitätsfaktor entspricht, über den die von dem jeweiligen ersten Netzknoten bereitgestellte Primärregelleistung beeinflusst wird, und der Eintrag für alle anderen Netzknoten Null;
wobei B eine Inzidenzmatrix mit einer der Anzahl an Netzknoten im Stromnetz entsprechenden Anzahl an Zeilen und einer der Anzahl an Stromleitungen im Stromnetz entsprechenden Anzahl an Spalten ist, wobei jede Stromleitung durch eine gerichtete Kante repräsentiert wird, welche von einem Netzknoten startet und an einem Netzknoten endet;
wobei gilt

wobei L^✝ die Pseudoinverse der Laplace-Matrix L = BKB^T ist;
wobei K eine Diagonalmatrix ist, welche auf der Diagonalen einen Eintrag für jede, eine Stromleitung repräsentierende gerichtete Kante enthält, wobei der Eintrag für eine Kante, welche bei einem Netzknoten i startet und bei einem Netzknoten j endet, wie folgt lautet:

wobei u_i bzw. u_j die Effektivwerte der Spannungen in den jeweiligen Netzknoten i bzw. j sind;
wobei x_ij der Blindwiderstand der Stromleitung ist, welche am Netzknoten i startet und am Netzknoten j endet;
wobei Δf_max der erste Schwellwert ist;
wobei γ der zweite Schwellwert ist, der die maximale betragsmäßige Phasendifferenz aus allen Phasendifferenzen repräsentiert, die zwischen den Spannungen von zwei über eine Stromleitung verbundenen Netzknoten im Stromnetz auftreten.In a preferred embodiment, the set of inequalities is as follows: AΔP <b in which

where 1 is a unit vector and II is a unit matrix;
wherein ΔP is a vector containing an entry for each network node of the power network, the entry for a respective first network node being the secondary control power provided by the respective first network node, and wherein the entry for a respective second and third network node is zero;
where P _{0 is} a vector containing an entry for each network node of the power network, the entry for each respective first and second network node corresponding to the power generated in this network node at rated frequency, and wherein the entry for a respective third network node is that taken from that network node Performance (with negative showing) corresponds
where ΔP _{W is} a vector containing an entry for each network node of the power network, the entry for a respective second network node being smaller than the associated entry of the vector P ₀ if the respective second network node has not failed, and if the respective one fails second network node corresponding to the power generated at the current time in the respective second network node, ie ΔP _{W, i} = P _{0, i} , and wherein the entry for a respective first and third network node is zero;
where k _{P is} a vector containing an entry for each network node of the power network, the entry for a respective first network node corresponding to a proportionality factor over which the primary control power provided by the respective first network node is affected, and the entry for all other network nodes being zero ;
where B is an incidence matrix having a number of rows corresponding to the number of network nodes in the power network and a number of columns corresponding to the number of power lines in the power network, each power line being represented by a directed edge starting from a network node and terminating at a network node ;
where is true

where L ^{✝ is} the pseudoinverse of the Laplace matrix L = BKB ^T ;
where K is a diagonal matrix containing on the diagonal an entry for each directed edge representing a power line, the entry for an edge starting at a network node i and terminating at a network node j is as follows:

where u _i and u _{j are} the rms values of the voltages in the respective network nodes i and j, respectively;
where x _{ij is} the reactance of the power line starting at node i and terminating at node j;
where Δf _{max is} the first threshold value;
where γ is the second threshold value representing the maximum magnitude phase difference from all phase differences that occur between the voltages of two network nodes connected via a power line in the power grid.

The current time defined above is the time of the currently executed control according to the invention with the associated calculations. In the above formulas and also in the following, the superscript letter "T" denotes the transpose of a matrix in a manner known per se.

In one embodiment of the method according to the invention, the proportions of the secondary control powers provided in the respective network nodes are predefined on the total secondary control power provided, wherein in step c) a permissible factor fulfilling the predetermined condition is determined by multiplying by the proportion of a respective first Network node results in the available secondary power of the respective first network node in the power grid.

In a further variant, in step c), separately for each first network node, assuming that the other first network nodes do not provide secondary control power, the system searches for permissible values for the secondary control power of the respective first network node that satisfy the predetermined condition, thereby producing a set of vectors permissible secondary control power of all first network nodes is determined. The secondary control powers available in the power grid are then set by selecting a vector from the convex hull of the set of vectors and the zero vector.

In a further refinement of the method according to the invention, in step c) the secondary control powers available in the power grid are determined based on the maximization of the sum of the secondary control outputs of all the first network nodes under the predetermined condition from step b) as a secondary condition. The maximization can be done with known methods for solving linear optimization problems, such. As the simplex method or the inside-points method, are solved.

The existing in the power grid first network nodes are usually conventional generator nodes, such. B. fossil power plants or nuclear power plants. The second network nodes are preferably one or more wind turbines (eg wind farms) and / or one or more photovoltaic systems.

In addition to the method described above, the invention further relates to a device for computer-aided control of the power in an electrical power network, wherein the device comprises one or more means for carrying out the method according to the invention or one or more variants of the method according to the invention.

The invention further relates to an electric power network comprising the above-described device according to the invention for controlling the power generated in the power grid.

Embodiments of the invention are described below in detail with reference to the accompanying drawings.

Show it:

1 a schematic representation of a section of a power grid, in which an embodiment of the method according to the invention is performed; and

2 a diagram illustrating the problem solved by the invention problem.

This in 1 schematically illustrated power grid is a transmission network in the form of a high voltage network, eg. B. with high voltages at 110 kV, 220 kV and 380 kV. However, the invention is not limited to high voltage grids and may optionally be used for power distribution networks in the form of medium and low voltage networks.

The in 1 indicated section of the power grid includes a plurality of (purely inductive) power lines PL interconnected network nodes N1, N2, N3, N4 and N5, the power grid as a whole includes a much larger number of network nodes. The network nodes can represent sources, via which electrical power is fed into the power grid, or sinks, via which power is taken from the power grid. In each of the network nodes, a voltage is established with a frequency identical in all network nodes, which in the ideal case corresponds to the nominal frequency of the power network. This nominal frequency is for example 50 Hz or 60 Hz.

In 1 are provided as sources among other generator nodes G, which also provide primary control power in the context of a primary control and secondary control power in a secondary control in addition to the generation of electrical power. These are the network nodes N1, N4 and N5. To provide the primary control power, a proportional regulator is provided in each of these nodes in a manner known per se, which sets the active power generated in the respective network node as a function of the deviation of the frequency in the power grid from the rated frequency, as will be explained in more detail below. As mentioned, secondary control power is also provided in the respective generator node G to compensate for power fluctuations in the power grid, which takes place in contrast to the frequency-dependent primary control via the intervention of a control center or control room. The generator nodes G are usually conventional power plants in the form of fossil power plants or nuclear power plants.

As further sources, the power grid contains the 1 Regenerative power generation plants, of which a wind farm WP is exemplified as a network node N2. Instead of or in addition to wind farms, other renewable energy generation systems, such. As photovoltaic systems, be provided. Due to variations in the energy production of renewable energy generation plants, these plants are not suitable for the provision of primary or secondary control power. The sinks in the power network, via which power is taken, are so-called load nodes L. In the illustration of 1 the network node N3 is such a load node. The supply of electricity in the power grid is z. Eg via synchronous generators, inverters or inverters. For the removal of electrical power from the mains z. As resistive loads, asynchronous machines, rectifiers and the like. A respective network node may also represent a conglomeration of multiple sources and sinks.

In the embodiment of the 1 is a central control unit CO z. B. in a control center, which monitors all nodes of the network and can communicate with them via communication lines, which are indicated by dashed lines. With this central control unit, the embodiment of the method according to the invention described below is carried out.

The aim of the method according to the invention is to guarantee a stable network state in the event of a failure of regenerative power generation plants in the power grid. This is done by means of a suitable modeling of the steady-state network status after failure of the power generation plants and a subsequent adjustment of the secondary reserve reserve so that network stability is ensured after failure of the network nodes and taking into account the primary control capacity. This objective is shown in the diagram of 2 clarified.

Along the abscissa of 2 is the time t and along the ordinate the power P generated in the power grid reproduced. The line L shows the power taken over the entire power grid via load nodes, which in this example is assumed to be constant. The power generation by the generator nodes is represented by the corresponding line G and the power generation by the regenerative power generation nodes by the corresponding line WP. As it turned out 2 For example, an increase in power generation by the regenerative power generation nodes (indicated by the arrow PI) causes the generator nodes G to provide secondary control power at the same level of power gain. This secondary control power is in 2 represented by the arrow SRL. The secondary control power is negative, ie the corresponding power generation of the generator node G is abgeregelt.

According to 2 t0 represents the current time of the control according to the invention. If now at time t1 a failure of at least part of the regenerative power generation nodes (in FIG 2 is a total failure of all regenerative power generation nodes shown), this leads to a drop in performance, which in 2 indicated by the arrow PD. As a consequence, there is a variation of the frequency in the power grid, with the result that over the provided in the generator node G primary control, the power loss is compensated, with a stationary frequency deviation is maintained until it is compensated by a further use of secondary control power. In other words, by the generator nodes G primary control power PRL is provided, so that the load L out can be supplied to the power grid. However, in the event of a failure of the regenerative power generation systems, it may not be ensured that the network assumes a stable network state again. In particular, too large phase differences in the voltages of nodes connected via power lines or an excessive deviation of the frequency from the nominal frequency occur, which can possibly lead to a power failure. In order to avoid this, an admissible secondary reserve reserve for the individual generator nodes G is determined within the scope of the invention, so that a stable network state is still ensured in the event of failure of the regenerative power generation systems. In other words, the maximum power increase correlated with the secondary reserve reserve is determined by regenerative power generation systems, so that a stable network state is still ensured in the event of failure of these systems.

For modeling or prediction of the stationary state of the network after time t1 (i.e., after failure of at least part of the regenerative power generation plants), in the embodiment described here, load flow equations are used for the powers occurring in the respective network nodes. These load flow equations are explained below. Optionally, there is also the possibility that the stationary state is modeled in other ways, such. Using a dynamic physical model (see reference [2]).

It is assumed that the power line between two adjacent network nodes i and j in the power network through the serial complex-valued impedance z _ij = r _ij + j _m x _ij and the shunt capacitance bc / ij is described, the latter being divided equally between the adjacent nodes. r _ij is commonly referred to as ohmic resistance (or resistance) and x _ij as reactive impedance (or reactance). The size of _m j denotes the complex unit, which is often referred to only j, but here to distinguish the indices j of the nodes is designated as j _m. The complex stress of the node i is given by u _i = u _i exp (j _m θ _i ). Analogously, the complex voltage of the node j is given by u _j = u _j exp (j _m θ _j ). In this case, θ _i or θ _{j is} the phase of the voltage in the respective network node i or j and u _i and u _j are the rms values of the voltages in the respective network nodes i and j, respectively. The complex current i _ij flowing from node i to node j results from the above voltages and the impedance as follows: i _ij = (u _i - u _j) / z _ij (1)

As is well known, the apparent power S _ij flowing from the node i to the node j is given as follows: S _ij = P _ij + j _m Q _ij = u _i i * / ij (2)

P _ij denotes the active power flowing from node i to node j. Analogously, Q _ij corresponds to the reactive power flowing from node i to node j. i * / ij is the conjugate complex value of i _ij .

This leads to the AC load flow equations for the grid of N nodes:

It is summed over all nodes j, which are adjacent to the node i. S _i denotes the apparent power generated at node i, P _i the active power generated at node i and Q _i the reactive power generated at node i. Spent active and reactive power are modeled by negative P _i and Q _i .

It is further assumed that the effective resistance between the nodes i and j is negligibly small compared to the reactance between the nodes i and j, ie r _ij << x _ij . This means that the ohmic Losses on the power lines can be neglected. By means of this assumption, the following simplified formula for the active power P _i results:

The above equation (4a) flows into the modeling of the stationary network state, as will be explained in more detail below.

The primary control in a respective generator node G is realized in a conventional manner via a proportional control (English: droop control), which depends on the deviation of the frequency f in the power grid from the nominal frequency f _tar . The proportional control is as follows: P _i = P _{o, i} + ΔP _i - k _{P, i} (f - f _tar ). (6)

In this case, P _{0 , i} > 0 denotes the nominal active power of a generator i. Hereinafter, generator nodes G, which provide primary and secondary control power, are simply referred to as generators for the sake of simplicity. In contrast, regenerative power plants are referred to as regenerative generators.

In the above proportional control according to equation (6), a proportionality factor k _{P, i} > 0 flows in, which is also referred to as "droop gain" or "gain". In the equation (6), there is further indicated an additional power amount ΔP _{i representing} a change in power generation of the generator due to the secondary control. In sum over all generators, this change is negative and is caused by an increase in power generation by the regenerative generators. However, in certain constellations, individual generators may have positive values for ΔP _i as long as other generators have negative values and the sum over all ΔP _{i is} negative.

Regenerative producers are modeled by their nominal power supply and an additional power generation outage term as follows: P _i = P _{o, i} - ΔP _{W, i} (7)

Here P _{0, i} > 0 denotes the nominal power feed of the regenerative generator. In the following applies ΔP _{W, i} = P _{0, i} for those regenerative generators, which in the considered scenario z. B. fail due to a short circuit. In contrast, ΔP _{W, i} <P _{0, i} for all other (not failed) regenerative generators. In particular, P _i > P _{0, i can} apply to these generators.

The loads are modeled in the grid by their nominal power consumption as follows: P _i = P _{0, i} <0 (8)

Generally, the real power of the various types of network nodes in the power grid is modeled by summarizing equations (6), (7), and (8) as follows: P _i = P _{o, i} + ΔP _i - ΔP _{W, i} - k _{P, i} (f - f _tar ) (9)

• – P_0,i < 0, ΔP_i = 0, ΔP_W,i = 0, k_P,i = 0, falls der Knoten i ein Lastknoten ist,
• – P_0,i > 0, ΔP_i ≤ 0, ΔP_W,i = 0, k_P,i ≥ 0, falls der Knoten i ein Generator ist, und
• – P_0,i > 0, ΔP_i = 0, ΔP_W,i ≤ P_0,i, k_P,i = 0, falls der Knoten i ein regenerativer Erzeuger ist. Dabei existiert zumindest ein ausgefallener regenerativer Erzeuger, für den ΔP_W,i = P_0,i gilt. Je nach Ausgestaltung des erfindungsgemäßen Verfahrens können die Werte von ΔP_W,i vollständig oder auch nur unvollständig bekannt sein.
• – Bei gemischten Last- und Erzeugerknoten können insbesondere die Werte von P_0,i außerhalb dieser Schranken liegen. Zur Vereinfachung werden im Folgenden keine gemischten Last- und Erzeugerknoten betrachtet, die Ergebnisse können aber ohne weiteres auf diese Knoten erweitert werden.

Where:

• P _{0, i} <0, ΔP _i = 0, ΔP _{W, i} = 0, k _{P, i} = 0 if the node i is a load node,
• P _{0, i} > 0, ΔP _i ≤ 0, ΔP _{W, i} = 0, k _{P, i} ≥ 0 if the node i is a generator, and
• -P _{0, i} > 0, ΔP _i = 0, ΔP _W, i≤P _{0, i} , k _{P, i} = 0 if the node i is a regenerative generator. At least one failed regenerative generator exists, for which ΔP _{W, i} = P _{0, i} . Depending on the embodiment of the method according to the invention, the values of ΔP _{W, i may be} completely or even incompletely known.
• In the case of mixed load and generator nodes, the values of P _{0, i} in particular can be outside these limits. For the sake of simplicity, no mixed load and generator nodes will be considered below, but the results can easily be extended to these nodes.

The stationary state modeling of the power network considered here is based on the assumption that the power lines are lossless, so that Σ _i P _i = 0. By inserting P _i from the above equation (9) into this condition, the deviation Δf of the frequency in the power grid from the rated frequency after failure of corresponding regenerative generators can be described as follows:

In this equation (10), thick printed symbols were introduced which designate vectors from the corresponding entries for each of the N network nodes. In particular, k T / P = (k _{P, 1} , k _{P, 2} , ..., k _{P, N} ), 1 ^T = (1, 1, 1, ..., 1) and P ₀ = (P _0,1 , P _{0 , 2} , ..., P _{0, N} ). In the same way, the vectors ΔP, P and ΔP _{W are} defined.

It is further assumed that in the initial situation at the time t0 the power grid has rated frequency (ie f = f _tar ), so that 1 ^T P ₀ = 0 applies. Analogous results can also be achieved without this assumption. This results in the following relationship for the steady state frequency deviation after failure of regenerative generators:

As can be seen from equation (11), the frequency deviation depends only on the secondary control power ΔP (which corresponds to the change of the regenerative generation before the failure) and the change of the power ΔP _W after the failure of regenerative generators.

gegeben ist. Die Größen der Kopplungsmatrix entsprechen den Größen aus den obigen Lastflussgleichungen. Die Inzidenzmatrix lautet wie folgt:

In the following, the so-called incidence matrix of the graph introduced by the coupling matrix

given is. The sizes of the coupling matrix correspond to the quantities from the above load flow equations. The incidence matrix is as follows:

It is a sparsely populated matrix containing only the entries 1 and -1 in each column α for those rows corresponding to network nodes connected via a power line α. The power lines are represented as directed edges α between directly connected network nodes. The direction of the corresponding power line can be chosen arbitrarily.

With the incidence matrix of equation (12), equation (4a) can be written as follows:

N _{E represents} the number of edges or power lines in the considered power grid. In short notation and using equation (9), the following condition results for the stationary state of the network at time t1 after failure of regenerative generators:

Here, K denotes a diagonal matrix with entries K _α for each edge, ie with the corresponding value K _{ij of} the coupling matrix, where i and j are the starting node or end node of the considered edge.

Now, the problem of the invention can be formulated as follows: It is assumed that a power grid with a power generation P ₀ and a number of regenerative generators, which eventually fail. These regenerative generators are the elements of the vector ΔP _W which correspond to the associated elements of the vector P ₀ , ie P _{0, i} = ΔP _{W, i} . The remaining elements of ΔP _W , which are non-zero, describe regenerative generators that do not fail and generate more or less power at time t1 than at time t0. What is now the maximum power gain of all renewable generators before time t1 (which is the secondary control power or compensation 1 ^T .DELTA.P of the generators corresponds) so that the frequency deviation | .DELTA.f | in the power grid and the phase differences | B ^T θ | the voltages of the network nodes by the thresholds .DELTA.f _max or γ is limited? It is considered the maximum magnitude phase difference from all phase differences that occur between the voltages of two connected via a power line network nodes in the power grid. Possibly. For each power line separate thresholds for the phase differences can be considered. In this case, the terms "sin (γ) 1" in the following equation (17) would be replaced by separate entries for each power line, each separate entry being the sine of a separate threshold for the particular power line.

The above problem can be expressed by using equations (11) and (14) as follows:

In the embodiment described here, a limit for the phase differences of the voltages is given based on a result of the document [3]. A conservative approximation for the second condition from relation (15) is used as follows:

Where || · || _∞ the infinity norm, ie the absolute maximum entry of the vector for which the norm is calculated. Furthermore, L ^t denotes the pseudoinverse of the Laplace matrix L = BKB ^T. This results in a set of inequalities for the variable ΔP to be determined, with two inequalities for each power line in the power grid. The set of inequalities is as follows:

These inequalities are to be understood element by element for the corresponding vectors on each side of the inequality sign. The nominal active powers P _{0 of} the proportional control of the generators must be chosen such that the inequality is also satisfied at time t 0, ie for ΔP = 0 and ΔP _W = 0.

In addition to the inequality (17), the following two inequalities result from the first condition from relation (15):

The conditions according to relations (17) and (18) can now be summarized as follows: AΔP <b

Where II denotes the unit matrix.

It is now assumed first that the vector ΔP _{W is} completely known, ie also the entries for those regenerative generators that do not fail. Later it will be explained how the problem can be solved even without this assumption. Each of the 2 (N _E + 1) inequalities (19) introduces a hyperplane which divides the space of the vector ΔP into two halves. The valid points are on one side of the hyperplane. All of the above inequalities from relation (19) must be satisfied for a valid set of points ΔP. The valid set of points is thus the common intersection of all valid spaces on one side of the corresponding hyperplanes.

In the method according to the invention, the reserve of the secondary control power ΔP is now set to correspond to a vector ΔP satisfying the above inequality relation (19). This implies, conversely, that the power generation of the regenerative generators is equally limited because the provided (negative) secondary control power correlates with a corresponding increase in the power generation of the regenerative generators.

Now consider the more general case where the vector ΔP _{W is} not completely known. The entries of the renewable producers who fail at time t1 are known because they correspond to the entries of the vector P _0th The entries of the regenerative generators that do not fail at time t1 are not known, but it is known that 1 ^T (P ₀ -ΔP _W ) ≦ 1 ^T ΔP (19a) must apply, because the total change of the regenerative generation including the failure can not exceed the total used secondary control power 1 ^T ΔP. Thus, all unknown entries are represented by (19a) and P ₀ ≥ ΔP _W (19b) limited (see the descriptions according to equation (9)). These two inequalities (19a) and (19b) describe a convex set Ξ in which the unknown elements of ΔP _W must lie. Since the inequality conditions (19) are linear in the unknown parameters ΔP _W and these uncertain parameters lie in a convex set Ξ, the inequalities (19) for all allowable values of ΔP _W within Ξ can be determined using robust linear optimization methods known per se be checked. One possibility is to examine the inequalities (19) for all vertices of the set Ξ. These vertices are obtained by setting all unknown elements of ΔP _W to the upper bound (19b) and displacing exactly one element each onto the lower bound (19a). The maximum number of vertices and thus the complexity of the optimization problem is limited by the number of regenerative generator nodes. Using these uncertain entries of ΔP _W , it is also possible to describe scenarios in which the exact number of failed regenerative generators is unknown. Finally, with this method, insecure power draws in the load nodes can be considered.

In order to find permissible values of ΔP on the basis of which the reserve of the secondary control power is determined, different process variants can be used.

In a first variant of the method, it is assumed that the ratio of the secondary control outputs of the individual generator nodes is known, that is to say: ΔP _i = Δp k _{ΔP, i} (20)

The direction is k T / ΔP = (k _{ΔP, 1} , k _{ΔP, 2} , ..., k _{ΔP, N} ) and only the scalar Δp is unknown. The problem is thus reduced to finding a limit for the scalar Δp. For each of the 2 (N _E + 1) inequalities from the relation (19) there is a limit. The smallest of these limits is the solution with which then the corresponding reserves of secondary control power in the individual generators are set based on equation (20).

In a second variant of the method, the fact is used that ΔP = 0 is a solution of the inequality relation (19). The analysis can then be simplified by considering a vector ΔP whose entries are 0 except for the mth entry, where the mth entry represents a generator. This leads to the following conditions: A _lm ΔP _m <b _l (21)

These conditions must be fulfilled for all indices l. By considering limits according to the above relation (21) for all components m of the vector ΔP representing generators, one obtains a set of boundary points of M coordinate axes (M = number of generators) of the space of entries not equal to 0 of the vector ΔP, typically two points with different signs on each coordinate axis. By selecting one of these points on each of these coordinate axes, a hyperplane can be constructed containing the selected points on all coordinate axes. All these hyperplanes, which result from all 2 ^M combinations of boundary points on the coordinate axes, form a convex hull which approximates the exact convex hull. Each vector within the convex hull fulfills the above inequality relation (19). By selecting a corresponding vector from the convex hull, reserves are thus defined for the secondary control outputs of the generators.

In a third process variant, the following linear optimization problem is considered to determine reserves for the secondary control power: max _ΔP | 1 ^T ΔP | (22)

To solve this optimization problem, the above condition (19) is used as a constraint.

Thus, using this constraint, the amount of the sum of the secondary control powers of the generators is maximized. By means of the solution of this optimization problem, suitably determined reserves of the secondary control power are again determined. To solve the optimization problem known per se methods for solving linear optimization problems such. As the simplex method or the inside-points method can be used.

The embodiments of the invention described above have a number of advantages. In particular, the secondary control power is set in a power grid such that in the event of a failure of renewable energy generators, the stability of the network is further ensured. This is achieved by a prediction of the network state after failure of regenerative power generation plants, whereby a condition is formulated on the predefined network state to the secondary control power, which ensures a stable network state after failure of the regenerative generators when they are fulfilled. The inventive method can be implemented in a simple manner with manageable numerical effort and ensures a stable network operation in power grids with regenerative energy production by suitable definition of reserves of secondary control power and the associated limitation of regenerative energy production.

Bibliography:

• [1] A. Ahmadi-Khatir. Multi-Area Unit Scheduling and Reserve Allocation Under Wind Power Uncertainty. IEEE Transactions to Power Systems, No. 4, 2014, pages 1701-1710
• [2] WO 2014/076011 A2
• [3] Doerfler, M. Chertkov, and F. Bullo. Synchronization in Complex Oscillator Networks and Smart Grids. http://arxiv.org/pdf/1208.0045v1.pdf

Claims (13)

Method for computer-aided control of the power in an electrical power network, wherein the power grid has a predetermined nominal frequency and contains a plurality of network nodes (N1, N2, ..., N5) interconnected via power lines (PL), wherein the network nodes (N1, N2 , ..., N5) comprises one or more first network nodes (N1, N4, N5) and one or more second network nodes (N2) and one or more third network nodes (N3), wherein a respective first network node (N1, N4, N5 ) is a generator node that generates power in the grid and provides primary control power (PRL) and / or secondary control power (SRL), wherein a respective second network node (N2) is a generator node that generates power in the grid using regenerative power generation, and wherein a respective third Network node (N3) is a load node that draws power from the power grid (N3); characterized in that a) a stationary state of the power network, in which a constant frequency in the power network is established by means of the primary control power (PRL) of the first network node (s) (N1), is modeled after failure of at least part of the second network node (N2); b) based on the stationary state of the power network, a condition is set to the secondary control power (SRL) generated by the one or more network nodes (N1) before failure of the at least a part of the second network node (N2), if the condition is met in the case of Failure of at least a portion of the second network node (N2) is the magnitude deviation of the frequency in the mains from the nominal frequency below a first threshold and / or at least an absolute phase difference between the voltages of two via one or more power lines (PL) connected network node (N1, N2, ..., N5) occurs in the power grid, is below a second threshold; c) the power generation of the second network node or nodes (N2) is limited, wherein the limit of the power generation by the available in the power grid secondary control power (SRL) of the first network node (N1) is set such that the predetermined condition is met. A method according to claim 1, characterized in that the stationary state of the power grid is modeled based on load flow equations for the active power occurring in the respective network nodes (N1, N2, ..., N5). A method according to claim 2, characterized in that in the load flow equations the condition is taken into account that the ohmic resistance on the power lines (PL) between adjacent network nodes (N1, N2, ..., N5) in the power grid is negligibly small compared to the reactance to the Power lines (PL) between adjacent network nodes (N1, N2, ..., N5) is. Method according to claim 2 or 3, characterized in that the load flow equation for a respective network node i is as follows:

where P _{i is} the active power generated at the network node i; where θ _i or θ _{j is} the phase of the voltage in the respective network node i or j; where N _{i represents} the set of network nodes (N1, N2, ..., N5) adjacent to a respective network node i; where u _i and u _{j are} the rms values of the voltages in the respective network nodes i and j, respectively; where r _{ij is} the ohmic resistance and x _{ij is} the reactance of the power line between network nodes i and j. Method according to one of the preceding claims, characterized in that the predetermined condition is formulated as a set of inequalities which are linear with respect to the secondary control powers (SRL). Method according to claim 5, characterized in that the set of inequalities is as follows: AΔP <b in which

where 1 is a unit vector and II is a unit matrix; where ΔP is a vector containing an entry for each network node (N1, N2, ..., N5) of the power network, the entry for a respective first network node (N1) representing the secondary control power (N1) provided by the respective first network node (N1) ( SRL) and wherein the entry for a respective second and third network node (N2, N3) is zero; where P _{0 is} a vector that contains an entry for each network node (N1, N2, ..., N5) of the power network, the entry for a respective first and second network node (N1, N2) being in that network node (N1, N2) corresponds to power generated at nominal frequency and wherein the entry for a respective third network node (N3) corresponds to the power taken from this network node (N3); where ΔP _{W is} a vector containing an entry for each network node (N1, N2, ..., N5) of the power network, the entry for a respective second network node (N2) being less than the associated entry of the vector P ₀ , if the respective second network node (N2) has not failed, and if the respective second network node (N2) fails, the power generated in the respective second network node (N2) corresponds to the current time, and wherein the entry for a respective first and third network node (N1 , N3) is zero; where k _{P is} a vector containing an entry for each network node (N1, N2, ..., N5) of the power network, the entry for a respective first network node (N1) corresponding to a proportionality factor over that of the respective one Network node (N1) provided primary control power (PRL) is affected, and the entry for all other network nodes is zero; where B is an incidence matrix with a number of rows corresponding to the number of network nodes (N1, N2, ..., N5) in the power grid and a number of columns corresponding to the number of power lines (PL) in the power grid, each power line (PL) is represented by a directed edge starting from a network node (N1, N2, ..., N5) and ending at a network node (N1, N2, ..., N5); where is true

where L ^{✝ is} the pseudoinverse of the Laplace matrix L = BKB ^T ; where K is a diagonal matrix containing on the diagonal an entry for each directed edge representing a power line, the entry for an edge starting at a network node i and terminating at a network node j is as follows:

where u _i and u _{j are} the rms values of the voltages in the respective network nodes i and j, respectively; where x _{ij is} the reactance of the power line starting at node i and terminating at node j; where Δf _{max is} the first threshold value; where γ is the second threshold representing the maximum magnitude phase difference from all the phase differences occurring between the voltages of two network nodes (N1, N2, ..., N5) connected via a power line (PL) in the power grid. Method according to one of the preceding claims, characterized in that in step c) the proportional proportions of the secondary control powers (SRL) provided in the respective first network nodes (N1, N4, N5) are predetermined on the total provided secondary control power, wherein in step c) permissible, the predetermined condition fulfilling factor is determined from which results in multiplying by the proportion of a respective first network node (N1, N4, N5) available in the power grid secondary control power (SRL) of the respective first network node (N1, N4, N5). Method according to one of the preceding claims, characterized in that, in step c), separately for each first network node (N1), assuming that the other first network nodes (N4, N5) do not provide secondary control power (SRL), the predetermined condition satisfying values for the secondary control powers (SRL) of the respective first network node (N1), whereby a set of vectors of permissible secondary control performances (SRL) of all first network nodes (N1) is determined, wherein the secondary control power available in the power grid (SRL) is selected by selecting a Vector from the convex hull of the set of vectors and the zero vector. Method according to one of the preceding claims, characterized in that, in step c), the secondary control power (SRL) available in the power grid is determined as a constraint based on the maximization of the sum of the secondary control power of all first network nodes (N1) under the predetermined condition of step b) become. Method according to one of the preceding claims, characterized in that the second network nodes (N2) comprise one or more wind turbines and / or one or more photovoltaic systems. Apparatus for computer-aided control of the power in an electrical power network, wherein the power grid has a predetermined nominal frequency and a plurality of interconnected via power lines (PL) network nodes (N1, N2, ..., N5), wherein the network nodes (N1, N2 , ..., N5) comprises one or more first network nodes (N1, N4, N5) and one or more second network nodes (N2) and one or more third network nodes (N3), wherein a respective first network node (N1, N4, N5 ) is a generator node that generates power in the power grid and provides primary control power (PRL) and secondary control power (SRL), wherein a respective second network node (N2) is a generator node that generates power in the power grid by means of regenerative power generation, and wherein a respective third network node ( N3) is a load node that draws power from the power grid (N3); characterized in that the device is arranged to carry out a method in which a) a stationary state of the power network, in which a constant frequency in the power network is established by means of the primary control power (PRL) of the first network node (s) (N1), after failure at least a part of the second network nodes (N2) is modeled; b) based on the stationary state of the power network, a condition to the secondary control power (SRL) generated by the one or more network nodes (N1) before failure of at least a part of the second Network node (N2) is given, wherein when the condition is met in the event of failure of the at least a portion of the second network node (N2) the magnitude deviation of the frequency in the mains from the nominal frequency is below a first threshold and / or at least one magnitude phase difference, the between the voltages of two network nodes (N1, N2, ..., N5) connected via one or more power lines (PL) occurs in the power grid is below a second threshold value; c) the power generation of the second network node or nodes (N2) is limited, wherein the limit of the power generation by the available in the power grid secondary control power (SRL) of the first network node (N1) is set such that the predetermined condition is met. Apparatus according to claim 11, characterized in that the device is arranged for carrying out a method according to one of claims 2 to 10. Electric power network having a predetermined nominal frequency and containing a plurality of network nodes (N1, N2, ..., N5) interconnected via power lines (PL), the network nodes (N1, N2, ..., N5) having one or more first network node (N1, N4, N5) and one or more second network nodes (N2) and one or more third network nodes (N3), wherein a respective first network node (N1, N4, N5) is a generator node, which in operation power in Generating power grid as well as providing primary control power (PRL) and secondary control power (SRL), wherein a respective second network node (N2) is a generator node that generates power in operation via regenerative power generation, and wherein a respective third network node is a load node operating Power from the mains supply (N3); characterized in that the power network comprises a device for computer-aided control of the power according to claim 11 or 12.

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