CN115549131B - Online inertia assessment method considering frequency dynamic response real-time partition - Google Patents

Online inertia assessment method considering frequency dynamic response real-time partition Download PDF

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CN115549131B
CN115549131B CN202211369799.2A CN202211369799A CN115549131B CN 115549131 B CN115549131 B CN 115549131B CN 202211369799 A CN202211369799 A CN 202211369799A CN 115549131 B CN115549131 B CN 115549131B
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frequency
inertia
dynamic response
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CN115549131A (en
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曹斌
辛焕海
苗丽芳
毕天姝
刘家豪
王程
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Zhejiang University ZJU
North China Electric Power University
Inner Mongolia Electric Power Research Institute of Inner Mongolia Power Group Co Ltd
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Zhejiang University ZJU
North China Electric Power University
Inner Mongolia Electric Power Research Institute of Inner Mongolia Power Group Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/241—The oscillation concerning frequency
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

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Abstract

The invention discloses an inertia online evaluation method considering frequency dynamic response real-time partition, which comprises the following steps: s1, configuring a PMU (power management unit) in a transformer substation according to a PMU configuration requirement of a power grid, and acquiring the bus frequency of the transformer substation and active power data of an in-out line measured by the PMU; s2, calculating a dynamic time bending index between measuring points in a time window according to frequency data measured by a measuring point PMU; s3, realizing frequency dynamic response real-time partition by adopting a k-center point method; s4, utilizing active power of a regional boundary tie line and central node frequency of a regional cluster measured by a PMU, and adopting a Kalman filtering algorithm to identify regional inertia parameters on line; s5, calculating the total inertia of the system on line according to the identification result of the regional inertia parameter. According to the inertia online assessment method considering the frequency dynamic response real-time partition, the real-time dynamic partition and the area of the power system and the system inertia are accurately measured, and the frequency stability level of the power system is mastered by a dispatcher in real time.

Description

Online inertia assessment method considering frequency dynamic response real-time partition
Technical Field
The invention relates to the field of frequency stability control of power systems, in particular to an inertia online evaluation method considering frequency dynamic response real-time partition.
Background
Inertia is an important index for measuring the frequency stability of a power system, and directly reflects the falling rate of the system frequency after disturbance. The new energy power supply is connected into the power grid through the power electronic converter, the external characteristic of no inertia or weak inertia is reflected in the dynamic process of the system, the new energy is connected into and replaces the synchronous generator in the system in a large scale, and the inertia level of the power system is gradually reduced. Therefore, the on-line evaluation of the inertia level of the power system has important significance, so that a dispatcher can grasp the frequency stability level of the system, adjust the operation mode of the system in advance and ensure the frequency stability of the system.
And (3) monitoring the starting state of the synchronous machine by combining the SCADA system, and carrying out weighted summation on the experience inertia constants of the whole-network online synchronous machine to obtain the online inertia level of the system. However, the SCADA system has a slow feeding speed, cannot cover all synchronous machines of the whole network, and has inaccurate experience inertia parameters, so that the SCADA-based inertia online evaluation scheme cannot evaluate instantaneity and accuracy.
The synchronous phasor measurement device measures the frequency and the active power of the transformer substation on line and synchronously uploads the frequency and the active power to the PMU master station, has real-time performance and accuracy, and provides a new thought for on-line assessment of the inertia of the power system.
The frequency response of the power system has a partition characteristic, the active power variation of the regional interconnecting line can reflect the unbalanced power of the region, and online evaluation of the regional inertia is more feasible. At this time, the power system is partitioned, the regional inertia constants are identified by utilizing the regional tie active power and the regional inertia center frequency obtained by the PMU, and the total inertia of the system is obtained by summing the regional inertia constants. In the aspect of frequency dynamic response partitioning of an electric power system, a partitioning method based on model driving can only obtain a fixed partitioning scheme, and the partitioning result cannot be ensured to meet various disturbance and operation conditions of the system. In the aspect of inertia parameter identification, the inertia constant can be obtained by directly calculating the ratio of active power to the frequency change rate according to a swinging equation, but the method has low calculation accuracy and is easily influenced by noise; the parameter identification method based on the least square principle can be used for identifying inertia constants, such as an autoregressive moving average model, an output error model and the like, but the identification algorithm needs a certain data window length and cannot update the regional inertia level in real time.
Disclosure of Invention
The invention aims to provide an inertia online evaluation method considering frequency dynamic response real-time partition, which not only realizes accurate measurement of real-time dynamic partition, region and system inertia of a power system, but also improves the real-time grasping of the frequency stability level of the power system by a dispatcher.
In order to achieve the above purpose, the invention provides an inertia online evaluation method considering frequency dynamic response real-time partition, comprising the following steps:
according to the PMU configuration requirement of the power grid, PMU is configured in a transformer substation, transformer substation bus frequency measured by the PMU and active power data of an in-out line are obtained, and the data are uploaded to a PMU master station;
consider that the set formed by the network nodes and the synchronous machines of the whole system are N and M respectively, and the network nodes and the synchronous machines in the area i correspond to N respectively i A And M i A Satisfies the following conditions
Figure BDA0003924479900000021
And->
Figure BDA0003924479900000022
Region i is a set of +.>
Figure BDA0003924479900000023
The frequency dynamic response of region i satisfies:
Figure BDA0003924479900000024
Figure BDA0003924479900000025
in the method, in the process of the invention,
Figure BDA0003924479900000026
for the mechanical power of the synchronous machine, P n E And P l L The active power of the load and the active power of the connecting wire are respectively; f (f) i COI For the region COI frequency, all synchronous machine speeds in the region are weighted and summed according to the moment of inertia of the synchronous machine speeds to obtain +.>
Figure BDA0003924479900000027
For the rotational speed of the generator>
Figure BDA0003924479900000028
And->
Figure BDA0003924479900000029
The rotational inertia and rated capacity of the synchronous machine are respectively;
equation (1) is the moment of inertia of the region i, namely the region inertia, and is represented by weighted summation of all the moment of inertia of synchronous machines in the region i according to the rated capacity:
Figure BDA0003924479900000031
wherein S is N Taking the total rated capacity of the system;
the system is completely divided into multiple regions, i.e. U-shaped i N i A =n and- i M i A The frequency dynamic response and the area inertia of the other areas except the area i also satisfy the formula (1) and the formula (2), respectively;
s2, appointing the online evaluation time window length of inertia, and calculating a dynamic time bending index between measuring points in the time window according to frequency data measured by a measuring point PMU;
s3, adopting a k-center point method to aggregate the areas with similar frequency response curves, dividing the system into a plurality of areas, realizing frequency dynamic response real-time partition, and representing the average frequency dynamic of the whole area by the frequencies of the corresponding measuring points of the cluster center points screened by the k-center point method;
the frequency dynamic response real-time partitioning method based on the DTW distance index and the k-center point clustering algorithm comprises the following steps:
designating the number of areas, namely the number of clusters C; cluster center initialization: in the whole network nodes, randomly selecting a group of nodes X #
Figure BDA0003924479900000032
Card (X) =c) as the initial cluster center;
cluster division: calculating the DTW distance between each node frequency of the whole network and the cluster center node frequency:
Figure BDA0003924479900000033
further, dividing each node into each cluster according to the DTW distance; updating the cluster center: for each cluster N divided A (
Figure BDA0003924479900000034
) Calculating the sum of DTW distances of each point in the cluster and other points in the cluster, such as for node e (+)>
Figure BDA0003924479900000035
)：
Figure BDA0003924479900000036
r e The smallest node is used as the updated cluster center;
repeating the steps (3) and (4) to obtain a frequency dynamic response real-time partitioning result N A A regional frequency measuring point X;
s4, according to the frequency dynamic response real-time partitioning result, utilizing the active power of the regional boundary tie line and the central node frequency of the regional cluster, which are measured by the PMU, and adopting a Kalman filtering algorithm to identify regional inertia parameters on line;
the Kalman filtering model comprises a state equation and a measurement equation, and is as follows:
Figure BDA0003924479900000041
wherein x, u and z are respectively state quantity, input quantity and measurement quantity, and F and H are respectively nonlinear state equation and measurement equation;
based on the formula (4), selecting the area COI frequency and the area inertia constant as state quantities, namely x= [ f ] COI ,H A ] T The input is the sum of the link powers, i.e. u= [ ΣΔp L ]The state equation is:
Figure BDA0003924479900000042
the measurement is the area COI frequency, which can be replaced by the cluster center PMU measurement frequency in step 3, i.e., z= [ f M ]The measurement equation is:
f M ＝f COI ； (12)
s5, calculating the total inertia of the system on line according to the identification result of the regional inertia parameter.
Preferably, in step S1, the area inertia constant is extrapolated according to the parameter identification algorithm in combination with the area frequency dynamic response and the measurement data obtained in the step;
considering that the actual power grid frequency generally fluctuates in a small range around the rated frequency, regional inertia assessment should be completed under a small disturbance condition, and continuous monitoring is performed at a real inertia level; at the moment, the system frequency deviation does not touch the dead zone of the speed regulator, the mechanical power of the synchronous machine is unchanged, and the load power fluctuation in the zone is negligible compared with the exchange power of a connecting wire; thus, formula (1) can be simplified as:
Figure BDA0003924479900000051
wherein DeltaP l L ＝P l L -P l L,0 Is the amount of change in active power of the tie-line based on its steady state operating point.
Preferably, in step S1, the PMU in the step is combined to measure the real power of the area tie line and the COI frequency of the area online, and identify the online inertia level of the area; after obtaining the inertia of each region, the total inertia of the system is further calculated:
Figure BDA0003924479900000052
in each region inertia constant
Figure BDA0003924479900000053
The sum is calculated to the rated capacity of the system in the formula (3), and the sum is directly added.
Preferably, in step S2, a data-driven concept is adopted to directly define the metric according to the measured frequency response curve.
Preferably, in step S4, the kalman filter does not require a long data window.
Preferably, in step S4, a volumetric kalman filter algorithm with a better application effect in the electric power system is used to solve the nonlinear kalman filter equation.
Therefore, the inertia online evaluation method considering the frequency dynamic response real-time partition with the structure not only realizes the accurate measurement of the real-time dynamic partition, the area and the system inertia of the power system, but also improves the real-time grasping of the frequency stability level of the power system by the dispatcher.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flow chart of an inertia online evaluation method considering frequency dynamic response real-time partition;
FIG. 2 is a schematic diagram of node frequency dynamics of an inertia online evaluation method considering frequency dynamics response real-time partitioning according to the present invention;
FIG. 3 is a schematic diagram of a DTW path of an inertia online evaluation method considering frequency dynamic response real-time partitioning;
FIG. 4 is a schematic diagram of an IEEE39 node system topology of an inertia online evaluation method considering frequency dynamic response real-time partitioning;
FIG. 5 is a schematic diagram of a system frequency response curve of an inertia online evaluation method considering real-time frequency dynamic response partitioning according to the present invention;
FIG. 6 is a graph showing the partitioning result and partitioning frequency effect curve of an inertia online evaluation method considering real-time partitioning of frequency dynamic response according to the present invention;
FIG. 7 is a schematic diagram of a state variable tracking effect of an inertia online evaluation method considering frequency dynamic response real-time partition according to the present invention;
FIG. 8 is a schematic diagram of a system frequency influence curve in a frequency fluctuation scene of an inertia online evaluation method considering frequency dynamic response real-time partition;
FIG. 9 is a schematic diagram of a partitioning result and a partitioning frequency response curve of a frequency fluctuation scene of an inertia online evaluation method considering frequency dynamic response real-time partitioning.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Referring to fig. 1, a flow chart of an inertial online assessment method considering frequency dynamic response real-time partition according to the present invention includes: according to the PMU configuration requirement of the power grid, PMU is configured in a transformer substation, transformer substation bus frequency measured by the PMU and active power data of an in-out line are obtained, and the data are uploaded to a PMU master station;
the configuration mode meets the configuration principle of PMU in the power grid; considering that the electrical distance between all devices in the same transformer substation is close, the bus frequency of the transformer substation can be replaced by any measuring point frequency in the transformer substation; the active power of the access line does not include the active power of the low-voltage distribution line.
Designating the online inertia evaluation time window length, and calculating the dynamic time bending index between measuring points in the time window according to the frequency data measured by the measuring point PMU;
in this step, in order to realize real-time partitioning of frequency dynamic response, a measurement index of the frequency similarity of network nodes is given, and the degree of connection tightness between nodes is usually measured by using an electrical distance, however, the electrical distance does not directly reflect the frequency dynamic response of the nodes, and the difference of the partition characteristics of the power system under different disturbances cannot be considered, so that the method is not suitable for defining the measurement index of the frequency similarity of the nodes.
As shown in fig. 2, the frequency response curves of two adjacent nodes in the system should be divided into the same area, and the node frequency similarity is represented in the following two aspects: from the curve value, the two frequency response curve values under any time section are close; from the curve form, the two curves are close, and have short-time lead-lag characteristics, because disturbance propagation in a large power grid has wave process characteristics, and the sequence of the disturbance affecting the frequency of each node is related to the position of the disturbance point from the node. To sum up, the node frequency similarity measure index needs to simultaneously account for curve value differences and lead-lag characteristics.
The DTW distance index is suitable for calculating the similarity between two unsynchronized time sequences, the two sequences are consistent in form by bending the time sequences, the difference value is characterized, and meanwhile, the lead-lag characteristic is considered, so that the DTW distance index can be used as the node frequency similarityThe measurement index is set that the PMU master station obtains discrete frequency sequences measured by the nodes a and b as follows respectively
Figure BDA0003924479900000071
And->
Figure BDA0003924479900000072
Satisfy the following requirements
Figure BDA0003924479900000073
And->
Figure BDA0003924479900000074
The sequence lengths are K.
As shown in FIG. 3, the K X K-dimensional lattice matrix for DTW path analysis has horizontal and vertical axes corresponding to
Figure BDA0003924479900000075
And->
Figure BDA0003924479900000076
The matrix element is denoted as w s (p, q) represents->
Figure BDA0003924479900000077
P-th sample point of (2) and +.>
Figure BDA0003924479900000078
The relation between the q-th sampling points of (c). From the frequency initial sampling point w 1 (1, 1) to the end-of-frequency sampling point w S The path of (K, K) can be noted as w= { W 1 ,w 2 ,…,w s ,…,w S K is less than or equal to S is less than or equal to 2K, and continuity and monotonicity of the path are ensured:
continuity: some point on the path and one point on the path are respectively marked as w s (p, q) and w s-1 (p ', q') is required to satisfy (p-p ') less than or equal to 1 and (q-q') less than or equal to 1, ensuring consideration of
Figure BDA0003924479900000081
And->
Figure BDA0003924479900000082
Simultaneously warping the time series such that frequency lead-lag is accounted for;
monotonicity: also for w s And w s-1 The p 'is less than or equal to p and the q' is less than or equal to q, and the guarantee is ensured
Figure BDA0003924479900000083
And->
Figure BDA0003924479900000084
The association between the sampling points is not considered repeatedly.
Element w s (p, q) corresponding sample points
Figure BDA0003924479900000085
And->
Figure BDA0003924479900000086
The frequency difference between them is recorded as->
Figure BDA0003924479900000087
The total difference of the paths W is +.>
Figure BDA0003924479900000088
The path meeting the minimum total difference is the optimal path, and the corresponding minimum difference is equal to +.>
Figure BDA0003924479900000089
DTW distance between:
Figure BDA00039244799000000810
the optimal path calculation in the formula (6) is a global optimization problem, and the dynamic programming method shown in the formula (7) can be utilized to convert global optimization into local optimization:
Figure BDA00039244799000000811
where D (p, q) is the cumulative minimum frequency difference.
The k-center point method is adopted to aggregate the areas with similar frequency response curves, the system is divided into a plurality of areas, the frequency dynamic response real-time partition is realized, the frequencies of the corresponding measuring points of the cluster center points screened by the k-center point method represent the average frequency dynamic of the whole area;
in the step, when the DTW distance index between node frequencies is smaller, the frequency similarity degree is high, and the nodes can be divided into the same area, so that on the basis of the DTW distance index, the frequency dynamic response real-time partition can be completed through a clustering algorithm, and the clustering algorithm based on the distance mainly comprises a k-mean value method and a k-center point method.
As shown in the formula (2), the COI frequency of the area required for inertia evaluation needs to be calculated according to the rotational speeds of all synchronous machines in the area, but in an actual system, it cannot be guaranteed that each power plant is configured with a PMU, so that the COI frequency needs to be approximately replaced by a certain network node frequency in the area. Compared with the k-means method, the cluster center shown by the clustering algorithm of the k-center point method corresponds to the actual data point, namely, the system network node. Considering that the cluster center can reflect the shape of the whole cluster, namely the frequency of the corresponding node of the cluster center can represent the frequency response of the region, a k-center point clustering algorithm is adopted, and the cluster center PMU measurement frequency is used for replacing the frequency of the region COI.
According to the frequency dynamic response real-time partitioning result, utilizing the active power of the regional boundary tie line and the central node frequency of the regional cluster, which are measured by the PMU, and adopting a Kalman filtering algorithm to identify regional inertia parameters on line;
calculating the total inertia of the system on line according to the identification result of the regional inertia parameter;
in this step, the total inertia of the system is calculated according to equation (5);
the IEEE39 node system topology is shown in FIG. 4, the disturbance is set to increase or decrease the load active power small range, the system frequency offset does not exceed the governor dead zone, and the zone frequency dynamic response is described in equation (4). The rated capacity and inertia constant of each unit are shown in table 1, the total rated capacity of the system is 1000MVA, and the regional inertia and the system inertia are both based on the total rated capacity of the system. At time t=0s, the active power of the load connected to node 27 increases by 5MW, and the frequency response curves of all PMU configuration nodes in the system at t=1-4 s are shown in fig. 5, which also shows the frequencies of node 23 and node 29. It can be seen that the IEEE39 node system frequency response has a spatially distributed nature, and in order to evaluate the area inertia and further calculate the total inertia of the system, the system is first divided into a plurality of areas.
TABLE 1 inertia constant of generators
Figure BDA0003924479900000091
Figure BDA0003924479900000101
The system carries out an on-line power system inertia assessment method considering frequency dynamic response real-time partition:
according to the configuration principle of PMU in the actual power grid, PMU should be configured for the equivalent IEEE39 nodes shown in FIG. 4 except the generator end;
calculating DTW indexes among nodes;
as shown in fig. 5, the data of the t=1-4 s time period is used as a data window of the frequency dynamic response real-time partitioning method, and DTW indexes among curves in fig. 5 are calculated and clustered according to a k-center point method algorithm. As shown in fig. 5 (a), the system is divided into 4 areas, the area 2 contains generators G04, G05, G06 and G07, only a single generator in the areas 3 and 4 is G01 and G09 respectively, and the remaining four generators are divided into the area 1, and the corresponding nodes in the center of each area cluster are node 04, node 21, node 09 and node 28 respectively.
The time period frequency data of t=1-4 s in fig. 5 are sorted according to the partitioning result, and the node frequency response curves corresponding to the areas 1-4 are shown in fig. 6 (b) - (e), respectively. As can be seen from fig. 6 (b) - (e), for the nodes in the same area, the frequency response curves are close in value and have the same oscillation characteristics in morphology, and the frequency response curves of the nodes in different areas are different in value and morphology, which indicates that the partitioning result is reasonable. Further, as shown in table 2, the quantization index of the partitioning effect is characterized by the DTW distance index of the node frequency of each region, in mHz. In table 2, diagonal cells represent the average value of DTW index between nodes in an area and the area node, off-diagonal cells represent the average value of DTW index between two different area nodes, and the smaller the DTW index value is, the closer the frequency response between the two is, it can be seen that the diagonal cells correspond to the DTW index value is smaller and far smaller than the off-diagonal cells.
Table 2 node DTW index for each region (mHz)
Figure BDA0003924479900000102
Figure BDA0003924479900000111
FIGS. 6 (b) - (e) also show the frequencies of the central nodes of each cluster, the values of the curves are the average of all curves in the cluster, and can represent the average dynamic characteristics of the regional frequencies, which indicates that the central node frequencies of the clusters can replace the regional COI frequencies and can be further used for regional inertia evaluation;
based on the partitioning result, the active power of the regional tie line and the corresponding node frequency of the cluster center measured by the PMU in the period of t=1-4 s are obtained, and the regional inertia is identified by adopting a volume Kalman algorithm according to the formula (11) and the formula (12). Taking area 1 as an example, the active power of the tie lines {01-02,08-09,25-26,26-27,16-17,14-15} is the input, and the frequency of node 04 is the observed quantity.
As shown in FIG. 7, the Kalman filtering state variable tracking effect of region 1, FIGS. 7 (a) and (b) correspond to two state variables, namely region COI frequency f, respectively COI And a regional inertia constant H A It can be seen that the Kalman filtering algorithm can accurately track the state variable values, and the regional inertia constant estimated values quickly converge to a steady stateValues.
The inertia parameter identification results of the region 1 and other regions are shown in table 3, and the inertia constant is normalized according to the 1000MW capacity, wherein the inertia result is taken as the identification inertia result when the fluctuation range of the inertia estimated value is less than 1%. It can be seen that the inertia estimation error of each region is less than 7%, the identification result is accurate, and meanwhile, the frequency response partitioning method can accurately partition the system. It should be noted that, since the region 3 and the region 4 are configured with a single synchronous machine only at the boundary of the system, the region inertia distribution is seriously uneven, and the region COI frequency, that is, the rotational speed of the synchronous machine is greatly different from the node frequency in the region, and the inertia estimation error is relatively large.
TABLE 3 inertia estimation results
Numbering device Actual inertia(s) Identification inertia(s) Error (%)
Zone 1 13.24 12.84 -2.98
Zone 2 11.58 11.72 1.20
Zone 3 50.00 47.67 -4.67
Zone 4 3.45 3.21 -6.96
Full system 78.27 75.44 -3.62
The total inertia of the system calculated according to equation (5) is shown in table 3 with high accuracy.
Further, in order to verify the adaptability of the partition inertia evaluation method to the running state of the system, various position continuous disturbance is set in the IEEE39 node system to simulate the actual power grid frequency fluctuation scene, and the frequency response curves of all PMU configuration nodes in the system are shown in FIG. 8. At each moment the disturbance and the system operating point are different, and at t=0-16 s and t=16-32 s, the load disturbance locations are located at nodes {21,22,23,24} and {10,11,12,13} respectively.
The example analysis is performed taking the data window of two periods of t=5-8 s and t=17-20 s as an example. First, as qualitatively shown in fig. 8, the frequencies of the node 23 and the node 29 are almost not different at t=17-20 s, and can be divided into the same area, but the time difference is significant at t=5-8 s, and cannot be divided into the same area, i.e., the partition characteristics of the power system have real-time property.
As shown in fig. 9, fig. 9 (a) and (b) are the partitioning result and the area frequency response curve of the data window 1, respectively, and fig. 9 (c) and (d) correspond to the data window 2. As shown in fig. 9 (a) and (c), as the system operating point and the disturbance location change, the system partition result is different, and the cluster center corresponding node is also different. As can be seen from fig. 9 (b) and (d), the spatial distribution characteristics of the system frequency in the data window 1 are significant, the difference between the oscillation characteristics of each curve is large, the system is divided into 5 areas, and only three areas need to be divided in the data window 2.
The regional inertia identification results are shown in table 4, and the regional inertia and the total inertia estimation accuracy of the system are high, so that the Kalman filtering algorithm can adapt to different operation conditions of the system, and the accuracy of inertia parameter identification is ensured by the dynamic partitioning results.
TABLE 4 partition inertia estimation results in frequency fluctuation scenarios
Figure BDA0003924479900000121
Figure BDA0003924479900000131
According to the embodiment, the method can divide the region in real time according to the actually measured frequency response curve, ensure the accuracy of the partitioning result under various operation conditions and improve the region inertia estimation precision.
Therefore, the inertia online evaluation method considering the frequency dynamic response real-time partition with the structure not only realizes the accurate measurement of the real-time dynamic partition, the area and the system inertia of the power system, but also improves the real-time grasping of the frequency stability level of the power system by the dispatcher.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.

Claims (6)

1. An inertia online evaluation method considering frequency dynamic response real-time partition is characterized by comprising the following steps:
s1, configuring a PMU (power management unit) in a transformer substation according to a PMU configuration requirement of a power grid, acquiring the transformer substation bus frequency measured by the PMU and active power data of an in-out line, and uploading the data to a PMU master station;
consider that the set formed by the network nodes and the synchronous machines of the whole system are N and M respectively, and the network nodes and the synchronous machines in the area i correspond to N respectively i A And M i A Satisfies the following conditions
Figure FDA0003924479890000019
And->
Figure FDA00039244798900000110
The set of region i and other region links is
Figure FDA0003924479890000011
The frequency dynamic response of region i satisfies:
Figure FDA0003924479890000012
Figure FDA0003924479890000013
in the method, in the process of the invention,
Figure FDA0003924479890000014
for the mechanical power of the synchronous machine, P n E And P l L The active power of the load and the active power of the connecting wire are respectively; f (f) i COI Is the area COI frequency; all synchronous machine rotating speeds in the region are weighted and summed according to the moment of inertia to obtain +.>
Figure FDA0003924479890000015
The rotation speed of the generator; />
Figure FDA0003924479890000016
And->
Figure FDA0003924479890000017
The rotational inertia and rated capacity of the synchronous machine are respectively;
h in formula (1) i A The moment of inertia of the region i, namely the region inertia; the rotational inertia of the synchronous machine in the region i is expressed by weighted summation of rated capacity:
Figure FDA0003924479890000018
wherein S is N Is the total rated capacity of the system;
the system is completely divided into multiple regions, i.e. U-shaped i N i A =n and- i M i A The frequency dynamic response and the area inertia of other areas than the area i also satisfy the formulas (1) and (2), respectively, =m;
s2, appointing the online evaluation time window length of inertia, and calculating a dynamic time bending index between measuring points in the time window according to frequency data measured by a measuring point PMU;
s3, adopting a k-center point method to aggregate the areas with similar frequency response curves, dividing the system into a plurality of areas, realizing frequency dynamic response real-time partition, and representing the average frequency dynamic of the whole area by the frequencies of the corresponding measuring points of the cluster center points screened by the k-center point method;
the frequency dynamic response real-time partitioning method based on the DTW distance index and the k-center point clustering algorithm comprises the following steps:
designating the number of areas, namely the number of clusters C; cluster center initialization: in the whole network nodes, randomly selecting a group of nodes X #
Figure FDA0003924479890000024
Card (X) =c) as the initial cluster center;
cluster division: calculating the DTW distance between each node frequency of the whole network and the cluster center node frequency:
Figure FDA0003924479890000021
further, dividing each node into each cluster according to the DTW distance, and updating the cluster center; for each cluster divided
Figure FDA0003924479890000027
Calculating the sum of DTW distances of each point in the cluster and other points in the cluster, e.g. for node +.>
Figure FDA0003924479890000028
Figure FDA0003924479890000022
r e The smallest node is used as the updated cluster center;
repeating the steps (3) and (4) to obtain a frequency dynamic response real-time partitioning result N A A regional frequency measuring point X;
s4, according to the frequency dynamic response real-time partitioning result, utilizing the active power of the regional boundary tie line and the central node frequency of the regional cluster, which are measured by the PMU, and adopting a Kalman filtering algorithm to identify regional inertia parameters on line;
the Kalman filtering model comprises a state equation and a measurement equation, and is as follows:
Figure FDA0003924479890000023
wherein x, u and z are respectively state quantity, input quantity and measurement quantity, and F and H are respectively nonlinear state equation and measurement equation;
based on the formula (4), selecting the area COI frequency and the area inertia constant as state quantities, namely x= [ f ] COI ,H A ] T The input is the sum of the link powers, i.e. u= [ ΣΔp L ]The state equation is:
Figure FDA0003924479890000031
the measurement is the area COI frequency, which can be replaced by the cluster center PMU measurement frequency in step 3, i.e., z= [ f M ]The measurement equation is:
f M ＝f COI ； (12)
s5, calculating the total inertia of the system on line according to the identification result of the regional inertia parameter.
2. The online inertia assessment method considering real-time partitioning of frequency dynamic response according to claim 1, wherein: in step S1, the area inertia constant is reversely deduced according to the parameter identification algorithm by combining the area frequency dynamic response and the measurement data obtained in the step;
considering that the actual power grid frequency generally fluctuates in a small range around the rated frequency, regional inertia assessment should be completed under a small disturbance condition, and continuous monitoring is performed at a real inertia level; at this time, the system frequency deviation does not touch the dead zone of the speed regulator, the mechanical power of the synchronous machine is unchanged, and the load power fluctuation in the zone is negligible compared with the link exchange power, so the formula (1) can be further simplified into:
Figure FDA0003924479890000032
wherein DeltaP l L ＝P l L -P l L,0 Is the amount of change in active power of the tie-line based on its steady state operating point.
3. The online inertia assessment method considering real-time partitioning of frequency dynamic response according to claim 1, wherein: in step S1, the PMU in the step is combined to measure the active power of the area connecting line and the COI frequency of the area on line, and the area on-line inertia level is identified; after obtaining the inertia of each region, the total inertia of the system is further calculated:
Figure FDA0003924479890000041
in each region inertia constant
Figure FDA0003924479890000042
The sum is calculated to the rated capacity of the system in the formula (3), and the sum is directly added.
4. The online inertia assessment method considering real-time partitioning of frequency dynamic response according to claim 1, wherein: in step S2, a data-driven idea is adopted to directly define a measurement index according to the measured frequency response curve.
5. The online inertia assessment method considering real-time partitioning of frequency dynamic response according to claim 1, wherein: in step S4, the kalman filter does not require a long data window.
6. The online inertia assessment method considering real-time partitioning of frequency dynamic response according to claim 1, wherein: in step S4, a volume Kalman filtering algorithm with good application effect in the power system is adopted to solve a nonlinear Kalman filtering equation.
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