CN116231685B - QPSO-based electric power system inertia and primary frequency modulation capability assessment method - Google Patents
QPSO-based electric power system inertia and primary frequency modulation capability assessment method Download PDFInfo
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Abstract
The invention discloses a QPSO-based power system inertia and primary frequency modulation capability assessment method, which belongs to the field of power system frequency stability control and comprises the following steps: the method comprises the steps of monitoring and collecting frequency and active power data of a grid-connected bus of a power plant in real time through a synchronous phasor measurement device, partitioning a power system based on a power grid topology and a disturbed system frequency dynamic response curve, evaluating inertia and primary frequency modulation capacity of each region based on unbalanced power and regional inertia center frequency in the region, and evaluating inertia and primary frequency modulation capacity of the whole power system through weighting and aggregating equivalent inertia time constants and equivalent difference modulation coefficients of each region. By adopting the QPSO-based power system inertia and primary frequency modulation capability assessment method, the real-time tracking of the power system inertia and primary frequency modulation capability can be realized, system scheduling staff is helped to grasp the system frequency safety level in real time, the system operation mode is guided and adjusted, and the system operation stability is improved.
Description
Technical Field
The invention relates to the field of power system frequency stability control, in particular to a QPSO-based power system inertia and primary frequency modulation capability assessment method.
Background
With the continuous improvement of the access proportion of new energy, the overall inertia level of the power system is reduced, and the characteristic of uneven frequency modulation capability distribution is increasingly displayed, so that the online evaluation of the inertia and primary frequency modulation capability of the power system by using the measurement data of the synchronous phasor measurement unit (Phasor Measurement Unit, PMU) has important significance.
And the inertia and primary frequency modulation capability of the power system are evaluated on line by taking the apparent space-time distribution difference of the frequency dynamic response of the power system into consideration, so that the feasibility is realized. The zoning result of the system is influenced by the power grid topology and parameters, is related to the system operating point, the disturbance type and the disturbance position, and provides higher requirements for the rapidity of the online evaluation algorithm of the inertia and primary frequency modulation capability of the system in the dynamic zoning scene of the system.
In order to quantitatively analyze the frequency modulation capability of the power system, the system frequency dynamic response process is focused in an inertia response stage and a primary frequency modulation stage. Where inertia plays an important role in maintaining transient stability of the frequency of the power system, the level of inertia of the power system can characterize the ability of the system to dampen frequency changes under unbalanced power disturbances, typically expressed as an inertia time constant. In the primary frequency modulation stage, the synchronous unit speed regulator acts to regulate mechanical power output, and the equivalent difference adjustment coefficient of the power system can represent the frequency supporting capacity of the power system in the primary frequency modulation stage.
Meanwhile, as a new energy source is connected into a power grid through a power electronic converter and replaces a synchronous generator in the system, the inertia level of the system is further reduced, and the primary frequency modulation capability is weakened, so that the online evaluation of the inertia and the primary frequency modulation capability of the power system has important significance, and the online evaluation method can help system dispatcher to grasp the frequency safety level of the system in real time and guide and adjust the operation mode of the system, and improves the operation stability of the system.
In the aspect of system inertia and primary frequency modulation capability assessment based on PMU measurement data, the calculated amount is large when a single generator is taken as a minimum assessment unit, the rapid requirement of online assessment cannot be met, and when the whole system is taken as an assessment object, the problems of difficult acquisition of unbalanced power, poor frequency aggregation effect and low assessment precision of frequency modulation capability are faced.
Disclosure of Invention
In order to solve the problems, the invention provides the QPSO-based power system inertia and primary frequency modulation capability evaluation method, which can realize real-time tracking of the power system inertia and primary frequency modulation capability, help system schedulers to master the system frequency safety level in real time and guide and adjust the system operation mode, and improve the system operation stability.
In order to achieve the above purpose, the invention provides a QPSO-based power system inertia and primary frequency modulation capability assessment method, which comprises the following steps:
s1, monitoring and collecting frequency and active power data of a grid-connected busbar of a power plant in real time through a synchronous phasor measurement device;
s2, taking the fact that the frequency of the power system has space-time distribution characteristics into consideration, and partitioning the power system based on the power grid topology and a disturbed system frequency dynamic response curve;
s3, evaluating inertia of each area and primary frequency modulation capacity based on unbalanced power in the area and area inertia center frequency;
and S4, evaluating inertia and primary frequency modulation capacity of the whole power system by carrying out weighted aggregation on the equivalent inertia time constant and the equivalent difference modulation coefficient of each region.
Preferably, the step S2 specifically includes the following steps:
based on Euclidean distance and K-means algorithm, the collected power plant grid-connected busbar frequency time series are clustered, the frequency time series and the cluster center closest to the frequency time series are classified, and the power system is divided into a plurality of areas by combining the power grid topology.
Preferably, the step S2 specifically includes the following steps:
s21, measuring the frequency discrete time sequence of the node A through the PMU
And frequency discrete time sequence of node B +.>
For frequency discrete time series +.>
And->
Satisfy->
，/>
，/>
Is the length of the frequency discrete time series;
s22, representing the similarity between time sequences of different frequencies by using Euclidean distance, wherein the distance index is shown as follows:
in the method, in the process of the invention,
for frequency time series->
And->
A Euclidean distance between them;
s23, clustering the frequencies by adopting a K-means algorithm based on the defined Euclidean distance index;
s24, dividing the power system into a plurality of areas by combining the power grid topology.
Preferably, the step S23 specifically includes the following steps:
s231, designating the cluster number M, and calculating the distance between the sample and the cluster center assuming that each cluster has a center point:
in the method, in the process of the invention,
for the frequency-time series of acquisition, +.>
For the center point vector of the cluster where the sample is located, the sample and the nearest center point are divided into a cluster, +.>
For calculating the distance between two frequency time sequences, < >>
For the length of the frequency discrete time series, +.>
Is the distance between the sample and the cluster center;
s232, randomly selecting M points as center points of each cluster, and iteratively executing the following two steps:
finding respective sample data for each center point, and dividing the sample data into center points closest to each center point;
and (3) recalculating the center point in each cluster, wherein the new center point is the arithmetic average value of members in the cluster, so that the calculated L value of the new center point is necessarily smaller than or equal to the original L value, and the iterative loop is carried out until the clustering algorithm converges and then exits.
Preferably, the step S3 specifically includes the following steps:
s31, writing out a forward differential model and a fitness function of regional inertia evaluation, respectively aggregating frequency and active power data of a power plant grid-connected bus in each region, and dynamically estimating equivalent inertia time constants of each region by adopting a quantum particle swarm optimization algorithm in the length of each data sliding window by utilizing frequency data before primary frequency modulation action;
s32, writing out a forward differential model and a fitness function of regional primary frequency modulation capability evaluation, calculating regional inertia response power according to the evaluation result of the equivalent inertia time constant of each region, correcting unbalanced power of a system, and dynamically estimating the equivalent difference adjustment coefficient of each region by adopting a quantum particle swarm optimization algorithm in each data sliding window length by utilizing frequency data after primary frequency modulation action;
s33, setting the sliding window length of the estimated data, the data sampling time interval and the action dead zone of the synchronous machine set speed regulator, writing a forward differential model and a fitness function for estimating the regional inertia and primary frequency modulation capacity into a quantum particle swarm optimization algorithm for iteration until the termination condition of the quantum particle swarm optimization algorithm is met, and outputting the global optimal position of the particle swarm, namely the regional equivalent inertia time constant and the equivalent difference adjustment coefficient.
Preferably, the step S31 specifically includes the following steps:
s311, equating the power system of each region into a synchronous generator, and describing the active-frequency dynamic response process by the following rotor motion equation under unbalanced disturbance:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the power angle of the generator, < >>
Rated frequency of generator, < >>
For generator frequency deviation, < >>
Is generator inertia time constant, +.>
And->
Respectively the mechanical power per unit value and the electromagnetic power per unit value of the generator>
Is the damping coefficient of the generator, < >>
Is a time-domain differential operator;
s312, in the inertia response stage after the system is disturbed, the system frequency does not exceed the primary frequency modulation dead zone, and the mechanical power output of the generator is considered to be stable at the moment, namely
Simultaneously ignoring the influence of the damping coefficient of the generator, let ∈ ->
The above formula is written as:
the output of the generator before disturbance occurs meets
The following formula is obtained:
in the method, in the process of the invention,
and->
Mechanical power and electromagnetic power of the generator before the disturbance occurs, respectively,>
for the electromagnetic power increment after the disturbance occurs, +.>
An equivalent inertial time constant to be evaluated for the regional power system;
s313, obtaining a fitting formula of the following frequency curve by forward difference of the formula:
in the method, in the process of the invention,
fitting for Quantum particle swarm Algorithm +.>
Time-of-day frequency deviation +.>
Fitting for Quantum particle swarm Algorithm +.>
Time-of-day frequencyDeviation (F)>
For the sampling time interval of the frequency data, +.>
Is->
Unbalanced power of the time zone power system;
s314, estimating an adaptability function of an equivalent inertial time constant of the regional power system, wherein the adaptability function is shown in the following formula:
in the method, in the process of the invention,
to characterize the fitness function of the frequency curve fitting effect, +.>
Frequency deviation fitted for quantum particle swarm algorithm.
Preferably, the step S32 specifically includes the following steps:
s321, in a primary frequency modulation stage after system disturbance, the system frequency exceeds a primary frequency modulation dead zone, a generator speed regulator in the area starts to act, mechanical power output changes, and at the moment, the mechanical power increment of a generator set meets the following transfer function form:
in the method, in the process of the invention,
for the generator mechanical power increment after the disturbance has occurred, +.>
Equivalent difference coefficient to be evaluated for regional power system, +.>
For the system frequency +.>
Is a primary frequency modulation action dead zone->
Equivalent time constant of first-order inertia link of speed regulator, < >>
Is a frequency domain differential operator;
s322, evaluating the result based on the equivalent inertial time constant of the regional power system
And (3) taking inertia effect into account in the primary frequency modulation process, and correcting the unbalanced regional power into:
in the method, in the process of the invention,
unbalanced power for a regional power system;
s323, forward difference of the transfer function is obtained:
in the method, in the process of the invention,
is->
Frequency deviation of time,/->
Fitting for Quantum particle swarm Algorithm +.>
Time zone power system unbalanced power, +.>
Fitting for Quantum particle swarm Algorithm +.>
Unbalanced power of the power system in the time zone;
s324, estimating an adaptability function of an equivalent difference adjustment coefficient of the regional power system, wherein the adaptability function is shown in the following formula:
in the method, in the process of the invention,
to characterize the fitness function of the power curve fitting effect, +.>
And (5) unbalanced power of the regional power system fitted for the quantum particle swarm algorithm.
Preferably, the step S33 specifically includes the following steps:
s331, determining dimension of quantum particle swarm target search space
I.e. the number of decision variables to be solved; at this time, assume thatNThe particles form a group, and the movement of each particle not only needs to consider the optimal position searched by the particle, but also comprehensively considers the optimal position searched by the group; in quantum space, the velocity and position of the particles cannot be determined simultaneously, so the wavefunction +.>
Describing the state of the particle, wherein->
Is a position vector of a particle in a three-dimensional space, and the probability density of the occurrence of the particle at a certain point in the space is represented by the square of a wave function modulus, namely:
wherein Q is a probability density function that satisfies a normalization condition:
s332, describing the movement of particles in quantum mechanics by a Schrodinger equation:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is Manhattan operator,)>
Is Planck constant, +.>
For particle quality, < >>
Is the potential field where the particles are located;
s333, consider a single particle
The point is one-dimensional +.>
In the potential well, attracting particlesSon->
Marked as->
The position of the particles is marked->
The potential energy function is as follows:
in the method, in the process of the invention,
is Euler-Ma Xieluo Niconstant;
s334, determining the position of the particles by adopting a Monte Carlo method:
wherein, the liquid crystal display device comprises a liquid crystal display device,Lis that
Characteristic length of potential well->
Is section->
On uniformly distributed random numbers, i.e. +.>
；
The particles are
First->
The basic evolution equation for the coordinates of the dimensions is:
in the method, in the process of the invention,
for the time t+1 particle->
First->
Coordinates of dimension->
For time t particle->
First->
The attractor of the dimension is a three-dimensional attractor,
for time t particle->
First->
Wei->
Characteristic length of potential well->
For time interval t->
Random numbers uniformly distributed on the base;
s335, introducing an average best position
Defined as the average of the best positions of all particle individuals,/->
By passing through
To evaluate, the evolution equation of the particles is rewritten as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
for the contraction-expansion coefficient, +.>
For time t particle->
First->
Coordinates of dimension->
For the number of particle populations,
is->
The best position is averaged.
Preferably, the step S4 specifically includes the following steps:
setting reference capacity of the power system, aggregating evaluation results of inertia and primary frequency modulation capacity of each area, and calculating equivalent inertia time constant and equivalent difference adjustment coefficient of the power system on line.
Preferably, the step S4 specifically includes the following steps:
dividing an electrical power system into
Setting rated capacity of the system, aggregating evaluation results of inertia and primary frequency modulation capacity of each region, and calculating equivalent inertia time constant and equivalent difference adjustment coefficient of the power system on line;
wherein, the equivalent inertia of the power system is expressed as:
in the method, in the process of the invention,
for the equivalent inertia of the power system->
For the kinetic energy stored by all generators in the area, +.>
Equivalent inertial time constant for each region, +.>
Rated capacity for each zone;
the system equivalent inertial time constant is represented by a weighted average of the equivalent inertial time constants of the respective regions:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the equivalent inertia time constant of the electric power system, +.>
Is a reference capacity of the power system;
likewise, the power system equivalent difference coefficient is represented by a weighted average of the regional equivalent difference coefficients:
in the method, in the process of the invention,
is the equivalent difference adjustment coefficient of the power system, +.>
Is the equivalent difference adjustment coefficient of each region.
The invention has the following beneficial effects:
the synchronous phasor measurement device configured at the positions of the grid-connected buses and other key buses of the power plant is fully utilized, the frequency and active power data of the buses are collected, the topological structure of the power grid is obtained, real-time tracking of the inertia and primary frequency modulation capacity of the power system can be realized, system scheduling staff is helped to master the frequency safety level of the system in real time, the operation mode of the system is guided and adjusted, and the operation stability of the system is improved.
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 a QPSO-based power system inertia and primary frequency modulation capability assessment method of the present invention;
FIG. 2 is a schematic diagram of an IEEE 39 node system topology as employed by an embodiment of the present invention;
FIG. 3 is a graph of a result of frequency clustering of busbar nodes according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an IEEE 39 node system partition in accordance with an embodiment of the invention;
FIG. 5 is a box plot of the results of the equivalent inertial time constant evaluation for each region in an embodiment of the present invention;
FIG. 6 is a box diagram of the evaluation result of the equivalent adjustment coefficient of each region according to the embodiment of the invention;
FIG. 7 is a graph of dynamic evaluation results of inertia of an electric power system according to an embodiment of the present invention;
fig. 8 is a graph of a dynamic evaluation result of primary frequency modulation capability of an electric power system according to an embodiment of the invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, and it should be noted that, while the present embodiment provides a detailed implementation and a specific operation process on the premise of the present technical solution, the protection scope of the present invention is not limited to the present embodiment.
The QPSO-based power system inertia and primary frequency modulation capability evaluation method comprises the following steps of:
s1, monitoring and collecting frequency and active power data of a grid-connected busbar of a power plant in real time through a synchronous phasor measurement device;
in the power system in this embodiment, synchronous phasor measurement devices should be configured at grid-connected buses of the power plant, and other key bus positions should be configured as much as possible.
S2, taking the fact that the frequency of the power system has space-time distribution characteristics into consideration, and partitioning the power system based on the power grid topology and a disturbed system frequency dynamic response curve;
preferably, the step S2 specifically includes the following steps:
the frequency of the power system has space-time distribution characteristics, and the similarity of frequency and time sequences of generator sets or busbar nodes with similar distances is higher, so that the acquired power plant grid-connected busbar frequency and time sequences are clustered based on Euclidean distance and a K-means algorithm, the frequency and time sequences and cluster centers with the closest distances are classified, and the power system is divided into a plurality of areas by combining with the power grid topology.
Preferably, the step S2 specifically includes the following steps:
s21, measuring the frequency discrete time sequence of the node A through the PMU
And frequency discrete time sequence of node B +.>
For frequency discrete time series +.>
And->
Satisfy->
，/>
，/>
Is the length of the frequency discrete time series;
s22, representing the similarity between time sequences of different frequencies by using Euclidean distance, wherein the distance index is shown as follows:
in the method, in the process of the invention,
for frequency time series->
And->
A Euclidean distance between them;
s23, clustering the frequencies by adopting a K-means algorithm based on the defined Euclidean distance index;
preferably, the step S23 specifically includes the following steps:
s231, designating the cluster number M, and calculating the distance between the sample and the cluster center assuming that each cluster has a center point:
in the method, in the process of the invention,
for the frequency-time series of acquisition, +.>
For the center point vector of the cluster where the sample is located, the sample and the nearest center point are divided into a cluster, +.>
For calculating the distance between two frequency time sequences, < >>
For the length of the frequency discrete time series, +.>
Is the distance between the sample and the cluster center;
s232, randomly selecting M points as center points of each cluster, and iteratively executing the following two steps:
finding respective sample data for each center point, and dividing the sample data into center points closest to each center point;
and (3) recalculating the center point in each cluster, wherein the new center point is the arithmetic average value of members in the cluster, so that the calculated L value of the new center point is necessarily smaller than or equal to the original L value, and the iterative loop is carried out until the clustering algorithm converges and then exits.
S24, dividing the power system into a plurality of areas by combining the power grid topology.
S3, evaluating inertia of each area and primary frequency modulation capacity based on unbalanced power in the area and area inertia center frequency;
preferably, the step S3 specifically includes the following steps:
s31, writing out a forward differential model and a fitness function of regional inertia evaluation, respectively aggregating frequency and active power data of a power plant grid-connected bus in each region, and dynamically estimating equivalent inertia time constants of each region by adopting a quantum particle swarm optimization algorithm in the length of each data sliding window by utilizing frequency data before primary frequency modulation action;
preferably, the step S31 specifically includes the following steps:
s311, the frequency dynamic response of the regional power systems is similar, each regional power system is equivalent to a synchronous generator, and the active-frequency dynamic response process is described by the following rotor motion equation under unbalanced disturbance:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the power angle of the generator, < >>
Rated frequency of generator, < >>
For generator frequency deviation, < >>
Is generator inertia time constant, +.>
And->
Respectively the mechanical power per unit value and the electromagnetic power per unit value of the generator>
Is the damping coefficient of the generator, < >>
Is a time-domain differential operator;
s312, in the inertia response stage after the system is disturbed, the system frequency does not exceed the primary frequency modulation dead zone, and the mechanical power output of the generator is considered to be stable at the moment, namely
Simultaneously ignoring the influence of the damping coefficient of the generator, let ∈ ->
The above formula is written as:
the output of the generator before disturbance occurs meets
The following formula is obtained:
in the method, in the process of the invention,
and->
Mechanical power and electromagnetic power of the generator before the disturbance occurs, respectively,>
for the electromagnetic power increment after the disturbance occurs, +.>
An equivalent inertial time constant to be evaluated for the regional power system;
s313, obtaining a fitting formula of the following frequency curve by forward difference of the formula:
in the method, in the process of the invention,
fitting for Quantum particle swarm Algorithm +.>
Time-of-day frequency deviation +.>
Algorithm for quantum particle swarmFitting +.>
Time-of-day frequency deviation +.>
For the sampling time interval of the frequency data, +.>
Is->
Unbalanced power of the time zone power system;
s314, estimating an adaptability function of an equivalent inertial time constant of the regional power system, wherein the adaptability function is shown in the following formula:
in the method, in the process of the invention,
to characterize the fitness function of the frequency curve fitting effect, +.>
Frequency deviation fitted for quantum particle swarm algorithm.
S32, writing out a forward differential model and a fitness function of regional primary frequency modulation capability evaluation, calculating regional inertia response power according to the evaluation result of the equivalent inertia time constant of each region, correcting unbalanced power of a system, and dynamically estimating the equivalent difference adjustment coefficient of each region by adopting a quantum particle swarm optimization algorithm in each data sliding window length by utilizing frequency data after primary frequency modulation action;
preferably, the step S32 specifically includes the following steps:
s321, in a primary frequency modulation stage after system disturbance, the system frequency exceeds a primary frequency modulation dead zone, a generator speed regulator in the area starts to act, mechanical power output changes, and at the moment, the mechanical power increment of a generator set meets the following transfer function form:
in the method, in the process of the invention,
for the generator mechanical power increment after the disturbance has occurred, +.>
Equivalent difference coefficient to be evaluated for regional power system, +.>
For the system frequency +.>
Is a primary frequency modulation action dead zone->
Equivalent time constant of first-order inertia link of speed regulator, < >>
Is a frequency domain differential operator;
s322, evaluating the result based on the equivalent inertial time constant of the regional power system
And (3) taking inertia effect into account in the primary frequency modulation process, and correcting the unbalanced regional power into:
in the method, in the process of the invention,
unbalanced power for a regional power system;
s323, forward difference of the transfer function is obtained:
in the method, in the process of the invention,
is->
Frequency deviation of time,/->
Fitting for Quantum particle swarm Algorithm +.>
Time zone power system unbalanced power, +.>
Fitting for Quantum particle swarm Algorithm +.>
Unbalanced power of the power system in the time zone;
s324, estimating an adaptability function of an equivalent difference adjustment coefficient of the regional power system, wherein the adaptability function is shown in the following formula:
in the method, in the process of the invention,
to characterize the fitness function of the power curve fitting effect, +.>
And (5) unbalanced power of the regional power system fitted for the quantum particle swarm algorithm.
S33, setting the sliding window length of the estimated data, the data sampling time interval and the action dead zone of the synchronous machine set speed regulator, writing a forward differential model and a fitness function for estimating the regional inertia and primary frequency modulation capacity into a quantum particle swarm optimization algorithm for iteration until the termination condition of the quantum particle swarm optimization algorithm is met, and outputting the global optimal position of the particle swarm, namely the regional equivalent inertia time constant and the equivalent difference adjustment coefficient.
Preferably, the step S33 specifically includes the following steps:
s331, determining dimension of quantum particle swarm target search space
I.e. the number of decision variables to be solved; at this time, assume thatNThe particles form a group, and the movement of each particle not only needs to consider the optimal position searched by the particle, but also comprehensively considers the optimal position searched by the group; in quantum space, the velocity and position of the particles cannot be determined simultaneously, so the wavefunction +.>
Describing the state of the particle, wherein->
Is a position vector of a particle in a three-dimensional space, and the probability density of the occurrence of the particle at a certain point in the space is represented by the square of a wave function modulus, namely:
wherein Q is a probability density function that satisfies a normalization condition:
s332, describing the movement of particles in quantum mechanics by a Schrodinger equation:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is Manhattan operator,)>
Is Planck constant, +.>
For particle quality, < >>
Is the potential field where the particles are located;
s333, consider a single particle
The point is one-dimensional +.>
Motion in the potential well, attractor of particles +.>
Marked as->
The position of the particles is marked->
The potential energy function is as follows:
in the method, in the process of the invention,
is Euler-Ma Xieluo Niconstant;
s334, determining the position of the particles by adopting a Monte Carlo method:
wherein, the liquid crystal display device comprises a liquid crystal display device,Lis that
Characteristic length of potential well->
Is section->
On uniformly distributed random numbers, i.e. +.>
；
The particles are
First->
The basic evolution equation for the coordinates of the dimensions is:
in the method, in the process of the invention,
for the time t+1 particle->
First->
Coordinates of dimension->
For time t particle->
First->
Dimension(s)The suction device is used for sucking the liquid,
for time t particle->
First->
Wei->
Characteristic length of potential well->
For time interval t->
Random numbers uniformly distributed on the base;
s335, introducing an average best position
Defined as the average of the best positions of all particle individuals,/->
By passing through
To evaluate, the evolution equation of the particles is rewritten as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
for the contraction-expansion coefficient, +.>
For time t particle->
First->
Coordinates of dimension->
For particle population quantity, +.>
Is->
The best position is averaged.
And S4, evaluating inertia and primary frequency modulation capacity of the whole power system by carrying out weighted aggregation on the equivalent inertia time constant and the equivalent difference modulation coefficient of each region.
Preferably, the step S4 specifically includes the following steps:
setting reference capacity of the power system, aggregating evaluation results of inertia and primary frequency modulation capacity of each area, and calculating equivalent inertia time constant and equivalent difference adjustment coefficient of the power system on line.
Preferably, the step S4 specifically includes the following steps:
dividing an electrical power system into
Setting rated capacity of the system, aggregating evaluation results of inertia and primary frequency modulation capacity of each region, and calculating equivalent inertia time constant and equivalent difference adjustment coefficient of the power system on line;
wherein, the equivalent inertia of the power system is expressed as:
in the method, in the process of the invention,
for the equivalent inertia of the power system->
For the kinetic energy stored by all generators in the area, +.>
Equivalent inertial time constant for each region, +.>
Rated capacity for each zone;
the system equivalent inertial time constant is represented by a weighted average of the equivalent inertial time constants of the respective regions:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the equivalent inertia time constant of the electric power system, +.>
Is a reference capacity of the power system;
likewise, the power system equivalent difference coefficient is represented by a weighted average of the regional equivalent difference coefficients:
in the method, in the process of the invention,
is the equivalent difference adjustment coefficient of the power system, +.>
Is the equivalent difference adjustment coefficient of each region.
The method according to the invention is illustrated by means of a specific example:
as shown in fig. 2, based on the system, the system performs the evaluation of inertia and primary frequency modulation capability of the power system based on the quantum particle swarm optimization algorithm and taking into account the dynamic response partition of the system frequency, and the operation steps are as follows:
1. a50 MW disturbance with a sudden load increase is arranged at the position of an IEEE 39 node system bus 25, and the system frequency passes through a primary frequency modulation action dead zone of a synchronous machine speed regulator. Firstly, collecting the frequency of a grid-connected bus position of a power plant for system partition; and secondly, collecting active power data of a grid-connected bus of the power plant for evaluating inertia and primary frequency modulation capability of the power system.
2. Based on the Euclidean distance and the K-means clustering algorithm, the frequency is clustered, and as can be seen from fig. 3, the space-time distribution of the frequency dynamic response of the IEEE 39 node system has a difference. According to the frequency clustering result of the bus nodes, the system is divided into a plurality of areas, the frequency dynamic response curves of the bus nodes in each area are similar, and the partitioning result of the system is shown in fig. 4.
3. Setting the sliding window length of inertia evaluation data, the data sampling time interval and the action dead zone of a synchronous machine set speed regulator, writing a forward differential model and a fitness function of regional inertia evaluation into a quantum particle swarm optimization algorithm for iteration when the frequency does not exceed the primary frequency modulation action dead zone until the termination condition of the quantum particle swarm optimization algorithm is met, and outputting the global optimal position of the particle swarm, namely the regional equivalent inertia time constant, wherein the regional equivalent inertia time constant evaluation result box diagram is shown in figure 5.
TABLE 1 estimation error of equivalent inertial time constant of the method of the invention
As can be seen from table 1, the estimation error of the equivalent inertial time constant is not more than 5%.
4. And correcting unbalanced power of each region by using an evaluation result of an equivalent inertia time constant, when the frequency exceeds a primary frequency modulation action dead zone, writing a forward differential model and an adaptability function for primary frequency modulation capability evaluation into a quantum particle swarm optimization algorithm for iteration until a termination condition of the quantum particle swarm optimization algorithm is met, and outputting a global optimal position of the particle swarm, namely a region equivalent difference adjustment coefficient, wherein a box diagram of the evaluation result of the region equivalent difference adjustment coefficient is shown in fig. 6.
TABLE 2 estimation error of equivalent differential coefficient in the method of the invention
As can be seen from table 2, the estimation error of the equivalent difference coefficient is not more than 10%.
5. The system equivalent inertia time constant is represented by the weighted average of the equivalent inertia time constants of all areas, and the dynamic evaluation result is shown in fig. 7; similarly, the system equivalent difference coefficient is represented by a weighted average of the difference coefficients, and the dynamic evaluation result is shown in fig. 8.
Therefore, the system and the method can realize real-time tracking of the inertia and primary frequency modulation capacity of the power system, help system schedulers to master the safety level of the system frequency in real time and guide and adjust the operation mode of the system, and improve the operation stability of the system.
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 (7)
1. The power system inertia and primary frequency modulation capability assessment method based on QPSO is characterized by comprising the following steps of: the method comprises the following steps:
s1, monitoring and collecting frequency and active power data of a grid-connected busbar of a power plant in real time through a synchronous phasor measurement device;
s2, taking the fact that the frequency of the power system has space-time distribution characteristics into consideration, and partitioning the power system based on the power grid topology and a disturbed system frequency dynamic response curve;
s3, evaluating inertia of each area and primary frequency modulation capacity based on unbalanced power in the area and area inertia center frequency;
the step S3 specifically comprises the following steps:
s31, writing out a forward differential model and a fitness function of regional inertia evaluation, respectively aggregating frequency and active power data of a power plant grid-connected bus in each region, and dynamically estimating equivalent inertia time constants of each region by adopting a quantum particle swarm optimization algorithm in the length of each data sliding window by utilizing frequency data before primary frequency modulation action;
s32, writing out a forward differential model and a fitness function of regional primary frequency modulation capability evaluation, calculating regional inertia response power according to the evaluation result of the equivalent inertia time constant of each region, correcting unbalanced power of a system, and dynamically estimating the equivalent difference adjustment coefficient of each region by adopting a quantum particle swarm optimization algorithm in each data sliding window length by utilizing frequency data after primary frequency modulation action;
s33, setting a sliding window length of evaluation data, a data sampling time interval and a synchronous unit speed regulator action dead zone, writing a forward differential model and a fitness function for evaluating regional inertia and primary frequency modulation capacity into a quantum particle swarm optimization algorithm for iteration until the termination condition of the quantum particle swarm optimization algorithm is met, and outputting the global optimal position of the particle swarm, namely a regional equivalent inertia time constant and an equivalent difference adjustment coefficient;
the step S31 specifically includes the following steps:
s311, equating the power system of each region into a synchronous generator, and describing the active-frequency dynamic response process by the following rotor motion equation under unbalanced disturbance:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the power angle of the generator, < >>
Rated frequency of generator, < >>
For generator frequency deviation, < >>
Is generator inertia time constant, +.>
And->
Respectively the mechanical power per unit value and the electromagnetic power per unit value of the generator>
Is the damping coefficient of the generator, < >>
Is a time-domain differential operator;
s312, in the inertia response stage after the system is disturbed, the system frequency does not exceed the primary frequency modulation dead zone, and the mechanical power output of the generator is considered to be stable at the moment, namely
Simultaneously ignoring the influence of the damping coefficient of the generator, let ∈ ->
The above formula is written as:
the output of the generator before disturbance occurs meets
The following formula is obtained:
in the method, in the process of the invention,
and->
Mechanical power and electromagnetic power of the generator before the disturbance occurs, respectively,>
for the electromagnetic power increment after the disturbance occurs, +.>
An equivalent inertial time constant to be evaluated for the regional power system;
s313, obtaining a fitting formula of the following frequency curve by forward difference of the formula:
in the method, in the process of the invention,
fitting for Quantum particle swarm Algorithm +.>
Time-of-day frequency deviation +.>
Fitting for Quantum particle swarm Algorithm +.>
Time-of-day frequency deviation +.>
For the sampling time interval of the frequency data, +.>
Is->
Unbalanced power of the time zone power system;
s314, estimating an adaptability function of an equivalent inertial time constant of the regional power system, wherein the adaptability function is shown in the following formula:
in the method, in the process of the invention,
to characterize the fitness function of the frequency curve fitting effect, +.>
Fitting frequency deviation for a quantum particle swarm algorithm;
the step S32 specifically includes the following steps:
s321, in a primary frequency modulation stage after system disturbance, the system frequency exceeds a primary frequency modulation dead zone, a generator speed regulator in the area starts to act, mechanical power output changes, and at the moment, the mechanical power increment of a generator set meets the following transfer function form:
in the method, in the process of the invention,
for the generator mechanical power increment after the disturbance has occurred, +.>
Equivalent difference coefficient to be evaluated for regional power system, +.>
For the system frequency +.>
Is a primary frequency modulation action dead zone->
Equivalent time constant of first-order inertia link of speed regulator, < >>
Is a frequency domain differential operator;
s322, evaluating the result based on the equivalent inertial time constant of the regional power system
And (3) taking inertia effect into account in the primary frequency modulation process, and correcting the unbalanced regional power into:
in the method, in the process of the invention,
unbalanced power for a regional power system;
s323, forward difference of the transfer function is obtained:
in the method, in the process of the invention,
is->
Frequency deviation of time,/->
Fitting for Quantum particle swarm Algorithm +.>
Time zone power system unbalanced power, +.>
Fitting for Quantum particle swarm Algorithm +.>
Unbalanced power of the power system in the time zone;
s324, estimating an adaptability function of an equivalent difference adjustment coefficient of the regional power system, wherein the adaptability function is shown in the following formula:
in the method, in the process of the invention,
to characterize the fitness function of the power curve fitting effect, +.>
Unbalanced power of a regional power system fitted for a quantum particle swarm algorithm;
and S4, evaluating inertia and primary frequency modulation capacity of the whole power system by carrying out weighted aggregation on the equivalent inertia time constant and the equivalent difference modulation coefficient of each region.
2. The QPSO-based power system inertia and primary frequency modulation capability assessment method according to claim 1, wherein: the step S2 specifically comprises the following steps:
based on Euclidean distance and K-means algorithm, the collected power plant grid-connected busbar frequency time series are clustered, the frequency time series and the cluster center closest to the frequency time series are classified, and the power system is divided into a plurality of areas by combining the power grid topology.
3. The QPSO-based power system inertia and primary frequency modulation capability assessment method according to claim 2, wherein: the step S2 specifically comprises the following steps:
s21, measuring the frequency discrete time sequence of the node A through the PMU
And frequency discrete time sequence of node B +.>
For frequency discrete time series +.>
And->
Satisfy->
，
，/>
Is the length of the frequency discrete time series;
s22, representing the similarity between time sequences of different frequencies by using Euclidean distance, wherein the distance index is shown as follows:
in the method, in the process of the invention,
for frequency time series->
And->
A Euclidean distance between them;
s23, clustering the frequencies by adopting a K-means algorithm based on the defined Euclidean distance index;
s24, dividing the power system into a plurality of areas by combining the power grid topology.
4. The QPSO-based power system inertia and primary frequency modulation capability assessment method according to claim 3, wherein: the step S23 specifically includes the following steps:
s231, designating the cluster number M, and calculating the distance between the sample and the cluster center assuming that each cluster has a center point:
in the method, in the process of the invention,
for the frequency-time series of acquisition, +.>
For the center point vector of the cluster where the sample is located, the sample and the nearest center point are divided into a cluster, +.>
For calculating the distance between two frequency time sequences, < >>
For the length of the frequency discrete time series, +.>
Is the distance between the sample and the cluster center;
s232, randomly selecting M points as center points of each cluster, and iteratively executing the following two steps:
finding respective sample data for each center point, and dividing the sample data into center points closest to each center point;
and (3) recalculating the center point in each cluster, wherein the new center point is the arithmetic average value of members in the cluster, so that the calculated L value of the new center point is necessarily smaller than or equal to the original L value, and the iterative loop is carried out until the clustering algorithm converges and then exits.
5. The QPSO-based power system inertia and primary frequency modulation capability assessment method according to claim 1, wherein: the step S33 specifically includes the following steps:
s331, determining dimension of quantum particle swarm target search space
I.e. the number of decision variables to be solved; at this time, assume thatNThe particles form a group, and the movement of each particle not only needs to consider the optimal position searched by the particle, but also comprehensively considers the optimal position searched by the group; in quantum space, the velocity and position of the particles cannot be determined simultaneously, so the wavefunction +.>
Describing the state of the particle, wherein->
Is a position vector of a particle in a three-dimensional space, and the probability density of the occurrence of the particle at a certain point in the space is represented by the square of a wave function modulus, namely:
wherein Q is a probability density function that satisfies a normalization condition:
s332, describing the movement of particles in quantum mechanics by a Schrodinger equation:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is Manhattan operator,)>
Is Planck constant, +.>
For particle quality, < >>
Is the potential field where the particles are located;
s333, consider a single particle
The point is one-dimensional +.>
Motion in the potential well, attractor of particles +.>
Marked as->
The position of the particles is marked->
The potential energy function is as follows:
in the method, in the process of the invention,
is Euler-Ma Xieluo Niconstant;
s334, determining the position of the particles by adopting a Monte Carlo method:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is->
Characteristic length of potential well->
Is section->
On uniformly distributed random numbers, i.e. +.>
；
The particles are
First->
The basic evolution equation for the coordinates of the dimensions is:
in the method, in the process of the invention,
for the time t+1 particle->
First->
Coordinates of dimension->
For time t particle->
First->
Attractor for vitamin, jersey>
For time t particle->
First->
Wei->
Characteristic length of potential well->
For time interval t->
Random numbers uniformly distributed on the base;
s335, introducing an average best position
Defined as the average of the best positions of all particle individuals,/->
By passing through
To evaluate, the evolution equation of the particles is rewritten as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
for the contraction-expansion coefficient, +.>
For time t particle->
First->
Coordinates of dimension->
For the number of particle populations,
is->
The best position is averaged.
6. The QPSO-based power system inertia and primary frequency modulation capability assessment method according to claim 1, wherein: the step S4 specifically comprises the following steps:
setting reference capacity of the power system, aggregating evaluation results of inertia and primary frequency modulation capacity of each area, and calculating equivalent inertia time constant and equivalent difference adjustment coefficient of the power system on line.
7. The QPSO-based power system inertia and primary frequency modulation capability assessment method of claim 6, wherein the method is characterized by: the step S4 specifically comprises the following steps:
dividing an electrical power system into
Setting rated capacity of the system, aggregating evaluation results of inertia and primary frequency modulation capacity of each region, and calculating equivalent inertia time constant and equivalent difference adjustment coefficient of the power system on line;
wherein, the equivalent inertia of the power system is expressed as:
in the method, in the process of the invention,
for the equivalent inertia of the power system->
For the kinetic energy stored by all generators in the area, +.>
Equivalent inertial time constant for each region, +.>
Rated capacity for each zone;
the system equivalent inertial time constant is represented by a weighted average of the equivalent inertial time constants of the respective regions:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the equivalent inertia time constant of the electric power system, +.>
Is a reference capacity of the power system;
likewise, the power system equivalent difference coefficient is represented by a weighted average of the regional equivalent difference coefficients:
in the method, in the process of the invention,
is the equivalent difference adjustment coefficient of the power system, +.>
Is the equivalent difference adjustment coefficient of each region.
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