CN104578051A - Power distribution network state estimation method based on firefly algorithm - Google Patents
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- GNBHRKFJIUUOQI-UHFFFAOYSA-N fluorescein Chemical compound O1C(=O)C2=CC=CC=C2C21C1=CC=C(O)C=C1OC1=CC(O)=CC=C21 GNBHRKFJIUUOQI-UHFFFAOYSA-N 0.000 claims abstract description 46
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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
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- G06Q50/06—Energy or water supply
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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
- 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]
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Abstract
The invention provides a power distribution network state estimation method based on a firefly algorithm. The method comprises steps as follows: Step 1, generating a power distribution network node admittance matrix; Step 2, initializing fluorescein and dynamic decision domains of fireflies; Step 3, updating the fluorescein of the fireflies; Step 4, calculating the distance between the fireflies to acquire neighborhoods; Step 5, calculating the movement probability of the fireflies; Step 6, updating positions of the fireflies; Step 7, updating the dynamic decision domains of the fireflies; Step 8, judging whether a convergence condition is satisfied or not, if the convergence condition is satisfied, ending the process, executing Step 9, and otherwise, executing Step 3; Step 9, outputting an optimal solution. According to the method, node voltage is used as a state variable, the node injection power is calculated, an objective function value of the least square method is taken as a firefly fitness function value and converted into the fluorescein of the fireflies, the state variable is updated continuously, and the firefly position with the highest fluorescein is taken as the optimal state estimation result. Experiments indicate that the method has good accuracy and adaptability.
Description
Technical Field
The invention relates to an estimation method, in particular to a firefly algorithm-based power distribution network state estimation method.
Background
The power distribution network state estimation is characterized in that the correlation and redundancy of measured data are utilized, a computer processing technology is applied, and a mathematical processing method is adopted to predict and correct the operation parameters of the power distribution network, so that the reliability and integrity of the data are improved, and the real-time operation state information of the power distribution network is effectively obtained.
With the development requirement of the power grid dispatching automation level, a power grid dispatching center needs to comprehensively and accurately master various data of power grid operation, so that high-quality state estimation is required to be used as a guarantee provided by real-time data; the power distribution network has the remarkable characteristics different from the power transmission network, a plurality of power transmission network state estimation algorithms cannot be directly applied to power distribution network state estimation, the real-time measurement configuration of the power distribution network is few, and the data redundancy is insufficient, so that the power distribution network state estimation needs to be deeply researched.
At present, a plurality of power distribution network state estimation methods are available, wherein the most common method is weighted least square method state estimation, and the basic principle is to find a group of state quantities so that the sum of the calculated network power and the measured variance of the quantity is minimum; the solution of the weighted least square method can be regarded as an optimization problem of an objective function, the traditional solution methods include a Newton iteration method, a gradient method and the like, the solution is generally carried out by the Newton method, but the Newton method has high requirement on an iteration initial value, and if a given initial value is far away from a correct value, the accurate convergence cannot be carried out, and even an iteration divergence result is caused.
The firefly algorithm is a new swarm intelligent bionic algorithm, has good capability of solving a global extreme value and searching a multi-extreme value, is applied to various aspects such as solving of a multi-extreme value function, localization of a signal source and the like, and achieves good effect.
The firefly algorithm is derived from the research on actions of firefly lighting, coupling, communication and the like in nature, is a group intelligent algorithm, and has the basic principle that firefly luciferin is used for inducing firefly to glow so as to attract a partner or a prey, the stronger the brightness is, the more attractive the glow is, the higher the fluorescein is, and the firefly moves to the firefly position with the highest fluorescein value; the fluorescein values correspond to fitness function values, so the firefly determines the optimal value of the fitness function by finding the location of the highest fluorescein firefly within the dynamic decision domain.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a power distribution network state estimation method based on a firefly algorithm, node voltage is taken as a state variable, the injection complex power of a node, branch current and the first and last segment complex power of a branch are calculated, a target function value calculated by a weighted least square method is taken as a fitness function value of the firefly, the fitness function value is converted into firefly fluorescein, the state variable is continuously updated, and finally the firefly position with the largest fluorescein is obtained as an optimal state estimation result.
In order to achieve the purpose of the invention, the invention adopts the following technical scheme:
the method for estimating the state of the power distribution network based on the firefly algorithm comprises the following steps:
step (1): loading a power distribution network system and measuring, and analyzing to generate a node admittance matrix;
step (2): initializing fluorescein and a dynamic decision domain of each firefly individual;
and (3): calculating a target function of a solution represented by each firefly, and updating the fluorescein of each firefly;
and (4): calculating the distance between each firefly and other fireflies, and obtaining the neighborhood of the firefly by combining the size of the fluorescein;
and (5): calculating the movement probability of each firefly and the firefly in the field;
and (6): selecting the best moving direction to move, and updating the position of the firefly;
and (7): updating the dynamic decision domain of each firefly;
and (8): judging whether a convergence condition is met, if so, finishing state estimation, and executing the step (9), otherwise, executing the step (3);
and (9): and outputting the firefly position with the maximum target function as the optimal solution.
In the step (1), topology analysis of the power distribution network is performed to generate a node admittance matrix.
In the step (2), n fireflies individuals are randomly distributed in the D-dimensional target search space, and each firefly has a fluorescein value of(ii) a All firefly individuals emit fluorescence to influence surrounding firefly individuals mutually and have respective dynamic decision domains（0<≤) (ii) a The size of the fluorescein of the individual firefly is related to the target function of the position of the firefly, and the larger the fluorescein is, the better the position of the firefly is, namely, the target value is better.
Firefly will find neighbor set in decision domainIn the set, the firefly with larger fluorescein has higher attraction to attract other fireflies to move towards the direction, and the moving direction of each time can change along with different selected neighbors; the size of the decision domain is influenced by the number of neighbors, and the smaller the neighbor density is, the larger the decision radius of the firefly is, so that more neighbors can be searched; the larger the neighbor density is, the smaller the decision radius of the firefly will be.
In the step (3), each fireflyFire insectIn the first placePosition of the sub-iterationCorresponding objective function valueConversion to fluorescein valueIs composed of
（1）
Wherein,the fluorescein turnover rate.
In the step (4), each firefly individual has a radius in its dynamic decision domainIn the method, firefly individuals with higher fluorescein value than self are selected to form a field set
（2）
Wherein,，is the radius of perception of the individual firefly.
In the step (5), each firefly individual has a radius in its dynamic decision domainIn, selection moves to a set of domainsInner bodyProbability of (2)Comprises the following steps: （3）。
in the step (6), the expression of each time the firefly updates the position is
（4）
Where s is the step of moving.
In the step (7), the dynamic decision-making domain radius updating expression of the firefly is obtained in each time
（5）
Wherein isThreshold value of the number of the fireflies in the field.
In the step (3), the target function value calculated by the weighted least square method is taken as the fitness function value of the firefly, the fitness function value is converted into the fluorescein of the firefly, and the ith firefly iterated adaptationThe degree function value is the target function value calculated by least square method, and the target function of the fireflyTaken as the inverse of the fitness function value
（6）
Wherein,for the number of measurements to be taken,the metrology weight for the mth metrology measurement,for the measurement of the m-th quantity,a state function measured for the mth quantity.
Compared with the prior art, the invention has the beneficial effects that:
1. the method is simple and effective, the precision can meet the requirements of engineering application, and the method is easy to implement;
2. the convergence is good, and the state estimation problem of a large-scale complex power distribution network can be solved.
Drawings
Fig. 1 is a flowchart of a power distribution network state estimation method based on a firefly algorithm according to the present invention.
Fig. 2 is a diagram illustrating a state estimation result according to an embodiment of the present invention.
Fig. 3 is a diagram of a variation curve of a fitness function of a state estimation result according to an embodiment of the present invention. . .
Detailed Description
The embodiment of the invention is further explained by combining the attached drawings, and a firefly algorithm-based power distribution network state estimation method comprises the following steps:
step (1): loading a power distribution network system and measuring, and analyzing to generate a node admittance matrix;
step (2): initializing fluorescein and a dynamic decision domain of each firefly individual;
and (3): calculating a target function of a solution represented by each firefly, and updating the fluorescein of each firefly;
and (4): calculating the distance between each firefly and other fireflies, and obtaining the neighborhood of the firefly by combining the size of the fluorescein;
and (5): calculating the movement probability of each firefly and the firefly in the field;
and (6): selecting the best moving direction to move, and updating the position of the firefly;
and (7): updating the dynamic decision domain of each firefly;
and (8): judging whether a convergence condition is met, if so, finishing state estimation, and executing the step (9), otherwise, executing the step (3);
and (9): and outputting the firefly position with the maximum target function as the optimal solution.
In the step (1), topology analysis of the power distribution network is performed to generate a node admittance matrix.
In the step (2), n fireflies individuals are randomly distributed in the D-dimensional target search space, and each firefly has a fluorescein valueIs composed of(ii) a All firefly individuals emit fluorescence to influence surrounding firefly individuals mutually and have respective dynamic decision domains（0<≤) (ii) a The size of the fluorescein of the individual firefly is related to the target function of the position of the firefly, and the larger the fluorescein is, the better the position of the firefly is, namely, the target value is better.
Firefly will find neighbor set in decision domainIn the set, the firefly with larger fluorescein has higher attraction to attract other fireflies to move towards the direction, and the moving direction of each time can change along with different selected neighbors; the size of the decision domain is influenced by the number of neighbors, and the smaller the neighbor density is, the larger the decision radius of the firefly is, so that more neighbors can be searched; the larger the neighbor density is, the smaller the decision radius of the firefly will be.
In the step (3), each fireflyIn the first placePosition of the sub-iterationCorresponding objective function valueConversion to fluorescein valueIs composed of
（1）
Wherein,the fluorescein turnover rate.
In the step (4), each firefly individual has a radius in its dynamic decision domainIn the method, firefly individuals with higher fluorescein value than self are selected to form a field set
（2）
Wherein,，is the radius of perception of the individual firefly.
In the step (5), each firefly individual has a radius in its dynamic decision domainIn, selection moves to a set of domainsInner bodyProbability of (2)Comprises the following steps: （3）。
in the step (6), the expression of each time the firefly updates the position is
（4）
Where s is the step of moving.
In the step (7), the dynamic decision-making domain radius updating expression of the firefly is obtained in each time
（5）
Wherein isThreshold value of the number of the fireflies in the field.
In the step (3), the target function value calculated by the weighted least square method is taken as the fitness function value of the firefly and is converted into the fluorescein of the firefly, and the fitness function value of the ith iteration of the firefly is taken as the target function value calculated by the least square method and is taken as the target function value of the fireflyTaken as the inverse of the fitness function value
（6）
Wherein,for the number of measurements to be taken,the metrology weight for the mth metrology measurement,for the measurement of the m-th quantity,a state function measured for the mth quantity.
Taking an IEEE33 node power distribution network as an example, a computer program is used for carrying out check calculation to verify the application of the power distribution network state estimation method based on the firefly algorithm in power distribution network state estimation.
Parameter setting of a power distribution network state estimation method based on a firefly algorithm comprises the following steps: firefly population scale n =50, fluorescein volatility coefficientDynamic decision domain update rate of =0.4=0.08, fluorescein turnover rate=0.6, initial value of fluorescein=5, radius of perception=3, field firefly number threshold=5, step size s =0.03, maximum number of iterations being 100.
Comparing the voltage value of each node estimated by the firefly algorithm state with the voltage value of each node estimated by the least square algorithm, as shown in fig. 2, the state estimation results are basically consistent, and the change of the minimum value of the fitness function is shown in fig. 3. Experimental results show that the method has the advantages of good precision, adaptability and convergence, high calculation speed and easiness in implementation, and can solve the problem of large-scale complex power distribution network state estimation engineering.
The above examples are only for illustrating the technical solutions of the present invention and not for limiting the same, and those skilled in the art can make modifications or equivalents to the embodiments of the present invention with reference to the above examples, but any modifications or equivalents without departing from the spirit and scope of the present invention are within the scope of the claims of the present invention.
Claims (10)
1. A power distribution network state estimation method based on a firefly algorithm is characterized by comprising the following steps:
step (1): loading a power distribution network system and measuring, and analyzing to generate a node admittance matrix;
step (2): initializing fluorescein and a dynamic decision domain of each firefly individual;
and (3): calculating a target function of a solution represented by each firefly, and updating the fluorescein of each firefly;
and (4): calculating the distance between each firefly and other fireflies, and obtaining the neighborhood of the firefly by combining the size of the fluorescein;
and (5): calculating the movement probability of each firefly and the firefly in the field;
and (6): selecting the best moving direction to move, and updating the position of the firefly;
and (7): updating the dynamic decision domain of each firefly;
and (8): judging whether a convergence condition is met, if so, finishing state estimation, and executing the step (9), otherwise, executing the step (3);
and (9): and outputting the firefly position with the maximum target function as the optimal solution.
2. The firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: in the step (1), topology analysis of the power distribution network is performed to generate a node admittance matrix.
3. The firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: in a D-dimensional target search space, n firefly individuals are randomly distributed, and each firefly has a fluorescein value of(ii) a All firefly individuals emit fluorescence to influence surrounding firefly individuals mutually and have respective dynamic decision domains（0<≤) (ii) a The size of the fluorescein of the individual firefly is related to the target function of the position of the firefly, and the larger the fluorescein is, the better the position of the firefly is, namely, the target value is better.
4. The firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: firefly will find neighbor set in decision domainIn the set, the firefly with larger fluorescein has higher attraction to attract other fireflies to move towards the direction, and the moving direction of each time can change along with different selected neighbors; the size of the decision domain is influenced by the number of neighbors, and the smaller the neighbor density is, the larger the decision radius of the firefly is, so that more neighbors can be searched; the larger the neighbor density is, the smaller the decision radius of the firefly will be.
5. The firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: every fireflyIn the first placePosition of the sub-iterationCorresponding objective function valueConversion to fluorescein valueIs composed of
（1）
Wherein,the fluorescein turnover rate.
6. The firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: each individual firefly is within its dynamic decision domain radiusIn the method, firefly individuals with higher fluorescein value than self are selected to form a field set
（2）
Wherein,，is the radius of perception of the individual firefly.
7. The firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: each individual firefly is within its dynamic decision domain radiusIn, selection moves to a set of domainsInner bodyProbability of (2)Comprises the following steps: （3）。
8. the firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: the expression of each time the firefly updates the position is
（4）
Where s is the step of moving.
9. The firefly algorithm-based power distribution network state estimation method according to claim 1, wherein: the dynamic decision domain radius updating expression of the firefly every time is as follows
（5）
Wherein isThreshold value of the number of the fireflies in the field.
10. The objective function of claim 5, wherein: taking the target function value calculated by the weighted least square method as the fitness function value of the firefly and converting the fitness function value into the fluorescein of the firefly, and taking the fitness function value of the ith iteration of the firefly as the target function value calculated by the least square methodTaken as the inverse of the fitness function value
（6）
Wherein,for the number of measurements to be taken,the metrology weight for the mth metrology measurement,for the measurement of the m-th quantity,a state function measured for the mth quantity.
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