CN112365196A - Spark-based power supply planning method for distributed improved differential evolution algorithm - Google Patents
Spark-based power supply planning method for distributed improved differential evolution algorithm Download PDFInfo
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Abstract
The invention provides a Spark-based power supply planning method for a distributed improved differential evolution algorithm, which comprises population calculation and population summarization, wherein the population calculation comprises the following steps: initializing parameters; different random initializations are carried out on the differential evolution according to the global or local search stage; s randomly selecting 3 individuals which are not repeated with the current individual to update the population; exchanging each dimension of the corresponding individuals of the new and old populations; calculating the total construction and operation cost of the distributed power supply, and taking the value as a fitness value of the DIDE; screening individuals meeting the constraint according to the load flow calculation constraint conditions of the power system, and if the individuals do not meet the load flow calculation constraint conditions, adjusting the individual fitness to be the maximum value; updating the individual historical optimal value; and updating the historical optimal value of the population. The invention solves the defects of low convergence rate, easy falling into local optimal solution and the like in the prior art for the addressing and constant volume of the distributed power supply.
Description
Technical Field
The invention relates to the field of power supply planning, in particular to a distributed power supply planning method based on a Spark calculation engine and a distributed improved differential evolution algorithm.
Background
The combination of distributed power generation and a large power grid is one of the development trends of power systems, and the two can make up for each other's deficiencies. The distributed power generation has the advantages of flexible power generation mode, investment saving, improvement of power quality and the like. However, when the distributed power supply is directly connected to the power grid, the distributed power supply has a great influence on the power grid, including voltage level, grid loss, reliability, flexibility and the like, and the influence is directly related to the installation position and capacity of the distributed power supply. Even an unreasonable access to distributed power sources can seriously threaten the safe and stable operation of the power grid. Therefore, the research on the site selection and the constant volume of the distributed power supply is particularly critical. In recent years, research on site selection and constant volume of distributed power sources has become a hot spot of domestic and foreign research. However, the research has the defects that the adopted algorithm is low in convergence speed and easy to fall into a local optimal solution, so that the invention provides an improved distributed differential evolution algorithm based on a Spark calculation engine based on the defects. And establishing a planning model taking the minimum total cost of the construction and operation of the distributed power supply as an optimization sub-objective, and carrying out site selection and volume fixing on the distributed power supply in the 14-node power distribution network testing system.
The differential evolution algorithm is used as a heuristic algorithm, has inherent defects in the aspect of search speed, and cannot be applied to the large-scale optimization problem. In order to effectively improve the search efficiency of the traditional Differential Evolution algorithm, a Distributed Improved Differential Evolution (did) is proposed, and the traditional Differential Evolution algorithm is Improved to adapt to the characteristics of a Spark Distributed computing framework, so that the computing resources of a Distributed cluster are fully utilized, and the search effect of the algorithm is Improved.
Disclosure of Invention
The invention aims to provide a Spark-based power supply planning method for a distributed improved differential evolution algorithm, which is used for overcoming the defects that the prior art is low in convergence rate, easy to fall into a local optimal solution and the like in the addressing and constant volume of a distributed power supply.
The invention adopts the following technical scheme: a Spark-based power supply planning method for a distributed improved differential evolution algorithm comprises population calculation and population summarization, wherein the population calculation comprises the following steps:
step 1: initializing parameters;
step 2: different random initializations are carried out on the differential evolution according to the global or local search stage;
step 3: randomly selecting 3 individuals which are not repeated with the current individual to update the population;
step 4: exchanging each dimension of the corresponding individuals of the new and old populations;
step5, calculating the total construction and operation cost of the distributed power supply, and taking the value as a fitness value of the DIDE;
step6, screening individuals meeting the constraint according to the load flow calculation constraint condition of the power system, and if the individuals do not meet the load flow calculation constraint condition, adjusting the individual fitness to the maximum value;
step 7: updating the individual historical optimal value;
step 8: and updating the historical optimal value of the population.
In an embodiment of the present invention, in a parameter initialization stage, a parallelism p of distributed computation is set, where the parallelism is to be divided into p groups of data according to an upper and lower bound of a data quantity, each group of data generates one RDD of Spark, which represents an example population, and then each population is computed in each RDD.
In an embodiment of the present invention, a formula used in the population random initialization step of the global search is as follows:
Xi＝rand*(ub-lb)+lb where i←(1：N) (1)
wherein, XiIs the position of the ith individual of the particle,
lb and ub are particle positions XiThe upper and lower bounds of (a) are,
rand is the average random number of (0,1),
number of individuals in N population.
In an embodiment of the present invention, a formula used in the step of initializing the population random for local search is as follows:
wherein, XiIs the position of the particle in the ith dimension,
beta is the searched known optimal fitness,
gaussian _ rand is a gaussian-distributed random number with a mean of 0 and a variance of 1,
number of individuals in N population.
Further, the global search phase accounts for 20% of the total calculation time, and the number of updates of population calculation is not limited. The local search phase accounts for 80% of the total computation time; and if the optimal value of the local search stage is not updated for n times continuously, adding 2 to the maximum update time of the local search stage on the original basis.
In an embodiment of the present invention, Step3 includes the following specific steps: randomly selecting 3 individuals which are not repeated with the current individual as Xr1，Xr2And Xr3Updating the population position according to the following formula:
wherein t is the current iteration number of the population calculation,
i is a preset maximum number of iterations,
is the position of the individual i in the generation t,
m is equal to 0.5.
In an embodiment of the present invention, Step 4: and exchanging each dimension of the corresponding individuals of the new and old populations according to the following probability:
p＝C/D (5)
wherein the content of the first and second substances,
c is equal to 0.9 of the total weight of the alloy,
d is the dimension value of the individual.
In an embodiment of the present invention, the total cost calculation function for building and operating the distributed power supply in Step5 is as follows:
in the formula: t ismaxIs the maximum number of hours of power generation of the distributed power supply; m is the total number of distributed power supplies in the power distribution network; sDGiIs the ith distributed typeRated capacity of the power supply; ceDGiThe unit electricity cost of the ith distributed power supply; etaiThe power factor of the ith distributed power supply; cDG1iThe installation cost for the ith distributed power supply; cDG2iA cost of operating and maintaining for the ith distributed power supply; cDG3iThe electricity generation fuel cost for the ith distributed power source.
In an embodiment of the present invention, the power flow calculation constraint conditions in Step6 include equality constraint conditions and inequality constraint conditions, where the equality constraint conditions are an active power balance equation:
in the formula: pDGiThe distributed power supply of the node i is active; pGiActive power is generated for the generator at the node i; pLIs the active network loss; pDIs the active load of the system.
In an embodiment of the present invention, the inequality constraint condition includes:
and (3) limiting the upper and lower limits of the node voltage: i Vi|min≤Vi≤|Vi|max (8)
And (3) branch current constraint: ii|≤|Ii|max (9)
Capacity constraint of distributed power supply:
in the formula:
and
respectively representing the lower limit and the upper limit of the capacity of the distributed power supply installed at the node i; pLDiThe load on the node i is active; eta is the maximum proportion of the active total amount of the distributed power supply to the active total amount of the system; n is a radical ofDGTotal number of distributed power source installations; n is the number of nodes; i Vi|minAnd | Vi|maxRespectively representing the minimum value and the maximum value of the voltage at the node i; iiI and Ii|maxThe magnitude of the current of the ith branch and the maximum value of the allowed current are respectively.
In an embodiment of the present invention, Step7 includes the following steps: and if the individual fitness in the population is smaller than the historical optimal fitness of the individual, taking the current individual as the historical optimal individual, and taking the current individual fitness as the historical optimal individual fitness.
In an embodiment of the present invention, Step8 includes the following steps: and if the individual fitness in the population is smaller than the historical optimal fitness of the population, updating the current individual as the historical optimal individual of the population, wherein the fitness of the current individual is the historical optimal individual fitness of the population.
In an embodiment of the invention, on an overall level, after each RDD completes iterative computation of each population, information interaction among the populations is required, that is, an optimal solution in a result generated when all the populations are subjected to the last iterative computation is found out; and if the solution is better than the optimal solution of all the current populations, updating the current optimal solution, and continuously transmitting the optimal solution to the next iterative computation of each population.
The distributed power supply planning method fully utilizes the computing resources of the distributed cluster, and improves the searching effect of the algorithm; and a planning model taking the minimum total cost of the construction and operation of the distributed power supply as an optimization sub-target realizes the optimal planning of the distributed power supply by the power distribution network testing system.
Drawings
FIG. 1 is a flow chart of population calculation according to the present invention.
Fig. 2 is a flow chart of the population summary information interaction of the invention.
Fig. 3 is a schematic diagram of a 14-node radiation type power distribution system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention, and it is obvious that the described embodiments are a part of the embodiments of the present invention, but not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Research on site selection and constant volume of the distributed power supply becomes a hot point of domestic and foreign research. However, the adopted algorithms are low in convergence speed and easy to fall into a local optimal solution, so that the defects that the invention adopts an improved distributed differential evolution algorithm based on a Spark calculation engine based on the above defects, a planning model with the minimum total construction and operation cost of the distributed power supply as an optimization sub-goal is established, and the distributed power supply is selected and fixed in a 14-node power distribution network test system.
The invention adopts the following technical scheme: a Spark-based power supply planning method for a distributed improved differential evolution algorithm comprises population calculation and population summarization, wherein the population calculation comprises the following steps:
step 1: initializing parameters;
step 2: different random initializations are carried out on the differential evolution according to the global or local search stage;
step 3: randomly selecting 3 individuals which are not repeated with the current individual to update the population;
step 4: exchanging each dimension of the corresponding individuals of the new and old populations;
step5, calculating the total construction and operation cost of the distributed power supply, and taking the value as a fitness value of the DIDE;
step6, screening individuals meeting the constraint according to the load flow calculation constraint condition of the power system, and if the individuals do not meet the load flow calculation constraint condition, adjusting the individual fitness to the maximum value;
step 7: updating the individual historical optimal value;
step 8: and updating the historical optimal value of the population.
In a parameter initialization stage, parallelism p of distributed computation needs to be set, the parallelism is divided into p groups of data according to the upper and lower bounds of the data quantity, each group of data generates an RDD of Spark, which represents an example population, and then each population is computed in each RDD.
In the distributed power supply planning, the individual dimensions in the did algorithm are set to be N ═ 14 dimensions, and the value in each dimension is a natural number and represents the number of power supply installation stations of the node in the power grid.
Population calculation is a specific search process of the algorithm on a solution space, and is an inseparable minimum calculation step in Spark.
Preferably, the number of iterations per calculation may be set to "total number of iterations × 0.8/p/5".
In one embodiment of the present invention, the population size is 10.
The population calculation procedures and steps are set forth in detail below. The specific steps and flow chart are shown in fig. 1.
Step 1: initializing parameters;
step 2: different random initializations are performed on the differential evolution according to the global or local search phase.
Preferably, the population random initialization step of the global search uses the following formula:
Xi＝rand*(ub-lb)+lb where i←(1：N) (1)
wherein the content of the first and second substances,
Xiis the position of the ith individual of the particle,
lb and ub are particle positions XiThe upper and lower bounds of (a) are,
rand is the average random number of (0,1),
number of individuals in N population.
The local search phase accounts for 80% of the total computation time.
Preferably, the population random initialization step of the local search uses the following formula:
wherein the content of the first and second substances,
Xiis the position of the particle in the ith dimension,
beta is the searched known optimal fitness,
gaussian _ rand is a gaussian-distributed random number with a mean of 0 and a variance of 1,
number of individuals in N population.
Step 3: randomly selecting 3 individuals which are not repeated with the current individual as Xr1,Xr2And Xr3：
Wherein the content of the first and second substances,
t is the current number of iterations of the population calculation,
i is a preset maximum number of iterations,
m is equal to 0.5.
Step 4: and exchanging according to the following probability for each dimension of the corresponding individual of the new and old populations.
p＝C/D (5)
Wherein the content of the first and second substances,
c is equal to 0.9 of the total weight of the alloy,
d is the dimension value of the individual.
Step5: and calculating the total construction and operation cost of the distributed power supply, and taking the value as the adaptability value of the DIDE.
In an embodiment of the present invention, the total cost calculation function for the construction and operation of the distributed power supply is:
in the formula, TmaxIs the maximum number of hours of power generation of the distributed power supply; m is the total number of distributed power supplies in the power distribution network; sDGiRated capacity for the ith distributed power supply; ceDGiThe unit electricity cost of the ith distributed power supply; etaiThe power factor of the ith distributed power supply; cDG1iThe installation cost for the ith distributed power supply; cDG2iA cost of operating and maintaining for the ith distributed power supply; cDG3iThe electricity generation fuel cost for the ith distributed power source.
Step6 individual screening. And screening individuals meeting the constraint according to the load flow calculation constraint conditions of the power system.
And if the individual does not meet the constraint condition of the load flow calculation, adjusting the individual fitness to be the maximum value.
In an embodiment of the invention, the load flow calculation constraint condition comprises an equality constraint condition and an inequality constraint condition.
Wherein, the equality constraint condition is an active power balance equation:
in the formula, PDGiThe distributed power supply of the node i is active;
PGiactive power is generated for the generator at the node i;
PLis the active network loss; pDIs the active load of the system.
Wherein, inequality constraint conditions include:
and (3) limiting the upper and lower limits of the node voltage:
|Vi|min≤Vi≤|Vi|max (8)
and (3) branch current constraint:
|Ii|≤|Ii|max (9)
capacity constraint of distributed power supply:
in the formula:
and
respectively representing the lower limit and the upper limit of the capacity of the distributed power supply installed at the node i; pLD iThe load on the node i is active; eta is the maximum proportion of the active total amount of the distributed power supply to the active total amount of the system; n is a radical ofDGTotal number of distributed power source installations; n is the number of nodes; i Vi|minAnd | Vi|maxRespectively representing the minimum value and the maximum value of the voltage at the node i; iiI and Ii|maxThe magnitude of the current of the ith branch and the maximum value of the allowed current are respectively.
Step 7: and updating the individual historical optimal value.
And if the individual fitness in the population is smaller than the historical optimal fitness of the individual, taking the current individual as the historical optimal individual, and taking the current individual fitness as the historical optimal individual fitness.
Step 8: and updating the historical optimal value of the population.
And if the individual fitness in the population is smaller than the historical optimal fitness of the population, updating the current individual as the historical optimal individual of the population, wherein the fitness of the current individual is the historical optimal individual fitness of the population.
Population summary: on the overall level, the algorithm is divided into two stages of global search and local search. The global search phase accounts for 20% of the total computation time, and the number of updates of the population computation is not limited. The local search phase accounts for 80% of the total computation time.
The general level of flow diagram is shown in figure 2.
In a preferred embodiment of the present invention, if the optimal value is not updated n times in succession, the maximum number of updates u in the local search stage is increased by 2 based on the original number.
In an embodiment of the present invention, the initial value of the maximum update time u in the local search stage is set to 15, and n is 5.
On the overall level, after each RDD completes the iterative computation of each population, information interaction among the populations is needed, namely, the optimal solution in the result generated by the last iterative computation of all the populations is found out; and if the solution is better than the optimal solution of all the current populations, updating the current optimal solution, and continuously transmitting the optimal solution to the next iterative computation of each population.
In a specific embodiment of the invention, a 14-node power distribution network test system is adopted as an example system to perform location and volume analysis on a distributed power supply.
As shown in FIG. 3, the node positions of the distributed power supply to be installed are 3, 4, 10 and 14, and the voltage class of the system is 23kV and Ptotal＝28.7MW，Qtotal7.75 Mvar. According to PDG≤0.25PtotalTaking PDGThe cos phi is 0.9 at 3MW, the power rating of each individual distributed power supply is 200kW, and the voltage deviation is specified to be within ± 5%. Installation cost C of ith DGDG1i1344 yuan/kW; operating maintenance cost C of ith DGDG2i0.052 yuan/kW; electricity generation fuel cost C of ith DGDG3i0.3 yuan/kW.
Table 1 shows the optimal solution obtained by performing the site selection and the volume fixing of the distributed power supply by using the did algorithm. From table 1, it can be seen that the power supplies installed at nodes 3, 4, 10 and 14 are found according to the did algorithm, and the optimal output powers are 799.3, 167.1, 400 and 194.9kW respectively. According to the actual equipment manufacturing situation, 4, 1, 2 and 1 distributed power supplies are respectively installed on the 3, 4, 10 and 14 nodes. The rated power of each distributed power supply is 200 kW. When the distributed power supply does not exist, the active network loss of the network is 0.5172MW, the lowest voltage of the network is 0.9713pu, and the average voltage is 0.9842 pu; the optimized active network loss is 0.4131MW, the minimum voltage of the network is 0.9740pu, and the average voltage is 0.9854 pu. Compared with the situation without a distributed power supply, the active network loss of the network is reduced by 20.1%, the operating cost of the power grid is effectively saved, and the economic stable operation of the power distribution network is greatly influenced.
Table 1 optimization of DG installation location and capacity of 14-node system using did algorithm
| Mounting location | Optimum output power/kW | Number of mounting units/unit | Power factor |
| 1 | 0 | 0 | - |
| 2 | 0 | 0 | - |
| 3 | 799.3 | 4 | 0.9 |
| 4 | 167.1 | 1 | 0.9 |
| 5 | 0 | 0 | - |
| 6 | 0 | 0 | - |
| 7 | 0 | 0 | - |
| 8 | 0 | 0 | - |
| 9 | 0 | 0 | - |
| 10 | 400.0 | 2 | 0.9 |
| 11 | 0 | 0 | - |
| 12 | 0 | 0 | - |
| 13 | 0 | 0 | - |
| 14 | 194.9 | 1 | 0.9 |
| Total up to | 1561.3 | 8 | - |
It can be known from table 1 that the distributed power supply planning method of the present invention fully utilizes the computing resources of the distributed cluster, and improves the search effect of the algorithm; and a planning model taking the minimum total cost of the construction and operation of the distributed power supply as an optimization sub-target realizes the optimal planning of the distributed power supply by the power distribution network testing system.
By adopting the optimal planning scheme, the active network loss of the network can be effectively reduced, the construction and operation cost of the distributed power supply can be reduced, and the voltage level of the system can be improved.
The above embodiments are provided only for illustrating the present invention, and those skilled in the art can make various changes or modifications without departing from the spirit and scope of the present invention, and therefore, all equivalent technical solutions should also fall within the scope of the present invention.
Claims (10)
1. A Spark-based power supply planning method for a distributed improved differential evolution algorithm is characterized by comprising the following steps: the method comprises the following steps of population calculation and population summarization, wherein the population calculation comprises the following steps:
step 1: initializing parameters;
step 2: different random initializations are carried out on the differential evolution according to the global or local search stage;
step 3: randomly selecting 3 individuals which are not repeated with the current individual to update the population;
step 4: exchanging each dimension of the corresponding individuals of the new and old populations;
step5: calculating the total construction and operation cost of the distributed power supply, and taking the value as a fitness value of the DIDE;
step6: screening individuals meeting the constraint according to the load flow calculation constraint conditions of the power system, and if the individuals do not meet the load flow calculation constraint conditions, adjusting the individual fitness to be the maximum value;
step 7: updating the individual historical optimal value;
step 8: and updating the historical optimal value of the population.
2. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 1, wherein: in a parameter initialization stage, setting parallelism p of distributed computation, wherein the parallelism is divided into p groups of data according to the upper and lower bounds of the data quantity, each group of data generates one RDD of Spark to represent an example population, and then, computing each population in each RDD.
3. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 1, wherein: the formula used in the population random initialization step of the global search is as follows:
Xi＝rand*(ub-lb)+lbwherei←(1：N) (1)
wherein, XiIs the position of the ith individual of the particle, lb and ub are the particle positions XiAnd rand is the average random number of (0,1), and the number of individuals in the N population.
4. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 1, wherein: the formula used in the random population initialization step of the local search is as follows:
wherein, XiIs the position of the ith dimension of the particle, beta is the known optimal fitness which is searched, gaussian _ rand is a Gaussian distribution random number with the mean value of 0 and the variance of 1,
the number of individuals in the N population is the known optimal individuals to search for.
5. A power supply planning method based on Spark distributed improved differential evolution algorithm according to claim 3 or 4, characterized in that: the global search phase accounts for 20% of the total computation time, and the number of updates of the population computation is not limited. The local search phase accounts for 80% of the total computation time; and if the optimal value of the local search stage is not updated for n times continuously, adding 2 to the maximum update time of the local search stage on the original basis.
6. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 1, wherein: step3 comprises the following specific steps: randomly selecting 3 individuals which are not repeated with the current individual as Xr1，Xr2And Xr3Updating the population position according to the following formula:
wherein t is the current iteration number of the population calculation, and I is the preset maximumThe number of iterations is,
m is equal to 0.5 for the position of the individual i in the generation t.
7. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 1, wherein: step 4: and exchanging each dimension of the corresponding individuals of the new and old populations according to the following probability:
p＝C/D (5)
where C is equal to 0.9 and D is the dimension value of the individual.
8. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 1, wherein: the total cost calculation function for the construction and operation of the distributed power supply in Step5 is as follows:
in the formula: t ismaxIs the maximum number of hours of power generation of the distributed power supply; m is the total number of distributed power supplies in the power distribution network; sDGiRated capacity for the ith distributed power supply; ceDGiThe unit electricity cost of the ith distributed power supply; etaiThe power factor of the ith distributed power supply; cDG1iThe installation cost for the ith distributed power supply; cDG2iA cost of operating and maintaining for the ith distributed power supply; cDG3iThe electricity generation fuel cost for the ith distributed power source.
9. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 1, wherein: the power flow calculation constraint conditions in Step6 include equality constraint conditions and inequality constraint conditions, wherein the equality constraint conditions are active power balance equations:
in the formula: pDGiThe distributed power supply of the node i is active; pGiActive power is generated for the generator at the node i; pLIs the active network loss; pDIs the active load of the system.
10. The Spark-based power supply planning method for the distributed improved differential evolution algorithm according to claim 9, wherein: the inequality constraint conditions include:
and (3) limiting the upper and lower limits of the node voltage: i Vi|min≤Vi≤|Vi|max (8)
And (3) branch current constraint: ii|≤|Ii|max (9)
Capacity constraint of distributed power supply:
in the formula:
and
respectively representing the lower limit and the upper limit of the capacity of the distributed power supply installed at the node i; pLDiThe load on the node i is active; eta is the maximum proportion of the active total amount of the distributed power supply to the active total amount of the system; n is a radical ofDGTotal number of distributed power source installations; n is the number of nodes; i Vi|minAnd | Vi|maxRespectively representing the minimum value and the maximum value of the voltage at the node i; iiI and Ii|maxThe magnitude of the current of the ith branch and the maximum value of the allowed current are respectively.
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