CN116388262A - Reactive power optimization method and system for distributed photovoltaic distribution network based on multi-objective optimization - Google Patents
Reactive power optimization method and system for distributed photovoltaic distribution network based on multi-objective optimization Download PDFInfo
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Abstract
Reactive power optimization method and system for distributed photovoltaic power distribution network based on multi-objective optimization, and the method comprises the following steps: building a photovoltaic power generation output probability model based on Beta distribution, and building a user load probability model based on Gaussian distribution; generating photovoltaic power generation time sequence data and load time sequence data respectively by using a Monte Carlo method; the minimum accumulated active network loss at 24 moments is a first objective function, the minimum average voltage deviation of all nodes is a second objective function, and the minimum voltage regulating operation times of the on-load voltage regulating transformer and the minimum switching times of the capacitor are a third objective function, so that a reactive power multi-objective optimization model of the power distribution network is formed; constructing a reactive power optimization model joint constraint condition of the power distribution network; and solving the reactive power optimization model and the joint constraint condition of the reactive power optimization model by adopting an intensity pareto evolution algorithm to obtain an optimal photovoltaic output solution, an optimal transformer voltage regulation solution and an optimal capacitor switching solution. The invention selects the network loss, the voltage and the adjustment cost as the reactive power solution.
Description
Technical Field
The invention belongs to the technical field of reactive power optimization operation of power distribution networks, and particularly relates to a reactive power optimization method and system for a distributed photovoltaic distribution network based on multi-objective optimization.
Background
The reactive power supply of the power distribution network is an important device for reducing network loss of the power distribution network, improving voltage level of the power distribution network and realizing reactive power on-site balancing. Reactive power compensation of a distribution system mainly comprises centralized compensation of a transformer substation, and along with continuous increase of grid frames of the distribution network and increasing of load demands, large line loss of a feeder line can be caused by long-distance transmission of reactive power, and problems of line blockage, low voltage of line ends and the like are easily caused.
In the prior art 1 (CN 114336658A), a reactive power control method for a distribution network including distributed photovoltaic and reactive power regulation devices is proposed, different control strategies are adopted through different control intervals of data, so that the voltage reactive power control system of a low-voltage distribution network station is ensured to act correctly, and the technical problem of distribution network control is solved, but the goal of the prior art 1 is to maintain the voltage and reactive power of the low-voltage distribution network station to be qualified, and the voltage and loss are not optimized through an intelligent optimization algorithm. In the prior art 2 (CN 108321810B), a distribution network multi-time-scale reactive power control method for inhibiting voltage fluctuation of a photovoltaic grid-connected point is proposed, and reactive power regulation of discrete equipment and a photovoltaic inverter in a distribution network is coordinated by using the multi-time-scale control method so as to inhibit severe voltage fluctuation caused by high-permeability photovoltaic grid-connected, and ensure the safety and economy of system operation. However, the optimization objective of the prior art 2 is that the total operation cost of the power distribution network is minimum, the total operation cost comprises the active loss, the adjustment cost of the on-load voltage-regulating transformer and the adjustment cost of the group switching capacitor, the two are different in dimension, the former is kilowatt-hour, the latter is the adjustment times, the adjustment cost of the on-load voltage-regulating transformer and the adjustment cost of the group switching capacitor cannot be accurately converted into the active network loss, and then the two are summed. In the prior art 3 (CN 105826946A), a dynamic reactive power optimization method of a power distribution network for large-scale photovoltaic access is provided, and the problems that SVR frequent actions are caused by large-scale distributed photovoltaic access to the power distribution network, equipment aging is accelerated and the like are solved. However, in the prior art 3, the optimization objective is that the network loss and the tap adjustment times are minimum, and the two objectives are converted into a single objective by adopting a weighting method, wherein the two objectives are different in dimension, the former is kilowatt-hour, the latter is the adjustment times, and the weights of the network loss and the tap adjustment times are difficult to select.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a reactive power optimization method and system for a distributed photovoltaic distribution network based on multi-objective optimization, which are used for constructing a photovoltaic power generation and load probability model aiming at the problem that the characteristic of the photovoltaic output time sequence is not considered in the reactive power optimization of the distributed photovoltaic distribution network, and generating photovoltaic and load time sequence data by applying a Monte Carlo method. And constructing a reactive power optimization model of the power distribution network by taking the minimum active network loss, the minimum average voltage deviation, the minimum voltage regulating operation times of the on-load voltage regulating transformer and the minimum switching times of the capacitor as targets, and solving a photovoltaic output strategy, a transformer voltage regulating strategy and a capacitor switching strategy by adopting an intensity pareto evolution algorithm.
The invention adopts the following technical scheme.
The invention provides a reactive power optimization method for a distributed photovoltaic power distribution network based on multi-objective optimization, which comprises the following steps:
step 1, building a photovoltaic power generation output probability model based on Beta distribution according to historical sunlight illumination of a target area, and building a user load probability model based on Gaussian distribution according to historical user load of the target area; according to the photovoltaic power generation output probability model and the user load probability model, generating photovoltaic power generation time sequence data and load time sequence data respectively by applying a Monte Carlo method;
Preferably, step 1 comprises:
step 1.1, historical solar illuminance of a target area is utilized to obtain historical clear air factor data of the target area, the average value and standard deviation of the historical clear air factors of all time points are calculated, and a probability density function of solar illuminance intensity of all time points of the target area based on Beta distribution, namely a photovoltaic power generation output probability model is constructed; generating sunlight illuminance data of the kth moment of the target area according to a photovoltaic power generation output probability model by adopting a Monte Carlo method, and forming photovoltaic power generation time sequence data by using the sunlight illuminance data of the target area at 24 moments;
step 1.2, calculating the maximum value, the minimum value, the mean value and the standard deviation of each time point in the historical user load data according to the historical user load of the target area, and constructing a user load probability density function at the kth moment of the target area based on Gaussian distribution, namely a user load probability model; and generating user load data of the kth moment service in the target area according to the user load probability model by adopting a Monte Carlo method, and forming load time sequence data by using the user load data of 24 moments in the target area.
The photovoltaic power generation output probability model meets the following relation:
in the method, in the process of the invention,
f(s k ) Is a probability density function of solar illumination intensity at the kth moment of a target area,
Γ (·) is a Gamma function (Gamma function),
s k solar illuminance data at the kth moment of the target area,
α k the first shape factor is distributed for Beta at the kth time, satisfying the following relation:
β k and distributing a second shape coefficient for Beta at the kth moment, wherein the following relation is satisfied:
wherein mu k Is the average value delta of the historic clear sky factors at the kth moment k And (5) the standard deviation of the clear sky factor is the history at the kth moment.
Step 1.1 further comprises: generating photovoltaic active power output curve data of the target area by using solar illuminance data of the target area at 24 moments according to the following relation:
in the method, in the process of the invention,
P PV,k photovoltaic power generation power at the kth moment of the target area,
P PV_r the rated power of photovoltaic power generation in the target area is obtained,
s k solar illuminance data at the kth moment of the target area,
s r and rated illuminance for the target area.
The user load probability model satisfies the following relation:
in the method, in the process of the invention,
f(p k ) A probability density function for the user load at the kth time of the target region,
η k is the average value of the historical load data at the kth moment,
σ k is the standard deviation of the historical load data at the kth time,
p k historical load data for the kth moment of the target area,
p k,low 、p k,up the lower limit value and the upper limit value of the user load at the kth moment of the target area are respectively set.
Preferably, in step 2, the first objective function is as follows:
in the method, in the process of the invention,
min f 1 as a function of the first object function,
P loss-k is the system loss at the kth time;
the second objective function is as follows:
in the method, in the process of the invention,
min f 2 as a function of the second objective function,
zm is the number of nodes of the distribution network,
U avg-i for the average voltage deviation of the voltage of the node i and the rated voltage, the U is satisfied avg-i ＝average(|U i -U n I), wherein U i U is the voltage value of the node i after being connected with the distributed photovoltaic n Is rated voltage;
the third objective function is as follows:
in the method, in the process of the invention,
min f 3 as a function of the third objective function,
i (·) is an indication function,
c k 、c k-1 the positions of the tap of the regulating transformer at the kth moment and the kth-1 moment respectively,
t k 、t k-1 the state of the capacitor at the kth moment and the state of the capacitor at the kth-1 moment are respectively obtained.
c k ＝c k-1 Or t k ＝t k-1 When I (&) is 0; c k ≠c k-1 Or t k ≠t k-1 The value of I (.cndot.) is 1.
Preferably, the joint constraint constructed in step 2 is as follows:
1. and considering the constraint condition that the distributed power supply is connected into the power distribution network, namely the power balance of the power distribution network containing the distributed power supply, and satisfying the following relation:
in the method, in the process of the invention,
P Li 、Q Li the active load and the reactive load of node i respectively,
P Gi 、Q Gi active power and reactive power injected at node i respectively,
P DGi 、Q DGi active power and reactive power which are respectively injected by the node i distributed photovoltaic;
U i 、U j the voltages at the first i and last j nodes of the branch,
δ ij for the power factor of the branch connecting node i and node j,
G ij 、B ij to connect the branch conductance and susceptance of node i and node j,
θ ij is the voltage phase angle difference between node i and node j;
2. the line active power constraint satisfies the following relation:
|P Lj |≤P Ljmax (14)
in the method, in the process of the invention,
P i for the active power of the Lj branch,
P imax maximum power is allowed for the Lj branch;
3. the distributed power supply operation constraint satisfies the following relation:
P DGi,min ≤P DGi ≤P DGi,max (15)
in the method, in the process of the invention,
P DGi active power injected for node i distributed photovoltaic,
P DGi,min 、P DGi,max respectively obtaining the minimum value and the maximum value of the distributed photovoltaic active power of the node i;
4. according to the current active power output and the capacity of the inverter, the reactive power output adjustable range of the photovoltaic power station is determined, and the following relation is satisfied:
in the method, in the process of the invention,
Q PV,max 、Q PV,min the upper limit and the lower limit of the reactive power output adjustable range of the photovoltaic power station are respectively,
S PV for the capacity of the photovoltaic inverter,
P PV active power output for photovoltaic;
5. the power distribution network to be connected must meet radial constraint and must be ensured to be in an open loop state during normal operation;
6. connectivity constraints, i.e., each load node communicates with a power node.
The invention also provides a reactive power optimization system of the distributed photovoltaic power distribution network based on multi-objective optimization, which comprises the following steps: the system comprises a data generation module, a multi-objective optimization model module and an optimal solution module;
the data generation module is used for constructing a photovoltaic power generation output probability model based on Beta distribution according to historical sunlight illumination of a target area, and constructing a user load probability model based on Gaussian distribution according to historical user loads of the target area; according to the photovoltaic power generation output probability model and the user load probability model, generating photovoltaic power generation time sequence data and load time sequence data respectively by applying a Monte Carlo method;
the multi-objective optimization model module is used for forming a reactive multi-objective optimization model of the power distribution network by taking the minimum accumulated active network loss at 24 moments as a first objective function, taking the minimum average voltage deviation of all nodes at 24 moments as a second objective function, taking the minimum voltage regulating operation times of the on-load voltage regulating transformer and the minimum switching times of the capacitor as a third objective function and taking three objective functions; meanwhile, constructing a joint constraint condition for the reactive power optimization model of the power distribution network;
and the optimal solution module is used for solving the reactive power optimization model of the power distribution network and the joint constraint condition thereof by using the photovoltaic power generation time sequence data and the load time sequence data and adopting an intensity pareto evolution algorithm to obtain a photovoltaic output optimal solution, a transformer voltage regulation optimal solution and a capacitor switching optimal solution.
Compared with the prior art, the method provided by the invention has the beneficial effects that the photovoltaic power generation and load probability model is built based on the photovoltaic historical power generation data and the load historical data, the Monte Carlo method is applied to generate the photovoltaic and load time sequence data, the photovoltaic output, the load randomness and the fluctuation are considered, and the prediction accuracy is higher. The method is characterized in that the reactive power optimization multi-objective model of the power distribution network is built by taking the minimum active network loss, the minimum average voltage deviation, the minimum voltage regulating operation times of the on-load voltage regulating transformer and the minimum switching times of the capacitor as targets in 24 time periods and adopting the intensity pareto evolution algorithm, and compared with the method of converting the multi-objective optimization problem into the single-objective optimization problem by a weighting method, the method of converting the multi-objective optimization problem into the single-objective optimization problem is avoided, and the problems that the active network loss is minimum, the average voltage deviation is minimum, the voltage regulating operation times of the on-load voltage regulating transformer and the switching times weight of the capacitor are unreasonable because the dimension is different are avoided. Meanwhile, the reactive multi-objective optimization solution of the photovoltaic-containing power distribution network is solved by adopting the strength pareto evolution algorithm, so that the diversity and convergence of the pareto optimal solution set of the solution are guaranteed, and the overall optimal solution of the network loss, the voltage and the adjustment cost is selected by adopting the TOPSIS, so that the optimal solution can be comprehensively, reasonably and effectively selected.
Drawings
FIG. 1 is a flow chart of a reactive power optimization method of a distributed photovoltaic power distribution network based on multi-objective optimization;
FIG. 2 is a schematic diagram of an improved IEEE33 node power distribution system in accordance with an embodiment of the invention;
FIG. 3 is a graph of typical output force of a distributed power supply (photovoltaic) in an embodiment of the present invention;
FIG. 4 is a graph of typical output force of a distributed power source (wind power) in an embodiment of the invention;
FIG. 5 is a graph of typical load of a resident load in an embodiment of the invention;
FIG. 6 is a graph of typical load of a commercial load in an embodiment of the present invention;
FIG. 7 is a graph of the optimal solution set of the pareto 24 hours per node for the voltage deviation mean value of each node after optimization in an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The embodiments described herein are merely some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art without inventive faculty, are within the scope of the invention, based on the spirit of the invention.
On the one hand, the invention provides a reactive power optimization method of a distributed photovoltaic power distribution network based on multi-objective optimization, which is shown in fig. 1 and comprises the following steps:
step 1, building a photovoltaic power generation output probability model based on Beta distribution according to historical sunlight illumination of a target area, and building a user load probability model based on Gaussian distribution according to historical user load of the target area; and respectively generating photovoltaic power generation time sequence data and load time sequence data by applying a Monte Carlo method according to the photovoltaic power generation output probability model and the user load probability model.
Specifically, step 1 includes:
step 1.1, historical solar illuminance of a target area is utilized to obtain historical clear air factor data of the target area, the average value and standard deviation of the historical clear air factors of all time points are calculated, and a probability density function of solar illuminance intensity of all time points of the target area based on Beta distribution, namely a photovoltaic power generation output probability model is constructed; and generating sunlight illuminance data of the kth moment of the target area according to the photovoltaic power generation output probability model by adopting a Monte Carlo method, and forming photovoltaic power generation time sequence data by using the sunlight illuminance data of the target area at 24 moments. Comprising the following steps:
step 1.1.1, acquiring historical sunlight illuminance data of a target area, wherein the historical sunlight illuminance data is represented by the following formula:
in the method, in the process of the invention,
s is historical sunlight illumination data of a target area,
s si,k for solar illuminance data at the kth time on the si day of the target area, si=1, 2, …, sn, sn is solar illuminance data history days, k=1, 2, …,24.
Step 1.1.2, acquiring historical clear sky factor data of a target area, wherein the data is specifically shown as the following formula:
in the method, in the process of the invention,
s' is historical clear sky factor data of a target area,
s max,k is the maximum value of the historical sunlight illuminance data S of the target area at the kth moment.
Step 1.1.3, calculating the mean value and standard deviation of historical clear sky factors of all time points, and constructing a probability density function of solar illumination intensity of all time points of a target area based on Beta distribution, namely a photovoltaic power generation output probability model, wherein the following relational expression is satisfied:
in the method, in the process of the invention,
f(s k ) At the kth time of the target areaA probability density function of the sun illumination intensity is carved,
Γ (·) is a Gamma function (Gamma function),
s k solar illuminance data at the kth moment of the target area,
α k the first shape factor is distributed for Beta at the kth time, satisfying the following relation:
β k and distributing a second shape coefficient for Beta at the kth moment, wherein the following relation is satisfied:
wherein mu k Is the average value delta of the historic clear sky factors at the kth moment k And (5) the standard deviation of the clear sky factor is the history at the kth moment.
And 1.1.4, generating sunlight illuminance data of the kth moment of the target area according to a photovoltaic power generation output probability model by adopting a Monte Carlo method, and forming photovoltaic power generation time sequence data by using the sunlight illuminance data of the 24 moments of the target area.
Further, step 1.1 further comprises:
step 1.1.5, generating photovoltaic active power output curve data of the target area by using solar illuminance data of the target area at 24 moments according to the following relation:
in the method, in the process of the invention,
P PV,k photovoltaic power generation power at the kth moment of the target area,
P PV_r the rated power of photovoltaic power generation in the target area is obtained,
s k solar illuminance data at the kth moment of the target area,
s r and rated illuminance for the target area.
Step 1.2, calculating the maximum value, the minimum value, the mean value and the standard deviation of each time point in the historical user load data according to the historical user load of the target area, and constructing a user load probability density function at the kth moment of the target area based on Gaussian distribution, namely a user load probability model; and generating user load data of the kth moment service in the target area according to the user load probability model by adopting a Monte Carlo method, and forming load time sequence data by using the user load data of 24 moments in the target area. Comprising the following steps:
step 1.2.1, acquiring historical user load data of a target area, wherein the historical user load data is shown in the following formula;
in the method, in the process of the invention,
p is historical user load data for the target region,
p pi,k for user load data at the kth time on the pi th day of the target area, pi=1, 2, …, pn, pn is the historical days of the user load data.
Step 1.2.2, calculating the maximum value, the minimum value, the mean value and the standard deviation of each time point in the historical user load data, constructing a user load probability density function at the kth moment of a target area based on Gaussian distribution, namely a user load probability model, and meeting the following relation:
in the method, in the process of the invention,
f(p k ) A probability density function for the user load at the kth time of the target region,
η k is the average value of the historical load data at the kth moment,
σ k is the standard deviation of the historical load data at the kth time,
p k historical load data for the kth moment of the target area,
p k,low 、p k,up the lower limit value and the upper limit value of the user load at the kth moment of the target area are respectively,
and 1.2.3, generating user load data of the kth moment service in the target area according to a user load probability model by adopting a Monte Carlo method, and forming load time sequence data by using the user load data of 24 moments in the target area.
The method provided by the invention constructs a photovoltaic power generation and load probability model based on photovoltaic historical power generation data and load historical data, generates photovoltaic and load time sequence data by applying a Monte Carlo method, considers photovoltaic output, load randomness and volatility, and has higher prediction accuracy.
The invention optimizes three objective functions as multiple targets without considering the relation among the three objective functions, so that the three objective functions, namely active network loss, voltage deviation and operation cost, are formed into three dimensions, the multiple targets are solved by adopting an intensity pareto evolution algorithm, the three equations are not solved simultaneously under constraint conditions, but are optimized in an operation solution space under constraint conditions, and a pareto optimal solution set is obtained as a result.
Specifically, step 2 includes:
step 2.1, the first objective function is as follows:
in the method, in the process of the invention,
min f 1 as a function of the first object function,
P loss-k is the system loss at the kth time;
wherein, is P loss-k Can be expressed as:
in the method, in the process of the invention,
P Lj-k the active power loss of the Lj branch at the kth time,
zn is the number of branches.
Step 2.2, the second objective function is as follows:
in the method, in the process of the invention,
min f 2 as a function of the second objective function,
zm is the number of nodes of the distribution network,
U avg-i for the average voltage deviation of the voltage of the node i and the rated voltage, the U is satisfied avg-i ＝average(|U i -U n I), wherein U i U is the voltage value of the node i after being connected with the distributed photovoltaic n Is rated voltage.
Step 2.3, the third objective function is as follows:
in the method, in the process of the invention,
min f 3 as a function of the third objective function,
i (·) is an indication function,
c k 、c k-1 the positions of the tap of the regulating transformer at the kth moment and the kth-1 moment respectively,
t k 、t k-1 the state of the capacitor at the kth moment and the kth-1 moment respectively,
wherein c k ＝c k-1 Or t k ＝t k-1 When I (&) is 0; c k ≠c k-1 Or t k ≠t k-1 The value of I (.cndot.) is 1.
In particular, the on-load tap changer voltage regulating operation and the capacitor switching operation require costs, so that the reactive power multi-objective optimization of the power distribution network is performed to minimize the times of the on-load tap changer voltage regulating and the capacitor switching.
Calculating the change times of the tap of the voltage regulating transformer in one day, and comparing whether the tap positions at the kth moment and the kth-1 moment are changed or not, wherein the change of the tap position is 1, and otherwise, the change of the tap position is 0; similarly, if the switching state of the capacitor at the kth moment and the kth-1 moment is changed, the switching state is changed to 1, and otherwise, the switching state is changed to 0.
Step 2.4, the constructed joint constraint conditions comprise:
1. and considering the constraint condition that the distributed power supply is connected into the power distribution network, namely the power balance of the power distribution network containing the distributed power supply, and satisfying the following relation:
in the method, in the process of the invention,
P Li 、Q Li the active load and the reactive load of node i respectively,
P Gi 、Q Gi active power and reactive power injected at node i respectively,
P DGi 、Q DGi active power and reactive power which are respectively injected by the node i distributed photovoltaic;
U i 、U j the voltages at the first i and last j nodes of the branch,
δ ij for the power factor of the branch connecting node i and node j,
G ij 、B ij to connect the branch conductance and susceptance of node i and node j,
θ ij is the voltage phase angle difference between node i and node j.
2. The line active power constraint satisfies the following relation:
|P Lj |≤P Ljmax (14)
in the method, in the process of the invention,
P i for the active power of the Lj branch,
P imax maximum power is allowed for the Lj leg.
3. The distributed power supply operation constraint satisfies the following relation:
P DGi,min ≤P DGi ≤P DGi,max (15)
in the method, in the process of the invention,
P DGi active power injected for node i distributed photovoltaic,
P DGi,min 、P DGi,max respectively the minimum value and the maximum value of the distributed photovoltaic active power of the node i.
4. According to the current active power output and the capacity of the inverter, the reactive power output adjustable range of the photovoltaic power station is determined, and the following relation is satisfied:
in the method, in the process of the invention,
Q PV,max 、Q PV,min the upper limit and the lower limit of the reactive power output adjustable range of the photovoltaic power station are respectively,
S PV for the capacity of the photovoltaic inverter,
P PV is the active power output of the photovoltaic.
5. The distribution network to be connected must meet radial constraints and must be guaranteed to be in an open loop state during normal operation.
6. Connectivity constraints, i.e., each load node communicates with a power node.
Specifically, the intensity pareto evolution algorithm in step 3 includes:
step 3.1, generating an initial group Pop, and setting an empty non-dominant set NDSet, or referred to as an archive set;
step 3.2, copying non-dominant individuals in the Pop into the NDSet;
step 3.3, deleting the dominant individuals in the NDSet;
and 3.4, if the number of individuals in the NDset exceeds a preset value, reducing the size of the ND set by using a clustering method.
Specifically, in step 3.4, the size of the non-dominant set NDSet is reduced based on the hierarchical clustering method.
Specifically, when the size of the non-support set exceeds N, the size of the non-support set is reduced by adopting a condensation hierarchical clustering algorithm, and the specific process is as follows:
step 3.4.1, initializing each non-dominant object with a cluster cl w ＝{o w W is greater than or equal to 1 and less than or equal to W, W is the number of non-dominant objects, o w Is an object.
Step 3.4.2, if the number of clusters is smaller than N, and N is the size of the group Pop, turning to step 3.5, otherwise turning to step 3.3.
Step 3.4.3, calculating the distance between the different two clusters:
in the method, in the process of the invention,
d is two different clusters cl w1 And cl w2 The distance between the two plates is set to be equal,
o w1 and o w2 Respectively cluster cl w1 And cl w2 ；
Step 3.4.4, merge the two clusters with the smallest distance, go to step 3.4.2.
And 3.4.5, selecting an individual with the standard from each cluster (the core of the subclass is selected, and the core has the smallest distance with other individuals in the subclass) to form a new non-dominant set.
And 3.5, calculating the fitness of individuals in the group Pop and the non-dominant set NDset.
Specifically, the individual xi fitness calculation method in the non-dominant set NDSet is as follows:
in the method, in the process of the invention,
fitness (xi) is the fitness of individual xi in the non-dominant set NDSet,
n i the number of individuals, n, of individuals xj, who are dominated by individual xi in the population Pop i = |{ xj e pop|xi > xj, xi e NDSet } |, where xj is the individual whose group Pop is dominated by individual xi,
n is the size of the population Pop.
The individual xj in the group Pop is calculated as follows:
in the method, in the process of the invention,
fitness (xj) is the fitness of an individual xj in the evolving population.
And 3.6, selecting individuals from the group Pop and the non-dominant set NDset to enter a pairing library by adopting a tournament algorithm.
And 3.7, performing evolutionary crossover and mutation operation on the pairing library.
And step 3.8, if the condition is not met, the step 3.2 is carried out, and if the condition is not met, the step is ended.
The method provided by the invention aims at minimum active network loss in 24 time periods, minimum average voltage deviation, minimum voltage regulating operation times of the on-load voltage regulating transformer and minimum switching times of the capacitor, and adopts the strength pareto evolution algorithm to construct a reactive power optimization multi-objective model of the power distribution network, so that the problem that the reactive power optimization multi-objective model is converted into a single-objective optimization problem by a weighting method is avoided, and the problem that the voltage regulating operation times of the on-load voltage regulating transformer and the weight settings of the switching times of the capacitor are unreasonable because the active network loss is minimum, the average voltage deviation is minimum and the dimension is different is avoided.
Meanwhile, the reactive multi-objective optimization solution of the photovoltaic-containing power distribution network is solved by adopting the strength pareto evolution algorithm, so that the diversity and convergence of the pareto optimal solution set of the solution are guaranteed, and the overall optimal solution of the network loss, the voltage and the adjustment cost is selected by adopting the TOPSIS, so that the optimal solution can be comprehensively, reasonably and effectively selected.
Taking an improved IEEE33 node power distribution system as an example, the validity of the algorithm presented herein is verified. The improved distribution network topology containing distributed power sources is shown in figure 2, the numbers 0 to 32 in figure 2 respectively represent 33 nodes, the nodes 10 and 17 are respectively connected with photovoltaic PV1 and PV2 with the capacity of 800kVA, and the power factor adjusting range is [0.95,1 ]]The method comprises the steps of carrying out a first treatment on the surface of the Node 30 has an access capacity of 800kVA wind power WG, and a power factor adjusting range [0.95,1 ]]The method comprises the steps of carrying out a first treatment on the surface of the 24. The 27 nodes are respectively connected with reactive power compensation devices C1 and C2 with the capacity of 800kVar, each reactive power compensation device comprises four groups of parallel capacitor groups, and the capacity of each group of parallel capacitor groups is 200kVar; an on-load voltage regulating transformer T1 is connected between the nodes 8 and 9, the initial transformation ratio is 1, and the adjustment interval is [0.9,1.1 ]]The step size is adjusted to 0.025. Let 0 point time decision become x 0 ＝[x(0,1),x(0,2),x(0,3),x(0,4),x(0,5),x(0,6)]Individual codes x= [ X ] for 24 periods 0 ,x 1 ,x 2 ,...,x 23 ]。
And taking a day as a unit, simulating the photovoltaic power generation output and the load by applying a Monte Carlo method according to the photovoltaic and load probability model parameters, and generating time sequence simulation data. Typical output curves of the distributed power source (photovoltaic and wind power) in the embodiment of the invention are shown in fig. 3 and 4, and typical load curves of residential and commercial loads are shown in fig. 5 and 6.
The average voltage deviation of each node, the 24-hour loss of each node and the reactive power multi-objective optimization of the 33-node power distribution system after improvement are shown in table 1.
TABLE 1 Voltage deviation and loss before optimization
The power factor, the transformer transformation ratio and the capacitor capacity switching of the 24-hour distributed power supply are optimized by adopting the intensity pareto evolution algorithm, and the voltage deviation mean value of each node and the 24-hour pareto optimal solution set of each node after optimization are shown in figure 7.
The distance and the closeness between each pareto optimal solution and the positive and negative ideal solutions are calculated by adopting a TOPSIS method for the operation times of the transformer and the capacitor of the final pareto optimal solution set, the voltage deviation mean value of each node and the 24-hour loss and normalization of each node, and the result is shown in table 2.
Table 2 solutions and ideal solution distances and closeness
| Sequence number | Distance from ideal | Distance from negative ideal solution | Proximity degree |
| Operation scheme 1 | 0.799 | 1.183 | 0.597 |
| |
1.112 | 1.023 | 0.479 |
| |
1.250 | 0.996 | 0.444 |
| |
0.725 | 1.180 | 0.620 |
| |
0.640 | 1.145 | 0.641 |
| |
0.832 | 1.059 | 0.560 |
| … | … | … | … |
The operation scheme has the maximum closeness and optimal scheme, and the operation times of the transformer and the capacitor, the voltage deviation average value of each node, the 24-hour loss of each node and 16,0.04132,6.9931 are respectively. Comparing the node voltage deviation and the loss sum before optimization, the average value of the node voltage deviation and the 24-hour loss sum of each node are improved after optimization, and the effectiveness of the algorithm model is proved.
The invention also provides a reactive power optimization system of the distributed photovoltaic distribution network based on multi-objective optimization, which comprises the following components:
the system comprises a data generation module, a multi-objective optimization model module and an optimal solution module;
the data generation module is used for constructing a photovoltaic power generation output probability model based on Beta distribution according to historical sunlight illumination of a target area, and constructing a user load probability model based on Gaussian distribution according to historical user loads of the target area; according to the photovoltaic power generation output probability model and the user load probability model, generating photovoltaic power generation time sequence data and load time sequence data respectively by applying a Monte Carlo method;
the multi-objective optimization model module is used for forming a reactive multi-objective optimization model of the power distribution network by taking the minimum accumulated active network loss at 24 moments as a first objective function, taking the minimum average voltage deviation of all nodes at 24 moments as a second objective function, taking the minimum voltage regulating operation times of the on-load voltage regulating transformer and the minimum switching times of the capacitor as a third objective function and taking three objective functions; meanwhile, constructing a joint constraint condition for the reactive power optimization model of the power distribution network;
and the optimal solution module is used for solving the reactive power optimization model of the power distribution network and the joint constraint condition thereof by using the photovoltaic power generation time sequence data and the load time sequence data and adopting an intensity pareto evolution algorithm to obtain a photovoltaic output optimal solution, a transformer voltage regulation optimal solution and a capacitor switching optimal solution.
The present disclosure may be a system, method, and/or computer program product. The computer program product may include a computer readable storage medium having computer readable program instructions embodied thereon for causing a processor to implement aspects of the present disclosure.
The computer readable storage medium may be a tangible device that can hold and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium would include the following: portable computer disks, hard disks, random Access Memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static Random Access Memory (SRAM), portable compact disk read-only memory (CD-ROM), digital Versatile Disks (DVD), memory sticks, floppy disks, mechanical coding devices, punch cards or in-groove structures such as punch cards or grooves having instructions stored thereon, and any suitable combination of the foregoing. Computer-readable storage media, as used herein, are not to be construed as transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., optical pulses through fiber optic cables), or electrical signals transmitted through wires.
The computer readable program instructions described herein may be downloaded from a computer readable storage medium to a respective computing/processing device or to an external computer or external storage device over a network, such as the internet, a local area network, a wide area network, and/or a wireless network. The network may include copper transmission cables, fiber optic transmissions, wireless transmissions, routers, firewalls, switches, gateway computers and/or edge servers. The network interface card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium in the respective computing/processing device.
Computer program instructions for performing the operations of the present disclosure can be assembly instructions, instruction Set Architecture (ISA) instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, c++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions may be executed entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any kind of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computer (for example, through the Internet using an Internet service provider). In some embodiments, aspects of the present disclosure are implemented by personalizing electronic circuitry, such as programmable logic circuitry, field Programmable Gate Arrays (FPGAs), or Programmable Logic Arrays (PLAs), with state information of computer readable program instructions, which can execute the computer readable program instructions.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.
Claims (11)
1. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization is characterized by comprising the following steps of:
step 1, building a photovoltaic power generation output probability model based on Beta distribution according to historical sunlight illumination of a target area, and building a user load probability model based on Gaussian distribution according to historical user load of the target area; according to the photovoltaic power generation output probability model and the user load probability model, generating photovoltaic power generation time sequence data and load time sequence data respectively by applying a Monte Carlo method;
step 2, taking the minimum accumulated active network loss at 24 moments as a first objective function, taking the minimum average voltage deviation of all nodes at 24 moments as a second objective function, taking the minimum voltage regulating operation times of the on-load voltage regulating transformer and the minimum switching times of the capacitor as a third objective function, and forming a reactive multi-objective optimization model of the power distribution network by three objective functions; meanwhile, constructing a joint constraint condition for the reactive power optimization model of the power distribution network;
step 3, solving a reactive power optimization model of the power distribution network and joint constraint conditions thereof by using photovoltaic power generation time sequence data and load time sequence data and adopting an intensity pareto evolution algorithm to obtain a photovoltaic output optimal solution, a transformer voltage regulation optimal solution and a capacitor switching optimal solution; and combining the optimal solution of the photovoltaic output, the optimal solution of the voltage regulation of the transformer and the optimal solution of the capacitor switching to obtain a reactive power optimization result of the distributed photovoltaic power distribution network.
2. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization according to claim 1, wherein,
the step 1 comprises the following steps:
step 1.1, historical solar illuminance of a target area is utilized to obtain historical clear air factor data of the target area, the average value and standard deviation of the historical clear air factors of all time points are calculated, and a probability density function of solar illuminance intensity of all time points of the target area based on Beta distribution, namely a photovoltaic power generation output probability model is constructed; generating sunlight illuminance data of the kth moment of the target area according to a photovoltaic power generation output probability model by adopting a Monte Carlo method, and forming photovoltaic power generation time sequence data by using the sunlight illuminance data of the target area at 24 moments;
step 1.2, calculating the maximum value, the minimum value, the mean value and the standard deviation of each time point in the historical user load data according to the historical user load of the target area, and constructing a user load probability density function at the kth moment of the target area based on Gaussian distribution, namely a user load probability model; and generating user load data of the kth moment service in the target area according to the user load probability model by adopting a Monte Carlo method, and forming load time sequence data by using the user load data of 24 moments in the target area.
3. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization according to claim 2, wherein,
the photovoltaic power generation output probability model meets the following relation:
in the method, in the process of the invention,
f(s k ) Is a probability density function of solar illumination intensity at the kth moment of a target area,
Γ (·) is a Gamma function (Gamma function),
s k solar illuminance data at the kth moment of the target area,
α k the first shape factor is distributed for Beta at the kth time, satisfying the following relation:
β k and distributing a second shape coefficient for Beta at the kth moment, wherein the following relation is satisfied:
wherein mu k Is the average value delta of the historic clear sky factors at the kth moment k And (5) the standard deviation of the clear sky factor is the history at the kth moment.
4. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization according to claim 3, wherein,
step 1.1 further comprises: generating photovoltaic active power output curve data of the target area by using solar illuminance data of the target area at 24 moments according to the following relation:
in the method, in the process of the invention,
P PV,k photovoltaic power generation power at the kth moment of the target area,
P PV_r the rated power of photovoltaic power generation in the target area is obtained,
s k is the target areaSunlight illuminance data at the kth time,
s r and rated illuminance for the target area.
5. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization according to claim 2, wherein,
the user load probability model satisfies the following relation:
in the method, in the process of the invention,
f(p k ) A probability density function for the user load at the kth time of the target region,
η k is the average value of the historical load data at the kth moment,
σ k is the standard deviation of the historical load data at the kth time,
p k historical load data for the kth moment of the target area,
p k,low 、p k,up the lower limit value and the upper limit value of the user load at the kth moment of the target area are respectively set.
6. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization according to claim 1, wherein,
in step 2, the first objective function is as follows:
in the method, in the process of the invention,
min f 1 as a function of the first object function,
P loss-k is the system loss at time k.
7. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization according to claim 6, wherein,
the second objective function is as follows:
in the method, in the process of the invention,
min f 2 as a function of the second objective function,
zm is the number of nodes of the distribution network,
U avg-i for the average voltage deviation of the voltage of the node i and the rated voltage, the U is satisfied avg-i ＝average(|U i -U n I), wherein U i U is the voltage value of the node i after being connected with the distributed photovoltaic n Is rated voltage.
8. The reactive power optimization method for the distributed photovoltaic power distribution network based on multi-objective optimization according to claim 7, wherein,
the third objective function is as follows:
in the method, in the process of the invention,
min f 3 as a function of the third objective function,
i (·) is an indication function,
c k 、c k-1 the positions of the tap of the regulating transformer at the kth moment and the kth-1 moment respectively,
t k 、t k-1 the state of the capacitor at the kth moment and the state of the capacitor at the kth-1 moment are respectively obtained.
9. The reactive power optimization method for the distributed photovoltaic power distribution network based on the multi-objective optimization according to claim 8, wherein,
c k ＝c k-1 or t k ＝t k-1 When I (&) is 0; c k ≠c k-1 Or t k ≠t k-1 The value of I (.cndot.) is 1.
10. The reactive power optimization method for the distributed photovoltaic power distribution network based on the multi-objective optimization according to claim 8, wherein,
the joint constraint conditions constructed in step 2 are as follows:
1) And considering the constraint condition that the distributed power supply is connected into the power distribution network, namely the power balance of the power distribution network containing the distributed power supply, and satisfying the following relation:
in the method, in the process of the invention,
P Li 、Q Li the active load and the reactive load of node i respectively,
P Gi 、Q Gi active power and reactive power injected at node i respectively,
P DGi 、Q DGi active power and reactive power which are respectively injected by the node i distributed photovoltaic;
U i 、U j the voltages at the first i and last j nodes of the branch,
δ ij for the power factor of the branch connecting node i and node j,
G ij 、B ij to connect the branch conductance and susceptance of node i and node j,
θ ij is the voltage phase angle difference between node i and node j;
2) The line active power constraint satisfies the following relation:
|P Lj |≤P Ljmax (14)
in the method, in the process of the invention,
P i for the active power of the Lj branch,
P imax maximum power is allowed for the Lj branch;
3) The distributed power supply operation constraint satisfies the following relation:
P DGi，min ≤P DGi ≤P DGi，max (15)
in the method, in the process of the invention,
P DGi active power injected for node i distributed photovoltaic,
P DGi，min 、P DGi，max respectively obtaining the minimum value and the maximum value of the distributed photovoltaic active power of the node i;
4) According to the current active power output and the capacity of the inverter, the reactive power output adjustable range of the photovoltaic power station is determined, and the following relation is satisfied:
in the method, in the process of the invention,
Q PV，max 、Q PV，min the upper limit and the lower limit of the reactive power output adjustable range of the photovoltaic power station are respectively,
S PV for the capacity of the photovoltaic inverter,
P PV active power output for photovoltaic;
5) The power distribution network to be connected must meet radial constraint and must be ensured to be in an open loop state during normal operation;
6) Connectivity constraints, i.e., each load node communicates with a power node.
11. A reactive power optimization system of a distributed photovoltaic power distribution network based on multi-objective optimization for implementing the method of any one of claims 1 to 10, comprising:
the system comprises a data generation module, a multi-objective optimization model module and an optimal solution module;
the data generation module is used for constructing a photovoltaic power generation output probability model based on Beta distribution according to historical sunlight illumination of a target area, and constructing a user load probability model based on Gaussian distribution according to historical user loads of the target area; according to the photovoltaic power generation output probability model and the user load probability model, generating photovoltaic power generation time sequence data and load time sequence data respectively by applying a Monte Carlo method;
the multi-objective optimization model module is used for forming a reactive multi-objective optimization model of the power distribution network by taking the minimum accumulated active network loss at 24 moments as a first objective function, taking the minimum average voltage deviation of all nodes at 24 moments as a second objective function, taking the minimum voltage regulating operation times of the on-load voltage regulating transformer and the minimum switching times of the capacitor as a third objective function and taking three objective functions; meanwhile, constructing a joint constraint condition for the reactive power optimization model of the power distribution network;
and the optimal solution module is used for solving the reactive power optimization model of the power distribution network and the joint constraint condition thereof by using the photovoltaic power generation time sequence data and the load time sequence data and adopting an intensity pareto evolution algorithm to obtain a photovoltaic output optimal solution, a transformer voltage regulation optimal solution and a capacitor switching optimal solution.
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| CN117353378A (en) * | 2023-11-22 | 2024-01-05 | 兰州理工大学 | Distributed power distribution network line loss optimization method based on whale algorithm |
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| CN117096962B (en) * | 2023-08-08 | 2024-04-09 | 国网浙江省电力有限公司宁海县供电公司 | Photovoltaic-considered power grid dynamic reactive power compensation optimization method and system |
| CN117353378A (en) * | 2023-11-22 | 2024-01-05 | 兰州理工大学 | Distributed power distribution network line loss optimization method based on whale algorithm |
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