CN111860950B - Probability assessment method for power adjustability of virtual power plant - Google Patents
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Abstract
The invention provides a probability evaluation method for the power adjustability of a virtual power plant, and belongs to the technical field of operation and control of power systems. The method comprises the following steps: decoupling linear approximation is carried out on the power flow model of the virtual power plant, and a power flow equation in a matrix form is constructed; carrying out linearization processing on active-reactive power ranges output by various types of power generation equipment and energy storage equipment; constructing a Gaussian mixture model to perform probability distribution function fitting on uncertain factors such as photovoltaic, fan and load; calculating the power adjustable range of the virtual power plant at the grid-connected point under equal confidence by using an opportunity constraint method; and calculating a scalar field function of an adjustable range and confidence coefficient in an active-reactive two-dimensional plane to obtain the power adjustability of the virtual power plant under different confidence coefficients. The method fully considers the influence of uncertainty factors on the power adjustability of the virtual power plant, effectively improves the calculation speed, can obtain more accurate assessment results, and promotes the optimal scheduling of the power system.
Description
Technical Field
The invention belongs to the technical field of operation control of power systems, and particularly relates to a probability assessment method for power adjustability of a virtual power plant.
Background
The virtual power plant organically integrates the distributed generator set, the controllable load and the distributed energy storage facility, and the integrated regulation and control of various distributed energy sources are realized by utilizing an advanced regulation and control technology and a communication technology. In a region, a virtual power plant can participate in optimal scheduling of a power system as a special power plant. However, since the distributed power generation resources are large in number and small in scale, the distributed power generation resources are distributed in the power distribution network and have large characteristic differences. Therefore, there are difficulties with the system in directly controlling all distributed generation resources. The virtual power plant can integrate the distributed power supplies, but due to different equipment characteristics, network constraint conditions exist, and uncertain factors such as a large amount of loads, new energy output and the like exist, so that the power adjustability of the virtual power plant is difficult to accurately evaluate at present.
The existing method for evaluating the power adjustability of the virtual power plant adopts a deterministic evaluation method and does not consider the influence caused by the uncertainty of renewable energy sources and loads in the virtual power plant. In some methods, a plurality of scenes are generated through a Monte Carlo method, and then a power adjustability model of the virtual power plant under uncertain factors is constructed, but the method is huge in calculated amount and low in calculating speed, and effective evaluation results are difficult to obtain quickly.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a probability evaluation method for the power adjustability of a virtual power plant. The method fully considers the influence of uncertain factors on the power adjustability of the virtual power plant, effectively improves the calculation speed, can obtain more accurate assessment results, promotes the optimal scheduling of the power system, and has higher value in practical application.
The invention provides a probability evaluation method for the power adjustability of a virtual power plant, which is characterized by comprising the following steps of:
1) Constructing a network model of a virtual power plant;
based on a decoupled linearized power flow model, defining each node inside a virtual power plant as a PQ node, defining a grid-connected node as a balance node, and establishing a network power flow model of the virtual power plant as follows:
V L =L -1 Q-L -1 G LL B′ LL -1 P (1)
θ L =H -1 P+H -1 G LL B LL -1 Q (2)
wherein, V L A vector representing the magnitude of the voltage at the PQ node; theta.theta. L A vector representing the phase angle of the PQ node; g LL A self-conductance matrix representing the PQ nodes; b' LL Represents the PQ node from the na matrix without considering the parallel capacitors; b LL Represents the self-susceptance matrix at the PQ node considering the parallel capacitor; p represents an injection active power vector formed by the balance node and the PQ type node; q represents the injected active power vector of the PQ-type node; l, a,Is a system parameter;
the active and reactive power of the branch ij power flow in the virtual power plant are respectively expressed as follows:
P ij =g ij (V i -V j )-b ij (θ i -θ j ) (3)
Q ij =-b ij (V i -V j )-g ij (θ i -θ j ) (4)
wherein, P ij And Q ij Respectively representing active power and reactive power passing through the branch ij; v i And V j Respectively representing the voltage amplitudes of the node i and the node j; theta.theta. i And theta j Respectively representing voltage phase angles of a node i and a node j; g ij And b ij Respectively representing the conductance and susceptance of branch ij;
2) Constructing an equipment model of a virtual power plant;
distributed power generation equipment of a virtual power plant is divided into five types, namely synchronous machine type equipment, photovoltaic power generation type equipment, doubly-fed fan type equipment, energy storage type equipment and load, and the operation constraint conditions of each type of equipment are respectively expressed as follows:
2.1 Active power constraints for synchronous machine type devices:
wherein the content of the first and second substances,the active output power of the synchronous machine type equipment at the node i at the moment t is represented;andrespectively representing the minimum value and the maximum value of the active output power of the synchronous machine type equipment at the node i;
reactive power constraint of synchronous machine type equipment:
wherein, the first and the second end of the pipe are connected with each other,representing the reactive output power of the synchronous machine type equipment at a node i at the time t;andrespectively representing the minimum value and the maximum value of the reactive output power of the synchronous machine type equipment at the node i;
2.2 Active power constraints for photovoltaic power generation type devices:
wherein the content of the first and second substances,representing the active output power of the photovoltaic power generation type equipment at a node i at the moment t;representing the minimum value of the active output power of the photovoltaic power generation type equipment at the node i;representing the maximum value of the active output power of the photovoltaic power generation type equipment at the node i;
capacity constraint of photovoltaic power generation type device:
wherein the content of the first and second substances,representing the reactive output power of the photovoltaic power generation type equipment at the node i at the time t;represents the maximum capacity of the photovoltaic power generation type device at node i;
the approximation of equation (8) is reduced to the linear constraint of the following octagon:
photovoltaic power generation type equipment prediction error constraint:
wherein the content of the first and second substances,respectively representing an actual value and a predicted value of active power output of the photovoltaic power generation type equipment at a node i at the moment t;representing the light abandonment quantity of the photovoltaic power generation type equipment at a node i at the time t;the prediction error of the output active power of the photovoltaic power generation type equipment at the node i at the time t is represented;
2.3 Active power constraints for doubly-fed fan-type devices:
wherein, the first and the second end of the pipe are connected with each other,indicating presence of doubly-fed fan-type equipment at node i at time tA work output power;representing the minimum value of the active output power of the doubly-fed fan equipment at the node i;representing the maximum value of the active output power of the doubly-fed fan type equipment at the node i;
reactive power constraint of doubly-fed fan type equipment:
wherein the content of the first and second substances,representing the reactive output power of the doubly-fed fan-type equipment at a node i at the time t;andrespectively representing the minimum value and the maximum value of the reactive output power of the doubly-fed fan type equipment at the node i;
capacity constraint of doubly-fed fan-type equipment:
wherein the content of the first and second substances,representing the maximum capacity of doubly-fed fan-type equipment at node i;
the approximation of equation (18) is reduced to the linear constraint of the following octagon:
the prediction error constraints of doubly-fed fan-type equipment are as follows:
wherein the content of the first and second substances,respectively representing an actual value and a predicted value of active output power of the doubly-fed fan type equipment at a node i at the time t;representing the air abandoning amount of the doubly-fed fan type equipment at a node i at the time t;representing the prediction error of the active output power of the doubly-fed fan type equipment at the node i at the time t;
2.4 Active power constraints of energy storage devices:
wherein the content of the first and second substances,representing the net active output power of the energy storage type device at node i at time t;representing the maximum value of the discharge active power of the energy storage type equipment at the node i;representing the maximum value of the charging active power of the energy storage type equipment at the node i;
capacity constraints of energy storage devices:
wherein, the first and the second end of the pipe are connected with each other,representing the reactive output power of the energy storage type equipment at the node i at the time t;represents the maximum capacity of the energy storage type device at node i;
the approximation of equation (27) is simplified to the linear constraint of the following octagon:
2.5 Load power constraints;
wherein the content of the first and second substances,andrespectively representing the real load with work and the real load without work at a node i at the moment t;representing an active load predicted value at a node i at a time t;representing the active load prediction error at the node i at the time t;power factor of the load at node i;
2.6 Calculate net injected power of virtual plant internals at each node:
wherein the content of the first and second substances,andrespectively representing the net injection power with work and the net injection power without work at a node i at the time t;
3) Modeling uncertainty variables in the virtual power plant by using a Gaussian mixture model to obtain opportunity constraint conditions;
setting random variablesFor the prediction error of the photovoltaic power generation device at the time t node iPrediction error of doubly-fed fan type equipmentActive load prediction error at node i at time tThe composed vector is:
fitting with N Gaussian distribution functions using a Gaussian mixture modelDistribution function of (d):
wherein, the first and the second end of the pipe are connected with each other,is shown inIs the mean of the jth Gaussian distribution at time t, andthe distribution is a high-dimensional normal distribution of the variance, a subscript j represents a jth normal distribution function, and a superscript t represents a tth moment;representing the weight of the jth normal distribution function, and N representing the number of Gaussian distribution functions;
using the model formula Error created in step 1)! Reference source not found, -Error! Determining opportunity constraint conditions met by branch power flow and node voltage:
wherein the content of the first and second substances,representing the voltage amplitude of the node i at the time t;representing the active power flow of the branch ij at the moment t;representing the reactive power flow of the branch ij at the moment t; 1- ε represents the confidence with which the constraint is satisfied;
4) The chance constraint formula Error!obtained in the step 3) is! Reference source not found, -Error! Reference source not found. Is transformed into an equivalent deterministic constraint, the expression is as follows:
wherein the content of the first and second substances,representing a node i voltage constraint margin;representing the constraint margin of the active power of the branch ij tide;representing branch ij reactive power constraint margin;representing the sum of active power and reactive power of the branch ij as a constraint margin;representing the difference constraint margin between active power and reactive power of the branch ij; lambda [ alpha ] P Representing the output active power constraint margin of the renewable energy power generation equipment; each constraint margin calculation expression is as follows:
wherein, the first and the second end of the pipe are connected with each other,representing random variables1-epsilon quantile of;representing random variables1-epsilon quantile of;representing random variables1-epsilon quantile of;representing random variablesDividing the digit;representing random variables1-epsilon quantile of (c);representing random variablesThe 1-epsilon quantile of (c),is defined as follows:
5) Establishing a probability evaluation model of the adjustable capacity of the power of the virtual power plant, and evaluating the adjustable capacity of the power of the virtual power plant under a set confidence coefficient; the method comprises the following specific steps:
5.1 Output active and reactive variables of various types of equipment of the virtual power plant are arranged into a vector form, which is expressed as follows:
wherein the content of the first and second substances,respectively representing vectors formed by output active and reactive variables of synchronous machine type equipment at the moment t;respectively representing vectors formed by output active and reactive variables of the photovoltaic power generation equipment at the moment t;respectively representing vectors formed by output active and reactive variables of the doubly-fed fan type equipment at the moment t;respectively representing vectors formed by output active and reactive variables of the energy storage type equipment at the moment t;
5.2 ) construct a decision variable vector X t As follows:
5.3 Define (b) definition ofAndrespectively establishing a probability evaluation model of the power adjustability of the virtual power plant for active power and reactive power output to a main network by the virtual power plant at a grid-connected point at the moment t under the confidence coefficient of 1-epsilon;
the model objective function is as follows:
the constraint of the model is given by the formula Error! Reference source not found, -Error! Reference source not found and formula Error! Reference source not found;
wherein, alpha is a power factor alpha epsilon [0,2 pi);
5.4 For any given power factor alpha, solving a probability evaluation model of the power adjustability of the virtual power plant to obtain a corresponding optimal solution under a set confidence coefficient of 1-epsilon
5.5 A convex function piecewise linear fitting algorithm is used for representing the solving results of the step 5.4) under different confidence coefficients into a piecewise linear function form, and a probability function analytic expression of the power adjustability of the virtual power plant is formed as follows:
wherein ReLU (·) represents a rectifying linear unit function; y is t Representing two-dimensional independent variable vector formed by virtual power plant output active power and output reactive power at moment tRepresenting a virtual plant power tunability; a is j And b j Respectively representing coefficients of jth piecewise function at the moment t; m represents the number of piecewise linear functions;
using equation (52), given a confidence level of 1- ε, let Conf t (Y t ) More than or equal to 1-epsilon, and solving to obtain Y of the corresponding power adjustability of the virtual power plant t Range, evaluation ends.
The invention has the characteristics and beneficial effects that:
the invention provides a probability evaluation method for the power adjustability of a virtual power plant, which is characterized in that a mixed Gaussian model is utilized to accurately fit the probability distribution of uncertainty factor prediction errors according to historical data; by utilizing linear approximation and converting the opportunity constraint condition into the equivalent certainty constraint condition, the problem is changed into a convex optimization model, the calculation difficulty is simplified, and the calculation speed is accelerated. By the method, a more accurate evaluation result of the power adjustability of the virtual power plant can be obtained, and optimal scheduling of the power system is promoted.
Drawings
FIG. 1 is an overall flow diagram of the process of the present invention.
FIG. 2 is a schematic diagram of a process for solving the power adjustable range under the confidence of a virtual power plant and the like.
Detailed Description
The invention provides a probability evaluation method for power adjustability of a virtual power plant, which is further described in detail in the following by combining the accompanying drawings and specific embodiments.
The invention provides a probability evaluation method for the power adjustability of a virtual power plant, the whole flow is shown in figure 1, and the method comprises the following steps:
1) Constructing a network model of a virtual power plant;
based on a decoupled linearized power flow model, defining each node inside a virtual power plant as a PQ node, defining a grid-connected node as a balance node, and establishing a network power flow model of the virtual power plant as follows:
V L =L -1 Q-L -1 G LL B′ LL -1 P (1)
θ L =H -1 P+H -1 G LL B LL -1 Q (2)
wherein, V L A vector representing the magnitude of the voltage at the PQ node; theta L A vector representing the PQ nodal phase angle; g LL A self-conductance matrix representing a PQ node; b' LL Represents the self-capacitance matrix at the PQ node without considering the parallel capacitor; b is LL Represents the PQ node from the capacitance matrix under consideration of the parallel capacitor; p represents an injection active power vector formed by the balance node and the PQ type node; q represents the injected active power vector of the PQ-type node; l, a,All the parameters are system parameters, and the values of the parameters can be solved by utilizing a decoupled linearized power flow model.
The active and reactive power of the branch ij power flow in the virtual power plant are respectively expressed as follows:
P ij =g ij (V i -V j )-b ij (θ i -θ j ) (3)
Q ij =-b ij (V i -V j )-g ij (θ i -θ j ) (4)
wherein, P ij And Q ij Respectively representing active power and reactive power passing through the branch ij; v i And V j Respectively representing the voltage amplitudes of the node i and the node j; theta i And theta j Respectively representing voltage phase angles of a node i and a node j; g is a radical of formula ij And b ij Respectively representing conductance and susceptance of branch ij。
2) Constructing an equipment model of a virtual power plant;
distributed power generation equipment existing in a virtual power plant can be divided into five types, namely synchronous machine type equipment, photovoltaic power generation type equipment, doubly-fed fan type equipment, energy storage type equipment and load, and the operation constraint conditions of each type of equipment can be respectively expressed as follows:
2.1 Active power constraints for synchronous machine type devices:
wherein the content of the first and second substances,representing the active output power of the synchronous machine type equipment at a node i at the time t;andand respectively representing the minimum value and the maximum value of the active output power of the synchronous machine type equipment at the node i.
Reactive power constraint of synchronous machine type equipment:
wherein, the first and the second end of the pipe are connected with each other,the reactive output power of the synchronous machine type equipment at the node i at the time t is represented;andrespectively representing reactive power transmission of synchronous machine type equipment at node iAnd outputting a power minimum value and a power maximum value.
2.2 Active power constraints for photovoltaic power generation type devices:
wherein, the first and the second end of the pipe are connected with each other,representing the active output power of the photovoltaic power generation type equipment at a node i at a time t;representing the minimum value of the active output power of the photovoltaic power generation type equipment at the node i;and (4) representing the maximum value of the active output power of the photovoltaic power generation type equipment at the node i.
Capacity constraint of photovoltaic power generation type equipment:
wherein the content of the first and second substances,representing the reactive output power of the photovoltaic power generation type equipment at the node i at the time t;representing the maximum capacity of the photovoltaic power generation type device at node i. To simplify the complexity of the optimization problem, the capacity constraint of the photovoltaic power generation type device of equation (8) is generally reduced approximately to the following octagonal linear constraint:
the photovoltaic power generation type equipment prediction error constraint representing the relation among the actual value, the predicted value and the prediction error of the photovoltaic power generation type equipment output active power is as follows:
wherein, the first and the second end of the pipe are connected with each other,respectively representing an actual value and a predicted value of active power output of the photovoltaic power generation type equipment at a node i at the time t;representing the light abandonment quantity of the photovoltaic power generation type equipment at a node i at the time t;and (4) representing the prediction error of the output active power of the photovoltaic power generation type equipment at the node i at the time t.
2.3 Active power constraints for doubly-fed fan-type devices:
wherein, the first and the second end of the pipe are connected with each other,representing the active output power of the doubly-fed fan-type equipment at a node i at the moment t;representing the minimum value of the active output power of the doubly-fed fan equipment at the node i;and the maximum value of the active output power of the doubly-fed fan type equipment at the node i is represented.
Reactive power constraint of doubly-fed fan type equipment:
wherein the content of the first and second substances,representing the reactive output power of the doubly-fed fan-type equipment at a node i at the time t;andand respectively representing the minimum value and the maximum value of the reactive output power of the doubly-fed fan type equipment at the node i.
Capacity constraint of doubly-fed fan-type equipment:
wherein, the first and the second end of the pipe are connected with each other,representing the maximum capacity of the doubly-fed fan-type equipment at node i.
The capacity constraint of the doubly-fed fan-type plant of equation (18) is reduced approximately to the linear constraint of the following octagon:
the prediction error constraint of the doubly-fed fan type equipment representing the relationship among the actual value, the predicted value and the prediction error of the output active power of the doubly-fed fan type equipment is as follows:
wherein, the first and the second end of the pipe are connected with each other,respectively representing active power of doubly-fed fan type equipment at t moment node iActual and predicted values of output power;representing the air abandon quantity of the doubly-fed fan type equipment at the node i at the time t;and (4) representing the prediction error of the active output power of the doubly-fed fan type equipment at the node i at the time t.
2.4 The energy storage type renewable energy device has two states of charging and discharging, and the active power of the energy storage type device is constrained as follows:
wherein the content of the first and second substances,representing the net active output power of the energy storage type device at node i at time t;representing the maximum value of the discharge active power of the energy storage type equipment at the node i;and represents the maximum value of the charging active power of the energy storage type equipment at the node i.
Capacity constraints of energy storage devices:
wherein the content of the first and second substances,representing the reactive output power of the energy storage type equipment at the node i at the time t;representing the maximum capacity of the energy storage type device at node i.
The capacity constraint problem of the energy storage device of equation (27) is reduced approximately to the following linear constraint condition of octagon:
2.5 Load power constraints;
wherein the content of the first and second substances,andrespectively representing the real load with work and the real load without work at a node i at the moment t;an active load predicted value at a node i representing a moment t;representing the active load prediction error at the node i at the time t;power factor of the load at node i.
2.6 According to the positions of various types of equipment in the nodes, the net injection power of the internal equipment of the virtual power plant at each node can be obtained:
wherein, the first and the second end of the pipe are connected with each other,andrespectively representing the active and reactive net injected power at node i at time t.
3) Modeling uncertainty variables in the virtual power plant by using a Gaussian mixture model to obtain opportunity constraint conditions;
setting random variablesPredicting error for photovoltaic power generation type equipment at time t node iPrediction error of doubly-fed fan type equipmentActive load prediction error at node i at time tThe composed vector, namely:
wherein the content of the first and second substances,is shown inIs the mean value of the jth Gaussian distribution at the time t, andthe subscript j represents the jth normal distribution function, and the superscript t represents the tth moment;and the weight of the jth normal distribution function is represented, N represents the number of Gaussian distribution functions, the specific value of the weight is determined according to the precision requirement of the model, and the higher the precision requirement is, the larger the value of N is obtained.
By using the linearized power flow model expressions (1) - (4) established in the step 1), the voltage amplitude of the node i and the active reactive power of the branch ij can be expressed as a linear combination of the node injection active power and the node injection reactive power. Because uncertain factors such as renewable energy power generation equipment, load and the like exist in the virtual power plant, the predicted maximum output point of the renewable energy and the node load value are in a probability distribution form, so that the constraint condition met by the branch flow and the node voltage is an opportunity constraint, namely the constraint condition is met under certain confidence coefficient:
wherein, the first and the second end of the pipe are connected with each other,representing the voltage amplitude of the node i at the time t;representing the active power flow of the branch ij at the moment t;representing the reactive power flow of the branch ij at the moment t; 1- ε represents the confidence with which the constraint is satisfied.
4) Converting the opportunity constraint conditions obtained in the step 3) into equivalent certainty constraint conditions;
for the opportunity constraint problem, the uncertainty variable in the opportunity constraint problem can be changed into a constraint margin, and then the opportunity constraint conditions (38) - (40) obtained in the step 3) are converted into a certainty constraint condition.
Namely:
wherein the content of the first and second substances,representing node i voltage constraint margin;Representing the constraint margin of the active power of the branch ij tide;representing branch ij reactive power constraint margin;representing the sum of the active power and the reactive power of the branch ij as a constraint margin;representing the difference constraint margin between active power and reactive power of the branch ij; lambda [ alpha ] P And the output active constraint margin of the renewable energy power generation device is represented. The constraint margin may be represented by the following equation:
wherein, the first and the second end of the pipe are connected with each other,representing random variables1-epsilon quantile of (c);representing random variables1-epsilon quantile of;representing random variables1-epsilon quantile of (c);representing random variablesQuantile division;representing random variables1-epsilon quantile of;representing random variablesThe 1-epsilon quantile of (c),is defined as follows:
5) Establishing a probability evaluation model of the adjustable capacity of the power of the virtual power plant, and evaluating the adjustable capacity of the power of the virtual power plant under certain confidence;
the output active and reactive variables of various types of equipment in the virtual power plant are arranged into a vector form and are expressed as follows:
wherein the content of the first and second substances,respectively representing vectors formed by output active and reactive variables of synchronous machine type equipment at the moment t;respectively representing vectors formed by output active and reactive variables of the photovoltaic power generation type equipment at the moment t; respectively representing vectors formed by output active and reactive variables of the doubly-fed fan type equipment at the moment t;and respectively representing vectors formed by the active variables and the reactive variables of the output of the energy storage type equipment at the moment t.
Further arranging vectors formed by active and reactive variables of various types of equipment into decision variable vector X t As follows:
definition ofAndthe active power and the reactive power output to the main network by the virtual power plant at the confidence level of 1-epsilon and the grid-connected point at the time t are respectively. And (3) establishing a probability evaluation model of the power adjustability of the virtual power plant, and solving the adjustable power range of the virtual power plant at the time t under the level of the confidence coefficient 1-epsilon, wherein the equations (5) - (35) and (41) are integrally used as constraint conditions. The objective function of the probability evaluation model of the power adjustability of the virtual power plant is to solve the power output limit of the virtual power plant under each given constant power factor alpha, namely to solve the following problems within the range of alpha epsilon [0,2 pi ]:
for any given power factor alpha, solving an optimization problem formula (51) to obtain a corresponding optimal solution under a set confidence coefficient of 1-epsilonAnd solving results under different alpha to obtain scattered points formed by multiple groups of optimal solutions. A solving process schematic diagram is shown in fig. 2, wherein horizontal and vertical coordinates respectively represent active power and reactive power output by a grid-connected point of a virtual power plant; the arrow indicates the direction in which the optimal solution is sought in the optimization problem; scatter represents a solution obtained by solving the optimization problem through the variation parameter alpha; the outer boundary range represented by a number of discrete points represents the solved virtual plant output power regulation range.
5.5 Constructing an analytic representation form representing the adjustable capacity of the power of the virtual power plant;
in step 5.4) the power tunability range of the virtual power plant at constant power factor at the level of confidence 1-epsilon at time t has been solved. Outputting active power, output reactive power and confidence level in virtual power plantIn the three-dimensional space formed, for each confidence 1-epsilon, step 5.4) obtains the solution in the modelA contour on the curved surface is formed. And solving the obtained result based on the confidence coefficients 1-epsilon to form a three-dimensional curved surface representing the output active power and output reactive power range and the confidence coefficient level. And expressing the solving result in a piecewise linear function form by using a convex function piecewise linear fitting algorithm to form a probability function analytic expression of the power adjustability of the virtual power plant as follows:
wherein ReLU (·) represents a rectifying linear unit function; y is t Representing two-dimensional independent variable vector formed by virtual power plant output active power and output reactive power at moment tRepresenting a virtual plant power tunability; a is a j And b j Respectively representing coefficients of jth piecewise function at time t; m represents the number of piecewise linear functions. Using equation (52), given a confidence level of 1- ε, let Conf t (Y t ) More than or equal to 1-epsilon, the Y of the corresponding virtual power plant power adjustability can be solved t Range, evaluation ends.
In addition, by utilizing the model established in the step (2) of the invention, the cost function of the virtual power plant can be calculated, and the specific steps are as follows:
6) Constructing a cost model of the virtual power plant, and piecewise linearly fitting a cost function of the virtual power plant;
aiming at various devices in the virtual power plant, constructing a corresponding cost model:
6.1 Power generation cost for synchronous type equipment is in the form of a quadratic function, i.e.:
wherein the functionThe synchronous machine type equipment at the node i outputs active power at the moment tCost of power generation; a is a i,GEN ,b i,GEN And c i,GEN Respectively a secondary cost parameter, a primary cost parameter and a cost constant parameter of the synchronous machine type equipment at the node i.
6.2 Photovoltaic power generation type devices mainly consider the cost of abandoned light, namely:
wherein the functionRepresenting the photovoltaic power generation type equipment at node i outputs active power at time t ofThe cost of electricity generation;and represents the power grid price at the moment t.
6.3 Doubly-fed fan-type equipment mainly considers the cost of abandoned wind, namely:
wherein the functionThe doubly-fed fan type equipment at the node i outputs active power at the moment tThe cost of electricity generation.
6.4 Cost of energy storage devices takes into account charge-discharge costs, namely:
wherein the functionIndicating that the energy storage type equipment at the node i outputs active power at the moment tCost of power generation;andrespectively representing the cost coefficients of discharging and charging of the energy storage type equipment at the node i; Δ t represents the time interval between two adjacent decision time points.
6.5 ) constructing a virtual power plant cost optimization model, solving sample points of a virtual power plant cost fitting function
According to the cost functions of the various types of equipment, a virtual power plant cost optimization model is constructed, constraint conditions of the virtual power plant cost optimization model are represented by the constraint conditions of (5) - (35) and (41), and the total running cost of the internal equipment of the virtual power plant is represented by an objective function, namely:
wherein, the first and the second end of the pipe are connected with each other,representing the total cost of all equipment operations of the virtual power plant at time t.
Based on the result in step 5), the range of the power output outwards of the virtual power plant at the time t can be determinedIn the interval, K samples are randomly extracted, the specific value of the K samples is determined according to the precision requirement of the model, and the higher the precision requirement is, the larger the value of K is obtained. Let the kth sample beMake the output power of the virtual power plant at the momentTo minimize virtual plant operating costsFor the purpose, an optimization problem is solved to obtain a minimum operating cost ofTherefore, the output power-power generation cost point corresponding to the kth sample can be obtainedAnd repeating the sampling and optimizing processes to obtain K output power-power generation cost points in total to form a fitting data set of a virtual power plant power generation cost curve.
6.6 Piecewise linear fit cost function of the virtual power plant;
and fitting the output power-power generation cost curve formed by K sample points in the section r (the value of r is usually 3-7 according to different requirements of fitting precision) by using a convex function piecewise linear fitting algorithm to form the piecewise linear function of fitting 6.5). The form is as follows:
wherein, c l ,d l The first order coefficient and the constant coefficient of the I-th affine function. By means of the formula (58), any active power value of the virtual power plant at the grid-connected point is input, and the corresponding operation cost can be obtained.
Claims (1)
1. A probability assessment method for power adjustability of a virtual power plant is characterized by comprising the following steps:
1) Constructing a network model of a virtual power plant;
based on a decoupled linearized power flow model, defining each node inside a virtual power plant as a PQ node, defining a grid-connected node as a balance node, and establishing a network power flow model of the virtual power plant as follows:
θ L =H -1 P+H -1 G LL B LL -1 Q (2)
wherein, V L A vector representing the magnitude of the voltage at the PQ node; theta L A vector representing the PQ nodal phase angle; g LL A self-conductance matrix representing the PQ nodes; b' LL Represents the PQ node without considering the parallel capacitor from the susceptance matrix; b is LL Represents the self-susceptance matrix at the PQ node considering the parallel capacitor; p represents an injection active power vector formed by the balance node and the PQ type node; q represents the injected active power vector of the PQ-type node; l, a,Is a system parameter;
the active and reactive power of the branch ij power flow in the virtual power plant are respectively expressed as follows:
P ij =g ij (V i -V j )-b ij (θ i -θ j ) (3)
Q ij =-b ij (V i -V j )-g ij (θ i -θ j ) (4)
wherein, P ij And Q ij Respectively representing active power and reactive power passing through the branch ij; v i And V j Respectively representing the voltage amplitudes of the node i and the node j; theta.theta. i And theta j Respectively representing the voltage phase angles of a node i and a node j; g ij And b ij Respectively representing the conductance and susceptance of branch ij;
2) Constructing an equipment model of a virtual power plant;
distributed power generation equipment of a virtual power plant is divided into five types, namely synchronous machine type equipment, photovoltaic power generation type equipment, doubly-fed fan type equipment, energy storage type equipment and load, and the operation constraint conditions of each type of equipment are respectively expressed as follows:
2.1 Active power constraints for synchronous machine type devices:
wherein the content of the first and second substances,representing the active output power of the synchronous machine type equipment at a node i at the time t;andrespectively representing the minimum value and the maximum value of the active output power of the synchronous machine type equipment at the node i;
reactive power constraint of synchronous machine type equipment:
wherein the content of the first and second substances,representing the reactive output power of the synchronous machine type equipment at a node i at the time t;andrespectively representing the minimum value and the maximum value of the reactive output power of the synchronous machine type equipment at the node i;
2.2 Active power constraint of photovoltaic power generation type devices:
wherein, the first and the second end of the pipe are connected with each other,representing the active output power of the photovoltaic power generation type equipment at a node i at a time t;representing the minimum value of the active output power of the photovoltaic power generation type equipment at the node i;representing the maximum value of the active output power of the photovoltaic power generation type equipment at the node i;
capacity constraint of photovoltaic power generation type device:
wherein the content of the first and second substances,representing the reactive output power of the photovoltaic power generation type device at node i at time t;represents the maximum capacity of the photovoltaic power generation type device at node i;
the approximation of equation (8) is reduced to the linear constraint of the following octagon:
photovoltaic power generation type equipment prediction error constraint:
wherein the content of the first and second substances,respectively representing an actual value and a predicted value of active power output of the photovoltaic power generation type equipment at a node i at the moment t;representing the light abandoning amount of the photovoltaic power generation type equipment at the node i at the time t;the prediction error of the output active power of the photovoltaic power generation type equipment at the node i at the moment t is represented;
2.3 Active power constraints for doubly-fed fan-type devices:
wherein, the first and the second end of the pipe are connected with each other,representing the active output power of the doubly-fed fan-type equipment at a node i at the moment t;representing the minimum value of the active output power of the doubly-fed fan equipment at the node i;representing the maximum value of the active output power of the doubly-fed fan type equipment at the node i;
reactive power constraint of doubly-fed fan type equipment:
wherein the content of the first and second substances,the reactive output power of the doubly-fed fan type equipment at the node i at the moment t is represented;andrespectively representing the minimum value and the maximum value of the reactive output power of the doubly-fed fan type equipment at the node i;
capacity constraint of doubly-fed fan-type equipment:
wherein, the first and the second end of the pipe are connected with each other,representing the maximum capacity of the doubly-fed fan-type equipment at node i;
equation (18) is simplified to the linear constraint of the following octagon:
the prediction error constraints for doubly-fed fan-type devices are as follows:
wherein, the first and the second end of the pipe are connected with each other,respectively representing an actual value and a predicted value of the active output power of the doubly-fed fan type equipment at a node i at the moment t;representing the air abandon quantity of the doubly-fed fan type equipment at the node i at the time t;representing the prediction error of the active output power of the doubly-fed fan type equipment at the node i at the time t;
2.4 Active power constraints of energy storage devices:
wherein, the first and the second end of the pipe are connected with each other,representing the net active output power of the energy storage type device at node i at time t;representing the maximum value of the discharge active power of the energy storage type equipment at the node i;representing energy storage type devices at node iMaximum value of active power of charging;
capacity constraints of energy storage devices:
wherein, the first and the second end of the pipe are connected with each other,representing the reactive output power of the energy storage type equipment at a node i at a time t;represents the maximum capacity of the energy storage type device at node i;
the approximation of equation (27) is reduced to the linear constraint of the following octagon:
2.5 Load power constraints;
wherein the content of the first and second substances,andrespectively representing the real load with work and the real load without work at a node i at the moment t;representing an active load predicted value at a node i at a time t;representing the active load prediction error at the node i at the time t;power factor of the load at node i;
2.6 Calculating net injection power of internal equipment of the virtual power plant at each node:
wherein, the first and the second end of the pipe are connected with each other,andrespectively representing the net injection power with work and the net injection power without work at a node i at the time t;
3) Modeling uncertainty variables in the virtual power plant by using a Gaussian mixture model to obtain opportunity constraint conditions;
setting random variablesFor the prediction error of the photovoltaic power generation device at the time t node iPrediction error of doubly-fed fan type equipmentActive load prediction error at node i at time tThe composed vector is as follows:
fitting with N Gaussian distribution functions using a Gaussian mixture modelThe distribution function of (c):
wherein the content of the first and second substances,is shown inIs the mean value of the jth Gaussian distribution at the time t, andthe distribution is a high-dimensional normal distribution of the variance, a subscript j represents a jth normal distribution function, and a superscript t represents a tth moment;representing the weight of the jth normal distribution function, wherein N represents the number of Gaussian distribution functions;
determining opportunity constraint conditions met by branch power flow and node voltage by using model expressions (1) - (4) established in the step 1):
wherein, the first and the second end of the pipe are connected with each other,representing the voltage amplitude of the node i at the time t;representing the active power flow of the branch ij at the moment t;representing the reactive power flow of the branch ij at the moment t; 1- ε represents the confidence with which the constraint is satisfied;
4) Converting the chance constraint conditions (38) - (40) obtained in the step 3) into equivalent deterministic constraint conditions, wherein the expression is as follows:
wherein the content of the first and second substances,representing a node i voltage constraint margin;representing the constraint margin of the active power of the branch ij tide;representing branch ij reactive power constraint margin;representing the sum of the active power and the reactive power of the branch ij as a constraint margin;representing the difference constraint margin between the active power and the reactive power of the branch ij; lambda [ alpha ] P Representing the output active power constraint margin of the renewable energy power generation equipment; each constraint margin calculation expression is as follows:
wherein the content of the first and second substances,representing random variables1-epsilon quantile of;representing random variables1-epsilon quantile of;representing random variables1-epsilon quantile of;representing random variables1-epsilon quantile of;representing random variables1-epsilon quantile of (c);representing random variablesThe 1-epsilon quantile of (c),is defined as follows:
5) Establishing a probability evaluation model of the adjustable capacity of the power of the virtual power plant, and evaluating the adjustable capacity of the power of the virtual power plant under a set confidence coefficient; the method comprises the following specific steps:
5.1 Output active and reactive variables of various types of equipment of the virtual power plant are arranged into a vector form, which is expressed as follows:
wherein, the first and the second end of the pipe are connected with each other,respectively representing vectors formed by output active and reactive variables of synchronous machine type equipment at the moment t;respectively representing vectors formed by output active and reactive variables of the photovoltaic power generation equipment at the moment t;respectively representing vectors formed by output active and reactive variables of the doubly-fed fan type equipment at the moment t;respectively representing vectors formed by output active and reactive variables of the energy storage type equipment at the moment t;
5.2 ) construct a decision variable vector X t As follows:
5.3 Define (c) definitionAndrespectively establishing a probability evaluation model of the power adjustability of the virtual power plant for the active power and the reactive power output to the main network by the virtual power plant at the grid-connected point at the moment t under the confidence coefficient of 1-epsilon;
the model objective function is as follows:
the constraint conditions of the model are equations (5) - (35) and (41);
wherein, alpha is a power factor alpha epsilon [0,2 pi);
5.4 For any given power factor alpha, solving a probability evaluation model of the power adjustability of the virtual power plant to obtain a corresponding optimal solution under a set confidence coefficient of 1-epsilon
5.5 A convex function piecewise linear fitting algorithm is used for representing the solving results of the step 5.4) under different confidence coefficients into a piecewise linear function form, and a probability function analytic expression of the power adjustability of the virtual power plant is formed as follows:
wherein ReLU (·) represents a rectifying linear unit function; y is t Representing two-dimensional independent variable vector formed by virtual power plant output active power and output reactive power at moment tRepresenting a virtual plant power tunability; a is j And b j Respectively representing coefficients of jth piecewise function at the moment t; m represents the number of piecewise linear functions;
using equation (52), let Conf give a confidence level of 1- ε t (Y t ) More than or equal to 1-epsilon, and solving to obtain Y of corresponding virtual power plant power adjustability t Range, evaluation ends.
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