CN114268102B - Power system running state quantization method based on analytic probability power flow model - Google Patents
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Abstract
The invention relates to a method for quantifying the running state of an electric power system based on an analytic probability power flow model, which comprises the following steps: step 1), establishing a linear probability power flow model; step 2) a frequency regulation model of a node n is established by combining with a linear probability power flow model, a frequency modulation factor for controlling the frequency of the node n by the unbalance amount of active power is introduced on the basis of the frequency regulation model, and the linear power flow model related to the active power, the reactive power X and the running state Y of the power system is obtained after deduction; and 3) according to the linear invariance of the Gaussian mixture model and the Gaussian mixture model parameter set of X, the Gaussian mixture model parameter set of Y is obtained analytically, and finally the distribution of the running state of the power system is obtained. The beneficial effects are that: the method constructs the analysis expression of the random distribution of the running state of the power system, and can more efficiently perform the subsequent work of safety analysis, power system optimization and the like of the power system.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a power system running state quantification method based on an analytic probability power flow model.
Background
Large scale wind grid integration will bring non-negligible randomness to the power system. One of the effects of this randomness of the injected power in the operation of the power system is to cause fluctuations in the line transmission power and even line overload. To quantify this risk of line flow out of limits due to wind randomness, researchers have proposed a "probabilistic power flow (Probabilistic Load Flow, PLF)" approach. The mature method for calculating the joint probability distribution in the method is only a Monte Carlo simulation method. The biggest disadvantage of the monte carlo simulation method is that it takes a long time. In order to quickly and accurately perform probability flow calculation (especially to calculate joint probability distribution of power of multiple lines), development of an analytical probability flow calculation method is urgently needed. At present, a great deal of literature is used for researching an analytical probability power flow calculation method, and research focuses on finding a high-precision linear power flow calculation method.
Aiming at the problem of describing the operation state of the wind-solar power station containing uncertainty, a large number of researchers adopt probability distribution to describe the uncertainty of wind-solar output. Such as with gaussian distribution, beta distribution, cauchy distribution, etc. However, in practice, wind power is used as a non-gaussian variable, and a gaussian distribution is used to describe the wind power, so that a large error is caused. Meanwhile, gaussian distribution, beta distribution and Cauchy distribution cannot be applied to wind and light output probability modeling under different time scales. In addition, the output of the wind-solar power station often has extremely strong correlation, and if the correlation is ignored when the probability distribution modeling is carried out on the output, the output is difficult to capture and accords with actual uncertainty information.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a power system running state quantization method based on an analytic probability power flow model, which is realized by the following technical scheme:
the method for quantifying the running state of the power system based on the analytic probability power flow model is characterized by comprising the following steps of:
step 1) establishing a description of active and reactive power injection for each node according to equation (1)And power system operating state->A linear probabilistic power flow model of the relationship between them,
wherein θ and V represent the voltage phase angle and magnitude, respectively; p and Q respectively represent active power and reactive power injected by the nodes; Λ and C are parameter matrices composed of conductivity and susceptance elements of the power system; subscript ofRepresents the set of V theta nodes, +.>Represents the set of PV and V.theta.,>representing PV and PQ node formationsSet of->Representing a set of PQ nodes;
step 2) constructing a frequency adjustment model about the node n according to the formula (2) by combining the linear probability power flow model, and introducing an active power unbalance amount P for controlling the frequency of the node n on the basis of the frequency adjustment model Δ Deriving a linear power flow model of the formula (3) about active power and reactive power X and the running state Y of the power system,
wherein K is d,n Represents the load frequency characteristic coefficient, K, of the bus n g,n Represents the response coefficient, K, of the speed regulator of a conventional generator at the same bus u,n ＝K g,n +K d,n ，f A Frequency threshold for automatic power generation control, f D Is the average frequency threshold of all generator dead zones, P Δ,max To the maximum regulation capacity of the system, H g,n Is the climbing rate of the automatic power generation control device at the position of the bus n, and meets the requirements of
Wherein alpha is i 、E i 、D i Are all matrix expressions of intermediate parameters related to frequency modulation factors, M represents the number of PQ nodes in the system, N represents the sum of the numbers of PV nodes and PQ nodes in the system,representing a real matrix of size (n+m) × (n+m), Δ 1 ＝0,Δ 2 ＝K D f D ,Δ 3 ＝K U f A ,Δ 4 ＝P Δ,max ，i∈{1,2,3}；
And 3) according to the linear invariance of the Gaussian mixture model and the Gaussian mixture model parameter set of X, analyzing to obtain the Gaussian mixture model parameter set of Y, and finally obtaining the distribution of the running state of the electric power system.
The method for quantifying the running state of the power system based on the analytic probability power flow model is further designed in that the frequency adjustment model is divided into three sections from top to bottom, wherein the first section represents primary frequency modulation when only the load responds to the frequency change, the second section represents primary frequency modulation when the load and the generator both respond to the frequency change, and the third section represents secondary frequency modulation when the load and the generator both respond to the frequency change.
The method for quantifying the running state of the power system based on the analytic probability power flow model is further designed in that the deducing process of the step 2) specifically comprises the following steps: setting up
Δ 1 ＝0,Δ 2 ＝K D f D ,Δ 3 ＝K U f A ,Δ 4 ＝P Δ,max
According to equation (2), the generator active power adjustment amount P at bus n Δ,n The method comprises the following steps: p (P) Δ,n ＝α n,i P Δ ifΔ i ＜|P Δ |≤Δ i+1 ，
Compared with the active power injection at the node n when the frequency adjustment is ignored, the frequency modulation factor combined with the active power injection at the node n after frequency modulation is alpha n,i P Δ Active power P injected at node n n The expression of (2) becomes
Wherein,subscript g represents a conventional generator, subscript w represents a wind driven generator, subscript d represents a load, and n∈s;
in order to matrix describe node power injection, set up:
the node injects active powerThe method comprises the following steps:
node injection of reactive powerThe expression of (c) is not affected by primary and secondary frequency modulation and can still be written in the same way as when frequency control is not considered:
wherein I is an identity matrix with dimension M,and gamma is
Let X be the active power and reactive power injected by the wind driven generator, Y be the vector formed by the running state of the power system, D i Beta is i And gamma, i.e. vector
Combining the deductions, and taking into consideration the active power condition quantity of the node controlled by the frequency in the formula (2) to obtain a relational expression of the active power and reactive power X injected by the wind driven generator and the running state Y of the power system
Wherein,
the invention has the following advantages:
in the method for quantifying the running state of the electric power system based on the analytic probability tide model, unbalanced power is jointly born by units participating in frequency modulation through the whole network, so that the method is more in line with the actual situation of an actual system. If the frequency control is ignored, the unbalanced power of the whole system is only born by the balance nodes, and the actual situation of the power system is not met.
Compared with the Monte Carlo method, the analytical probability power flow algorithm in the quantization method samples a large number of wind power random injection scenes, so that the calculated amount is greatly reduced; and by constructing an analysis expression of the random distribution of the running states of the power system, the subsequent work such as safety analysis of the power system and optimization of the power system can be more efficiently performed.
Detailed Description
The following describes the technical scheme of the invention in detail.
The method for quantifying the running state of the power system based on the analytic probability power flow model of the embodiment comprises the following steps:
step 1) establishing a description of active and reactive power injection for each node according to equation (1)And power system operating state->A linear probabilistic power flow model of the relationship between them,
wherein θ and V represent the voltage phase angle and magnitude, respectively; p and Q respectively represent active power and reactive power injected by the nodes; Λ and C are parameter matrices composed of conductivity and susceptance elements of the power system; subscript ofRepresents the set of V theta nodes, +.>Represents the set of PV and V.theta.,>representing the set of PV and PQ nodes, < >>A set of PQ nodes is represented.
Step 2) constructing a frequency adjustment model about the node n according to the formula (2) by combining the linear probability power flow model, and introducing an active power unbalance amount P for controlling the frequency of the node n on the basis of the frequency adjustment model Δ Deriving a linear power flow model of the formula (3) about active power and reactive power X and the running state Y of the power system,
wherein K is d,n Represents the load frequency characteristic coefficient, K, of the bus n g,n Represents the response coefficient, K, of the speed regulator of a conventional generator at the same bus u,n ＝K g,n +K d,n ，f A P is the frequency threshold of AGC Δ,max To the maximum regulation capacity of the system, H g,n Is the climbing rate of the AGC device at the position of the bus n and meets the requirements of
Wherein alpha is i 、E i 、D i Are all matrix representations of intermediate parameters with respect to the frequency modulation factor,representing a real matrix of size (n+m) × (n+m), Δ 1 ＝0,Δ 2 ＝K D f D ,Δ 3 ＝K U f A ,Δ 4 ＝P Δ,max ，i∈{1,2,3}。
The deduction process in the formula (2) in the step 2) is specifically as follows:
with P n And Q m Representing the active power and the reactive power injected by the node n and the node m respectively, and the expressions thereof can be written as
P n ＝P g,n +P w,n -P d,n n∈S
Q m ＝Q g,m +Q w,m -Q d,m m∈L
Wherein the subscript g represents a conventional generator, the subscript w represents a wind generator, and the subscript d represents a load. In addition, P and Q represent active power and reactive power, respectively. Due to P w,n Is a random variable and therefore the system is often faced with a problem of power imbalance as the wind power injection fluctuates. If the active loss of the line in the system is ignored, the active power unbalance amount P of the system Δ Can be written as
Wherein N is the size of the set S, P Δ The magnitude of the value determines the frequency control measures that the system should take.
To avoid frequent generator governor action, the dispatcher will manually set the generator dead zone in the primary frequency modulation. When P Δ Or frequency deviation f Δ When the frequency is smaller than the dead zone threshold value, only the rotation load response frequency changes; when P Δ Or frequency deviation f Δ Above the deadband threshold, both the load and the generator respond to changes in frequency. When primary frequency modulation is able to keep the frequency variation within the allowed range, secondary frequency modulation is not required. To this end, the operator will set an AGC threshold for the AGC unit. When P Δ Or frequency deviation f Δ When the value is smaller than the AGC threshold value, only one frequency modulation action is performed; when P Δ Or frequency deviation f Δ And when the frequency deviation is larger than the AGC threshold value, performing secondary frequency modulation and eliminating the frequency deviation. Based on the above, P Δ And frequency deviation f Δ Relation setting of (2)
Wherein f D Is the average frequency threshold value of dead zone of all generators, K D And K U Is defined as follows
Wherein K is d,n Represents the load frequency characteristic coefficient, K, of the bus n g,n Representing the governor response coefficient of a conventional generator at the same bus. If the bus n is not loaded or has no generator, K d,n =0 or K g,n ＝0。
Based on the formula (2) and the segmentation characteristics of the frequency adjustment, a frequency adjustment model can be established, and then the active power adjustment quantity segmented expression at the node n shown in the formula (2) is obtained. The frequency adjustment model of this embodiment is composed of three segments from top to bottom, the first segment represents the primary frequency modulation when only the load response frequency changes, the second segment represents the primary frequency modulation when both the load and the generator respond to the frequency changes, and the third segment represents the secondary frequency modulation when both the load and the generator respond to the frequency changes.
The deduction process in the formula (3) in the step 2) is specifically as follows:
setting up
Δ 1 ＝0,Δ 2 ＝K D f D ,Δ 3 ＝K U f A ,Δ 4 ＝P Δ,max
According to equation (2), the generator active power adjustment amount P at bus n Δ,n The method comprises the following steps: p (P) Δ,n ＝α n,i P Δ ifΔ i ＜|P Δ |≤Δ i+1 ，
Compared with the active power injection at the node n when the frequency adjustment is ignored, the frequency modulation factor combined with the active power injection at the node n after frequency modulation is alpha n,i P Δ Active power P injected at node n n The expression of (2) becomes
Wherein,subscript g represents a conventional generator, subscript w represents a wind driven generator, subscript d represents a load, and n∈s;
in order to matrix describe node power injection, set up:
the node injects active powerThe method comprises the following steps:
node injection of reactive powerThe expression of (c) is not affected by primary and secondary frequency modulation, and can be written and not consideredThe same form as in frequency control:
wherein I is an identity matrix with dimension M,and gamma is
Let X be the active power and reactive power injected by the wind driven generator, Y be the vector formed by the running state of the power system, D i Beta is i And gamma, i.e. vector
Combining the deductions, and taking into consideration the active power condition quantity of the node controlled by the frequency in the formula (2) to obtain a relational expression of the active power and reactive power X injected by the wind driven generator and the running state Y of the power system
Wherein,
and 3) according to the linear invariance of the Gaussian mixture model (hereinafter referred to as GMM), and according to the Gaussian mixture model parameter set of X, the Gaussian mixture model parameter set of Y is obtained analytically, and finally the distribution of the running state of the power system is obtained.
In order to make the piecewise linear power flow model more general, formula (3) is rewritten as
Wherein,
wherein i=1, a method of treating a subject suffering from a disorder, I, I is 3 in the piecewise linear power flow model of equation (3). In order to make the piecewise linear power flow model more general, the above formula adoptsInstead of delta i ＜|P Δ |≤Δ i+1 。
GMM piecewise linear invariance can be expressed as: when Y is a piecewise linear function of X, and the expression of Y is determined by the value of the linear transformation of X, if the distribution of X can be represented by GMM, the distribution of Y can be represented by infinite GMM.
The GMM piecewise linear invariance proving process is: if the distribution of X can be represented by GMM, the distribution of X is as follows, according to the definition of GMM:
wherein,expressed in mu j Is mean value, sigma j Is the variance, w j The j-th Gaussian distribution is the weight, and the parameters of the j-th Gaussian distribution can be obtained by an EM algorithm according to the historical data of X. Due to->Is a linear transformation of X, known from the linear invariance of GMM, +.>Is also a GMM, and can be expressed in particular as:
wherein,
i is an identity matrix of dimension (N + M),is an all 1 vector.
According to the edge probability invariance of GMM, forGiven->Conditional probability distribution of XAlso conforms to GMM and its expression can be defined by +.>GMM expression derivation of (i.e.)
Wherein,
for a given oneFunctional relation determination of Y and X is linear transformation y=a i X+b i . From the linear invariance of GMM, we know the conditional probability distribution of Y +.>Also a GMM whose expression satisfies
In omega i As a complete event group, the full probability formula using probability theory can be known
Wherein the method comprises the steps of
Due toIs a GMM, and the linear invariance of the GMM is combined, as can be seen from formulas (5) and (6)Also a GMM.
To be used forAs a complete event group, the full probability formula using probability theory can be known
Wherein the method comprises the steps of
Is known to beIs a GMM, from formula (7)>Is->Linear combination of (2), thus->Also a GMM. In combination of formula (6) and formula (7),>the expression of (c) can be written as:
due to omega i In (a) and (b)There are infinite numbers, thus->And->The number of gaussian components included is also infinite, and is not entirely consistent with the finite number of gaussian components included in a conventional GMM. Thus, the present embodiment uses "infinite GMM" to refer to a GMM composed of an infinite number of gaussian components. To this end, piecewise linear invariance of the GMM was demonstrated.
According to the piecewise linear invariance of the GMM, the embodiment further provides two calculation methods, namely a GMM direct method and a GMM indirect method, which are analytically defined byThe GMM expression of +.>GMM expression of (a).
GMM direct method: direct pairing using the expression in formula (8)And (5) performing calculation. Since the infinite Gaussian components cannot be weighted and summed in the actual calculation, the method uses the formula (8) to count ++>And performing approximate solution.
The above formula is represented by a large number L, expressed in Ω, compared with formula (8) i Extracting LInstead of in actual case at Ω i Extracting infinite number +.>Obviously, the value of L will affect the calculation accuracy of the method, and when the value of L is larger, +.>Will contain a large number of Gaussian components, p->Further, the method is used for analysis of the power system, so that a large calculation amount is brought.
GMM indirect method: the method aims at improving the larger calculation amount caused by too many Gaussian components in the GMM direct method. To be used forAs a complete event group, a full probability formula using probability theory is available:
wherein the method comprises the steps of
From (9), it can be seen thatIs a weighted sum of an infinite number of gaussian distributions, i.e., an infinite GMM.
However, unlikeThe history data of X is easy to obtain, so that +.>Without adding a large number of gaussian components to approximate its GMM expression using equation (9).
Obtained directly by using EM algorithmThe expression can be written in the form of a conventional GMM, i.e
Wherein due to the givenThus the functional relationship of Y and X is determined for linear transformation y=a i X+b i . Using the linear invariance of GMM, the +.>GMM expression of (a), i.e.)
According to the aboveThe linear invariance of GMM can be analytically obtained +.>GMM expression of (a).
Historical data acquisition with X due to GMM indirectionIs the normal GMM expression of (2), the final +.>The GMM expression of (2) only comprises I multiplied by J Gaussian distributions, which are far less than L Gaussian distributions in the GMM direct method, thus greatly reducing +.>The complexity of the GMM expression of (c).
The present embodiment thus far proposes that the GMM direct method and the GMM indirect method are analytically defined byGMM expression of (2)GMM expression of (a).
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (3)
1. The utility model provides a power system running state quantization method based on analytic probability power flow model, which is characterized by comprising the following steps:
step 1) establishing and describing active power and reactive power injection of each node according to the formula (1)And power system operating state->A linear probabilistic power flow model of the relationship between them,
wherein θ and V represent the voltage phase angle and magnitude, respectively; p and Q respectively represent active power and reactive power injected by the nodes; Λ and C are parameter matrices composed of conductivity and susceptance elements of the power system; subscript ofRepresents the set of V theta nodes, +.>Represents the set of PV and V.theta.,>representing the set of PV and PQ nodes, < >>Representing a set of PQ nodes;
step 2) constructing a frequency adjustment model related to the bus n according to the formula (2) by combining the linear probability power flow model, and introducing an active power unbalance amount P for controlling the frequency of the bus n on the basis of the frequency adjustment model Δ Deriving a linear power flow model of the formula (3) about active power and reactive power X and the running state Y of the power system,
wherein K is d,n Represents the load frequency characteristic coefficient, K, of the bus n g,n Representing the convention at the same busSpeed regulator response coefficient, K of generator u,n ＝K g,n +K d,n ，f A Frequency threshold for automatic power generation control, f D Is the average frequency threshold of all generator dead zones, P Δ,max To the maximum regulation capacity of the system, H g,n Is the climbing rate of the automatic power generation control device at the position of the bus n, and meets the requirements of
Wherein alpha is i 、E i 、D i Are all matrix expressions of intermediate parameters related to frequency modulation factors, M represents the number of PQ nodes in the system, N represents the sum of the numbers of PV nodes and PQ nodes in the system,representing a real matrix of size (N + M) x (N + M),
Δ 1 ＝0,Δ 2 ＝K D f D ,Δ 3 ＝K U f A ,Δ 4 ＝P Δ,max ，i∈{1,2,3}；
and 3) according to the linear invariance of the Gaussian mixture model and the Gaussian mixture model parameter set of X, analyzing to obtain the Gaussian mixture model parameter set of Y, and finally obtaining the distribution of the running state of the electric power system.
2. The method for quantifying the running state of the electric power system based on the analytical probabilistic power flow model according to claim 1, wherein the frequency adjustment model is characterized in that from top to bottom, the first segment represents the primary frequency modulation when only the load responds to the frequency change, the second segment represents the primary frequency modulation when both the load and the generator respond to the frequency change, and the third segment represents the secondary frequency modulation when both the load and the generator respond to the frequency change.
3. The method for quantifying the operation state of the power system based on the analytical probabilistic power flow model according to claim 1, wherein the deriving process of the step 2) specifically comprises the following steps: setting up
Δ 1 ＝0,Δ 2 ＝K D f D ,Δ 3 ＝K U f A ,Δ 4 ＝P Δ,max
According to equation (2), the generator active power adjustment amount P at bus n Δ,n The method comprises the following steps: p (P) Δ,n ＝α n,i P Δ ifΔ i ＜|P Δ |≤Δ i+1 The frequency modulation factor alpha combined with the active power injection at the frequency modulated bus n is compared to the active power injection at node n when frequency modulation is ignored n,i P Δ Active power P injected by bus n n The expression of (2) becomes
Wherein,subscript g represents a conventional generator, subscript w represents a wind driven generator, subscript d represents a load, and n∈s;
in order to matrix describe node power injection, set up:
the node injects active powerThe method comprises the following steps:
node injection of reactive powerThe expression of (c) is not affected by primary and secondary frequency modulation, and is still the same form when frequency control is not considered:
wherein I is an identity matrix with dimension M,and gamma is
Let X be the injection of the wind driven generatorActive power and reactive power of (2), Y is a vector formed by the running states of the power system, D i Beta is i And gamma, i.e. vector
Combining the deductions, and taking into consideration the active power condition quantity of the node controlled by the frequency in the formula (2) to obtain a relational expression of the active power and reactive power X injected by the wind driven generator and the running state Y of the power system
Δ i ＜|P Δ |≤Δ i+1
Wherein,
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