CN109190956B - Industrial electrical load decomposition method based on low-rank representation - Google Patents
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Abstract
The invention discloses an industrial electric load decomposition method based on low-rank representation, which comprises the following steps of: step S1, load node data are collected through non-invasive monitoring of the load nodes, and a load data matrix is obtained; step S2, performing low-rank representation on the load data matrix, and respectively obtaining a shared coefficient matrix and a proprietary coefficient matrix, wherein the shared coefficient matrix is used for representing the total load, and the proprietary coefficient matrix is used for representing the relationship between the sub-load and the total load; step S3, analyzing the sharing coefficient matrix and the proprietary coefficient matrix through low-rank variables, and judging the switching state of each electric device in the load; in step S4, load breakdown is performed to obtain the contribution ratio of each electric device to the total load. The invention can carry out load decomposition and modeling through the daily load curve, thereby preliminarily realizing the judgment criterion of the switching load of industrial users, providing an accurate user power consumption prediction algorithm, formulating a more flexible electricity price mechanism and achieving the aims of energy conservation and environmental protection of the whole society.
Description
Technical Field
The invention relates to the technical field of power management, in particular to an industrial power load decomposition method based on low-rank representation.
Background
The load of the power system is divided into a comprehensive load, a power supply load and a power generation load, wherein the comprehensive load refers to the sum of electric power consumed by electric equipment of users of the power system, the power supply load is the sum of the comprehensive load and power loss of a power grid, and the power generation load is the sum of the power supply load and station service power. It can be seen that among the loads of the power system, the integrated load is the most critical part thereof and is also the basis for calculating other loads. Therefore, understanding and analysis of the integrated load is an important component of overall power energy management. In the industry, the most common monitoring and analysis of electrical loads is the electrical load profile. The power load curve is a curve describing the change rule of the power load in a certain period of time along with the time. In the power load curve, time is an independent variable. According to different time, the power load curve can be divided into a daily load curve, a monthly load curve, a quarterly load curve and an annual load curve. Obviously, the daily load curve is the basis for the formation of other load curves.
To understand the load demand of the user, what needs to be done first is the monitoring and analysis of the user load. Load monitoring is classified into two methods, invasive monitoring and non-invasive monitoring. The intrusive monitoring means that after the intrusive monitoring device penetrates into a load, a corresponding sensor or a corresponding meter is added to each electric device, so that the load is counted. Obviously, the method has obvious defects that a large amount of manpower and material resources are required to be input, and the sensing and measuring equipment needs to be replaced along with the updating of the electric equipment, so that the deployment cost is greatly increased. Therefore, non-invasive monitoring is currently prevalent internationally. Non-intrusive monitoring only makes critical data measurements at the load inlet, without having to reach deep into the specific consumer. Although the non-intrusive monitoring has the characteristics of low cost and high efficiency, the switching state and the load proportion of each electric device in the load cannot be directly obtained, so that some difficulties exist in demand allocation and dynamic scheduling.
Disclosure of Invention
The present invention is directed to provide a method for decomposing an industrial electrical load based on low-rank representation, which can decompose the industrial electrical load more effectively.
In order to solve the above-mentioned problems, the present invention provides a method for decomposing an industrial electrical load based on low-rank expression, comprising:
step S1, load node data are collected through non-invasive monitoring of the load nodes, and a load data matrix is obtained;
step S2, performing low-rank representation on the load data matrix, and respectively obtaining a shared coefficient matrix and a proprietary coefficient matrix, wherein the shared coefficient matrix is used for representing the total load, and the proprietary coefficient matrix is used for representing the relationship between the sub-load and the total load;
step S3, analyzing the sharing coefficient matrix and the proprietary coefficient matrix through low-rank variables, and judging the switching state of each electric device in the load;
in step S4, load breakdown is performed to obtain the contribution ratio of each electric device to the total load.
In step S2, a first target equation is established:
wherein X is a load data matrix, A is a base matrix, E is a correction data matrix, and ZCIs a shared coefficient matrix, ZSIs a proprietary coefficient matrix, rank represents the rank of the matrix, | E | | luminance1L represents E1Norm, α>0 is the balance parameter and s.t. represents the constraint.
Wherein, the step S3 specifically includes:
and obtaining the states of the columns in the shared coefficient matrix and the special coefficient matrix by optimizing the first objective equation, if the columns are 0, judging that each electric device in the sub-load corresponding to the columns is in a closed state, otherwise, judging that the electric device is in an operating state.
Wherein in the optimization of the first objective equation, the rank of the matrix is approximately optimized using the kernel norm of the matrix, and the data set is initialized with the base matrix itself, thereby expressing the objective equation as the following second objective equation:
wherein, | | Zc||*Representing a shared coefficient matrix ZcNuclear norm, | | Zs||*Representing a proprietary coefficient matrix ZsThe nuclear norm of (d).
The second target equation is optimized by an augmented Lagrange method, two relaxation variables J and Q are introduced, and the Lagrange equation of the second target equation is expressed as the following third target equation:
wherein,<>traces representing matrix multiplication (Trace), i.e.<Y2，Zc-J>＝tr(Y2 T(Zc-J)), subscript F representing the Frobenius norm of the matrix, Y1，Y2And Y3Is three lagrange multipliers, and μ > 0 is a balance parameter.
Wherein optimizing the third objective equation by an alternating direction multiplier method specifically includes:
all variables except for J in the third objective equation are determined as constants, and then the third objective equation calculates the partial derivative of the variable J, so that the optimization mode of the variable J is as follows:
all variables except for Q in the third objective equation are determined as constants, and then the third objective equation is used for solving the partial derivative of the variable Q, so that the optimization mode of the variable Q is as follows:
all variables except for E in the third objective equation are determined as constants, and then the third objective equation is used for solving the partial derivative of the variable E to obtain the variable E in the following optimization mode:
and solving the three optimization modes by a singular value threshold method to obtain the optimal solution of J, Q and E.
Wherein the optimization of the third objective equation further comprises:
all but Z in the third objective equationcAll other variables are considered as constants, and the third objective equation is then applied to variable ZcCalculating the partial derivative, and making the derivative be 0 to obtain variable ZcThe optimization solution is as follows:
all but Z in the third objective equationsAll other variables are considered as constants, and the third objective equation is then applied to variable ZsCalculating the partial derivative, and making the derivative be 0 to obtain variable ZsThe optimization solution is as follows:
wherein the optimization of the third objective equation further comprises:
sequentially optimizing the three Lagrange multipliers as follows:
Y1＝Y1+μ(X-X(Zc+Zs)-E)
Y2＝Y2+μ(Zc-J)
Y3＝Y3+μ(Zs-Q)
wherein, the overall optimization of the third objective equation obtains the optimized Z by continuously iteratively updating each variable to finally satisfy the convergence conditioncAnd Zs。
Wherein for the total load X monitoredGeneral assemblyEach of the sub-loads Y is obtained by the following equation:
Y＝Xgeneral assembly(ZC+ZS)+E
Wherein each column of the sub-loads Y represents the total load X of the corresponding electric equipmentGeneral assemblyThe ratio of contribution of (1).
The embodiment of the invention has the beneficial effects that: by analyzing the characteristics of the daily load curve, the power utilization condition of the load node can be known, and load decomposition and modeling can be further carried out through the daily load curve, so that the judgment criterion of switching load of industrial users is preliminarily realized, a reasonable power grid peak and capacity regulation mechanism is formulated, an accurate user power consumption prediction algorithm is provided, a more flexible power price mechanism is formulated, and the purposes of energy conservation and environmental protection in the whole society are achieved. Compared with the existing algorithm, the load decomposition and optimization method has the advantages of higher accuracy and better robustness.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flow chart of an industrial electrical load decomposition method based on low rank representation according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a discrete observation value of a load in one day of a certain load node in the embodiment of the present invention.
Fig. 3 is a schematic diagram of the daily load curve corresponding to fig. 2.
Detailed Description
The following description of the embodiments refers to the accompanying drawings, which are included to illustrate specific embodiments in which the invention may be practiced.
Referring to fig. 1, an embodiment of the present invention provides a low rank representation-based method for decomposing an industrial electrical load, which can be used for load decomposition in non-intrusive electrical load monitoring, and includes the following steps:
step S1, load node data are collected through non-invasive monitoring of the load nodes, and a load data matrix is obtained;
step S2, performing low-rank representation on the load data matrix, and respectively obtaining a shared coefficient matrix and a proprietary coefficient matrix, wherein the shared coefficient matrix is used for representing the total load, and the proprietary coefficient matrix is used for representing the relationship between the sub-load and the total load;
step S3, analyzing the sharing coefficient matrix and the proprietary coefficient matrix through low-rank variables, and judging the switching state of each electric device in the load;
in step S4, load breakdown is performed to obtain the contribution ratio of each electric device to the total load.
Specifically, in practical applications, since time can be divided into smaller units indefinitely, daily load curves usually employ observed values of data dispersion, and then these dispersion points are connected to draw a graph. For observations over a certain period of time, a vector x ═ x may be used1，x2，...，xn]And (4) showing. For example, during a day, the data collected by a certain load node is shown in fig. 2. By connecting the individual load observations, a daily load curve as shown in fig. 3 can be obtained.
In the load curve shown in fig. 3, time is an independent variable and the load amount is a dependent variable, and it is apparent that the load can be expressed as a function of time. Assuming that time is represented by the variable t, there are:
x＝f(t)
for comprehensive analysis, not only a small load node is monitored, but also the total load of a plurality of load nodes in a certain area is monitored in a centralized manner, so that a total load curve determined by all the sub-load curves is obtained. Each sub-load curve represents the load of a particular load node, each of which may correspond to one or more load devices.
In the industrial energy management, an industrial user needs to perform load decomposition according to a total load curve, so that a judgment criterion of switching load is formed, and a reasonable power grid peak and capacitance regulation mechanism is further formulated. In the analysis of the load curve, two basic problems are involved, namely how to obtain a total load curve according to the load curve of each load node, and how to analyze the switching state of each load according to the total load curve. The means for solving this problem is to perform load decomposition. Since each device is stable in voltage, current, power and other information during a period of time when it is working normally, it has definite statistical characteristics. Therefore, the characteristics of each electric device in the load can be obtained through statistics of the historical state, and the switching condition and the load proportion of each electric device in the load can be judged according to the current load state.
First, assuming that the total load is composed of a plurality of sub-loads, each sub-load is represented as a vector X, the plurality of sub-loads jointly form a matrix X ═ X1，X2，...，Xn]The total load curve is thus a function of the time variation of x. It is clear that at a given point in time any one of the sub-loads can be represented as the sum of the total load and a correcting variable, which can be either positive or negative, i.e. there is a sharing factor for each sub-load and the total load, which can be reconstructed from a set of identical bases (bases) plus different parameters. Assuming that this common basis is a, there is a coefficient matrix Z and a correction matrix E such that:
X＝AZ+E (1)
as mentioned above, the total load curve is formed by a plurality of sub-load curves, both the total load curve and the sub-load curves have their own characteristics, but each sub-load curve is closely related to the total load curve. In order to separate each sub-load from the total load, the present embodiment decomposes the coefficient matrix, assuming that the load of the i-th load node can be expressed as:
Xi＝AZi+Ei (2)
wherein Z isiParameter corresponding to the ith load node in the total load, EiA correction value corresponding to the ith load node in the total load. In order to associate each sub-load with the total load, while preserving the characteristics of each sub-load itself, Z is represented as the sum of two parts, one of which is used to represent the total load, and the other is used to represent the relationship between the sub-load itself and the total load, the following steps are performed:
X＝A(Zc+Zs)+E (3)
where the subscript C denotes common, i.e. the part sharing the total load, and the subscript s denotes specific, i.e. the specific relationship of the sub-load itself to the total load. In recent years, relevant studies of machine learning have shown that low rank representation is helpful in discovering the truest features in the confounding data. Since only the total load and the total number of sub-loads that may generate the load are known in the total load, the specific switching state of each load is not known. To judge ZcAnd ZsThe switching state of the medium load, which is Z in this embodimentcAnd ZsAnd adding low-rank constraint, and learning Z with a low-rank structure by an optimization method. The objective equation to be optimized is:
wherein rank represents the rank of the matrix, | E | | non-calculation1L represents E1Norm, α>0 is a balance parameter; s.t. is an abbreviation for subject to, representing a constraint. Z obtained by optimizing the above objective equationcAnd ZsThe switching state of the sub-load can be judged in the state of the middle column, if the column is 0 (the low rank constraint is helpful to find the column of 0), the electric equipment in the sub-load corresponding to the column can be judged to be in the off state, otherwise, the electric equipment is in the running state. Meanwhile, the sub-load curve can be obtained by the foregoing formula (2).
In an actual optimization process, since minimizing the rank of a matrix is an NP (Non-deterministic Polynomial) difficult problem, the rank of the matrix is generally approximately optimized using a kernel norm of the matrix. Meanwhile, the related research of low rank optimization suggests that a common basis matrix a may be initialized with the dataset itself. Thus, the objective equation (4) can be expressed as:
wherein, | | Zc||*Represents ZcNuclear norm, | | Zs||*Represents ZsThe nuclear norm of (d). The target equation (5) can be optimized by the augmented lagrangian method. In detail, first two relaxation variables J and Q are introduced, representing the lagrangian equation of the target equation (5) as:
wherein,<>traces representing matrix multiplication (Trace), i.e.<Y2，Zc-J>＝tr(Y2 T(Zc-J)). The subscript F denotes the Frobenius Norm (Frobenius Norm), Y of the matrix1，Y2And Y3Is three lagrange multipliers, and μ > 0 is a balance parameter. The objective equation (6) is optimized by Alternating Direction Method Of Multipliers (ADMM).
First, in order to optimize the variable J, all variables except J in the objective equation (6) are considered as constants, and then the objective equation (6) is used to calculate the partial derivative of the variable J, the optimization method of the variable J can be obtained as follows:
similarly, in order to optimize the variable Q, all variables except Q in the objective equation (6) are considered as constants, and then the objective equation (6) is used to make a partial derivative of the variable Q, the variable Q can be optimized in the following way:
thirdly, in order to optimize the variable E, all variables except for E in the objective equation (6) are considered as constants, and then the objective equation (6) is used to calculate the partial derivative of the variable E, so that the variable E can be optimized in the following way:
the three formulas (7), (8) and (9) can be solved by a singular value threshold method, and after optimal J, Q and E are obtained, other variables are optimized.
Fourth, to optimize the variable ZcAll of the target equation (6) are divided by ZcAll variables except for Z are considered as constants, and then the objective equation (6) is applied to the variable ZcCalculating the partial derivative and making the derivative 0 to obtain the variable ZcThe optimization solution is as follows:
fifthly, to optimize the variable ZsAll of the target equation (6) are divided by ZsAll variables except for Z are considered as constants, and then the objective equation (6) is applied to the variable ZsCalculating the partial derivative, and making the derivative be 0, and obtaining the variable Z in the same waysThe optimization solution is as follows:
sixthly, after all the main variables are optimized, three Lagrange multipliers are optimized in sequence, and the three Lagrange multipliers are respectively as follows:
Y1＝Y1+μ(X-X(Zc+Zs)-E) (12)
Y2＝Y2+μ(Zc-J) (13)
Y3＝Y3+μ(Zs-Q) (14)
the overall optimization of the objective equation can be realized by continuously iteratively updating each variable to finally meet the convergence condition, so that the optimized ZcAnd Zs。
Finally, Z is obtained by trainingc，ZsAfter E, for the total load X monitoredGeneral assemblyEach of the sub-loads Y can be obtained by the following equation:
Y＝Xgeneral assembly(ZC+ZS)+E
Wherein each column of the sub-loads Y represents the total load X of the corresponding electric equipmentGeneral assemblyThe ratio of contribution of (1). As described above, a column of Y is 0, which indicates that its corresponding electrical device is in an off state, and the contribution ratio in the total load is 0.
According to the description, the embodiment of the invention has the advantages that the electricity utilization condition of the load node can be known by analyzing the characteristics of the daily load curve, and the load decomposition and modeling can be further carried out through the daily load curve, so that the judgment criterion of the switching load of an industrial user is preliminarily realized, a reasonable power grid peak and capacity regulating mechanism is formulated, an accurate user electricity consumption prediction algorithm is provided, a more flexible electricity price mechanism is formulated, and the purposes of energy conservation and environmental protection in the whole society are achieved. Compared with the existing algorithm, the load decomposition and optimization method has the advantages of higher accuracy and better robustness.
The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention, and it is therefore to be understood that the invention is not limited by the scope of the appended claims.
Claims (5)
1. An industrial electrical load decomposition method based on low rank representation is characterized by comprising the following steps:
step S1, load node data are collected through non-invasive monitoring of the load nodes, and a load data matrix is obtained;
step S2, performing low-rank representation on the load data matrix, and respectively obtaining a shared coefficient matrix and a proprietary coefficient matrix, wherein the shared coefficient matrix is used for representing the total load, and the proprietary coefficient matrix is used for representing the relationship between the sub-load and the total load;
step S3, analyzing the sharing coefficient matrix and the proprietary coefficient matrix through low-rank variables, and judging the switching state of each electric device in the load;
step S4, carrying out load decomposition to obtain the contribution proportion of each electric device to the total load;
the step S2 includes establishing a first target equation:
wherein X is a load data matrix, A is a base matrix, E is a correction data matrix, and ZCIs a shared coefficient matrix, ZSIs a matrix of proprietary coefficients, rank representing the rank of the matrix, | E |1L represents E1Norm, α>0 is a balance parameter, and s.t. represents a constraint condition;
the step S3 specifically includes:
obtaining the states of columns in the shared coefficient matrix and the special coefficient matrix by optimizing the first objective equation, if the columns are 0, judging that each electric device in the sub-load corresponding to the columns is in a closed state, otherwise, judging that the electric device is in an operating state;
in the optimization of the first objective equation, the rank of the matrix is approximately optimized using the kernel norm of the matrix, and the matrix is initialized with the data set itself, so that the first objective equation is expressed as the following second objective equation:
wherein, | | Zs||*Representing a shared coefficient matrix ZcNuclear norm, | | Zs||*Representing a proprietary coefficient matrix ZsThe nuclear norm of (d);
the second target equation is optimized by an augmented Lagrange method, two relaxation variables J and Q are introduced, and the Lagrange equation of the second target equation is expressed as the following third target equation:
wherein,<>traces representing matrix multiplication (Trace), i.e. < Y2，Zc-J＞＝tr(Y2’(Zc-J)), subscript F representing the Frobenius norm of the matrix, Y1，Y2And Y3Is three Lagrange multipliers, μ>0 is a balance parameter;
optimizing the third objective equation by an alternating direction multiplier method, specifically comprising:
all variables except for J in the third objective equation are determined as constants, and then the third objective equation calculates the partial derivative of the variable J, so that the optimization mode of the variable J is as follows:
all variables except for Q in the third objective equation are determined as constants, and then the third objective equation is used for solving the partial derivative of the variable Q, so that the optimization mode of the variable Q is as follows:
all variables except for E in the third objective equation are determined as constants, and then the third objective equation is used for solving the partial derivative of the variable E to obtain the variable E in the following optimization mode:
and solving the three optimization modes by a singular value threshold method to obtain the optimal solution of J, Q and E.
2. The method of claim 1, wherein the optimization of the third objective equation further comprises:
all but Z in the third objective equationcAll other variables are considered as constants, and the third objective equation is then applied to variable ZcCalculating the partial derivative, and making the derivative be 0 to obtain variable ZcThe optimization solution is as follows:
all but Z in the third objective equationsAll other variables are considered as constants, and the third objective equation is then applied to variable ZsCalculating the partial derivative, and making the derivative be 0 to obtain variable ZsThe optimization solution is as follows:
3. the method of claim 2, wherein the optimization of the third objective equation further comprises:
sequentially optimizing the three Lagrange multipliers as follows:
Y1＝Y1+μ(X-X(Zc+Zs)-E)
Y2＝Y2+μ(Zc-J)
Y3＝Y3+μ(Zs-Q) 。
4. the method of claim 1, wherein the global optimization of the third objective equation obtains the optimized Z by continuously iteratively updating the variables to eventually satisfy the convergence conditioncAnd Zs。
5. Method according to claim 4, characterized in that for the monitored total load XGeneral assemblyEach of the sub-loads Y is obtained by the following equation:
Y＝Xgeneral assembly(ZC+ZS)+E
Wherein each column of the sub-loads Y represents the total load X of the corresponding electric equipmentGeneral assemblyThe ratio of contribution of (1).
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