CN114221343B - Optimal power flow solving method considering wind power plant output randomness based on point distribution method - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
- H02J2300/20—The dispersed energy generation being of renewable origin
- H02J2300/28—The renewable source being wind energy
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- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/70—Wind energy
- Y02E10/76—Power conversion electric or electronic aspects
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Abstract
The invention discloses an optimal power flow solving method considering the randomness of new energy output based on a point matching method. By considering the influence of the random change of the wind power plant output on the optimal power flow solution of the system, the requirements of safety analysis and control of the power system are met and further perfected, and the influence of the steady-state optimal power flow of the system on the output of new energy sources such as the wind power plant can be reflected more comprehensively. The method is applicable to solving the optimal power flow under various complex working conditions of the power system, has wide application range and high solving speed, and can provide a scientific and reasonable analysis scheme for safety and stability analysis and control of the power system.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to the field of steady-state analysis and control of power systems in the power market environment, and provides an optimal power flow solving method considering the randomness of new energy output based on a point distribution method.
Background
The optimal power flow problem is an effective tool for coordinating the economy and the safety of the power system, and is also one of important tools for planning and running the power system. The optimal power flow problem of the power system is a complex nonlinear programming problem, and the optimal system stable state of a preset target is required to be realized by adjusting available control means in the system under the condition that the specific power system operation and safety constraint conditions are met. In recent years, as a large number of wind farms are connected into a traditional power system, the output of wind power has stronger randomness, volatility and intermittence along with the influence of natural conditions (such as wind speed, time and the like), and the uncertainty factors influence the solving of the optimal power flow problem.
In order to solve the optimal power flow considering the randomness of the wind power plant output, an optimal power flow model considering the influence of random factors needs to be established first. There are two methods to solve this problem according to the method of processing variable parameters. 1) Probability type optimal power flow: the disadvantage of this approach is that it relies on an assumed probability density function of the variable parameter and typically requires a large number of samples to find the probability density function of the system variable. 2) Robust optimal power flow: the purpose of the robust optimal power flow is to solve a control scheme which enables the system to have robust stability to parameter changes. It does not need to assume the probability distribution of the variable parameter, only to know its range of variation. However, since this approach ignores the probabilistic nature of the system variables, a more conservative solution in the worst case is typically obtained.
Disclosure of Invention
The invention aims to solve the problems in the background technology and provides an optimal power flow solving method considering wind power output randomness based on a point matching method. The solution is the quantitative relation between the optimal solution and the wind power output. Compared with the probability type optimal power flow, the parameterized optimal power flow has the advantages that probability distribution of random parameters is not needed to be assumed, and only the change range of the random parameters is needed to be set; compared with the robust optimal power flow, the solution of the method can ensure the safe operation of the system and avoid the conservation of the optimal solution.
According to a first aspect of the object of the invention, the invention adopts the following technical scheme:
the optimal power flow solving method considering the wind power plant output randomness based on the point matching method is characterized by comprising the following steps of:
(1) And establishing a steady-state mathematical model of the power system considering the output randomness of the wind power plant.
And establishing a steady-state mathematical model of elements such as new energy sources including wind power, synchronous generators, transformers, loads, power networks and the like according to the actual conditions of the power networks. The power network equation is:
wherein S is B Is node set, S R For the collection of reactive power sources, P Gi Active power, Q, generated by a conventional power supply for node i Ri Reactive power, P, emitted by various reactive sources of node i Wi And Q Wi Active power and reactive power sent by the node i wind farm are respectively; p (P) Li And Q Li Active power and reactive power of the node i load respectively; v (V) i The voltage amplitude of the node i; y is Y ij Is a node admittance matrix element.
The output power of the wind power plant depends on the output power of each wind turbine generator in the wind power plant, the power generation power of the wind turbine generator changes along with the fluctuation of wind speed, and the relation between the power generation power and the wind speed is as follows:
wherein v is wind speed; v in Is the cut-in wind speed; v out To cut out wind speed; v r Is the rated wind speed; p (P) r Is wind powerRated output power of the unit;the actual output power of the wind turbine generator is obtained; a=p r v in /(v in -v r )，b＝P r /(v r -v in ) Are all constant.
Thus, the output power P of the node i wind farm Wi Is that
P Wi ＝N Wi P Wgi (1.3)
Wherein N is Wi The number of wind turbine generators P of the wind power plant with the node i Wgi The actual output power of the ith wind turbine generator system.
Assuming that the wind turbine generator runs in a constant power factor mode, the reactive power Q absorbed by the node i wind power plant Wi The method comprises the following steps:
Q Wi ＝P Wi tanθ i (1.4)
wherein θ is i And (3) the power factor angle of the wind turbine generator set of the node i wind power plant.
Therefore, the formulas (1.1) - (1.4) form a power system steady state power flow mathematical model considering the uncertainty of the wind power plant output. For simplicity, equations (1.1) - (1.4) may be reduced to the following function vectors:
0＝g(y,u；p) (1.5)
wherein y is algebraic variable describing the steady-state operation state of the system, including node voltage, line power flow and the like, u is a control parameter, which can comprise the output of a generator, terminal voltage, load size, reference value of a compensation device and the like, p is a random parameter which is influenced by wind speed and represents the output of a wind power plant, and g is a function vector of a steady-state model of the power system, including formulas (1.1) - (1.4).
(2) Based on the mathematical model obtained in the step (1), establishing a parameterized power system optimal power flow mathematical model considering the randomness of the new energy output, and expressing the parameterized power system optimal power flow mathematical model as a parameterized nonlinear programming problem;
the proposed parameterized optimal power flow problem can be expressed as a nonlinear programming problem, where u is the variable to be optimized, and the variable parameter p is freely variable as a variable within its range:
wherein, the optimization objective is:
the constraint condition is that
0＝g(y,u；p) (2.2)
H min ≤H(y,u；p)≤H max (2.3)
Wherein c (y, u; p) is an objective function of the optimization problem, and can represent fuel cost, network loss or line transmission capacity, etc., formula (2.2) is a steady-state mathematical model of the power system, formula (2.3) represents a steady-state inequality constraint condition, H represents a function vector expressing a system state, and the upper bound is H min The lower bound is H max Including bus voltage amplitude, generator active and reactive output limits, etc.
In order to find an optimal steady-state operating point y with transient stability, we need to adjust the control parameter u, such as rearranging the active power or adjusting the generator terminal voltage, taking into account the random output p of the wind farm. Since the optimal power flow model (2.1) - (2.3) of the power system is a parameterized nonlinear programming optimization model, the random parameter p can freely change in the definition domain of the parameterized nonlinear programming model, so the optimal steady-state operating point y and the optimal control scheme u are variables about p. Therefore, the key to solving parameterized nonlinear programming is how to effectively evaluate the effect of the random parameter p on the optimal solution.
The optimal solution method based on the point matching method is an optimal method for algebraic parameterized nonlinear programming, and aims to explicitly approximate the relation between the optimal solution and the variable parameters through a polynomial expression.
(3) Constructing a parameterized Karush-Kuhn-Tucker condition, namely a KKT condition, based on the mathematical model of the parameterized nonlinear programming problem obtained in the step (2);
based on the classical original dual interior point method, introducing the relaxation variables of inequality constraint into formulas (2.1) - (2.3) and adding the logarithmic barrier function to the objective function, the algebraic parameterized nonlinear programming model types (2.1) - (2.3) can be reconstructed into the following sub-problems:
the objective function is:
the constraint conditions are as follows:
0＝g(y,u；p) (3.2)
H(y；p)+v(p)＝H max (3.3)
H(y；p)+v(p)＝H min (3.4)
where μ is an obstacle parameter decreasing toward zero in the optimization process, l, v are relaxation variables of the inequality constraint formula (2 c), respectively, and r is the number of the steady-state inequality constraint formula (2 c). When μ approaches zero, the solutions of the reconstructed sub-problem formulas (3 a) - (3 d) approach those of the original optimized pattern formulas (2 a) - (2 c).
Since the state variable y and the control parameter u are the same variables to be optimized in the optimization model, they can be put together for convenience. Thus, here we meanAs a compact form of both. Thus, the Lagrangian function L of the sub-problem formulas (3.1) - (3.4) μ The method comprises the following steps:
wherein ζ (p), z (p), w (p) are Lagrangian multipliers of constraint formulas (3 a) to (3 d), respectively.
The optimal solutions of the sub-problem formulas (3.1) - (3.4) satisfy the following parameterized KKT first order conditions:
in the middle ofFor gradient arithmetic notation, e= [1, ], 1] T ,L＝diag(l 1 ,...,l r ),Z＝diag(z 1 ,...,z r ),U＝diag(v 1 ,...,v r ),U＝diag(v 1 ,...,v r )。
So far, the solution to algebraic parameterized nonlinear programming formulas (2.1) - (2.3) has been converted to a solution to a set of parameterized algebraic equations (3.6) - (3.11). Next we will use the fitting method to approximate a hidden function describing the relationship of the parameter p and the optimal solution.
(4) And (3) solving the parameterized KKT conditions based on a point matching method according to the parameterized KKT conditions obtained in the step (3).
First, all variables in parameterized KKT conditional expressions (3.6) - (3.11) can be expressed as linear combinations of polynomial basis functions { Φ (p) } as follows:
in the middle ofIs a compact form of the variable in parameterized KKT conditions, < >>Is->Approximation of N b Is the number of polynomial basis functions, +.>The approximation coefficient corresponding to the kth polynomial basis function is represented by k, which is a counting variable, and Φ (p) is a polynomial basis function.
Then, the coefficient is to be determined by the point matching methodCan be solved by the following equation:
wherein χ is k ＝∫ D Φ k (p)Φ k (p) ω (p) dp is the modulus of the polynomial basis function, D is the domain of p, ω (p) is the probability density function of p; p is p (m) M=1,..m is a configuration point (also called integration point), α m Is p (m) Integral coefficient of (a), configuration point and corresponding integral coefficient alpha m Is determined by a sparse grid method. It should be noted that when the polynomial basis function is selected, χ k ，α m ，p (m) Has been designed in advance in the dot placement method, soWill be affected by the value of parameter p.
According to a second aspect of the object of the present invention, there is provided a non-transitory computer readable storage medium having stored thereon a computer program, characterized in that the computer program, when executed by a processor, implements the steps of the above-mentioned optimal power flow solving method based on a point matching method, which considers wind farm output randomness.
According to a third aspect of the object of the present invention, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-mentioned optimal power flow solving method based on the point allocation method and considering the wind farm output randomness.
The invention has the beneficial effects that: by providing the optimal power flow calculation method considering the wind power plant output randomness based on the point distribution method, the influence of the wind power plant output random change on the optimal power flow solution of the system is considered, the requirements of safety analysis and control of the power system are met and further perfected, and the influence of the steady-state optimal power flow of the system on the output of new energy sources such as the wind power plant can be reflected more comprehensively. The method is applicable to solving the optimal power flow under various complex working conditions of the power system, has wide application range and high solving speed, and can provide a scientific and reasonable analysis scheme for safety and stability analysis and control of the power system.
Drawings
Fig. 1 is a topology diagram of a 3-machine 9-node system.
Detailed Description
The present invention is further illustrated in the accompanying drawings and detailed description which are to be understood as being merely illustrative of the invention and not limiting of its scope, since various modifications of the invention, which are equivalent to those skilled in the art, will fall within the scope of the invention as defined in the appended claims after reading the invention.
In this embodiment, taking a 3-machine 9-node system power system as an example, in order to verify the effectiveness of the proposed method, the change range of the power generation amount of each wind power plant along with the environment is [0,25 ] in the nodes 5, 6 and 8 respectively]MW，[0,18]MW，[0,20]MW. The topology and detailed data of the system can be obtained in fig. 1. Balance generator at node 1, so the controllable parameter is the output P of synchronous generators at node 2 and node 3 G2 ∈[135,155]MW and P G3 ∈[45,155]MW. The objective function is defined as the following fuel costs:
wherein P is Gi Is the active power of the ith generator. [ a ] 1 ,a 2 ,a 3 ] T ＝[2,1,1] T ,[b 1 ,b 2 ,b 3 ] T ＝[3,1,1] T And [ c ] 1 ,c 2 ,c 3 ] T ＝[3,1,1] T Is a fuel cost factor for the generator.
Referring to fig. 1, the optimal power flow solving method considering wind power plant output randomness based on the point matching method comprises the following steps:
(1) A quasi-steady state model of the long term process in the power system is established.
Wherein S is B Is node set, S R For the collection of reactive power sources, P Gi Active power, Q, generated by a conventional power supply for node i Ri Reactive power, P, emitted by various reactive sources of node i Wi And Q Wi Active power and reactive power sent by the node i wind farm are respectively; p (P) Li And Q Li Active power and reactive power of the node i load respectively; v (V) i The voltage amplitude of the node i; y is Y ij Is a node admittance matrix element; n (N) Wi The number of wind turbines in the wind power plant is node i; θ i And (3) the power factor angle of the wind turbine generator set of the node i wind power plant.
(2) And establishing a mathematical model for solving the optimal power flow of the power system by considering the randomness of the new energy output.
The optimization targets are as follows:
the constraint condition is that
Wherein C is G Is fuel cost; p (P) Gi Is the active power of the ith generator. [ a ] 1 ,a 2 ,a 3 ] T ＝[2,1,1] T ,[b 1 ,b 2 ,b 3 ] T ＝[3,1,1] T And [ c ] 1 ,c 2 ,c 3 ] T ＝[3,1,1] T Is a fuel cost factor for the generator. S is S G For the node set of the generator, S W For the collection of wind power places at nodes, other symbol definitions are shown in step 2.
(4) Parameterized Karush-Kuhn-Tucker (KKT) conditions were constructed and solved:
the order of the selected polynomial basis function is 2, and the result of solving the parameterized KKT condition by the point matching method is shown in Table 1.
Table 1,3 machine 9 node system example parameterized control scheme
From the description of the embodiments above, it will be apparent to those skilled in the art that the facility of the present invention may be implemented by means of software plus necessary general hardware platforms. Embodiments of the invention may be implemented using existing processors, or by special purpose processors used for this or other purposes for appropriate systems, or by hardwired systems. Embodiments of the invention also include non-transitory computer-readable storage media including machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. Such machine-readable media may include, for example, RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of machine-executable instructions or data structures and that can be accessed by a general purpose or special purpose computer or other machine with a processor. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the connection is also considered to be a machine-readable medium.
Thus far, the technical solution of the present invention has been described in connection with the specific embodiments, but it is easily understood by those skilled in the art that the scope of protection of the present invention is not limited to these specific embodiments. Equivalent modifications and substitutions for related technical features may be made by those skilled in the art without departing from the principles of the present invention, and such modifications and substitutions will fall within the scope of the present invention.
Claims (4)
1. The optimal power flow solving method considering the wind power plant output randomness based on the point matching method is characterized by comprising the following steps of:
step (1): establishing a steady-state mathematical model of the power system considering the output randomness of the wind power plant;
step (2): based on the mathematical model obtained in the step (1), setting a variation range of random parameters, establishing a parameterized power system optimal power flow mathematical model considering the randomness of the new energy output, and expressing the parameterized power system optimal power flow mathematical model as a parameterized nonlinear programming problem;
the step (2) specifically comprises the following steps: the proposed parameterized optimal power flow problem is expressed as a nonlinear programming problem, where u is the variable to be optimized, and the random parameter p is freely variable as a variable within its range:
wherein, the optimization objective is:
the constraint condition is that
0＝g(y,u；p) (2.2)
H min ≤H(y,u；p)≤H max (2.3)
Wherein y is algebraic variable containing node voltage and line power flow and describing the steady-state operation state of the system, u is a control parameter comprising the output of the generator, the terminal voltage, the load size and the reference value of the compensation device, and p is a random parameter influenced by wind speed and representing the output of the wind power plant; c (y, u; p) is the objective function of the optimization problem; g is a function vector containing a steady state model of the power system, H represents a function vector of steady state inequality constraint conditions, and the upper bound of the function vector is H min The lower bound is H max Including limits on bus voltage amplitude, generator active and reactive outputs;
step (3): solving parameterized Karush-Kuhn-Tucker conditions, namely parameterized KKT conditions, of the parameterized optimization model based on the mathematical model of the parameterized nonlinear programming problem obtained in the step (2);
step (4): solving the parameterized KKT condition based on a point allocation method according to the parameterized KKT condition obtained in the step (3), and obtaining a quantitative function relation between an optimal power flow solution and random parameters;
the step (3) specifically comprises the following steps: based on the classical original dual interior point method, introducing the relaxation variables of inequality constraint into formulas (2.1) - (2.3), and adding the logarithmic barrier function to the objective function, the algebraic parameterized nonlinear programming model forms (2.1) - (2.3) are reconstructed into the following sub-problems:
the objective function is:
the constraint conditions are as follows:
0＝g(y,u；p) (3.2)
H(y；p)+v(p)＝H max (3.3)
H(y；p)+v(p)＝H min (3.4)
wherein μ is an obstacle parameter decreasing toward zero in the optimization process, l, v are relaxation variables of the inequality constraint formula (2.3), and r is the number of the steady-state inequality constraint formula (2.3); when μ approaches zero, the solutions of the reconstructed sub-problem formulas (3.1) - (3.4) approach those of the original optimized model formulas (2.1) - (2.3);
thus, the Lagrangian function L of the sub-problem formulas (3.1) - (3.4) μ The method comprises the following steps:
wherein the method comprises the steps ofIn compact form of the state variable y and the control parameter u; ζ (p), z (p), w (p) are Lagrangian multipliers of constraint formulas (3.2) to (3.4), respectively;
the optimal solution of the sub-problem formula (3.1- (3.4) satisfies the following parameterized KKT first order conditions:
in the middle ofFor gradient arithmetic notation, e= [1, ], 1] T ,L＝diag(l 1 ,...,l r ),Z＝diag(z 1 ,...,z r ),U＝diag(v 1 ,...,v r ),U＝diag(v 1 ,...,v r )。
2. The optimal power flow solving method considering wind power plant output randomness based on the point matching method according to claim 1, wherein the optimal power flow solving method is characterized by comprising the following steps of: the step (4) specifically comprises the following steps: first, all variables in parameterized KKT conditional expressions (3.5) - (3.10) are represented as linear combinations of polynomial basis functions { Φ (p) } as follows:
in the middle ofIs a compact form of the variable in parameterized KKT conditions, < >>Is->Approximation of N b Is the number of polynomial basis functions, +.>The approximation coefficient corresponding to the kth polynomial basis function is adopted, and k is a counting variable;
then, the coefficient is to be determined by the point matching methodThe solution is as follows:
wherein χ is k ＝∫ D Φ k (p)Φ k (p) ω (p) dp is the modulus of the polynomial basis function, D is the domain of p, ω (p) is the probability density function of p; p is p (m) M=1,..m is the configuration point, α m Is p (m) Integral coefficient of (a), configuration point and corresponding integral coefficient alpha m Is determined by a sparse grid method; when the polynomial basis function is selected, χ k ，α m ，p (m) Has been designed in advance in the dot placement method, soWill be affected by the value of parameter p.
3. A non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor, implements the steps of a method for solving an optimal power flow based on a point allocation method, taking into account wind farm output randomness, according to claim 1 or 2.
4. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the optimal power flow solving method according to claim 1 or 2 based on the point matching method, taking into account wind farm output randomness.
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|---|---|---|---|---|
| JP2003134666A (en) * | 2001-10-16 | 2003-05-09 | Takeo Kawamura | Optimum power flow calculating system by nonlinear programming method |
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