CN116760062A - Power distribution network area self-balancing planning method based on two-stage robust optimization - Google Patents
Power distribution network area self-balancing planning method based on two-stage robust optimization Download PDFInfo
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Abstract
The application discloses a power distribution network area self-balancing planning method based on two-stage robust optimization, which comprises the following steps: establishing an uncertainty interval expression of load power and the maximum output of the distributed power supply; establishing a function model of a one-stage main body target; establishing a two-stage daily self-balancing cost evaluation target model, and carrying out linearization equation processing on an expression of the target model; based on the linearized two-stage daily self-balancing cost evaluation target model, establishing an evaluation stage dual problem and performing dual conversion; based on the single-layer maximum value optimization problem after dual transformation, a large M method constraint is established to process nonlinear items related to scene variables. According to the application, a self-balancing planning model of the power distribution network area can be constructed under the extreme scene of considering the fluctuation of the maximum output uncertainty of the load and the distributed power supply, so that the power fluctuation scene possibly encountered in actual operation is considered in the planning investment period, and the management and coping capacity of the power distribution network on the source load uncertainty is enhanced.
Description
Technical Field
The application belongs to the field of power distribution network planning, operation and optimization, and particularly relates to a power distribution network area self-balancing planning method based on two-stage robust optimization.
Background
The permeability of new energy power generation such as distributed photovoltaic, wind power and the like in the distribution network is gradually improved, and randomness and uncertainty of the new energy power generation with the improvement of the permeability bring higher challenges to the uncertain capability of the distribution network. At the same time, random fluctuation of load is also an unavoidable problem in the operation process, and the occurrence of the random fluctuation and the fluctuation of the distributed power supply in the power grid can seriously influence the safe and stable operation of the distribution network. Therefore, uncertainty scenes in actual operation are considered and evaluated in the regional power distribution network planning construction stage, and the self-balancing capacity of the regional power distribution network is improved, so that the problem worthy of research in the current power distribution network planning is solved.
Disclosure of Invention
The application aims to: in order to overcome the defects in the prior art, the self-balancing planning method for the power distribution network area based on two-stage robust optimization is provided, and a self-balancing planning model for the power distribution network area can be constructed under the extreme scene of considering the fluctuation of the maximum output uncertainty of a load and a distributed power supply, so that the power fluctuation scene possibly encountered in actual operation is considered in the planning investment period, and the management and coping capacity of the power distribution network on the source load uncertainty is enhanced.
The technical scheme is as follows: in order to achieve the above purpose, the application provides a power distribution network area self-balancing planning method based on two-stage robust optimization, which comprises the following steps:
s1: establishing an uncertainty interval expression of load power and the maximum output of the distributed power supply;
s2: establishing a function model of a one-stage main body target;
s3: establishing a two-stage daily self-balancing cost evaluation target model, and carrying out linearization equation processing on an expression of the target model;
s4: based on the linearized two-stage daily self-balancing cost evaluation target model, establishing an evaluation stage dual problem and performing dual conversion;
s5: based on the single-layer maximum value optimization problem after dual transformation, a large M method constraint is established to process nonlinear items related to scene variables, and self-balancing planning of a power distribution network area is achieved.
Further, in the step S1, an uncertainty interval expression of the load power and the maximum output of the distributed power supply is as follows:
in the formula (1), the components are as follows,load power values at the time of day evaluation and day-ahead stage t are respectively obtained; />The fluctuation amount of the load power value in the day and the day front two periods at the time t; />The upper and lower amplitude values of the fluctuation amount of the load power are respectively; in the formula (2), ->The maximum power value of the distributed power supply at the time t of the day-ahead stage is estimated in the day; />The fluctuation quantity of the maximum power value of the distributed power supply in the day and the first two time periods at the time t;the maximum output power fluctuation of the distributed power supply is respectively the upper and lower amplitude values.
Further, the function model of the one-stage subject object in step S2 is
F inv ＝L inv +ESS inv (3)
F DA ＝F GSP +F LM +F ESSM +F CUT (6)
In the formula (3), L inv The annual equivalent investment cost of the circuit; ESS (ESS) inv Annual equivalent investment cost for the energy storage system; a in the formula (4) is the discount rate; y is such thatAge of use;constructing a cost coefficient for investment of the line; />Investment variables for the line; omega shape L Is a set of circuit branches; in the formula (5), ->Building a cost coefficient for investment of the energy storage system; />Investment construction variables of the energy storage system; />The energy storage capacity at the position i; omega shape ESS Is an energy storage node set; omega shape S A selection set for energy storage construction capacity; in the formula (6), F DA 、F GSP 、F LM 、F ESSM 、F CUT The system is characterized in that the system comprises daily operation cost, upper power grid electricity purchasing cost, line operation and maintenance cost and energy storage system operation and maintenance cost, and load compensation cost can be reduced; in the formula (7), T i Days of occurrence for the ith scene; t (T) DA Taking one day as one period in the model, wherein the value is 24; s is S max The total number of running scenes; c d Purchasing electricity power unit price for the power distribution network to an upper power grid; />Purchasing electric power from the power distribution network to the upper power grid in the day-ahead stage; in the formula (8), c LM The unit price for line operation and maintenance; l (L) i The total length of the line in the scene i is calculated; in the formula (9), c ESSM The operation and maintenance unit price of the energy storage system; />Respectively charging and discharging power of the energy storage system j in the day-ahead stage scene i; />Respectively charging and discharging state variables of the energy storage system in the day-ahead stage; in the formula (10), c cut To reduce the load compensation coefficient; />The power regulation which can cut down the load is the j-th phase of the day; />Load adjustment state variables can be reduced for the day-ahead stage; omega shape CUT To cut down the load set.
Further, the linearization equation of the two-stage intra-day self-balancing cost evaluation target model in step S3 is expressed as follows:
in the formula (11), F unba Evaluating the cost for intra-day self-balancing; d, d unba Evaluating coefficients for self-balancing costs;purchasing power from a power distribution network to an upper power grid at a time t in a day stage in a scene i; />The day-ahead purchase power under the action of the adjustable load is corrected; t (T) ID ＝T DA A value of 24; in the formula (12), ->Variables are defined for assistance.
Further, in the step S4, the expression of establishing the evaluation stage dual problem and performing dual transformation is as follows:
in the formula (14), phi is a source load uncertainty scene set; u is a source load uncertainty variable; y is an intra-day optimization variable; d is a coefficient matrix of the optimization variable; in the formula (15), x is a one-stage optimization variable, and h is a constant vector; h (phi) 1 ,Φ 2 ) Is an uncertainty variable matrix; h is an optimization variable corresponding coefficient matrix; gamma, v, omega, pi 1 、π 2 The dual variables are respectively.
Further, in the step S5, based on the single-layer maximum optimization problem after the dual transformation, the expression of processing the nonlinear term related to the scene variable by establishing the large M-method constraint is as follows:
the [ (x) ray ]17 In the above-mentioned) process, a first step,0 and 1 variables of load fluctuation upwards and downwards respectively; />Auxiliary dual variables respectively; in formula (18), M is a sufficiently large constant term; in the formula (19), ω 1 、ω 2 Respectively the weight coefficients of two-stage targets in the overall robust model; c is a coefficient matrix of one-stage optimization variables. Here in equation (18), the large M method is used to linearize the equation constraint for the nonlinear term, so "large enough" depends on whether it can be constrained to Z and pi variables.
The beneficial effects are that: compared with the prior art, the method mainly considers investment planning stage cost and distribution network day-ahead scheduling operation cost in the existing power distribution network planning, and does not consider distributed power fluctuation and load power fluctuation which possibly occur in the day-in stage in actual operation. The application evaluates the actual self-balancing capability in the planning stage, and further improves the uncertainty self-management capability compared with the conventional distribution network planning. Meanwhile, the method is based on two-stage robust optimization, and the uncertainty scene is considered as a limit scene, so that the obtained planning result can be suitable for the worst fluctuation condition, and the safe and stable operation of the actual power distribution network is effectively ensured. The application has important reference function for planning and operation control of the distribution network under the enhancement of source load uncertainty.
Drawings
FIG. 1 is a flow chart of the method of the present application;
fig. 2 is a block diagram of a power distribution network employed in an example of the present application.
Detailed Description
The present application is further illustrated in the accompanying drawings and detailed description which are to be understood as being merely illustrative of the application and not limiting of its scope, and various modifications of the application, which are equivalent to those skilled in the art upon reading the application, will fall within the scope of the application as defined in the appended claims.
As shown in fig. 1, the application provides a power distribution network area self-balancing planning method based on two-stage robust optimization, which comprises the following steps:
s1: establishing an uncertainty interval expression of load power and maximum output of a distributed power supply:
the uncertainty interval expression of the load power and the maximum output of the distributed power supply is as follows:
in the formula (1), the components are as follows,load power values at the time of day evaluation and day-ahead stage t are respectively obtained; />The fluctuation amount of the load power value in the day and the day front two periods at the time t; />The upper and lower amplitude values of the fluctuation amount of the load power are respectively; in the formula (2), ->The maximum power value of the distributed power supply at the time t of the day-ahead stage is estimated in the day; />The fluctuation quantity of the maximum power value of the distributed power supply in the day and the first two time periods at the time t;the maximum output power fluctuation of the distributed power supply is respectively the upper and lower amplitude values.
S2: a functional model of a one-stage subject target is established as follows:
F inv ＝L inv +ESS inv (3)
F DA ＝F GSP +F LM +F ESSM +F CUT (6)
in the formula (3), L inv The annual equivalent investment cost of the circuit; ESS (ESS) inv Annual equivalent investment cost for the energy storage system; a in the formula (4) is the discount rate; y is the service life;constructing a cost coefficient for investment of the line; />Investment variables for the line; omega shape L Is a set of circuit branches; in the formula (5), ->Building a cost coefficient for investment of the energy storage system; />Investment construction variables of the energy storage system; />The energy storage capacity at the position i; omega shape ESS Is an energy storage node set; omega shape S A selection set for energy storage construction capacity; in the formula (6), F DA 、F GSP 、F LM 、F ESSM 、F CUT The system is characterized in that the system comprises daily operation cost, upper power grid electricity purchasing cost, line operation and maintenance cost and energy storage system operation and maintenance cost, and load compensation cost can be reduced; in the formula (7), T i Days of occurrence for the ith scene; t (T) DA Taking one day as one period in the model, wherein the value is 24; s is S max The total number of running scenes; c d Purchasing electricity power unit price for the power distribution network to an upper power grid; />Purchasing electric power from the power distribution network to the upper power grid in the day-ahead stage; in the formula (8), c LM The unit price for line operation and maintenance; l (L) i The total length of the line in the scene i is calculated; in the formula (9), c ESSM The operation and maintenance unit price of the energy storage system; />Respectively charging and discharging power of the energy storage system j in the day-ahead stage scene i; />Respectively charging and discharging state variables of the energy storage system in the day-ahead stage; in the formula (10), c cut To reduce the load compensation coefficient; />For the day ofThe j-th adjusting power capable of reducing load in the previous stage; />Load adjustment state variables can be reduced for the day-ahead stage; omega shape CUT To cut down the load set.
S3: establishing a two-stage daily self-balancing cost evaluation target model, and carrying out linearization equation processing on an expression of the target model:
the linearization equation for the two-stage intra-day self-balancing cost assessment objective model is expressed as follows:
in the formula (11), F unba Evaluating the cost for intra-day self-balancing; d, d unba Evaluating coefficients for self-balancing costs;purchasing power from a power distribution network to an upper power grid at a time t in a day stage in a scene i; />The day-ahead purchase power under the action of the adjustable load is corrected; t (T) ID ＝T DA A value of 24; in the formula (12), P t - 、P t + Variables are defined for assistance.
S4: based on the linearized two-stage daily self-balancing cost evaluation target model, establishing an evaluation stage dual problem and performing dual conversion:
the expression of establishing the evaluation stage dual problem and performing dual transformation is as follows:
in the formula (14), phi is a source load uncertainty scene set; u is a source load uncertainty variable; y is an intra-day optimization variable; d is a coefficient matrix of the optimization variable; in the formula (15), x is a one-stage optimization variable, and h is a constant vector; h (phi) 1 ,Φ 2 ) Is an uncertainty variable matrix; h is an optimization variable corresponding coefficient matrix; gamma, v, omega, pi 1 、π 2 The dual variables are respectively.
S5: based on the single-layer maximum value optimization problem after dual transformation, a large M method constraint is established to process nonlinear items related to scene variables, and self-balancing planning of a power distribution network area is achieved:
the expression is as follows:
in the formula (17), the amino acid sequence of the compound,respectively the load fluctuates upward and downward0. A 1 variable; />Auxiliary dual variables respectively; in formula (18), M is a sufficiently large constant term, and m=1000 in this embodiment; in the formula (19), ω 1 、ω 2 Respectively the weight coefficients of two-stage targets in the overall robust model; c is a coefficient matrix of one-stage optimization variables.
Based on the above, in order to verify the effectiveness of the solution of the present application, in this embodiment, the above solution is applied as an example, specifically as follows:
a node system of a power distribution network 49 in a certain area of Fujian is selected as an example basis, distributed photovoltaic power sources are respectively added to nodes 9, 40 and 45 on the basis of an original system, and nodes 4, 15 and 44 are selected as addresses of energy storage systems to be invested and constructed, as shown in fig. 2. Other parameters related to planning operation of the power distribution network such as energy storage, adjustable load and the like are shown in table 1 in detail. The time-of-use electricity prices employed in the example for the day-ahead schedule run period are shown in table 2.
Table 1 power distribution network planning operation parameters
Table 2 time-of-use electricity price units: meta/kilowatt-hour
According to the main parameters of related planning operation in the table 1 and the time-of-use electricity price parameters in the table 2, the two-stage robust optimization planning method is utilized to calculate, so that the corresponding planning operation cost under two sub-scenes in the following table 3 is obtained. In order to better verify the effectiveness of the method, the embodiment compares the two-stage robust optimization self-balancing planning method with the traditional deterministic power distribution network planning method. Compared with the prior art, the phase robustness planning is higher than the conventional deterministic distribution network planning which only considers the planning cost and the operation scheduling cost in terms of planning investment cost evaluation because the self-balancing cost evaluation of the distribution network in an extreme scene is considered. The annual equivalent planning investment cost evaluation value of the robust planning is 48.2803, while the annual equivalent investment cost evaluation value of the deterministic planning is 41.2364, and the economic performance of the running layer is better than that of the deterministic planning before the distribution network day due to the higher cost investment of the robust planning in the aspect of planning objects, and the running cost evaluation value is reduced 10.0149 compared with that of the deterministic planning. Because the energy storage device with higher capacity can flexibly respond to the change of the real-time electricity price and the maximum photovoltaic output, the distribution network economy is developed to a better direction.
Table 3 each class planning running cost
Scene 1 is based on a spring typical sub-scene, and the upward and downward uncertain parameters of the source charge of an actual curve in a day are set to be 2; scenario 2 based on the summer typical sub-scenario, the load up and down uncertainty parameter is set to 8, while the photovoltaic maximum output up and down uncertainty parameter is set to 4. The self-balancing cost evaluation combined with the distribution network planning results under the scenes 1 and 2 can find that the evaluation value under the robust planning in the scene 1 is smaller than the deterministic planning evaluation value 1.1338, and the evaluation value in the scene 2 is smaller than 3.2383, namely the result of the robust planning has more effective effect on the daily uncertainty management, and better effect is reflected along with the enhancement of the load and the photovoltaic maximum output uncertainty.
According to the example result, the two-stage robust optimization model formed by the investment construction period, the day-ahead period and the day-in period is constructed, on one hand, the self-balancing capacity of the planning result is evaluated by using the site selection and the constant volume of the energy storage device on the basis of selecting a limit scene, so that the power distribution network planning area with better robustness can cope with the source load uncertainty in the actual running state; on the other hand, the method has the advantages that the cost consideration of the planning object in the traditional power distribution network planning and the power distribution network economy under the typical scene operation scheduling are combined. Finally, the method provided by the application has the advantages of being beneficial to the construction of the power distribution network, and meanwhile, the safe and stable operation of the power distribution network can be effectively ensured.
Claims (7)
1. The power distribution network area self-balancing planning method based on two-stage robust optimization is characterized by comprising the following steps of:
s1: establishing an uncertainty interval expression of load power and the maximum output of the distributed power supply;
s2: establishing a function model of a one-stage main body target;
s3: establishing a two-stage daily self-balancing cost evaluation target model, and carrying out linearization equation processing on an expression of the target model;
s4: based on the linearized two-stage daily self-balancing cost evaluation target model, establishing an evaluation stage dual problem and performing dual conversion;
s5: based on the single-layer maximum value optimization problem after dual transformation, a large M method constraint is established to process nonlinear items related to scene variables, and self-balancing planning of a power distribution network area is achieved.
2. The method for self-balancing planning of a power distribution network area based on two-stage robust optimization according to claim 1, wherein an uncertainty interval expression of the load power and the maximum output of the distributed power supply in the step S1 is as follows:
in the formula (1), P t ID,load 、P t DA,load Load power values at the time of day evaluation and day-ahead stage t are respectively obtained;the fluctuation amount of the load power value in the day and the day front two periods at the time t; />The upper and lower amplitude values of the fluctuation amount of the load power are respectively; in the formula (2), P t ID,RDG,max 、P t DA,RDG,max The maximum power value of the distributed power supply at the time t of the day-ahead stage is estimated in the day; />The fluctuation quantity of the maximum power value of the distributed power supply in the day and the first two time periods at the time t;the maximum output power fluctuation of the distributed power supply is respectively the upper and lower amplitude values.
3. The method for self-balancing planning of a power distribution network area based on two-stage robust optimization according to claim 1, wherein the functional model of the one-stage subject objective in step S2 is
F inv ＝L inv +ESS inv (3)
F DA ＝F GSP +F LM +F ESSM +F CUT (6)
In the formula (3), L inv The annual equivalent investment cost of the circuit; ESS (ESS) inv Annual equivalent investment cost for the energy storage system; a in the formula (4) is the discount rate; y is the service life;constructing a cost coefficient for investment of the line; />Investment variables for the line; omega shape L Is a set of circuit branches; in the formula (5), ->Building a cost coefficient for investment of the energy storage system; />Investment construction variables of the energy storage system;the energy storage capacity at the position i; omega shape ESS Is an energy storage node set; omega shape S A selection set for energy storage construction capacity; in the formula (6), F DA 、F GSP 、F LM 、F ESSM 、F CUT The system is characterized in that the system comprises daily operation cost, upper power grid electricity purchasing cost, line operation and maintenance cost and energy storage system operation and maintenance cost, and load compensation cost can be reduced; in the formula (7), T i Days of occurrence for the ith scene; t (T) DA Number of operating cycle hours of 1; s is S max The total number of running scenes; c d Purchasing electricity power unit price for the power distribution network to an upper power grid; />Purchasing electric power from the power distribution network to the upper power grid in the day-ahead stage; in the formula (8), c LM The unit price for line operation and maintenance; l (L) i The total length of the line in the scene i is calculated; in the formula (9), c ESSM The operation and maintenance unit price of the energy storage system; />Respectively charging and discharging power of the energy storage system j in the day-ahead stage scene i; /> Respectively charging and discharging state variables of the energy storage system in the day-ahead stage; in the formula (10), c cut To reduce the load compensation coefficient; />The power regulation which can cut down the load is the j-th phase of the day; />Load-reducing adjustment for the daytimeA state variable; omega shape CUT To cut down the load set.
4. The two-stage robust optimization-based power distribution network area self-balancing planning method according to claim 1, wherein the linearization equation of the two-stage intra-day self-balancing cost evaluation target model in step S3 is expressed as follows:
in the formula (11), F unba Evaluating the cost for intra-day self-balancing; d, d unba Evaluating coefficients for self-balancing costs;purchasing power from a power distribution network to an upper power grid at a time t in a day stage in a scene i; />The day-ahead purchase power under the action of the adjustable load is corrected; t (T) ID ＝T DA The method comprises the steps of carrying out a first treatment on the surface of the In the formula (12), P t - 、P t + Variables are defined for assistance.
5. The method for self-balancing planning of a power distribution network area based on two-stage robust optimization according to claim 1, wherein the step S4 is to establish an evaluation stage dual problem and perform a dual transformation as follows:
in the formula (14), phi is a source load uncertainty scene set; u is a source load uncertainty variable; y is an intra-day optimization variable; d is a coefficient matrix of the optimization variable; in the formula (15), x is a one-stage optimization variable, and h is a constant vector; h (phi) 1 ,Φ 2 ) Is an uncertainty variable matrix; h is an optimization variable corresponding coefficient matrix; gamma, v, omega, pi 1 、π 2 The dual variables are respectively.
6. The distribution network area self-balancing planning method based on two-stage robust optimization according to claim 1, wherein in the step S5, based on the single-layer maximum optimization problem after dual transformation, the expression of processing nonlinear items related to scene variables by establishing large M-method constraint is as follows:
in the formula (17), the amino acid sequence of the compound,0 and 1 variables of load fluctuation upwards and downwards respectively; />Auxiliary dual variables respectively; in formula (18), M is a sufficiently large constant term; in the formula (19), ω 1 、ω 2 Respectively the weight coefficients of two-stage targets in the overall robust model; c is a coefficient matrix of one-stage optimization variables.
7. A method of self-balancing planning a power distribution network area based on two-stage robust optimization according to claim 6, wherein m=1000 in equation (18).
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