CN115115251A - Power distribution network power supply planning method and system considering net load optimal acceptable domain - Google Patents
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Abstract
The invention discloses a power distribution network power supply planning method and system considering an optimal admissible domain of a net load, which comprises the following steps: acquiring active and reactive output data, line tide and capacity data and node voltage and phase angle data of a generator set; establishing a power distribution network power supply planning target optimization model by taking the sum of the minimized annual unit investment cost, the operation cost and the reliability cost as a target and taking the constraint after the net load disturbance as a constraint condition; and carrying out square term elimination and uncertainty conversion processing on the constraint conditions, converting the target optimization model into an affine adjustment robust optimization model, converting the affine adjustment robust optimization model into a deterministic model without random parameters, and solving the deterministic model to obtain the optimal unit position and capacity. The method adopts a new reliability cost efficient calculation method, does not need to introduce 0/1 variables, can efficiently calculate the reliability cost, and greatly improves the calculation efficiency of the model.
Description
Technical Field
The invention relates to the technical field of power grid planning, in particular to a power distribution network power supply planning method and system considering an optimal acceptable net load domain.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Building a clean and efficient novel power system is an important target for planning and constructing a power distribution network. Different from the traditional power system, the permeability of renewable energy sources in the novel power system is high, and the high uncertainty caused by the renewable energy sources is one of the core factors to be considered in power supply planning of a power distribution network. Therefore, how to effectively deal with the uncertainty of high proportion is an urgent problem to be solved in power distribution network power supply planning.
Uncertainties considered in the planning problem include uncertainties in renewable energy output, uncertainties in load, uncertainties due to equipment failure, and the like. These uncertainties seriously affect the safety and economy of the system operation after the distribution network is planned, and therefore need to be properly considered in the planning stage. Modeling uncertainty based on the characteristics of the learned uncertainty information can be summarized as follows:
1) only knowing the variation range of the uncertainty, the uncertainty can be described by adopting an interval, and an interval optimization or robust optimization model is further established;
2) when the probability information of the uncertainty is known, the uncertainty can be described by adopting probability distribution or a scene after the probability distribution is dispersed, and models such as random optimization, opportunity constraint planning, cost/benefit compromise optimization and the like are further established.
To deal with the uncertainty caused by source-to-load bilateral power disturbances, one has proposed the concept of node admissible domain. The node admissible domain spatially perturbs the mapping at the source (i.e., the load and renewable energy access nodes) for backup regulation capabilities in the system, i.e., the disturbance rejection capabilities at the payload nodes. In an optimization model considering the node acceptable domain, the node power uncertainty is also regarded as a flexible object which can be optimized instead of fixed parametric information, the range of the object to be optimized in the model is expanded, and the optimal acceptable domain of the node power disturbance comprehensively considering the economy and the reliability can be decided. In addition, compared with the traditional optimization decision of the standby resources, the optimization decision of the node admissible domain fully considers the transfer capability of the standby in the network, and has stronger spatial pertinence.
In the prior art, a double-layer economic dispatching model is established, the safety is taken as a primary target, and an upper-layer target is the sum of node disturbance acceptable domains in a maximized system; and the economy is taken as a secondary target, the lower layer target is the minimum total operation cost of the system, and the sum of the optimal node admissible domains obtained by the upper layer optimization is taken as the constraint of the lower layer optimization, so that the range of the total admissible domain is still ensured. In the prior art, a scheduling model considering the maximum receiving capacity (do-not-exceeded limits) of renewable energy sources is established, and the problem can be converted into a robust optimization model with an optimizable uncertain parameter interval. In order to solve the problem, three modes, namely a fixed participation factor affine strategy, an optimal participation factor affine strategy and an adaptive control strategy, are respectively considered. In the prior art, a scheduling model based on a cost/benefit compromise concept is established, an objective function is to minimize the corresponding operation cost inside an admissible domain and the reliability cost outside the admissible domain, and simultaneously, an optimal admissible domain of an operation base point and a net load of a unit is determined.
However, the above studies have focused on the field of safe and economical operation of large power grids. In the distribution network planning problem, the node net load prediction error is more obvious, so that the research on the node admissible domain is more necessary in the distribution network planning, and the research on the node admissible domain is not considered in the distribution network planning at present.
The cost/benefit tradeoff optimization philosophy is particularly applicable to optimization decisions for node-admissible domains. In the cost/benefit compromise optimization model of the optimal acceptable domain of the decision node, the benefit is often represented by the reduction of the reliability cost corresponding to the external disturbance of the acceptable domain, and the calculation of the reliability cost is the difficulty of the calculation of the optimization model. The reliability cost is usually expressed as a product of a penalty price and a desired energy, such as Expected wind park (EWS)/Expected scarce power (EENS). Under the condition that the probability distribution of the power disturbance is known, the probability distribution is generally piecewise linearized, and 0/1 variables are introduced to each segment to indicate whether the segment has the EENS and the EWS, so that piecewise linear expressions of the EENS and the EWS are obtained. However, when the probability distribution is piecewise linearized, if the number of segments is too small, the calculation errors of the EENS and the EWS are too large; if the number of the segments is too large, in the problem of planning the power supply of the distribution network considering node net load disturbance, because each linear segment of the disturbance probability distribution of each net load node at each moment needs to introduce an 0/1 variable, a large number of 0/1 variables exist in the model, and the calculation efficiency of the model is seriously influenced.
The prior art establishes a unit combination model considering EENS and EWS indexes, and 0/1 variables are not introduced into EENS and EWS index calculation. In the prior art, after the EENS and the EWS are piecewise linearized, the piecewise localization function of the EENS and the EWS is automatically realized through an optimized objective function, however, the admissible domain of a node and the topology of a network are not considered, the total EENS and the EWS of the system are calculated, the EENS and the EWS on the node are not considered, the limitation of network constraints is not considered when the EENS and the EWS are calculated, and the values of the EENS and the EWS are significantly underestimated. In the prior art, after a wind power probability density function is discretized, EENS is further expressed as the product of discrete scene probability and relative load shedding rather than absolute load shedding under a scene, and the EENS value is seriously underestimated by the method.
Disclosure of Invention
In order to solve the problems, the invention provides a power distribution network power supply planning method and system considering an optimal acceptable net load domain, the acceptable net load domain of a node is introduced into power distribution network planning on the basis that the uncertainty of the net load is described by probability distribution, and a novel linear calculation method without introducing 0/1 variables is provided, so that the calculation efficiency of model solution is obviously improved.
In some embodiments, the following technical scheme is adopted:
a power distribution network power supply planning method considering an optimal acceptable net load domain comprises the following steps:
acquiring active and reactive output data, line tide and capacity data and node voltage and phase angle data of a generator set;
establishing a power distribution network power supply planning target optimization model by taking the sum of the minimized annual unit investment cost, the operation cost and the reliability cost as a target and taking the constraint after the net load disturbance as a constraint condition;
and carrying out square term elimination and uncertainty conversion processing on the constraint conditions, converting the target optimization model into an affine adjustment robust optimization model, converting the affine adjustment robust optimization model into a deterministic model without random parameters, and solving the deterministic model to obtain the optimal unit position and capacity.
In other embodiments, the following technical solutions are adopted:
a power distribution network power supply planning system that considers a net load optimal admissible domain, comprising:
the data acquisition module is used for acquiring active and reactive output data, line tide and capacity data and node voltage and phase angle data of the generator set;
the model construction module is used for establishing a power distribution network power supply planning target optimization model by taking the sum of the minimized annual unit investment cost, the operation cost and the reliability cost as a target and taking the constraint after the net load disturbance as a constraint condition;
and the model solving module is used for carrying out square term elimination and uncertainty conversion processing on the constraint conditions, converting the target optimization model into an affine adjustment robust optimization model, then converting the affine adjustment robust optimization model into a deterministic model without random parameters, and solving the deterministic model to obtain the optimal unit position and capacity.
In other embodiments, the following technical solutions are adopted:
a terminal device comprising a processor and a memory, the processor being arranged to implement instructions; the memory is configured to store a plurality of instructions adapted to be loaded by the processor and to perform the method for power distribution network power supply planning considering a payload optimal admissible domain as described above.
In other embodiments, the following technical solutions are adopted:
a computer readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to execute the above-mentioned method of power supply planning for a power distribution network taking into account a payload-optimized admissible domain.
Compared with the prior art, the invention has the beneficial effects that:
(1) the node net load admissible domain is introduced into the distribution network power supply planning problem, and the optimal admissible domain and the distributed power supply construction capacity of the node are determined; a power distribution network power supply planning model considering the net load optimal acceptable domain is provided efficiently. In the model, disturbance inside the optimal demarcation point and system call resources completely respond; and (4) punishing disturbance outside the optimal demarcation point in the objective function through reliability cost.
(2) Compared with the prior reliability cost calculation method, the new method does not need to linearize the known probability density function, replaces the absolute wind curtailment load by the sum of the relative wind curtailment load and does not need to introduce the intercept of 0/1 variable and piecewise linear function, can directly express the reliability cost as a linear primary expression, obviously simplifies the traditional reliability cost expression, can efficiently calculate the reliability cost, and greatly improves the calculation efficiency of the model.
(3) The invention considers that the optimal acceptable domain of the node can directly concern the space disturbance source of the net load, thereby ensuring the economy of planning and the reliability of the operation of the system after planning and realizing good compromise of cost and benefit; the new reliability cost calculation method can efficiently calculate the power loss of each node, greatly improves the calculation efficiency of the model, and has important application value.
Additional features and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
FIG. 1 is a schematic diagram of a net load perturbation probability density function according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a linearization of a probability density function according to an embodiment of the invention;
FIG. 3 is a schematic diagram of the EENS function of piecewise linearity in an embodiment of the present invention;
FIG. 4 is a schematic diagram of the load shedding and receivable domain values;
FIG. 5 is an improved IEEE-33 node system in an embodiment of the present invention;
FIG. 6 is a known active/reactive payload prediction value in an embodiment of the present invention;
FIG. 7 shows the time calculated for cases B and C in the example of the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
Example one
In one or more embodiments, a power distribution network power supply planning method considering an optimal acceptable net load domain is disclosed, and a new power distribution network power supply planning model considering the optimal acceptable net load domain is provided by introducing a node net load acceptable domain into power distribution network planning on the basis of describing net load uncertainty by probability distribution. Disturbance in the acceptable domain, based on the robust idea, calling resources to completely deal with the disturbance; receiving disturbance outside the domain, calculating the corresponding reliability cost, and performing soft punishment in the objective function; and the end points of the receivable domains are determined by the optimization of the compromise of investment cost, internal operation cost and external reliability cost.
When the external reliability cost is calculated, analysis shows that the wind power part with larger disturbance degree amplitude is to be discarded preferentially when wind is discarded, and the load part with larger disturbance degree amplitude is to be cut preferentially when the load is cut. If the net load disturbance probability density function has the characteristic of monotonous change on two sides of the predicted value, the larger the disturbance amplitude of the net load is, the smaller the probability of disturbance occurrence is. According to this rule, the calculation formula of the EENS and the EWS can be further simplified, thereby proposing a new expression of reliability cost calculation without introducing 0/1 variables. And further converting the model into a linear programming problem for solving through technologies such as a dual theory, an alternate iteration heuristic algorithm and the like. The new reliability cost expression avoids the introduction of 0/1 variables, thereby obviously improving the computational efficiency of the model. Finally, based on an IEEE 33 node calculation example of the power distribution network, the effectiveness of the method and the model is proved.
The method of the embodiment specifically comprises the following processes:
(1) acquiring active and reactive output data, line tide and capacity data and node voltage and phase angle data of a generator set;
(2) establishing a power distribution network power supply planning target optimization model by taking the sum of the minimized annual unit investment cost, the operation cost and the reliability cost as a target and taking the constraint after the net load disturbance as a constraint condition;
(3) and carrying out square term elimination and uncertainty conversion processing on the constraint conditions, converting the target optimization model into an affine adjustment robust optimization model, converting the affine adjustment robust optimization model into a deterministic model without random parameters, and solving the deterministic model to obtain the optimal unit position and capacity.
In particular toThe planning target of this embodiment is the location and capacity of the unit. Objective function is minimizing annual unit investment cost C inv Operating cost C oper (including operating cost C) run And spare cost C res ) And a reliability cost C rel The sum is specifically expressed as follows:
min(C inv +d·C oper +d·C rel ) (1)
M g ＝u g (1+u g ) yg /[(1+u g ) yg -1] (3)
in formulae (2) to (4): d is the number of planning typical days; g, t are indexes of the generator set and the optimization time period respectively; n is a radical of G ,
N T The method is characterized by comprising the steps of respectively collecting the existing generator set, the generator set to be expanded and the optimization time period of the system. In formula (2): m g The capital recovery factor for unit g, which can be represented by formula (3);
the initial investment cost of unit g capacity is obtained;
the operation and maintenance cost of the unit g unit capacity generally comprises labor cost and maintenance cost;
the residual value of unit g capacity is obtained; cap g Is the construction capacity of the unit g. In formula (3): u. u g The current rate is the current rate; y is g Is the economic service life of the unit gAnd (4) limiting. In formula (4):
the active and reactive running cost coefficients of the unit g are respectively; p g,t 、Q g,t Respectively setting the active power output reference value and the reactive power output reference value of the unit g in the optimization time period t;
respectively carrying out up-regulation and down-regulation standby cost coefficients on the unit g;
R dng,t and respectively carrying out up-regulation and down-regulation standby values of the unit g in the optimization time period t.
The constraint conditions of the objective function comprise a constraint based on a net load predicted value and a constraint after considering net load disturbance. The constraint based on the net load predicted value is the constraint under the reference value, and uncertainty does not exist; the constraint after the net load disturbance is considered ensures that the physical constraints such as the unit output, the line power flow and the like are not out of limit and have uncertainty after the net load disturbance is considered; both constraints need to be satisfied.
Wherein the constraint based on the net load predicted value is as follows:
1) power balance constraint
The active and reactive power output reference values of the generator set need to be balanced with the active and reactive net load predicted values.
In the formula: i is the node index, N I For all node sets, P fcsti,t ,Q fcsti,t And respectively predicting values of active and reactive net loads in a time period t at the node i.
2) Line flow and capacity constraints
Active power flow and reactive power flow are usually considered in the power distribution network, and the active power flow and the reactive power flow can be simplified into the following linear expressions:
in the formula: p ij,t ,Q ij,t The active power flow reference value and the reactive power flow reference value of the line ij in the time period t; g ij ,b ij The conductance value and susceptance value of the line ij; v i,t ,V j,t A voltage reference value of the nodes i and j in a time period t; theta i,t ,θ j,t Is the phase angle reference value of the nodes i, j in the time period t.
Based on the linear power flow expression (6), the line power flow can be expressed in a form of node injection power, and the specific expression is as follows:
in the formula: k is a node index and has the same meaning as i and j;
the active and reactive power generation load transfer factors of the node k to the line ij; bus (g) k means that unit g is installed at node k. The line capacity constraint may be expressed as follows:
in the formula: s. the maxij Is the upper capacity limit of line ij. The above equation indicates that the line load flow based on the net load prediction should not exceed its upper line capacity limit.
3) Node voltage, phase angle constraints
The matrix relationship of node voltage, phase angle and node injected power can be expressed as follows:
in the formula:
r is a real number matrix. Therefore, in the present embodiment model, equation (9) can be expressed as (10):
in the formula:
H θi,k the power generation load transfer factor for node i, j for voltage and phase angle. Further, equation (11) gives the node voltage, phase angle limit constraints.
In the formula: v maxi ,V mini The upper and lower limits of the voltage at the node i; theta maxi Is the upper limit of angular deviation at node i.
4) Unit output constraint
The unit output constraints in the system are expressed as follows. The upper-level power supply is also regarded as an equivalent unit, and the output of the equivalent unit is limited by factors such as the capacity of a transformer substation.
In the formula: lambda [ alpha ] g P maxg ,λ g P ming The product of the installed capacity coefficient and the upper limit and the lower limit of the active output of the unit represents the upper limit and the lower limit of the actual active output of the unit g. Lambda [ alpha ] g S maxg And the product of the installation coefficient and the upper limit of the apparent power of the unit represents the upper limit of the actual apparent power of the unit g.
5) Alternate adjustment constraints
The power generation units in the system need to meet the following standby regulation constraints:
equation (14) is the reserve capacity adjustment constraint for unit g; equation (15) is a standby justification rate constraint for unit g, where
The maximum climbing rate and the maximum climbing rate of the unit g in a unit time interval are respectively.
The constraints to consider net load disturbances are as follows:
1) power balance constraint
When the net load disturbance is considered, the active and reactive output values after the unit power adjustment need to be balanced with the active and reactive net load values after the disturbance.
In the formula:
in order to consider the active and reactive output values of the unit g in the time period t during disturbance;
to consider the active and reactive net load values at time period t at node i after the disturbance.
2) Line flow and capacity constraints
The line flow constraint after considering the power disturbance can be expressed as follows:
in the formula:
to account for the active and reactive tidal current values of line ij during time period t during a net load disturbance.
3) Node voltage, phase angle constraints
Similar to (10) - (11), the node voltage, phase angle constraint when considering net load disturbances may be represented by (19).
4) Unit output constraint
The above constraints indicate that the unit power when the net load disturbance is considered is still within its output constraints.
5) Standby adjustment capability constraints
The above formula gives the relationship between the up-down spare quantity after the net load disturbance and the output variation of the unit.
In this embodiment, the reliability cost is calculated as follows:
(ii) a net load acceptance capability
The present embodiment combines renewable energy sources with loads into a payload, taking into account its uncertainty. Taking a certain node in the system as an example, it is assumed that the net load disturbance situation of the node i in the time period t is as shown in fig. 1 (here, a normal distribution is taken as an example, and other distributions can be similarly expressed).
In FIG. 1, the abscissa x i,t To take into account the actual value of the net load power at node i after a disturbance, the ordinate Pr (x) i,t ) As a function of its probability density.
,ΔAR Li,t And the sizes of the upper and lower disturbance acceptable domains of the net load of the time period t at the node i are respectively represented, and are non-negative variables to be optimized.
ΔDR Li,t The sizes of the upper and lower perturbation domains of the net load of the time interval t at the node i are respectively expressed, and are given parameters which are not negative. It should be noted that, in the drawing, the shadow on the right side of the receivable domain corresponds to a node payload upper disturbance area that cannot be received by the system, and the shadow on the left side of the receivable domain corresponds to a node payload lower disturbance area that cannot be received by the system.
The uncertainty of the payload of this example is described using a box uncertainty set, expressed as follows:
in the formula:
the random disturbance quantity of the active and reactive net load power which can be responded by the system in the time period t at the node i can be positive or negative; eta i,t Is the proportionality coefficient between the active and reactive net loads in the time period t at the node i. In order to embody the relationship among the node disturbance domain, the node receivable domain and the node net load random disturbance quantity, the following constraints are supplemented:
equation (24) ensures that the node net load random disturbance amount is within the node admissible domain, and the node admissible domain is within the node disturbance domain.
Second expression of traditional reliability cost
The reliability cost of a system when the traditional node net load disturbance exceeds the upper and lower limits of the system acceptable domain can be expressed as follows:
in the formula: pi NL ,π WT The punishment unit price of load shedding cost and wind abandoning cost is respectively.
Wherein the net load disturbance at node i for a period t exceeds the expected energy loss at the upper and lower limits of the node admissible domain, EENS i,t And EWS i,t Can be expressed as follows:
visible, EENS i,t ，EWS i,t Are respectively a variable
As a function of (c). Since the EENS and EWS contain integral signs and are difficult to directly calculate, they can be subjected to piecewise linearization processing. Firstly, introducing a segmentation point to a node perturbation domain, and then calculating the EENS/EWS value at the segmentation point through integral expressions (26) - (27) to further obtain a piecewise linear expression of the EENS/EWS.
The specific linearization process is described below:
1) segmentation of node perturbation domains
Taking the disturbance on the net load of a certain node at a certain time as an example, the graph is shown in fig. 2. Firstly, firstlyThe probability density function curve Pr (x) at the upper limit of the upper disturbance domain up ) Truncation followed by introduction of segmentation points
The upper disturbance domain after being cut off is divided equally to make k up1 And P fcst And (6) overlapping. In fig. 2, 7 segmentation points are introduced schematically to divide the perturbation domain into 6 segments, and the ordinate of the blue point is the function value of the probability density at the segmentation point.
2) Calculation of piecewise Point EENS value and piecewise Linear EENS expression
Due to admissible domain ceiling
The reliability cost cannot be directly calculated for the variable to be optimized. Therefore, the admissible domain is first capped
Coinciding with the segment points, the EENS value of the admissible domain, taken at each discrete point, i.e. the ordinate value of the circle in fig. 3, is determined, which is calculated as follows:
calculating the slope of the piecewise linear EENS function according to the horizontal and vertical coordinate values at the circle point in FIG. 3
And intercept of
The piecewise linear EENS expression is obtained as follows.
In the formula:
to identify the 0/1 variable at node i whether the upper bound of the actual admissible domain during time period t lies in paragraph s. The second and third expressions in the expression (29) ensure that the upper limit coordinates of the acceptable domain can only be taken to a certain line segment of the EENS and not to a plurality of line segments simultaneously. Equation (30) gives the slope
And intercept of
The method of (3). The piecewise linearization of the EWS corresponding to the lower perturbation is similar and will not be described again.
Expression of reliability cost
In the traditional EENS and EWS piecewise linearization process, the more the number of segments is, the more accurate the reliability index numerical value is calculated. However, when the number s of segments is increased, and the number of load nodes i and optimization time t is large, a large number of 0/1 variables are contained in the EENS and EWS linear expressions, and the method needs to calculate the slope and intercept of the segmented linear expressions at the same time, so that the reliability cost expression is complex, the calculation efficiency is significantly reduced, and the value of the method is weakened. Therefore, the method is not suitable for accurate calculation of reliability cost in large power systems.
Therefore, the present embodiment proposes a new reliability index linearization method. According to the method, 0/1 variables are not required to be introduced, the expression of the model is simplified, and the calculation efficiency of the model is greatly improved. It should be noted that the new method proposed in this embodiment is applicable to the case where the probability density function of any uncertainty parameter has monotonicity (monotonicity increasing on the left side, monotonicity decreasing on the right side) on both sides of the expected value, and the probability density function is not required to be axisymmetrically distributed with the expected value.
1) EENS equivalent expression
From the physical point of view, the analysis is carried out in the example of FIG. 4 (for simplicity, the parameter and variable subscripts are omitted from the figure)I, t, if the net load disturbance is too large, the system needs to cut the load, the cut load quantity in the graph is inevitably taken from the disturbance upper limit point (the rightmost end round point) from right to left, the former section is taken to be full, the latter section can be taken, and the upper limit coordinate of the receivable domain can be taken by the same principle
Values must be taken from left to right, starting from the payload prediction point (leftmost dot). FIG. 4 EENS plotted on the left ordinate i,t Is shown as
I.e. (29), right ordinate is EENS i,t Expressed as the tangential load
The lower left/right arrows show
And
and the sum of the two is the total disturbance quantity on the net load of the node
Based on the above analysis, the length Δ k of each segment after uniform segmentation can be introduced upi,t EENS i,t From
Is rewritten as
To convert expression (29) to (31):
in the formula:
the load is taken as the value of the segmented load cutting amount. In the formula (31), the segment S needs to be fetched from right to left, i.e. the index S is from S max -1 starts to get 1 in descending order; 0/1 variable in second and third expressions
The existence of the (B) ensures that the tangential load must be taken from right to left, namely the tangential load is along the lower part P of the figure 4 NL The direction from right to left is monotonously valued. The fourth expression ensures that the total load shedding amount is the sum of the load shedding amounts of all the segments. The equation still contains a large number of 0/1 variables, and the solution is complex.
Since the reliability cost is minimized in the objective function, the EENS tends to be minimized. When the number of segments s changes from right to left, i.e. the index s takes values in descending order from large to small, if the following assumption condition is satisfied: slope of EENS expression in equation (31)
Constantly positive and monotonically increasing with the decreasing value of s, the increment of the corresponding EENS in each uniform segment
Monotonically increasing with decreasing values of s, i.e. inequality
This is true. At this time, if the load is cut
Is present to cause the appearance of EENS, then
The EENS corresponding to the right segment is taken from the right to the left, namely the EENS corresponding to the left segment begins to take the value after the EENS corresponding to the right segment is fully taken. In short, if the above assumptions are satisfied, the optimization model implies a phenomenon that the tangential load is inevitably taken from right to left. This and the introduction 0/1 in (31)Variables of
So that the 0/1 variables in (31) overlap
Can be deleted, whereby (31) can be expressed further simply as follows:
it can be seen from comparison of (29), (31) and (32) that there is no 0/1 variable in EENS in (32), and the expression is more concise.
The processing procedure of the EWS is consistent with the EENS, and the EWS is processed i,t From Δ AR Li,t The function of (a) is rewritten into a value delta P of the sectional air abandoning quantity WTs,i,t 0/1 variable is deleted.
2) Demonstration of piecewise linear EENS monotonicity
The above simplification from (31) to (32) is based on the assumption that: (31) middle slope
Is constant positive and monotonically increasing as s is valued in decreasing order. This assumption is always true, which is demonstrated below.
As can be seen from the view of figure 4,
the values increase monotonically with decreasing order of s. As can be seen in connection with expression (31),
is always a positive number. And (3) performing difference on two adjacent slope values:
when in use
In the case of a strictly convex function, equation (33) must be greater than 0, i.e., the slope monotonically increases. Due to the function
Is only that
Thus can pass through
About
Second derivative determination of
The concavity and convexity of (d):
in the formula:
is a known probability density function, therefore (34) is constantly greater than 0, further yielding
For a strictly convex function, so that (33) constantly greater than 0 holds, the slope
The constant positive and monotonically increasing conclusion is warranted.
3) Novel expression of reliability cost
Since the reliability cost calculation mechanism is completely the same when the net load is disturbed up/down, according to the EENS simplified calculation formula (32) in 2), a simplified linear expression (35) of the total reliability cost of the system can be obtained:
in the formula:
ΔP WTs,i,t the load and the air abandon quantity are continuously cut in a section within a time period t at the node i. Through the above conversion process, the reliability cost expression is converted from (25-27) to (35). Compared with the traditional reliability cost expression, the expression only introduces the slope of the sectional EENS and the EWS linear function and the sectional wind curtailment load shedding variable, and can eliminate the integral number without introducing the sectional EENS, the intercept of the EWS linear function and the 0/1 variable of sectional positioning, so that the model is obviously simplified. In addition, compared with the traditional EENS and EWS simplified calculation expression, the expression can efficiently calculate the EENS and the EWS at each time section of each node after considering the network topology constraint, can directly focus on the source of space disturbance, and is suitable for a large-scale power system.
In this embodiment, the converting the constraint condition specifically includes:
(ii) constraining the squaring term to linearize
In the model constraints (8), (13), (18), (21), non-linear square terms exist, and the square terms are eliminated by adopting a power circle linearization method in the embodiment. Taking (21) as an example, equation (21) can be converted into equation (36), and similar constraints (8), (13), and (18) can be eliminated by the same method, and are not described herein again for simplicity.
In the formula: m is the number of segments of a polyhedron inscribed in a power circle;
δ 2m ,δ 3m and the coefficients are corresponding to the selected inscribed polyhedron.
② uncertainty conversion treatment
The box type of this embodiment is not exactThe introduction of a set (23) is carried out, so that the constraint conditions of the model contain random parameters
And
it is difficult to solve directly. Therefore, the embodiment adopts an affine strategy to construct an affine relationship between the power variation of the unit and the net load disturbance power, establish an affine adjustment robust optimization model, and perform conversion processing on the constraint, and the specific steps are as follows:
1) constructing affine relationships
Assuming an affine relationship between the net load disturbance and the machine set contribution adjustment, as shown in (37):
in the formula:
the method comprises the steps of (1) considering the power adjustment quantity of a unit g after net load disturbance in a time period t; rho Pg,t ,ρ Qg,t And (4) responding to the distribution coefficient of the net load active/reactive disturbance for the unit g in the time period t. The backup justification capability constraint (22) may be translated into (39):
after the processing, the original model is converted into an affine adjustment robust optimization model. The system power balance (16) containing only random parameters is automatically satisfied, and the random parameters in the model only appear in inequality, thereby being convenient for further solving.
2) Model processing
In order to convert the affine adjustment robust optimization model into a deterministic model, an auxiliary variable v is introduced i,t ∈[0,1]To eliminate random parameters in the model. The power random perturbation can be expressed as follows:
processing inequality constraints with random parameters. Taking (36) as an example, substituting (37) and (40) into (36), the optimization problem can be expressed as follows:
in the formula: the max sign is used to find the solution, ω, under the worst disturbance condition i,g,t,m Are dual variables. According to dual theory, the optimization problem (41) can be converted into the following equation:
the same transformation procedures can be used for the formulae (18) to (19), and for the sake of brevity, the details are not repeated here.
After the processing, the affine adjustment robust optimization model is converted into a deterministic model without random parameters. The deterministic model still has nonlinear terms, the nonlinear terms are caused by multiplication of continuous distribution coefficient variables and receivable domain variables, and the nonlinear terms cannot be solved directly through a linear solver.
The method adopts an alternate iteration heuristic algorithm, converts the original bilinear problem into iterative solution of two linear optimization problems, thereby realizing the joint optimization of the distribution coefficient and the receivable domain, having the characteristic of high convergence speed and being capable of obtaining better optimization effect. At this time, the original simulation adjustment robust optimization model is converted into a deterministic linear optimization model, and an existing linear business solver can be called to solve the problem.
The distribution coefficient is a proportion coefficient of each unit corresponding to disturbance, the distribution coefficient of the unit is a proportion coefficient of the unit corresponding to net load disturbance, and the sum of the distribution coefficients of all the units is equal to 1 and is a variable to be optimized.
The admissible domain is the ability at a node to handle disturbances in power, and the effective admissible domain is within a given known disturbance domain. The admissible domain at a node is a mapping of the unit output at the source of the disturbance.
Example analysis
This embodiment was tested on a modified IEEE-33 node power distribution network system, the topology of which is shown in fig. 5, consisting of 33 nodes and 32 lines. Assuming that no distributed adjustable power supply exists in the system before planning, the initial power generation resources only comprise an upper-level power grid and part of wind turbines. The example is planned based on a typical day, and the predicted net load value of 24h in the day is shown in fig. 6. The node 1 is selected as a reference node, the upper limit and the lower limit of the node voltage are set to be 1.05p.u./0.95p.u., and the phase angle variation range is [ -180 degrees, 180 degrees ]. The controllable DG to be expanded in the model can be constructed at nodes numbered 6, 9, 13, 17, 21, 24, 27 and 31 in fig. 5, and the upper limit of installed capacity of each node is set to 1MW, and the detailed data is shown in table 1.
TABLE 1 Power Generation Unit specific data
Assuming that the net load disturbance of each node i in each optimization period t is subject to normal distribution
Wherein the mean value mu i,t Taking the predicted value P of the net load fcsti,t Standard deviation σ i,t Set to 5% of the predicted payload. Since the probability of disturbance of the normally distributed parameters within three standard deviations is 99.74%, the vast majority of the disturbance has been covered, so the embodiment is within + -3 sigma i,t Is cut off from the normal distribution, i.e.
ΔDR Li,t Are all taken as 3 sigma i,t (ii) a Net load disturbance proportionality coefficient eta i,t The ratio of the reactive payload to the active payload prediction value in fig. 6 is taken.
Initial investment cost of controllable DG unit volume
The cost of operation and maintenance is 1500000$/MW
Taking 3% of initial investment cost and residual value of equipment
Taking 5% of the initial investment cost; typical number of days d is 365 days, and discount rate u g 6 percent of the total economic service life y g Taking for 20 years; the up/down standby cost unit price provided by the controllable DG is 10% of the highest marginal cost, and the reactive operation cost coefficient
Set as an active operating cost coefficient
10% of; unit punishment price pi NL Taking 5000$/MWh, pi WT Get 500$/MWh, S when reliability cost is piecewise linearized max And 7, taking.
The model provided by the embodiment calls a CPLEX solver to solve based on GAMS optimization platform programming. The used computer is configured to be a Win10 system, the main frequency is 3.2GHz, the memory is 16GB, and the convergence precision is set to be 0.01%.
The node optimally accepts the impact of the domain:
in order to analyze the influence of the introduction of the node optimal admissible domain on the planning result and the cost of each part, the present embodiment provides the following calculation scenario:
and (3) CaseA: the node admissible domain is not considered, the safety and reliability are taken as the primary targets, namely the disturbance in the node perturbation domain needs to call the absolute response of system resources, the wind curtailment and load shedding are not allowed, and the reliability cost is 0. At this time, the whole optimization model is a Linear Programming (LP) model, and a CPLEX solver is called to solve the model.
And (3) CaseB: considering the node optimal admissible domain, the reliability cost calculation uses the traditional expression (29) containing 0/1 variables. At this time, the optimization model is a Mixed Integer Linear Programming (MILP) model, and a CPLEX solver is called to solve the model.
After the optimization, the planning results of Case a and B are shown in table 2, and the cost results are shown in table 3. For the sake of simplicity, the node information of the set which is not built is not shown.
TABLE 2Case A, B planning results
TABLE 3Case A, B cost results
As can be seen from table 2, compared to Case B, Case a selects fewer nodes for building DG, but increases the total planned building capacity by 6.93%, because in the cost/benefit tradeoff method considering the domain that the nodes can optimally accept, the system does not call resource responses, but penalizes in the objective function, where the net load disturbance occurrence probability is smaller. Therefore, the model considering the node optimal acceptable domain has relatively low requirement on system resources, and the investment cost can be reduced.
As can be seen from Table 3, the operation cost of Case B is substantially unchanged compared to Case A, and the remaining costs, except for the reliability cost, are reduced to different extents. Because the receivable domain of the net load disturbance is optimized and decided by the Case B, the complete acceptance of the net load disturbance is not required to be ensured, so that the demand of the model in the Case B on standby resources is relatively low, and the standby cost is reduced by 24.5%. Although Case B increases the reliability cost, the part of the cost is caused by the unresponsiveness of the net load disturbance outside the optimal admissible domain, the probability weighted value is small, the occurrence probability is low, and the influence on the reliability of the planned system is small. In addition, the investment cost of Case B is reduced by 6.51% compared with that of Case A. In conclusion, the planning model considering the node optimal acceptable domain can ensure the economy of planning and the reliability of system operation after planning, and has higher application value.
The effectiveness analysis of the new linearization method:
to analyze the effectiveness of the simplified linearization method proposed in this embodiment, this embodiment supplements the following example scenario:
case C: the new method for introducing the piecewise admissible domain proposed by the embodiment is adopted in the reliability cost linearization calculation by considering the node optimal admissible domain. At this time, the whole optimization model has no 0/1 variable, is an LP model, and calls a CPLEX solver to solve.
This example compares cases B, C. As the number of segments of the net load up/down perturbation domain gradually increases, the planning results of Case B, C are shown in Table 4, the calculation time pair is shown in FIG. 7, and the cost result pair is shown in Table 5.
TABLE 4Case B, C planning results
With the increase of the number of the segments, the planning results of the two linearization methods are completely the same, thereby verifying the effectiveness of the linearization method provided by the embodiment. From the planning results in table 4, it can be found that the planning capacity generally decreases with the increase of the number of segments, and when the number of segments is greater than 15, the planning total capacity tends to be unchanged, which indicates that the reliability cost is more accurately calculated when the number of segments is greater than 15, and the error of the number of segments is no longer a factor affecting the planning result.
From the calculation time of fig. 7, it can be seen that: with the increase of the number of the segments, the calculation efficiency is obviously reduced due to the fact that more 0/1 variables are introduced into the reliability cost calculation of Case B; when the number of segments is greater than 15, it can be known from table 4 that the power source planning result does not change any more, but the calculation efficiency decreases faster as the number of segments increases; the 0/1 variable is not introduced into the Case C cost calculation, and the calculation efficiency of the Case C cost calculation does not change greatly. When the number of segments is 15, the calculation efficiency of Case C compared with Case B is improved by 58.7%; when the number of segments was 18, the computational efficiency of Case C compared to Case B was improved by 61.9%. Therefore, in the model of this embodiment, a new reliability cost linearization method is adopted, and the number of segments is set to 15, so that not only better accuracy but also higher solving efficiency can be obtained.
TABLE 5Case B, C cost results
Comparing the cost results of Case B and C, it can be known that the cost results of the two linearization methods are basically the same as the number of segments increases, wherein the reliability cost calculation is more precise and gradually approaches to a stable value, and the effectiveness of the linearization method provided by the embodiment is further verified. When the number of segments is greater than 15, the cost of each segment is substantially unchanged. Therefore, in the model of this embodiment, a new reliability cost linearization method is adopted, and the number of segments is set to 15, so that not only better accuracy but also higher solving efficiency can be obtained.
Example two
In one or more embodiments, a power distribution network power supply planning system considering a net load optimal admissible domain is disclosed, comprising:
the data acquisition module is used for acquiring active and reactive output data, line tide and capacity data and node voltage and phase angle data of the generator set;
the model construction module is used for establishing a power distribution network power supply planning target optimization model by taking the sum of the minimized annual unit investment cost, the operation cost and the reliability cost as a target and taking the constraint after the net load disturbance as a constraint condition;
and the model solving module is used for carrying out square term elimination and uncertainty conversion processing on the constraint conditions, converting the target optimization model into an affine adjustment robust optimization model, then converting the affine adjustment robust optimization model into a deterministic model without random parameters, and solving the deterministic model to obtain the optimal unit position and capacity.
It should be noted that, the specific implementation of each module described above has been described in detail in the first embodiment, and is not described in detail here.
EXAMPLE III
In one or more embodiments, a terminal device is disclosed that includes a processor and a memory, the processor to implement instructions; the memory is configured to store a plurality of instructions adapted to be loaded by the processor and to perform the method for power supply planning for a power distribution network considering a net load optimal admissible domain as described in the first embodiment.
Example four
In one or more embodiments, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored, the instructions being adapted to be loaded by a processor of a terminal device and to perform the method for power supply planning of a power distribution network considering a net load optimal admissible domain as described in the first embodiment.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (10)
1. A power distribution network power supply planning method considering an optimal admissible domain of a net load is characterized by comprising the following steps:
acquiring active and reactive output data, line tide and capacity data and node voltage and phase angle data of a generator set;
establishing a power distribution network power supply planning target optimization model by taking the sum of the minimized annual unit investment cost, the operation cost and the reliability cost as a target and taking the constraint after the net load disturbance as a constraint condition;
and carrying out square term elimination and uncertainty conversion processing on the constraint conditions, converting the target optimization model into an affine adjustment robust optimization model, converting the affine adjustment robust optimization model into a deterministic model without random parameters, and solving the deterministic model to obtain the optimal unit position and capacity.
2. The method according to claim 1, wherein the reliability cost is calculated by considering a net load optimal admissible domain as follows:
introducing a subsection point into a node disturbance domain, calculating an expected power shortage EENS/expected air abandoning amount EWS value at the subsection point, and further solving a piecewise linear expression of the EENS/EWS;
introducing the length of each segment after uniform segmentation, and EENS i,t From
Rewriting the function of (A) into the value of the segment load-cutting quantity
Is a function of, will EWS i,t From Δ AR Li,t The function of (a) is rewritten into a value delta P of the sectional air abandoning quantity WTs,i,t The 0/1 variable is removed, resulting in a simplified overall system reliability cost.
3. The method for planning a power distribution network power supply considering a net load optimal admissible domain as claimed in claim 2, wherein the simplified total system reliability cost is specifically:
wherein, C rel For reliability cost, pi NL ,π WT Respectively the punishment unit price of load shedding cost and wind abandoning cost,S max the number of the segmentation points is shown,
respectively taking the values of the sectional load cutting quantity and the sectional air abandoning quantity,
respectively taking the values of the total load capacity and the air abandoning capacity,
the slopes of the piecewise linear EENS and EWS functions in segment s,
each segment length of the upper disturbance and the lower disturbance after the uniform segmentation is respectively a given parameter.
4. The method according to claim 1, wherein the considering of constraints after the net load disturbance includes:
and considering power balance constraint, line tide and capacity constraint, node voltage, phase angle constraint, unit output constraint and standby adjustment capability constraint after net load disturbance.
5. The method for planning a power distribution network power supply considering the net load optimal admissible domain according to claim 1, wherein the process of eliminating the square term and converting uncertainty for the constraint conditions comprises:
eliminating a square term in a constraint condition by adopting a power circle linearization method;
an affine strategy is adopted, an affine relation between the power variation of the unit and the net load disturbance power is constructed, and an affine adjustment robust optimization model is established.
6. The method of claim 1, wherein the auxiliary variable v is introduced into the power distribution network power supply planning method taking into account the net load optimal admissible domain i,t ∈[0,1]Processing inequality constraints with random parameters to eliminate the random parameters in the model; thereby converting the affine adjustment robust optimization model into a deterministic model without random parameters.
7. The method for planning a power distribution network power supply considering an optimal admissible domain of a payload as claimed in claim 1, wherein the deterministic model is solved to obtain an optimal unit position and capacity, specifically:
and (3) converting the original bilinear problem into iterative solution of two linear optimization problems by adopting an alternate iteration heuristic algorithm, thereby realizing the joint optimization of the distribution coefficient and the receivable domain and further obtaining the optimal result of the position and the capacity of the unit.
8. A power distribution network power supply planning system that considers an optimally acceptable net load domain, comprising:
the data acquisition module is used for acquiring active and reactive output data, line tide and capacity data and node voltage and phase angle data of the generator set;
the model construction module is used for establishing a power distribution network power supply planning target optimization model by taking the sum of the minimized annual unit investment cost, the operation cost and the reliability cost as a target and taking the constraint after the net load disturbance as a constraint condition;
and the model solving module is used for carrying out square term elimination and uncertainty conversion processing on the constraint conditions, converting the target optimization model into an affine adjustment robust optimization model, then converting the affine adjustment robust optimization model into a deterministic model without random parameters, and solving the deterministic model to obtain the optimal unit position and capacity.
9. A terminal device comprising a processor and a memory, the processor being arranged to implement instructions; the memory for storing a plurality of instructions, wherein the instructions are adapted to be loaded by the processor and to perform the method for power supply planning for a power distribution network in view of a payload optimized admissible domain as claimed in any of claims 1-7.
10. A computer-readable storage medium, in which a plurality of instructions are stored, characterized in that said instructions are adapted to be loaded by a processor of a terminal device and to perform the method for power supply planning of a power distribution network taking into account a net load optimally receivable domain according to any of the claims 1-7.
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