CN116611192A - Flexible power distribution network random expansion planning method and system considering operation risk - Google Patents
Flexible power distribution network random expansion planning method and system considering operation risk Download PDFInfo
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Abstract
The invention relates to a flexible power distribution network random expansion planning method and system considering operation risk, wherein the method comprises the following steps: constructing an uncertainty factor probability distribution model of the flexible power distribution network; based on the flexible power distribution network uncertainty factor probability distribution model, introducing a conditional risk value theory, and constructing a flexible power distribution network energy-abandoning load-shedding conditional risk constraint; constructing a flexible power distribution network two-stage random expansion planning model, wherein the flexible power distribution network two-stage random expansion planning model aims at minimizing annual comprehensive cost, and constraint conditions comprise risk constraint of the flexible power distribution network energy-abandoning load-shedding condition; and solving the two-stage random expansion planning model of the flexible power distribution network to obtain an optimal planning scheme. Compared with the prior art, the invention can effectively improve the distributed renewable energy source consumption level of the flexible power distribution network, reduce the load shedding risk, exert the power flow regulating capability of the multi-terminal intelligent soft switch, and simultaneously show good performance in the aspects of economy and risk resistance.
Description
Technical Field
The invention relates to the technical field of power distribution networks, in particular to a random expansion planning method and system for a flexible power distribution network, which are used for considering operation risks.
Background
Compared with the traditional mechanical switch, the multi-terminal intelligent soft switch avoids potential safety hazards caused by frequent deflection, realizes flexible and rapid adjustment of network power flow of the power distribution network, ensures that the network morphological structure of the power distribution network is more flexible, and integrates the advantages of radial and ring network power supply modes. In addition, the multi-terminal intelligent soft switch is connected into the power distribution network, so that the functions of reducing network loss, balancing feeder load, improving power supply reliability, providing voltage reactive power support, promoting distributed renewable energy consumption and the like can be achieved. With the wide application of flexible interconnection devices represented by multi-terminal intelligent soft switches in power distribution networks, conventional power distribution networks are evolving towards flexible power distribution networks. Patent application CN105449713a discloses an active power distribution network intelligent soft switch planning method considering the characteristics of a distributed power source, and the access of a flexible power electronic device is considered in a planning layer. But the uncertain factors in the power distribution network are continuously increased, so that the applicability of the planning method is affected.
For example, fluctuation and intermittence of distributed renewable energy source output and randomness of diversified load electricity consumption exacerbate the 'source-load' supply and demand mismatch degree of a flexible power distribution network, so that part of renewable energy sources may not be effectively consumed, part of user electric energy supply cannot be reliably ensured, and the problems of energy abandoning and load cutting are serious. Therefore, how to further solve the problems of energy abandoning and load shedding in the planning stage with prospective and global perspectives, and reduce the operation risk caused by uncertainty factors becomes an important task of flexible power distribution network expansion planning.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a random expansion planning method and a random expansion planning system for a flexible power distribution network, which take operational risk into account, and can provide guarantee for the flexible power distribution network to effectively cope with 'source-load' uncertainty and properly avoid the operational risk.
The aim of the invention can be achieved by the following technical scheme:
the invention provides a random expansion planning method of a flexible power distribution network considering operation risk, which is applied to the flexible power distribution network with multi-terminal intelligent soft switch and comprises the following steps:
constructing an uncertainty factor probability distribution model of the flexible power distribution network;
based on the flexible power distribution network uncertainty factor probability distribution model, introducing a conditional risk value theory, and constructing a flexible power distribution network energy-abandoning load-shedding conditional risk constraint;
constructing a flexible power distribution network two-stage random expansion planning model, wherein the flexible power distribution network two-stage random expansion planning model aims at minimizing annual comprehensive cost, and constraint conditions comprise risk constraint of the flexible power distribution network energy-abandoning load-shedding condition;
and solving the two-stage random expansion planning model of the flexible power distribution network to obtain an optimal planning scheme.
Further, the flexible power distribution network uncertainty factors include distributed renewable energy source output and load power.
Further, the flexible power distribution network energy-abandoning load-shedding condition risk constraint is expressed as:
0≤CVaR β (x)≤q CVaR
wherein CVaR is as follows β (x) Representing the CVaR value of the loss function f (x, y) at a given confidence level β, x being a decision vector, y being a random vector that triggers an uncertainty event, q CVaR Is a conditional risk threshold.
Further, the flexible power distribution network uncertainty factor probability distribution model comprises a wind speed and distributed wind power output probability distribution model, an illumination intensity and distributed photovoltaic output probability distribution model and a load power uncertainty probability distribution model;
the flexible power distribution network energy discarding and load shedding condition risk constraint comprises a distributed wind power energy discarding condition risk constraint, a distributed photovoltaic energy discarding condition risk constraint and an end user load shedding condition risk constraint.
Further, constraint conditions of the two-stage random expansion planning model of the flexible power distribution network further comprise equipment investment construction constraint, network topology structure constraint and flexible power distribution network operation safety constraint.
Further, in the two-stage random expansion planning model of the flexible power distribution network, the first stage is to acquire an investment decision for equipment, and the second stage is to perform simulation operation optimization on each random scene after determining the investment decision.
Further, the apparatus includes one or more of a transformer, a line, a multi-terminal intelligent soft switch, distributed wind power, distributed photovoltaic, a static var compensator.
Further, solving the two-stage random expansion planning model of the flexible power distribution network by adopting an algorithm framework based on Benders decomposition, and specifically comprises the following steps:
dividing a solving problem of a two-stage random expansion planning model of the flexible power distribution network into a main problem and a sub-problem, wherein the main problem is used for determining the investment decision, and the sub-problem is a simulation running problem in a random scene and is used for solving the optimal running state of the flexible power distribution network;
solving the sub-problem after determining the investment decision, introducing auxiliary variables into the main problem, adding a cutting set containing dual variables of the sub-problem, and feeding back the optimization result of the sub-problem to the main problem in the successive iteration process to finish the solution.
The invention also provides a flexible power distribution network random expansion planning system considering operation risk, which comprises a memory, a processor and computer program instructions stored on the memory and capable of being operated by the processor, wherein the method steps are realized when the processor operates the computer program instructions.
The present invention also provides a computer readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, the one or more programs comprising instructions for performing the method as described above.
Compared with the prior art, the invention has the following beneficial effects:
1. the flexible power distribution network uncertainty factor probability distribution model is built, uncertainty of distributed renewable energy sources and loads can be accurately described, a foundation is laid for optimizing planning of the flexible power distribution network, and planning reliability is improved.
2. According to the invention, based on a conditional risk value theory, a flexible power distribution network energy-abandoning load-shedding conditional risk constraint is constructed, the operation risk under a certain confidence level can be reasonably controlled, and the expected operation risk exceeding the given confidence level can be fully considered.
3. According to the invention, a planning scheme is obtained by the established two-stage random expansion planning model of the flexible power distribution network, so that the distributed renewable energy consumption of the flexible power distribution network can be effectively promoted, the distributed renewable energy consumption level of the flexible power distribution network is effectively improved, the load shedding risk is reduced, and the risk coping capability of the flexible power distribution network is improved while the economy is ensured.
4. According to the application, the algorithm framework based on the Benders decomposition is adopted for solving, so that the solving efficiency can be effectively improved.
5. By implementing the method, the power flow regulating capability of the multi-terminal intelligent soft switch can be exerted, and meanwhile, the method has good performance in the aspects of economy and risk resistance.
Drawings
Fig. 1 is a schematic diagram of a random expansion planning flow of a flexible power distribution network according to an embodiment of the present application;
fig. 2 is a two-stage stochastic expansion planning solution flow chart of a flexible power distribution network according to an embodiment of the application;
FIG. 3 is a schematic diagram of an example system of a flexible distribution network according to an embodiment of the present application;
FIG. 4 is a graph of load, photovoltaic, wind power history data for an embodiment of the present application;
fig. 5 is an influence diagram of risk weight coefficients on a random expansion planning result of a flexible power distribution network according to an embodiment of the present application.
Detailed Description
The application will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present application, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present application is not limited to the following examples.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
As shown in fig. 1, this embodiment provides a flexible power distribution network random expansion planning method including multi-terminal intelligent soft switches, which takes operational risk into account, and includes:
step S1: and constructing an uncertainty factor probability distribution model of the flexible power distribution network.
The uncertainty factors of the flexible power distribution network considered in the embodiment comprise distributed renewable energy sources such as distributed wind power, distributed photovoltaic and the like, and load power. Correspondingly, the flexible power distribution network uncertainty factor probability distribution model comprises a wind speed and distributed wind power output probability distribution model, an illumination intensity and distributed photovoltaic output probability distribution model and a load power uncertainty probability distribution model.
1) Wind speed and distributed wind power output probability distribution model
The wind speed is fitted by adopting the double-parameter Weibull distribution with ideal application effect in practice, and the probability density function is as follows:
wherein: k is a shape parameter reflecting the asymmetry of wind speed distribution; c is a scale parameter reflecting the expected mean of wind speed.
In general, under the condition of standard air density, the relation between the output and the wind speed of the distributed wind turbine unit can be expressed as follows:
wherein: p (P) WTG Representing active power of the distributed wind turbine generator;representing rated power of the distributed wind turbine generator; v ci 、v r And v co And respectively representing the cut-in wind speed, the rated wind speed and the cut-out wind speed of the distributed wind turbine generator.
If the distributed wind turbine runs according to a constant power factor, the reactive power of the distributed wind turbine is as follows:
wherein:and the power factor angle of the distributed wind turbine generator is represented.
2) Probability distribution model for illumination intensity and distributed photovoltaic output
It is generally considered that the illumination intensity within a certain period approximately follows the Beta distribution, and the probability density distribution function is:
wherein: r represents the actual illumination intensity, r max Representing its maximum value; Γ represents a Gamma function; a and b are both shape parameters of the Beta distribution.
The relationship between the distributed photovoltaic output and the illumination intensity can be approximated as:
wherein:and r rated Respectively representing the rated capacity and the rated value of the illumination intensity of the distributed photovoltaic.
If the distributed photovoltaic is controlled by a constant power factor, the reactive power of the distributed photovoltaic is as follows:
wherein:representing the power factor angle of the distributed photovoltaic system.
3) Load power uncertainty probability distribution model
The uncertainty of the load prediction error is described by selecting a common normal distribution, and the probability density function is as follows:
wherein: mu (mu) P Sum sigma P Respectively representing the expected and standard deviations of the load active power prediction errors; mu (mu) Q Sum sigma Q The expected and standard deviations of the load reactive power prediction errors are represented, respectively.
Step S2: based on the flexible power distribution network uncertainty factor probability distribution model, a conditional risk value theory is introduced, and a flexible power distribution network energy-abandoning load-shedding conditional risk constraint is constructed.
In the embodiment, a condition risk value (conditional value-at-risk, CVaR) theory is introduced to describe the tail risk brought by various uncertainty factors to the flexible power distribution network planning and operation.
For any decision vector x, let the uncertainty event be caused by a random vector y, and the loss function caused by the uncertainty event be f (x, y), ρ (y) be the probability density function of the random vector y, and the probability that the loss function f (x, y) does not exceed the loss threshold α is shown as (8).
ψ(x,α)＝∫ f(x,y)≤α ρ(y)dy (8)
Wherein: ψ (x, α) is a function of α at any fixed x, and has properties of monotonically non-decreasing and right continuous.
Given the confidence level β, the risk value (VaR) of the loss function f (x, y) may be defined as shown in equation (9), i.e., representing the potential maximum loss due to uncertainty factors at a certain confidence level.
Wherein: vaR (Var) β (x) Indicating that P is satisfied r [f(x,y)≤α]Alpha minimum value of ≡beta, here P r [·]Representing the probability of an event occurring.
Based on equation (9), the higher than VaR portions of the loss function f (x, y) are averaged to obtain the CVaR value for f (x, y) at a given confidence level β, as shown in equation (10).
Wherein: CVaR (Compound CVaR) β (x) Indicating all of the satisfaction P r [f(x,y)≤α]And (3) the expected value of alpha under the condition of beta.
Based on equations (9) and (10), vaR and CVaR are calculated for the distributed renewable energy waste and cut loads, respectively. Considering uncertainty of distributed wind power, photovoltaic and load power in flexible power distribution network, under the condition that given confidence level is beta, simultaneously setting risk threshold q of energy discarding and load shedding conditions CVaR Therefore, the distributed renewable energy waste energy and flexible power distribution network load shedding condition risk constraint shown by the formula (11) is established.
Wherein: the decision vector x represents a planning scheme of the flexible power distribution network; the random vector y represents the output and load power of renewable energy sources such as distributed wind power, photovoltaic and the like in the flexible power distribution network; ρ (y) represents a joint probability density function of y; f (x, y) represents the distributed renewable energy waste energy and cut load due to uncertainty when the planning scheme is x and the distributed wind power, photovoltaic output or load demand is y.
To solve the problem that the integral term in the formula (11) leads to non-convex nonlinearity of the planning model and is difficult to directly and effectively solve, a transformation function F shown as the formula (12) is further introduced β (x, α) the process of solving for the CVaR value is linearized.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
to further discretize the integration process in equation (12), the probability density function may be randomly sampled using historical data or using Monte Carlo simulation methods to integrate the term ≡ [ f (x, y) - α] + ρ (y) dy is converted into a linear combination of transform functions in multiple scenarios. The transformation function can thus be reduced to the expression (14) given in u scenarios.
Accordingly, the CVaR constraint should be converted to equation (15):
in addition, if let Z u ＝[f(x,y u )-α] + Then there is Z u Not less than 0 and Z u ≥f(x,y u )-α。
Therefore, in the flexible power distribution network expansion planning problem, conditional risk constraint can be constructed for risks of energy rejection of different types of distributed renewable energy sources or load shedding of power users according to the form of a formula (15).
Step S3: and constructing a two-stage random expansion planning model of the flexible power distribution network by taking the minimum annual comprehensive cost as a target and taking constraint conditions including the risk constraint of the energy rejection load shedding condition of the flexible power distribution network as constraints.
A flexible power distribution network random expansion planning model considering operation risks takes the minimum annual comprehensive cost in a planning period as an objective function, and comprises the step of converting the annual planning investment cost C INV And simulated operating cost C OPE As shown in formula (16). C (C) INV The method comprises the steps of newly-built and capacity-expanded cost of a transformer substation, newly-built cost of a circuit, investment cost of a multi-terminal intelligent soft switch, distributed wind power investment cost, distributed photovoltaic investment cost and investment cost of a static reactive compensator, and C OPE Including various equipment operation and maintenance costs C OM Higher power grid purchase cost C PU Punishment cost C corresponding to wind discarding, light discarding and load shedding CUR Wherein C CUR Including the expected penalty value and the CVaR tail risk value. The specific calculation method is as follows:
min F＝C INV +C OPE (16)
C OPE ＝C OM +C PU +C CUR (18)
wherein:a present value-to-equal annual value coefficient representing the device o; r represents the discount rate;indicating the economic life of the device o; omega shape U And omega T Respectively representing a typical day scene and a simulated running period set; u and t represent the current typical day scene and time period, respectively; p is p u Probability of being the u-th typical day scene; psi S 、Ψ S0 、Ψ L 、Ψ N 、Ψ SOP 、Ψ PVG 、Ψ WTG And psi is SVC The method comprises the steps of respectively representing a node set of a transformer substation to be newly built, a node set of a transformer substation to be expanded, a line set, a load node set, an intelligent soft switch node set to be selected, a distributed photovoltaic node set to be selected, a distributed wind power node set to be selected and a static reactive compensator node set to be selected; />And c L The new construction cost of the transformer substation, the capacity expansion cost of the transformer substation and the new construction cost of the unit length line are respectively represented; c SOP 、c PVG 、c WTG And c SVC The unit capacity investment cost of the intelligent soft switch, the distributed photovoltaic, the distributed wind power and the static var compensator is respectively represented; />And->Decision variables of new construction of a transformer substation, capacity expansion of the transformer substation and new construction of a circuit are respectively determined; />And->Decision variables of the installation quantity of the intelligent soft switch, the distributed photovoltaic, the distributed wind power and the static var compensator are respectively determined; l (L) ij Representing the length of the line ij; />Representing active power transmitted by a transformer substation; />And->Respectively representing distributed photovoltaic and distributed wind power active output; />And->Representing annual operation and maintenance costs of transformers and substations; c L,OM Representing annual operation and maintenance cost of the line; c SOP,OM Annual operation and maintenance cost for representing installation capacity of the intelligent soft switch unit; c PVG,OM And c WTG,OM The operation and maintenance cost of the unit electric quantity generated by the distributed photovoltaic and the distributed wind power generation is respectively represented; c SVC,OM Annual operation and maintenance costs representing the unit installation capacity of the static var compensator; />Representing the electricity purchasing price of the transformer substation to the upper power grid; c PVG,C And c WTG,C The unit waste light and waste wind punishment cost of the distributed photovoltaic and the distributed wind power are respectively represented; c L,C Representing unit load shedding penalty cost; /> And->Respectively representing the light rejection, the wind rejection and the load shedding power; CVaR (Compound CVaR) PVG ,C 、CVaR WTG,C And CVaR L,C The risk values of the conditions of light abandoning, wind abandoning and load shedding are respectively represented; omega E And omega C Weighting coefficients of expected loss value and CVaR tail risk value, respectively, and omega E +ω C ＝1。
The flexible power distribution network random expansion planning model taking economical efficiency and abandoning energy and load shedding operation risk into consideration, constraint conditions to be considered comprise distributed renewable energy abandoning energy risk and load shedding risk constraint (namely flexible power distribution network abandoning energy and load shedding condition risk constraint), equipment investment construction constraint, network topological structure constraint, flexible power distribution network operation safety constraint and the like based on CVaR theory, and specifically comprises the following steps:
1) Distributed renewable energy waste energy risk and load shedding risk constraint
In this embodiment, the uncertainty factors of the flexible power distribution network include distributed renewable energy output and load power such as distributed wind power and distributed photovoltaic, and accordingly, the distributed renewable energy discarding risk and load shedding risk constraint include distributed wind power discarding energy condition risk constraint, distributed photovoltaic discarding energy condition risk constraint and end user load shedding condition risk constraint.
And (3) generating power by renewable energy sources such as distributed wind power, distributed photovoltaic and the like which are connected in the range of the flexible power distribution network, and establishing linear energy discarding condition risk constraint as shown in formulas (22) to (29).
Wherein: vaR (Var) WTG,C And VaR PVG,C The energy risk values are respectively distributed wind power and distributed photovoltaic energy discarding values;andare all introduced auxiliary variables; beta is the confidence level; />And->The upper limit of the risk value of the energy discarding condition of the distributed wind power and the distributed photovoltaic respectively.
And similarly, establishing a linear flexible power distribution network load shedding condition risk constraint as shown in formulas (30) to (33).
Wherein: vaR (Var) L,C Cutting the risk value of the load quantity for the flexible power distribution network;as an introduced auxiliary variable; />To cut the upper limit of the risk value of the load condition.
2) Equipment investment construction constraints
The equipment investment construction constraint comprises a transformer substation newly-built and capacity-expanded state constraint, a line construction state constraint, a multi-terminal intelligent soft switch installation port number and installation capacity constraint, a distributed wind turbine generator set and distributed photovoltaic turbine generator set installation capacity constraint and a static reactive compensator installation capacity constraint.
The newly-built and capacity-expansion state constraints of the transformer substation are shown in formulas (34) to (35).
Wherein:taking 1 to represent a newly built transformer station i, and taking 0 to represent that no new building is performed; />Taking 1 to represent the capacity expansion of the transformer substation i, and taking 0 to represent the non-capacity expansion.
The line construction state constraint is:
wherein:taking 1 to represent the route ij is built, and taking 0 to represent the route ij is not built.
The number of the installation ports and the installation capacity constraint of the multi-terminal intelligent soft switch are shown in formulas (37) to (39).
Wherein:representing the maximum installation number of the intelligent soft switch with unit capacity on the node i; />Whether the node to be installed of the intelligent soft switch is provided with the intelligent soft switch or not is indicated; t (T) SOP Representing the maximum port number of the intelligent soft switch to be installed; />Indicating the unit installation capacity of the intelligent soft switch.
The installation capacity constraint of the distributed wind turbine and the distributed photovoltaic turbine is shown in formulas (40) to (42).
Wherein:and->The unit installation capacity of the distributed wind power and the distributed photovoltaic is respectively represented; />Representing the rated load at node i; ζ is the total maximum permeability of the distributed wind power and the distributed photovoltaic in the flexible power distribution network; />And->And respectively representing the maximum allowable installation quantity of the distributed wind power and the distributed photovoltaic with unit capacity at the installation node i to be selected.
The static var compensator installation capacity constraint is as shown in equations (43) to (44).
Wherein:the number of the static var compensators is maximally installed at the node i; />And (3) installing an upper limit of the number of the static var compensators in the flexible power distribution network.
3) Network topology constraints
The flexible distribution network is typically in radial operation, but it is contemplated that the intelligent soft switch will be in flexible closed loop operation after it is switched in. In order to ensure that the parts of the flexible power distribution network except the intelligent soft switch still meet the radial condition, and meanwhile, the analysis is convenient, the circuit of each end connected with the intelligent soft switch is considered to be disconnected. The open loop and connectivity constraint of the flexible power distribution network is realized by establishing a virtual network with a topological structure consistent with a radial network of the flexible power distribution network, wherein the virtual network assumes that a substation node is a source node and the virtual load of a load node is 1. The network topology constraints are shown in (45) - (48).
Wherein: kappa (i) and rho (i) represent a child node set and a parent node set of node i, respectively; f (F) ij Representing the virtual power flowing from node i to node j; the number of elements in the set is denoted by i.
4) Flexible power distribution network operation safety constraint
The flexible power distribution network operation safety constraint comprises a transformer substation node power constraint, an on-load voltage regulating transformer regulation constraint, a node voltage constraint, a branch current constraint, a power balance constraint, a multi-terminal intelligent soft switch operation constraint, a distributed wind power and distributed photovoltaic operation constraint, a static reactive compensator power regulation constraint and a demand side management constraint.
Substation node power constraints are shown in (49) - (51).
Wherein:and->The rated capacities of transformers of a transformer substation to be newly built and an existing transformer substation at the node i are respectively represented; />And the rated capacity of the transformer to be expanded of the existing substation is represented.
Equation (51) may be written in the form of a rotating cone as in equation (52).
The on-load tap changer regulation constraints are shown in (53) - (54).
Wherein: v (V) rated,i Rated voltage is set for a node of the transformer substation; deltaV represents the per unit value of the regulating voltage of each tap of the on-load regulating transformer; k (k) i,u,t Representing the contact position of the on-load tap changing transformer; k (K) min And K max Representing minimum and maximum allowable regulation positions of the on-load tap changers, respectively.
If the allowable fluctuation range of the voltage per unit value of the substation node is limited to 0.95-1.05, and the on-load tap changing transformer is supposed to be adjustable in + -8 steps, at this time Δv=0.00625 (per unit value). Equation (53) can be fit linearly well by equation (55). The sum of squares of the errors after fitting was 1.183×10 -5 The coefficient was determined to be 0.9998.
The node voltage constraint can be expressed as:
wherein: v i,u,t Representing the square of the voltage amplitude at node i; v (V) max,i And V min,i Representing the upper and lower limits, respectively, of the voltage amplitude at node i.
The branch current constraint can be expressed as:
wherein: l (L) ij,u,t Representing the square of the current amplitude of branch ij; i max,ij Indicating the upper limit of the current amplitude through which the branch ij is allowed to flow.
The power balance constraints are shown in (58) - (64).
Wherein: p (P) ij,u,t And Q ij,u,t Respectively representing active power and reactive power flowing on the branch ij; r is R ij And X ij The resistance and reactance of branch ij are shown respectively;and->Respectively representing active power and reactive power injected from a node i, and taking a corresponding item as 0 if no corresponding equipment is installed at the node i; m is a sufficiently large positive number; /> Respectively representing the active power generated by the intelligent soft switch, the distributed photovoltaic and the distributed wind power at the node i; /> And->And respectively representing reactive power emitted by the intelligent soft switch, the distributed photovoltaic, the distributed wind power and the static reactive compensator at the node i.
Based on the convex relaxation technique, equation (62) is converted to a second order cone form, specifically as follows:
/>
the multi-terminal intelligent soft switch operating constraints are shown in (66) - (69).
Wherein:representing the loss coefficient of the multi-terminal intelligent soft switching converter at the node i; />And the active loss of the multi-terminal intelligent soft switching converter at the node i is represented.
The formula (67) is converted into a second order cone form, and the specific steps are as follows:
equation (68) may be written in the form of a rotating cone as in equation (71).
The distributed wind power and distributed photovoltaic operation constraints are shown in (72) - (79).
Wherein:and->Respectively representing distributed wind power and distributed photovoltaic power predicted values at a node i; />And->Respectively representing the maximum values of distributed wind power and distributed photovoltaic power factor angles at a node i; />And->Respectively represent distributed wind power and division at node iMinimum value of the photovoltaic power factor angle.
The formulas (73) and (76) may be written as rotary cone forms as shown in formulas (80) to (81).
/>
The static var power regulation constraints can be expressed as:
wherein:representing the unit installation capacity of the static var compensator.
The demand side management includes a number of measures, and this embodiment considers a common interruptible load measure that interrupts or cuts out a partial load for a user in a system peak load, an emergency state, and the constraint conditions thereof are as shown in (83) to (84).
Wherein:the power factor angle is rated for the load at node i.
For convenience of subsequent description, the expansion planning model of the flexible power distribution network with the multi-terminal intelligent soft switch, which takes the running risk into consideration, is written into a compact form, and the method is as follows:
wherein: a and b represent coefficient vectors in the objective function, including all cost coefficients, cost transformation coefficients, other parameters, and the like; x represents a variable vector related to a planning investment, including a planning decision variable y u Representing all of the run-related variable vectors; A. b, C, D, G i C, d, f, g are parameter matrices in constraints; o represents the number of second order pyramid form constraints in the planning model.
In the compact expression, the expression (85) corresponds to the objective functions (16) to (21). The first line of the expression (86) represents investment plan-related constraints including expressions (34) to (38) and expressions (40) to (48), the second line represents investment and operation logic relationships and related constraint constraints including expression (39), expression (49) to (50), expression (57), expression (60) to (61) and expression (82), the third line represents simulation operation-related constraints including expressions (22) to (33), expression (54) to (56), expression (58) to (59), expression (63) to (64), expression (66), expression (69), expression (72), expression (74) to (75), expression (77) to (79) and expression (83) to (84), and the fourth line represents second order taper constraint in the planning model including expression (52), expression (65), expression (70) to (71) and expression (80) to (81).
In fact, the constructed random planning model of the flexible power distribution network mainly comprises two stages of equipment investment decision-making and optimization simulation operation. Specifically, the first stage takes the minimum annual comprehensive cost as a target, considers constraint conditions such as equipment investment construction constraint, network topology structure constraint and the like, performs site selection and volume fixation optimization on equipment, and determines the state of a grid structure; and the second stage is to take the minimum annual simulated operation cost as a target after the investment decision in the previous stage is determined, consider constraint conditions such as risk constraint of abandoned energy load shedding conditions and operation safety constraint of the flexible power distribution network, and perform simulated operation optimization in various random scenes.
Step S4: and solving the two-stage random expansion planning model of the flexible power distribution network by adopting an algorithm framework based on Benders decomposition to obtain an optimal planning scheme.
The Benders decomposition method divides the original problem into a main problem and a sub problem, and carries out iterative solution, specifically:
the main problem is a planning problem, is related to complex variables x and is used for determining various equipment investment and net rack expansion schemes. After determining the investment decision, solving the sub-problem, then introducing auxiliary variables into the main problem and adding a cutset containing the dual variables of the sub-problem, and feeding back the optimization result of the sub-problem to the main problem in a successive iteration process in this way. The main problem is the original problem after relaxation, which can be expressed as:
Wherein: η is an auxiliary variable, and the running cost under each random scene is fed back.
The sub-problems of the Benders decomposition are simulation running problems under random scenes, and are related to a variable yu, namely, each sub-problem corresponds to one random scene. Because no coupling relation exists between each random scene, the method can solve in parallel, and therefore the solving efficiency is greatly improved. The sub-problems are solved by taking the annual simulated operation cost in each random planning scene as a target, and the optimal operation state of the flexible power distribution network in the random scene is obtained. Optimizing the value x at the known main problem * On the premise of (1), the sub-problem generalization model can be expressed as:
wherein: lambda (lambda) 1 、λ 2 Sigma and mu are the dual variables corresponding to the constraints, respectively.
Thus, the dual problem is obtained as follows:
if there is no feasible solution to the dipole problem, then the atomic problem is unbounded or has no feasible solution. If the dipole problem is unbounded, a candidates feasibility cut is generated by solving the auxiliary sub-problem (90) described below, as shown in formula (91).
If a feasible solution exists in the dipole problem, the strong dipole theorem indicates that an optimal solution exists in the atomic problem, and the atomic problem is equal to the optimal solution of the dipole problem. Thus, the Benders optimality cut for the sub-question is returned to the main question, as shown in equation (92).
The main problem of considering the Benders feasibility cut set and the optimality cut set is shown in formula (93).
Wherein: u (U) 1 And U 2 The number of sub-questions for returning feasibility and optimality cuts, respectively, is U 1 +U 2 ＝U。
As shown in fig. 2, the two-stage stochastic expansion planning model solution for the flexible power distribution network based on Benders decomposition specifically includes:
step S401, initializing parameters. The specific initialization settings include: upper bound value UB = +++ is a function of, the lower bound LB = - ≡, iteration number m=1, convergence allowance error epsilon=10 -5 。
Step S402, solving the main problem of the first stage to obtain an optimal solution (x * ,η * ) Simultaneously updating the lower bound: lb=max { LB, min a T x * +η * }。
Step S403, the optimal decision variable x of the main question * Substituting the binary problem and solving to obtain the optimal solution (lambda 1 * ，λ 2 * ，σ * ，μ * )。
Step S404, if the solution is an unbounded solution, generating and adding a Benders feasibility cut in the main problem:let m=m+1, return to step S402.
Step S405, if the solution is a bounded optimal solution, generating and adding a Benders optimal score to the main problem:
step S406, updating the upper limit value:
step S407, judging whether (UB-LB)/UB is less than or equal to epsilon, if yes, ending the solution, otherwise, letting m=m+1, and returning to step S402.
In another embodiment, a flexible power distribution network random expansion planning system including a multi-terminal intelligent soft switch is provided that accounts for operational risk, including a memory, a processor, and computer program instructions stored on the memory and executable by the processor, when executed by the processor, are capable of performing the method steps as described above.
Examples
In this embodiment, the flexible distribution network to be planned shown in fig. 3 is used as a test example for analysis. In the example of the flexible distribution network to be planned shown in fig. 3, there are 72 load nodes, 27 existing load nodes, 45The load nodes to be newly built, wherein node 1 is a transformer substation node to be expanded, and node 51 is a transformer substation node to be newly built; there are 26 established lines, 54 lines to be established. The system voltage class is 10kV, and the rated load is 70MW. The information and the cost of the transformer substation are shown in table 1, the main transformer on-load voltage regulating transformer of the transformer is an YNd11 three-phase double-winding transformer, 9 regulating gears are provided, the regulating range is 0.95p.u. to 1.05p.u., and the electricity purchasing price of the upper power grid is 0.5 yuan/kW.h. The unit length resistance and reactance of the line to be constructed are 0.0601 ohm/km and 0.0885 ohm/km, the maximum capacity of the line is 9.49 MV.A, the investment cost is 40 ten thousand yuan/km, and the annual operation and maintenance cost is 3000 yuan/strip. The distributed power supply mainly considers two types of distributed photovoltaic and distributed wind power, the information to be installed, the investment cost and the operation and maintenance cost of unit electric quantity are shown in the table 2, the power factor adjustable range of the distributed power supply is from 0.95 to 0.95 of the slow phase, the maximum permeability of the distributed power supply is 60%, and the punishment cost of unit waste wind and waste light is 0.35 yuan/kW.h; the interruptible load is interrupted according to the rated power factor, the interruptible proportion is 0-100%, and the unit load shedding penalty cost is 7 yuan/kW.h; the confidence of the abandoned energy and cut load CVaR is 90 percent, and the CVaR upper limit value And->Respectively setting the power to be 2 MW.h, 3 MW.h and 1 MW.h; setting omega E ＝0.1，ω C =0.9. The to-be-selected installation nodes of the static var compensator are 10, 47, 61 and 71, the unit installation capacity is 100kVar, the construction cost is 7000 yuan/kVar, the upper limit of the installation number of each node is 2, and the upper limit of the installation number of the static var compensator in the flexible power distribution network is 6. Due to actual requirements, 2 groups of multi-terminal intelligent soft switches are considered to be installed, and a group of multi-terminal intelligent soft switches are provided with 34, 40, 44, 50 and 53 to be installed nodes to be selected; the other group of multi-terminal intelligent soft switch candidate installation nodes are 6, 18, 20, 61 and 68. Considering the application situation of the intelligent soft switch with multiple ends in actual engineering, setting the maximum number of the intelligent soft switch to be installed as 4 ends, and setting the maximum access capacity of the voltage source type converter with the intelligent soft switch portsThe amount is 6 MV.A, the unit installation capacity is 100 kV.A, the investment cost is 1000 yuan/kV.A, the loss coefficient is 0.02, and the annual operation maintenance cost coefficient is 0.01. The node voltage amplitude constraint is 0.93p.u. -1.07 p.u., the load rated power factor is 0.9, the discount rate is 5%, and the planning period is 10 years. Based on annual historical data of distributed wind power, distributed photovoltaic and load given in fig. 4, fitting to obtain probability distribution (obeying Weibull distribution, beta distribution and normal distribution respectively) of power values of each time period in the day of the distributed wind power, the distributed photovoltaic and the load, and then forming a basic planning scene by the mean value of the probability distribution of each time period. On this basis, consider taking 0 as the mean value, taking the variances of the base values of 5%, 3% and 3% as the prediction errors, respectively, randomly generating 1000 groups of scenes, and then reducing the number of scenes to 10 groups by adopting a scene reduction method in order to reduce the complexity of solving.
Table 1 substation parameters
Table 2 distributed power supply parameters
In order to more thoroughly study the random expansion planning method of the flexible power distribution network and analyze the influence of the abandoned energy cut load operation risk on the planning scheme, 3 planning methods are set for comparison, and the comparison is shown in table 3.
Table 3 planning method setup
The method I does not consider the uncertainty of source-load and the risk of abandoned energy load shedding operation, and performs expansion planning on the flexible power distribution network containing the multi-terminal intelligent soft switch under a determined basic scene; the method II considers the uncertainty of source-load, but does not consider the management and control of the abandoned energy load shedding risk, and performs expansion planning on the flexible power distribution network with the multi-terminal intelligent soft switch by a random optimization method; the method III is used for considering random expansion planning of the flexible power distribution network with the multi-terminal intelligent soft switch, which is free from the risk of load shedding.
The results of the planning cost obtained by the methods I, II and III are shown in Table 4, and the planning schemes are shown in Table 5.
Table 4 Flexible Power distribution network expansion planning costs under different methods
Table 4 compares the impact of taking into account "source-load" uncertainty and whether the curtailed load is running risk or not on the planning cost. Scheme I does not take into account "source-load" uncertainty and operational risk, and annual composite cost is the lowest of the three planning schemes. Scheme II is a planning scheme obtained after the uncertainty of 'source-load' is processed by adopting a random optimization method, the annual comprehensive cost is increased by 751 ten thousand yuan compared with scheme I, wherein the annual operation cost is increased by 945 ten thousand yuan, and the energy rejection and load shedding penalty cost is respectively increased by 13 ten thousand yuan and 51 ten thousand yuan. The scheme III is a planning scheme obtained by simultaneously considering the uncertainty of source-load and the management and control of the abandoned energy cut load operation risk, the annual comprehensive cost is highest in three planning schemes, and the annual comprehensive cost is increased by 5.65 percent compared with the scheme I and 1.29 percent compared with the scheme II; and the abandoned energy penalty cost is reduced by 60 ten thousand yuan and 73 ten thousand yuan compared with the scheme I and the scheme II, and the load penalty cost is reduced by 5 ten thousand yuan and 56 ten thousand yuan compared with the scheme I and the scheme II. It should be noted, however, that both the reject penalty and the cut load penalty in scheme III are weighted sums of the expected values and their conditional risk values, whereas only the expected values are included in schemes I and II.
Table 5 expansion planning scheme for flexible power distribution network under different methods
The method I does not consider the uncertainty of source-load and the operation risk, so that the obtained planning scheme I has certain advantages in economical efficiency compared with other two planning schemes, but is only an optimal solution under a basic scene, and the planning scheme is difficult to meet the requirements of different scenes. From subsequent analysis, the planning scheme lacks resistance to risks caused by future uncertainty factors, and can face extremely high energy-saving load shedding operation risks in actual operation. The method II does not consider the management and control of the operation risk, namely only the expected values of the abandoned energy punishment cost and the cut load punishment cost are considered in the objective function, meanwhile, the abandoned energy and cut load risk constraint is not considered in the constraint condition, and the obtained planning scheme II has better performance in economical efficiency compared with the planning scheme III. As can be seen from table 5, scheme II is more biased to carry more renewable energy sources, so as to save the energy purchasing cost to a greater extent, but the energy discarding phenomenon is serious, and at the same time, is more sensitive to fluctuation of the load of the user, and is biased to adopt a load cutting means to meet the economic operation requirement when necessary, so that the annual comprehensive cost is reduced. And the scheme III is more conservative, compared with the scheme II, the scheme II realizes the consumption of renewable energy sources and the power supply to loads as much as possible, so that certain economical efficiency is sacrificed to control the risk of discarding energy and cutting loads, and the possible high running risk is reduced. From the configuration of the multi-terminal intelligent soft switch, the scheme III has larger installation capacity, which proves that the capacity of the flexible power distribution network for absorbing renewable energy sources and the reliability of power supply to end users can be effectively improved through the multi-terminal intelligent soft switch.
In order to further analyze the risks possibly faced by the planning schemes obtained by different planning methods in actual operation scenes, 100 scenes are randomly generated by adopting a Monte Carlo simulation method, then under the investment decisions respectively determined by the planning schemes I, II and III, the energy abandoning risks and the load shedding risks in the operation scenes are calculated with the minimum annual operation cost as targets, the relevant parameter settings of the examples in the test process are kept unchanged, and the test results are shown in Table 6.
Table 6 actual running risk test results of flexible distribution network under different planning schemes
As can be seen from table 6, the planning scheme III has smaller curtailed load and risk than the schemes I and II, indicating the effectiveness of the planning method of this embodiment. And the operation risk is considered in the planning stage, so that the obtained planning scheme has obvious risk avoidance characteristics, and the possibility that the flexible power distribution network is subjected to high-energy-rejection load shedding risk in actual operation is effectively reduced.
The influence of the energy-abandoning load-shedding condition risk on the expansion planning result of the flexible power distribution network is further and deeply analyzed.
Based on the planning method III, CVaR confidence values are 80%,90%,95% and 99% respectively, and the obtained abandoned energy cutting load VaR value and the CVaR value thereof in the planning scheme are shown in table 7.
TABLE 7 VaR and CVaR values for energy rejection and load shedding at different confidence levels
As can be seen from the results of table 7, the VaR values of the distributed renewable energy waste energy and cut load of the flexible power distribution network in each planning scheme do not exceed the corresponding CVaR values, the advantages of CVaR theory in measuring the risk of losing tail are illustrated. Specifically, taking the result of the scheme III as an example, the calculation result of the VaR value shows that the probability of 90% under the planning scheme can ensure that the air discarding quantity, the light discarding quantity and the cut load quantity of the flexible power distribution network in unit time are respectively less than 1.9 MW.h, 1.3 MW.h and 0.08 MW.h. The calculation result of the CVaR value shows that under the planning scheme, when the flexible power distribution network has the condition that the air rejection amount, the light rejection amount and the cut load amount in unit time exceed the VaR value due to the uncertainty of source-load, the probability of 90 percent can ensure that the extremely potential cut load amount cannot exceed (or the expected value is 2.2MW h, 1.5MW h and 0.1MW h under the condition that the cut load amount exceeds the VaR). It follows that CVaR values can represent more tail risk information. In the flexible power distribution network expansion planning stage, distributed renewable energy waste energy and flexible power distribution network load shedding operation risks are considered, conditional risk constraint is constructed, the operation risk under a certain confidence level can be reasonably measured, and the expected risk beyond the given confidence level can be fully considered.
Further analysis of risk weighting coefficient omega C Influence on the planning result.
As shown in fig. 5, the risk weight coefficient ω is shown when the CVaR risk confidence β is kept 90% C When the values are {0.10,0.30,0.50,0.70,0.80,0.85,0.90,0.95,1.00}, the annual comprehensive expense and annual rejection of the planning scheme can cut the change condition of the load. From the graph, it can be seen that with ω C The annual comprehensive cost of the flexible power distribution network expansion planning is gradually increased, but the energy rejection and load shedding amount is gradually reduced, and the operation risk is correspondingly gradually reduced. Thus, the planning decision maker may determine the risk by increasing the risk weight coefficient ω C The running risk is managed and controlled, but the balance of economy and risk of the planning scheme is also noted, the economic efficiency of the planning scheme is strived for, meanwhile, the distributed renewable energy source consumption level of the flexible power distribution network is effectively improved, and the load shedding risk is reduced according to the actual source-load historical information of the area to be planned and the running condition of the system.
In summary, analysis is performed, operation risk management and control is considered in a planning stage, comprehensive resources such as a flexible power distribution network transformer, a circuit, a multi-terminal intelligent soft switch, a distributed power supply and reactive compensation are optimally configured by considering renewable energy waste energy condition risk constraint and load shedding condition risk constraint, so that the obtained planning scheme can effectively avoid waste energy load shedding risk, balance between economy and risk leakage is realized, and effectiveness of the planning method of the embodiment is proved.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (10)
1. A flexible power distribution network random expansion planning method considering operation risk is characterized by comprising the following steps:
constructing an uncertainty factor probability distribution model of the flexible power distribution network;
based on the flexible power distribution network uncertainty factor probability distribution model, introducing a conditional risk value theory, and constructing a flexible power distribution network energy-abandoning load-shedding conditional risk constraint;
constructing a flexible power distribution network two-stage random expansion planning model, wherein the flexible power distribution network two-stage random expansion planning model aims at minimizing annual comprehensive cost, and constraint conditions comprise risk constraint of the flexible power distribution network energy-abandoning load-shedding condition;
and solving the two-stage random expansion planning model of the flexible power distribution network to obtain an optimal planning scheme.
2. The flexible power distribution network stochastic expansion planning method for accounting for operational risk of claim 1, wherein the flexible power distribution network uncertainty factors include distributed renewable energy output and load power.
3. The flexible power distribution network random expansion planning method considering operation risk according to claim 1, wherein the flexible power distribution network energy-abandoning and load-shedding condition risk constraint is expressed as:
0≤CVaR β (x)≤q CVaR
Wherein CVaR is as follows β (x) Representing the CVaR value of the loss function f (x, y) at a given confidence level β, x being a decision vector, y being a random vector that triggers an uncertainty event, q CVaR Is a conditional risk threshold.
4. The flexible power distribution network random expansion planning method considering operation risks according to claim 1, wherein the flexible power distribution network uncertainty factor probability distribution model comprises a wind speed and distributed wind power output probability distribution model, an illumination intensity and distributed photovoltaic output probability distribution model and a load power uncertainty probability distribution model;
the flexible power distribution network energy discarding and load shedding condition risk constraint comprises a distributed wind power energy discarding condition risk constraint, a distributed photovoltaic energy discarding condition risk constraint and an end user load shedding condition risk constraint.
5. The flexible power distribution network random expansion planning method considering operation risks according to claim 1, wherein the constraint conditions of the flexible power distribution network two-stage random expansion planning model further comprise equipment investment construction constraint, network topology constraint and flexible power distribution network operation safety constraint.
6. The flexible power distribution network random expansion planning method considering operation risk according to claim 1, wherein in the flexible power distribution network two-stage random expansion planning model, the first stage is to obtain investment decisions for equipment, and the second stage is to perform simulated operation optimization on each random scene after determining the investment decisions.
7. The flexible power distribution network random expansion planning method taking into account operational risks of claim 6, wherein the equipment comprises one or more of transformers, lines, multi-terminal intelligent soft switches, distributed wind power, distributed photovoltaics, static var compensators.
8. The flexible power distribution network random expansion planning method considering operation risk according to claim 6, wherein the two-stage random expansion planning model of the flexible power distribution network is solved by adopting an algorithm framework based on Benders decomposition, and the method specifically comprises the following steps:
dividing a solving problem of a two-stage random expansion planning model of the flexible power distribution network into a main problem and a sub-problem, wherein the main problem is used for determining the investment decision, and the sub-problem is a simulation running problem in a random scene and is used for solving the optimal running state of the flexible power distribution network;
solving the sub-problem after determining the investment decision, introducing auxiliary variables into the main problem, adding a cutting set containing dual variables of the sub-problem, and feeding back the optimization result of the sub-problem to the main problem in the successive iteration process to finish the solution.
9. A flexible power distribution network random expansion planning system taking into account operational risk, comprising a memory, a processor and computer program instructions stored on the memory and executable by the processor, when executing the computer program instructions, performing the method steps of any of claims 1-8.
10. A computer readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, the one or more programs comprising instructions for performing the method of any of claims 1-8.
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