CN110867866B - UPFC optimal configuration method based on direct current power flow - Google Patents

UPFC optimal configuration method based on direct current power flow Download PDF

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CN110867866B
CN110867866B CN201911117948.4A CN201911117948A CN110867866B CN 110867866 B CN110867866 B CN 110867866B CN 201911117948 A CN201911117948 A CN 201911117948A CN 110867866 B CN110867866 B CN 110867866B
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吴军
刘畅
陈俊锋
郝露茜
李保林
徐剑冰
甘佩莹
周辉
幸相渝
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
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Abstract

The invention discloses a UPFC optimal configuration method based on direct current power flow, belongs to the field of steady-state operation of power systems, and provides a UPFC optimal configuration model based on direct current power flow on the background of reducing transmission pressure of the power systems and optimizing the structure of modern power systems. The UPFC device can be used for adjusting the line power flow distribution in the power system and improving the economic cost of the system, the method model is a UPFC optimal configuration mathematical model which is established by taking the economic cost of a generator as an objective function on the basis of a constructed UPFC direct current power flow model, and is matched with a Big-M method to process a nonlinear power flow equation of the UPFC, so that the mixed integer nonlinear programming problem is converted into a mixed integer linear programming problem which is suitable for more solvers, and the installation position and the capacity of the UPFC in a line are optimized. The model is beneficial to adjusting the power transmission capability of the line and changing the power distribution in the system so as to ensure that the system operates efficiently.

Description

UPFC optimal configuration method based on direct current power flow
Technical Field
The invention belongs to the field of steady-state operation of power systems, and particularly relates to a UPFC optimal configuration method based on direct current power flow.
Background
With the reorganization of the power market and the access of renewable energy sources, the power industry is undergoing a deep revolution of technical, economic and organizational problems, and the modern power system structure is continuously optimized while considering that the degree of grid congestion is increased due to the increasing power consumption, the low predictive power flow and the wide adoption of renewable energy sources. The expansion of the power system is used as a basic means for reducing transmission pressure, and relates to newly-built power plants and newly-added power transmission lines in key areas, so that the construction cost is high, and the construction time is long. The Flexible Alternating Current Transmission Systems (FACTS) greatly improve the power flow control capability of the power system. By installing a power flow control device, the effective transmission line reactance can be changed, thereby transferring power to a nearby underutilized transmission line to increase the power transmitted on that line.
A Unified Power Flow Controller (UPFC) is one of the most widely used devices in the current flexible ac Power transmission family, combines with the excellent performance of various devices, not only can adjust the line transmission Power, but also can change the Power distribution of the system to realize the optimized operation of the system, and obtains the extensive attention of the Power industry by virtue of the flexibility and accuracy thereof, so that the research on how to realize the optimized configuration of the UPFC has important significance for Power planners.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a UPFC optimal configuration method based on direct current flow, so that the problem of how to realize the optimal configuration of the UPFC is solved.
In order to achieve the above object, the present invention provides a method for optimally configuring a UPFC based on a dc power flow, comprising:
(1) on the basis of the alternating current power flow calculation model, neglecting the line resistance and the reactive power flow of the branch to obtain a direct current power flow model;
(2) injecting the direct current power flow of the UPFC into the direct current power flow model through construction to obtain a steady-state equivalent model of the UPFC in the direct current power flow, and obtaining a UPFC optimal configuration mathematical model under an optimal constraint condition;
(3) and on the basis of the UPFC optimal configuration mathematical model, reconstructing the UPFC optimal configuration mathematical model and constrained mixed integer nonlinear constraint into mixed integer linear constraint, and solving the UPFC optimal configuration mathematical model to obtain the optimal installation position and the optimal capacity of the UPFC.
Preferably, in step (1), the nonlinear power flow equation system of the alternating current power flow calculation model is as follows:
Figure BDA0002274598160000021
wherein, PijRepresenting the active power flow of the line between node i and node j, QijRepresenting the reactive power flow, theta, of the line between node i and node jijRepresents the difference between the power angles at node i and node j, BijRepresenting the mutual susceptance, G, between node i and node jijRepresenting the mutual conductance, V, between node i and node jiRepresents the magnitude of the voltage at node i, VjRepresenting the magnitude of the voltage at node j.
Preferably, in step (1), the dc power flow model is:
Figure BDA0002274598160000022
wherein x isijRepresenting the line reactance, θ, of the line between node i and node jiRepresenting the power angle, theta, at node ijRepresenting the power angle at node j.
Preferably, in step (2), the obtaining a steady-state equivalent model of the UPFC in the dc power flow by constructing to inject the dc power flow of the UPFC into the dc power flow model includes:
according to UPFC input voltage VIInput current IISeries voltage V of injection current transformerTParallel current I injected into the converterT，VTWith respect to the output current IoDecomposed in-phase component VPTo the orthogonal component Vq，ITWith respect to the input voltage VIComponent I of orthogonal decompositionPAnd IqTo obtain the output voltage V of UPFCoOutput current IoAnd the power of the transmission line is injected by the series transformer, so that a steady-state equivalent model of the UPFC in the direct current power flow is obtained.
Preferably, the steady-state equivalent model of the UPFC in the dc power flow is: vI·IP＝VP·IoUnder the condition of neglecting the loss of the UPFC, the active input is equal to the active output, and the reactive imbalance is realized, and the influence of the adjustable variable of the UPFC on the system is directly transplanted to a line between nodes.
Preferably, in step (2), the objective function of the UPFC optimal power flow in the UPFC optimal configuration mathematical model is:
Figure BDA0002274598160000031
where Φ is the total power generation cost of the system, ciFor each generator corresponding economic parameter, NGFor a set of generators in the system, PGiThe active output of each generator node i.
Preferably, in step (2), the optimization constraints present in the UPFC optimization configuration mathematical model are inequality constraints consisting of a series of state variable and control variable constraints.
Preferably, step (3) comprises:
order to
Figure BDA0002274598160000032
Introducing an input variable lambda to obtain the active power on the transmission line a, wherein xijRepresenting the line reactance, x, of the line between node i and node jaIs the variable reactance of the UPFC injected into transmission line a;
introducing virtual variables
Figure BDA0002274598160000033
Further rewriting the active power, theta, on said transmission line aaRepresenting the phase angle difference, delta, across the lineaA variable of 0-1 is represented to measure whether the corresponding line is provided with the UPFC;
introducing a binary variable and linearizing the active power on the transmission line a after rewriting by using a Big-M method;
introduction of variable betaa＝θaδaTo continue the linearization process, and to use Big-M method again to make betaaAnd constraining, then solving the objective function of the UPFC optimal power flow according to constraint conditions, and obtaining the optimal installation position and the optimal capacity of the UPFC after relaxation.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects: the method improves the power flow calculation of the system under the large background of recombination and renewable energy access of the power market, can adjust the power flow distribution of the circuit and improve the economic cost in the power system, converts the mixed integer nonlinear programming problem in the original alternating current power flow calculation into the mixed integer linear programming problem which is suitable for more solvers, and is favorable for optimizing the installation position and the capacity of the UPFC in the circuit.
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Fig. 1 is a schematic flowchart of a method for configuring an UPFC optimization based on a dc power flow according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a UPFC simplified model according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a steady-state equivalent model of a UPFC according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a UPFC optimal configuration method based on direct current flow, which is used for optimally configuring the installation capacity and the installation position of the UPFC in a system, and is beneficial to adjusting the power transmission capability of a line and changing the power distribution in the system so as to enable the system to operate efficiently.
Fig. 1 is a schematic flow diagram of a method for configuring an UPFC optimization based on a dc power flow according to an embodiment of the present invention, where the method shown in fig. 1 includes the following steps:
step 1: based on a conventional alternating current power flow calculation model, a direct current power flow model is obtained through simplified analysis on the basis of the alternating current power flow calculation model from the mathematical angle;
fig. 2 is a schematic diagram of a UPFC simplified model provided in an embodiment of the present invention, and a specific implementation manner of step (1) is as follows:
in the embodiment of the present invention, the nonlinear power flow equation system of the conventional alternating current power flow calculation model in step 1 is:
Figure BDA0002274598160000051
wherein, Pij、QijRespectively is the active power flow and the reactive power flow of a line between the node i and the node j; thetaijIs the difference between the power angles at node i and node j; b isij、GijIs the mutual susceptance, mutual conductance, V, between node i and node ji、VjIs the voltage magnitude at node i, node j.
The nonlinear power flow equation system is obtained by iterating the node injection power equation of the n-node power system until convergence, wherein the power equation is as follows:
Figure BDA0002274598160000052
wherein j belongs to i and refers to other adjacent nodes j near the node i; pi、QiThe active power and the reactive power of a node i are indicated; vi、VjIs the voltage magnitude at node i, node j; b isij、GijRespectively, the mutual susceptance and the mutual conductance between node i and node j.
In the embodiment of the present invention, the alternating current power flow model in step 1 is simplified as follows: and (4) neglecting the line resistance and the reactive power flow of the branch circuit on the alternating current power flow model to solve to obtain a simplified power flow equation set.
In the embodiment of the present invention, the dc power flow model obtained in step 1 is:
Figure BDA0002274598160000053
wherein x isijIs the line reactance; thetai、θjThe power angles at node i and node j, respectively.
Step 2: the method comprises the steps of obtaining a steady-state equivalent model of the UPFC in the direct current flow by constructing and injecting the direct current flow of the UPFC, and obtaining a UPFC optimal configuration mathematical model under an optimal constraint condition;
in the embodiment of the invention, in the step 2, the steady-state equivalent model of the UPFC in the direct current power flow is derived from the simplified model of the UPFC itself, and is an equivalent model based on the consideration of the simplified model of the UPFC.
Fig. 3 is a schematic diagram of a UPFC steady-state equivalent model provided in an embodiment of the present invention, and the specific implementation manner is as follows:
in the embodiment of the present invention, in step 2, the calculation method of the UPFC steady-state equivalent model is as follows:
in the UPFC model, VI、VO、II、IOVoltage and current, V, respectively, of UPFC input and outputT、ITRespectively series voltage and parallel current injected into the converter, will VTResolved into in-phase components V with respect to output currentPTo the orthogonal component VqIn the same way as ITQuadrature decomposition into I with respect to input voltagePAnd IqThus, the output voltage V of UPFC can be obtainedoAnd an output current IoAnd power injected into the transmission line by the series transformer:
Figure BDA0002274598160000061
wherein, theta1Representing the phase angle, delta, of the UPFC input voltage0Representing the phase angle, δ, of the UPFC output current1Representing the phase angle of the UPFC input current.
The power injected into the transmission line by the series transformer is decomposed into two forms of active power and reactive power:
ST＝VP·Io+jVq·Io (5)
wherein S isTRepresenting the power injected into the transmission line by the series transformer, the active power PT(possibly negative) current I from the shunt transformerPProvided, therefore, a relationship can be derived for an ideal UPFC:
VI·IP＝VP·Io (6)
it can be seen that, ignoring the losses of the UPFC device itself, its active input equals the active output, while the reactive imbalance, the effect of the adjustable variables of the UPFC on the system is directly ported to the line between the nodes.
In the embodiment of the present invention, the objective function of the UPFC optimal power flow in the mathematical model optimized and configured in step 2 may be represented as:
Figure BDA0002274598160000062
and under the condition of not considering investment cost, the economic benefit of the generator is evaluated by adopting the power generation cost of the generator. Wherein phi is the total power generation cost of the system; c. CiThe economic parameters corresponding to each generator are obtained; n is a radical ofGIs a set of generators in the system; pGiThe active output of each generator node i.
In the embodiment of the present invention, the optimization constraint existing in the mathematical model for optimization configuration in step 2 is an inequality constraint composed of a series of state variable and control variable constraints, such as generator output constraint, UPFC control capacity constraint, transmission line thermal limit constraint, and the like. The method specifically comprises the following steps:
node i needs to maintain its balance constraint on active power:
Figure BDA0002274598160000071
wherein omegaiIs a line connected with the node i; II typeiLoad, P, carried by node ia、PLmRepresenting the corresponding active power.
Constraints such as generator output constraint, UPFC control capacity constraint, transmission line thermal limit constraint and the like:
Figure BDA0002274598160000072
wherein, BrefIs a reference node; sa maxIs the limit power on transmission line a; pGi min、PGi maxThe upper limit and the lower limit of the active power of the generator are set; pijmaxIs the thermal stability limit of the line transmission; thetai min、θi maxIs the upper and lower limits of the phase angle difference of the line, xaVariable reactance of UPFC for injection into transmission line a, xamin、xamaxThe upper and lower fluctuation limits of the equivalent reactance of the UPFC.
And step 3: and a Big-M method is adopted, and on the basis of the UPFC optimal configuration mathematical model, the model and the constrained mixed integer nonlinear programming model are reconstructed and converted into a mixed linear programming model, so that the calculation is simplified, and the optimization, the location and the volume fixing are facilitated.
In the embodiment of the invention, the Big-M method in the step 3 is an effective method for solving the programming problem, and the original nonlinear inequality constraint can be converted into the mixed integer linear constraint by introducing a plurality of binary variables of 0-1. Specifically, the Big-M method is applied as follows:
order to
Figure BDA0002274598160000073
The input variable lambda is introduced to facilitate linearization, and the active power P on the transmission line aaComprises the following steps:
Figure BDA0002274598160000081
wherein, thetaaRepresenting the phase angle difference, delta, across the lineaRepresents a 0-1 variable used to measure whether the corresponding line is equipped with UPFC, lambdamin、λmaxRepresenting the upper and lower limits of the introduced variables.
To linearize the non-linear term, a dummy variable is introduced
Figure BDA0002274598160000082
Further rewritten as:
Figure BDA0002274598160000083
at this time, a binary variable tau is introducedaAnd linearizing the above formula (11) using Big-M method:
Figure BDA0002274598160000084
wherein psiaDepends on the sign of the phase angle difference across the transmission line a, tauaThe value is related to the power flow direction of the transmission line a; throughout the optimization process, one of the two constraints, and only one of them, is active, the other constraint will always be satisfied, where MaA positive number which is large enough is taken, but the parameter cannot be selected to be too large so as not to cause the search range to be too large and influence the solving efficiency.
Introducing a variable betaa＝θaδaTo continue the linearization process, again using Big-M method for betaaAnd (4) carrying out constraint:
Figure BDA0002274598160000085
the above formula can be rewritten as:
Figure BDA0002274598160000086
wherein, thetaa maxRepresenting the upper limit of the phase angle difference across the line.
Under the constraint conditions, the objective function is solved, and after relaxation, the UPFC optimal localization and sizing research is converted into a mixed linear programming problem.
Specific examples of the present invention are given below.
And carrying out simulation analysis on UPFC addressing and capacity optimization in the constructed 2-machine 5-node system, the IEEE-14 node system and the IEEE-118 system.
Different installation locations affect the cost of power generation. When planning to install two UPFCs in combination in the system, the capacity of each UPFC is kept constant at 0.1, and candidate sites of 12 most probable configurations are selected in all installation cases. The optimal installation positions obtained by the method are on the line 4 and the line 5, the power generation cost is 6310.5($/h), and the objective function is the lowest in all configuration strategies.
Different UPFC equivalent capacities impact power generation costs. Fixing UPFC installation address on line 4, changing its control capacity, setting the upper limit of capacity to 0.15, observing the reduction of power generation cost, adopting the method of the invention to obtain the optimum installation capacity, with the UPFC equivalent capacity on line increasing, the power generation cost gradually reducing, when x equals to 0.08, the objective function reaches the lowest value.
The above is the optimized implementation scheme of the present invention, different installation positions and capacities of UPFC have obvious influence on investment and income, and after determining the most probable configuration of various modes, the method of the present invention can improve the optimization capability to obtain more accurate addressing information.
It should be noted that, according to the implementation requirement, each step/component described in the present application can be divided into more steps/components, and two or more steps/components or partial operations of the steps/components can be combined into new steps/components to achieve the purpose of the present invention.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (8)

1. A UPFC optimal configuration method based on direct current power flow is characterized by comprising the following steps:
(1) on the basis of the alternating current power flow calculation model, neglecting the line resistance and the reactive power flow of the branch to obtain a direct current power flow model;
(2) injecting the direct current power flow of the UPFC into the direct current power flow model through construction to obtain a steady-state equivalent model of the UPFC in the direct current power flow, and obtaining a UPFC optimal configuration mathematical model under an optimal constraint condition;
(3) and on the basis of the UPFC optimal configuration mathematical model, reconstructing the UPFC optimal configuration mathematical model and constrained mixed integer nonlinear constraint into mixed integer linear constraint, and solving the UPFC optimal configuration mathematical model to obtain the optimal installation position and the optimal capacity of the UPFC.
2. The method according to claim 1, wherein in step (1), the nonlinear power flow equation system of the alternating current power flow calculation model is:
Figure FDA0002819753500000011
wherein, PijRepresenting the active power flow of the line between node i and node j, QijRepresenting the reactive power flow, theta, of the line between node i and node jijRepresents the difference between the power angles at node i and node j, BijRepresenting the mutual susceptance, G, between node i and node jijRepresenting the mutual conductance, V, between node i and node jiRepresents the magnitude of the voltage at node i, VjRepresenting the magnitude of the voltage at node j.
3. The method according to claim 2, wherein in step (1), the direct current power flow model is:
Figure FDA0002819753500000012
wherein x isijRepresenting the line reactance, θ, of the line between node i and node jiRepresenting the power angle, theta, at node ijRepresenting the power angle at node j.
4. The method according to any one of claims 1 to 3, wherein in the step (2), the obtaining of the steady-state equivalent model of the UPFC in the DC power flow by constructing the direct current power flow model of the UPFC to be injected with the DC power flow model comprises:
according to UPFC input voltage VIInput current IISeries voltage V of injection current transformerTParallel current I injected into the converterT，VTWith respect to the output current IoDecomposed in-phase component VPTo the orthogonal component Vq，ITWith respect to the input voltage VIComponent I of orthogonal decompositionPAnd IqTo obtain the output voltage V of UPFCoOutput current IoAnd the power of the transmission line is injected by the series transformer, so that a steady-state equivalent model of the UPFC in the direct current power flow is obtained.
5. The method of claim 4, wherein the steady state equivalent model of the UPFC in DC power flow is: vI·IP＝VP·IoUnder the condition of neglecting the loss of the UPFC, the active input is equal to the active output, and the reactive imbalance is realized, and the influence of the adjustable variable of the UPFC on the system is directly transplanted to a line between nodes.
6. The method of claim 5, wherein in step (2), the objective function of the UPFC optimal power flow in the UPFC optimal configuration mathematical model is:
Figure FDA0002819753500000021
where Φ is the total power generation cost of the system, ciFor each generator corresponding economic parameter, NGFor a set of generators in the system, PGiThe active output of each generator node i.
7. The method according to claim 6, wherein in step (2), the optimization constraints present in the UPFC optimization configuration mathematical model are inequality constraints consisting of a series of state variable and control variable constraints, including: active power balance constraints, generator output constraints, UPFC control capacity constraints, and transmission line thermal limit constraints.
8. The method of claim 7, wherein step (3) comprises:
order to
Figure FDA0002819753500000022
Introducing an input variable lambda to obtain the active power on the transmission line a, wherein xijRepresenting the line reactance, x, of the line between node i and node jaIs the variable reactance of the UPFC injected into transmission line a;
introducing virtual variables
Figure FDA0002819753500000023
Further rewriting the active power, theta, on said transmission line aaRepresenting the phase angle difference, delta, across the lineaA variable of 0-1 is represented to measure whether the corresponding line is provided with the UPFC;
introducing a binary variable and linearizing the active power on the transmission line a after rewriting by using a Big-M method;
introduction of variable betaa＝θaδaTo continue the linearization process, and to use Big-M method again to make betaaAnd constraining, then solving the objective function of the UPFC optimal power flow according to constraint conditions, and obtaining the optimal installation position and the optimal capacity of the UPFC after relaxation.
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