CN114819281A - Method for optimizing coordinated power flow between flexible direct-current power grid stations - Google Patents
Method for optimizing coordinated power flow between flexible direct-current power grid stations Download PDFInfo
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Abstract
The invention relates to the technical field of flexible direct-current power transmission, in particular to a method for optimizing coordinated power flow between flexible direct-current power grid stations, which comprises the following steps: the method comprises the steps that firstly, control parameters of the flexible direct-current power grid are brought into an optimization category, the control parameters comprise an active power reference value and a droop coefficient, and a power flow optimization mathematical model of the flexible direct-current power grid is established by taking the minimum network loss as a target; and solving the mathematical model for the power flow optimization of the flexible direct-current power grid based on an interior point method to realize the power flow optimization of the flexible direct-current power grid. The method provides reference for power system scheduling and converter station control parameter setting, and is beneficial to improving the economy and stability of the power system.
Description
Technical Field
The invention relates to the technical field of flexible direct current transmission, in particular to a method for optimizing a collaborative power flow between flexible direct current power grid stations.
Background
The flexible direct current transmission is important power for promoting the development of new energy, plays an important role in a future power grid, and is very suitable for the fields of new energy large-scale grid connection, island power supply and the like. The design of the control strategy of the multi-end flexible direct-current power grid is one of important research directions, and the control strategy can directly determine the power flow distribution of the power grid and the wind power consumption capability. At present, the control strategy of the flexible direct current power grid mainly comprises fixed direct current voltage control, fixed active power control and droop control. For the flexible direct current power grid, the control strategy of the converter station and the power grid greatly influences the power flow distribution of the system, and the control parameters of the converter station are key factors in the control strategy, are inseparable from the power flow distribution condition of the system, and have an important position in the power flow optimization problem. However, at present, the active power reference value is designed mostly by depending on experience, the value of the droop coefficient is distributed according to the capacity of the converter station, and the control parameter is not designed by considering the optimal power flow. In addition, as the proportion of new energy to be connected into the power grid is higher and higher, the power of the converter station connected with the new energy fluctuates, so that the power setting value and the actual power are unbalanced, and the stable operation and the tide optimization effect of the flexible direct current power grid of the whole power grid are influenced.
Although a large number of scholars research the flow optimization problem of the flexible direct-current power grid, most of literature optimization methods only aim at a certain operation section, and few literature relates to flow optimization under dynamic scenes such as power grid load and new energy power generation output fluctuation.
Disclosure of Invention
The invention provides a method for optimizing coordinated power flow between flexible direct current power grid stations, which can overcome some or some defects in the prior art.
The invention discloses a method for optimizing a coordinated power flow between flexible direct current power grid stations, which comprises the following steps of:
the method comprises the steps that firstly, control parameters of the flexible direct-current power grid are brought into an optimization category, the control parameters comprise an active power reference value and a droop coefficient, and a power flow optimization mathematical model of the flexible direct-current power grid is established by taking the minimum network loss as a target;
and solving the mathematical model for the power flow optimization of the flexible direct-current power grid based on an interior point method to realize the power flow optimization of the flexible direct-current power grid.
Preferably, the mathematical model for power flow optimization of the flexible direct-current power grid is as follows:
the optimal power flow problem of the flexible direct current power grid is to solve a nonlinear optimization problem, and the nonlinear optimization problem is represented by a mathematical model containing an objective function and constraint conditions, namely:
wherein x represents a decision variable; (x) represents an objective function; h (x) represents an equality constraint; g (x) represents an inequality constraint;
and (3) incorporating the converter station control strategy and the corresponding control variable reference value into the load flow optimization calculation, and expressing the state variable as follows:
x T ＝[U dc ,U dcref ,P ref ,K] (23)
wherein U is dc Indicating the direct current bus voltage of the converter station; p ref And represents an active power reference value; k represents the droop coefficient, and the number of the converter stations is set to be N VSC ，U dcref Has a dimension of N u ，P ref Has a dimension of N P Dimension of K is N droop Then, the above dimensions satisfy:
N VSC ＝N u +N P +N droop (24)
the method comprises the following steps of selecting a single target of network loss to optimize the power flow of the flexible direct-current power grid, wherein the system network loss is expressed as:
wherein U is i And U j Representing a direct voltage, G ij Represents the conductance between nodes i and j;
the stable operation point of the flexible direct current power grid is related to the direct current bus voltage and the injected active power of the converter station, and a power flow constraint equation is written according to the four-end direct current power grid topology column:
wherein P is Gi Representing active power, P, injected into the converter station i Di Representing a load directly connected with a converter station i, and U represents a converter station direct current bus voltage;
the objects controlled by different control modes of the converter station are different, and the active equation is expressed as follows:
P ref -P＝K(U-U dcref ) (27)
P i ＝P ref (28)
wherein K represents the sag factor, P ref Representing an active power reference value;
the converter station adopts a droop control mode, and the direct-current voltage and the injected active power of the converter station meet the formula (6); the converter station adopting a fixed active power control mode satisfies the formula (7);
and (3) taking the power variation of the two sampling points into consideration, linearizing the new energy output curve according to the sampling points, and expressing the power variation as follows:
P'(t+t c )＝P(t)+ΔP(t) (29)
wherein P (t) represents the active power injected by the converter station accessed to the new energy at the time t, and P' (t + t) c ) The active power injection amount after a sampling period is represented, and delta P represents the active power fluctuation amount at the beginning and the end of the period;
active power reference value Pref and actual power P' (t + t) of converter station c ) Unbalance, not satisfying equation (7), thus introducing a new active power reference value P' ref And satisfies the following conditions:
P' ref ＝P'(t+t c ) (30)
the flexible direct-current power grid power flow optimization inequality constraint condition is expressed as follows:
U dcmin ≤U dc ≤U dcmax (31)
P min ≤P ref ≤P max (32)
Q min ≤Q ref ≤Q max (33)
K min ≤K≤K max (34)
wherein U is dcmin And U dcmax Respectively representing the upper limit and the lower limit of the direct current bus voltage, considering the capacity margin of the converter station, and if the capacity of the converter station is S, the upper limit P of the active power reference value and the upper limit P of the reactive power reference value max 、Q max All take 0.8S, lower limit P min 、Q min All take-0.8S, the lower limit K of the droop coefficient K min An upper limit of K of 0 max The derivation formula of (d) is taken as:
preferably, the method for solving the power flow optimization problem of the flexible direct-current power grid by adopting the interior point method comprises the following steps:
s1, introducing a relaxation variable and a penalty function, and converting the original problem into an optimization problem only containing equality constraint;
s2, initializing each variable; taking the result of load flow calculation as direct current voltage U dc The droop coefficient K is selected according to the capacity proportion of each converter station;
s3, eliminating equality constraint by utilizing a Lagrange multiplier method, and converting the equality constraint into an unconstrained optimization problem;
s4, making the partial derivative of each variable be 0 according to the unconditional extremum solving method, to obtain a series of nonlinear equations where f (x) is 0, that is, a correction equation set in the newton method; finally, solving a correction equation set by using a Newton method to obtain a correction quantity delta X;
s5, judging whether a convergence condition delta X is met and is less than an allowable error epsilon, if so, correcting the variable and outputting data; if not, the variables are corrected and the process returns to S4.
Preferably, a relaxation variable and a penalty function are introduced to convert the equation (1) into an optimization problem only containing equality constraint, and the mathematical model of the optimization problem is represented as follows:
wherein u and l are relaxation variables, mu is a barrier constant, and mu is more than 0;
inequality constraints are bound to occur when the optimal power flow of the flexible direct-current power grid is solved, and the inner point method is to always keep the iteration process in a feasible domain, so that the problem of out-of-range control variable or function inequality needs to be processed;
because the upper limit and the lower limit of the control variable are clear, when the out-of-range condition occurs, the control variable is directly taken as the upper limit or the lower limit to continue iteration, namely:
the function inequality constraint is different from the control variable constraint, the function value is jointly determined by a plurality of variables, and the boundary can not be directly selected to continue iteration like the border crossing of the processing control variable; introducing a penalty function to avoid the condition that the function inequality is out of bounds in the iteration process, and expanding a penalty term of the target function in the equation (15) as follows:
the subscript i denotes the order of the inequality constraint, and as the function h (x) approaches the boundary, the penalty function approaches infinity, which forces the control variable to iterate in the direction of decreasing penalty function, thus ensuring that the iterative process is always within the feasible region.
The invention provides a flexible direct current power grid inter-station cooperation power flow optimization strategy. Firstly, key control parameters of the direct current power grid are brought into an optimization category, and a flexible direct current power grid power flow optimization mathematical model is established by taking minimum network loss as a target. And then, solving the power flow optimization mathematical model of the flexible direct-current power grid based on an interior point method. The method provides reference for power system scheduling and converter station control parameter setting, and is beneficial to improving the economy and stability of the power system.
Drawings
Fig. 1 is a flowchart of a method for optimizing coordinated power flow between stations of a flexible direct-current power grid in embodiment 1;
FIG. 2 is a schematic diagram of a four-terminal MMC test system in example 1;
fig. 3 is a schematic diagram of a method for implementing an inter-station cooperative optimization strategy in embodiment 1;
FIG. 4 is a schematic diagram showing the relationship between the time of the optimization algorithm and the sampling interval time in embodiment 1;
fig. 5 is a flow chart of the power flow optimization of the flexible direct-current power grid based on the interior point method in embodiment 1;
FIG. 6 is a graph showing the convergence characteristics of the interior point method in example 1;
FIG. 7 is a schematic diagram showing the comparison of the grid losses before and after droop control optimization in example 1;
fig. 8 is a schematic diagram of the converter station injected active power before optimization in embodiment 1;
FIG. 9 is a schematic diagram of the converter station injected active power after optimization in embodiment 1;
FIG. 10 is a schematic diagram showing comparison of network loss before and after optimization in example 1;
fig. 11 is a schematic diagram of the converter station voltage variation during the optimization in embodiment 1.
Detailed Description
For a further understanding of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples. It is to be understood that the examples are illustrative of the invention and not limiting.
Example 1
As shown in fig. 1, the present embodiment provides a method for optimizing a coordinated power flow between flexible direct current power grid stations, which includes the following steps:
the method comprises the steps that firstly, control parameters of the flexible direct-current power grid are brought into an optimization category, the control parameters comprise an active power reference value and a droop coefficient, and a power flow optimization mathematical model of the flexible direct-current power grid is established by taking the minimum network loss as a target;
and solving the mathematical model for the power flow optimization of the flexible direct-current power grid based on an interior point method to realize the power flow optimization of the flexible direct-current power grid.
1. Optimal power flow model of flexible direct current power grid
Solving the optimal power flow problem of the flexible direct current power grid is actually solving a nonlinear optimization problem, and the nonlinear optimization problem can be represented by a mathematical model containing an objective function and constraint conditions, namely:
wherein x represents a decision variable; (x) represents an objective function; h (x) represents an equality constraint; g (x) represents an inequality constraint.
In this embodiment, a four-terminal high-voltage direct-current power transmission network based on an MMC voltage source converter developed by a modified CIGRE B4-57 working group is used as a test system, and a topological structure and a per unit resistance value of the test system are shown in fig. 2. The converter stations 1,2 and 4 are connected with an alternating current system, and the converter station 3 is connected with a new energy power generation system. The converter stations 1, 3 operate in a rectifying state and the converter stations 2 and 4 operate in an inverting state. FIG. 3 shows a block diagram of the optimization method provided by the embodiment, wherein 4 converter stations are provided with sampling devices and upload data to a terminal at certain intervalsAnd the terminal optimizes parameters, obtains the optimal control parameters at the time t through calculation of an optimization algorithm, and then sends the optimal control parameters to each converter station, so that the moisture flow distribution of the flexible direct-current power grid is improved. FIG. 4 shows the calculation time t of the optimization algorithm s With a sampling interval time t c If t is satisfied s <<t c Therefore, the flexible direct-current power grid can be ensured to be always in the optimal running state.
With the development of new energy power generation prediction technology, short-term or ultra-short-term prediction methods and theories are certainly developed, prediction accuracy is continuously improved, and the new energy power generation amount after accurate prediction can enable an optimization process to be better, so that the power flow distribution of a flexible direct current power grid is effectively improved.
1.1, state variables
The converter station control strategy and the corresponding control variable reference value are included in the load flow optimization calculation, and then the state variable can be expressed as:
x T ＝[U dc ,U dcref ,P ref ,K] (44)
wherein U is dc Indicating the direct current bus voltage of the converter station; p ref And represents an active power reference value; k represents a sag factor.
The number of the converter stations controlled by the constant direct current voltage is N u The number of the converter stations controlled by the constant active power is N P The number of the convertor stations adopting the droop control is N droop . Then U is dcref Has a dimension of N u ，P ref Has a dimension of N P Dimension of K is N droop (ii) a Setting the number of converter stations to N VSC Then, the above dimensions satisfy:
N VSC ＝N u +N P +N droop (45)
1.2, objective function
For an electric power system, the system power flow can be optimized from multiple angles, such as network loss, voltage deviation, power generation cost, pollution degree of the environment and the like. The voltage deviation is directly related to the voltage of the direct-current node, and the voltage deviation can be controlled by controlling the upper limit and the lower limit of the variable, so that the method selects a single goal of network loss to optimize the power flow of the flexible direct-current power grid, can improve the power flow and improve the calculation speed, and the time of the system running in the optimal power flow in an updating period is longer. Ignoring the node-to-earth admittance, the system loss can be expressed as:
wherein U is i And U j Representing a direct voltage, G ij Representing the conductance between nodes i and j.
1.3, constraint conditions
1) Flow restraint
The stable operating point of the flexible direct current power grid is related to the direct current bus voltage and the injected active power of the converter station, and a power flow constraint equation can be written according to the topology of the four-end direct current power grid:
wherein P is Gi Representing active power, P, injected into the converter station i Di Representing the load directly connected to the converter station i and U representing the converter station dc bus voltage.
2) Equality constraint under different control modes
Different objects are controlled by different control modes of the converter station, and the active equation of the four-terminal MMC direct-current system can be expressed as follows:
P ref -P＝K(U-U dcref ) (48)
P i ＝P ref (49)
wherein K represents the sag factor, P ref Representing the active power reference value.
The direct-current voltage and the converter station injection active power of the converter stations 1 and 2 adopting a droop control mode meet the formula (6); the converter stations 3,4 in the active power control mode should satisfy equation (7).
3) Equality constraint considering new energy power generation output or load fluctuation
The generated output of the new energy has fluctuation, and different from a conventional generator set, the generated energy of the new energy can be greatly changed in each sampling period. And (4) taking the power variation of the two sampling points into consideration, and linearizing the new energy output curve according to the sampling points. Its power variation can be expressed as:
P'(t+t c )＝P(t)+ΔP(t) (50)
wherein P (t) represents the active power injected by the converter station accessed to the new energy at the time t, and P' (t + t) c ) The active power injection amount after one sampling period is shown, and Δ P represents the active power fluctuation amount at the beginning and the end of the period.
Active power reference value Pref and actual power P' (t + t) of converter station c ) Unbalanced, and does not satisfy formula (7). Therefore, a new active power reference value P 'is introduced' ref And satisfies the following conditions:
P' ref ＝P'(t+t c ) (51)
at the moment, for the whole power grid, the fixed active power control converter station with unbalanced power is externally balanced, and the actual unbalanced power is jointly absorbed by the converter stations adopting the droop control mode.
Since the constraint (7) changes, all the converter station direct-current voltages and active powers related to the equation (5) change accordingly, and the constraint changes greatly, so that the optimal solution changes inevitably.
4) Constraint of state variable
The flexible direct-current power grid power flow optimization inequality constraint condition can be expressed as follows:
U dcmin ≤U dc ≤U dcmax (52)
P min ≤P ref ≤P max (53)
Q min ≤Q ref ≤Q max (54)
K min ≤K≤K max (55)
wherein U is dcmin And U dcmax Respectively representing the upper limit and the lower limit of the DC bus voltage, and generally taking 1.05U dcN And 0.95U dcN . Considering the capacity margin of the converter station, if the capacity of the converter station is S, the upper limits P of the active power reference value and the reactive power reference value max 、Q max All take 0.8S, lower limit P min 、Q min All take-0.8S. Lower limit K of sag factor K min An upper limit of K of 0 max The derivation formula of (d) is taken as:
2. optimization algorithm
The Interior Point Method (IPM) has the characteristics of strong robustness, good convergence performance, suitability for processing continuous variables and the like, is favored by optimization problem researchers, and is gradually and widely applied to solving the power flow optimization problem of the power system. Therefore, the method solves the problem of power flow optimization of the flexible direct-current power grid by adopting an interior point method. By introducing a relaxation variable and a penalty function, equation (1) can be converted into an optimization problem only containing equality constraint, and the mathematical model can be expressed as:
wherein u and l are relaxation variables, mu is a barrier constant, and mu is more than 0.
Inequality constraints are bound to occur when the optimal power flow of the flexible direct-current power grid is solved, and the core idea of the interior point method is to always keep the iteration process in a feasible domain, so that the problem of out-of-range control variable or function inequality needs to be processed.
Control variable crossing boundary
Because the upper limit and the lower limit of the control variable are clear, when the out-of-range condition occurs, the control variable can be directly taken as the upper limit or the lower limit to continue iteration. Namely:
function inequality out-of-range
The function inequality constraint is different from the control variable constraint, the function value is jointly determined by a plurality of variables, and the continuous iteration of directly taking the boundary as if the processing control variable is out of range can not be carried out. A penalty function is usually introduced to avoid the situation that the function inequality is out of bounds during the iteration process, and the penalty term of the objective function in equation (15) can be expanded as follows:
the subscript i denotes the order of the inequality constraint, and as the function h (x) approaches the boundary, the penalty function approaches infinity, which forces the control variable to iterate in the direction of decreasing penalty function, thus ensuring that the iterative process is always within the feasible region.
Equation (15) is an optimization problem only including equality constraint, and can be solved by converting the lagrange multiplier method into a nonlinear equation set, and the whole algorithm flow is shown in fig. 5, specifically:
s1, introducing a relaxation variable and a penalty function, and converting the original problem into an optimization problem only containing equality constraint;
s2, initializing each variable; the result of the load flow calculation is usually taken as the dc voltage U dc And an initial value of the active power P of the converter station, the droop coefficient K being based onThe capacity proportion of each converter station is an initial value properly selected according to the capacity proportion;
s3, eliminating equality constraint by utilizing a Lagrange multiplier method, and converting the equality constraint into an unconstrained optimization problem;
s4, making the partial derivative of each variable be 0 according to the unconditional extremum solving method, to obtain a series of nonlinear equations where f (x) is 0, that is, a correction equation set in the newton method; finally, solving a correction equation set by using a Newton method to obtain a correction quantity delta X;
s5, judging whether a convergence condition delta X is met and is less than an allowable error epsilon, if so, correcting the variable and outputting data; if not, the variables are corrected and the process returns to S4.
3. Examples and simulation analysis
In order to verify the correctness and the effectiveness of the method for optimizing the power flow of the flexible direct-current power grid, the method uses the four-terminal MMC flexible direct-current power grid as a test system and utilizes a PSCAD/EMTDC platform to perform simulation. Reference value of power S B 600MVA, reference value U of DC voltage N ＝400kV。
3.1 load flow optimization under droop control mode
The converter stations MMC1 and MMC2 adopt a droop control mode, and the converter stations MMC3 and MMC4 adopt a constant active power control mode. In order to more intuitively show the parameter changes of the converter station under different control modes, the generalized droop control coefficients alpha, beta and gamma are used as unified parameters, and the operation parameters and the voltage deviation of the converter station before and after optimization are shown in tables 1 and 2.
TABLE 1 converter station control parameters and DC Voltage deviations before optimization
TABLE 2 optimized converter station control parameters and DC voltage deviations
The maximum iteration number of the interior point method is 200, the iteration error epsilon is set to be 10e-8, iteration is terminated when the iteration number reaches 200 or the adjacent iteration result is smaller than epsilon, and the method is realized through compiling of an fmincon tool box in matlab. Fig. 6 shows the variation of the objective function value as the number of iterations increases, and the optimal solution converges when the number of iterations is 32.
The objective function values before and after optimization and the total loss of the flexible direct-current power grid are respectively shown in table 3 and fig. 7:
TABLE 3 before and after droop control optimization objective function values
As can be seen by comparing table 1 and table 2, the droop coefficient of the converter station MMC1 adopting the droop control mode is reduced and the droop coefficient of the converter station MMC2 is increased, which indicates that the initial droop coefficient selected according to the capacities of the converter stations MMC1 and MMC2 is not the optimal value. Similarly, the active power reference values of the converter stations MMC3 and MMC4 are greatly changed after being optimized, which indicates that the initial active power reference values of the converter stations MMC3 and MMC4 are not optimal values, and the control parameters can further improve the power flow distribution of the flexible direct-current power grid after being optimized, thereby proving the necessity of optimizing droop coefficients and the active power reference values in a droop control mode. As can be seen from table 3 and fig. 7, the power grid loss after the power flow optimization is significantly reduced compared with that before the optimization, and the correctness and the effectiveness of the optimization method provided by the embodiment are verified.
3.2 consideration of load flow optimization under load fluctuation
Under the background of high-permeability new energy grid connection, how to enable the optimal state of the tidal current distribution of the system not to be influenced by load and power generation output fluctuation is a problem worthy of research. In order to further verify that the optimization method provided by the embodiment has adaptability to the optimal distribution of the power flow of the flexible direct-current power grid under the condition of load and power generation output fluctuation, the section is based on a PSCAD/EMTDC platform, and a simulation model is used as a test system for simulation verification.
The simulation time length is taken as 5s, the system stably operates when t is 1s, the load of an alternating current system connected with the MMC4 is increased by 20% when t is 2s, and the output of an alternating current system generator connected with the MMC3 is reduced by 20% when t is 4 s. The simulation is performed based on the set 3 scenes, and fig. 8 and 9 show the change conditions of the injected active power before and after the optimization of the converter station respectively, so that the power of the converter station can still keep a stable operation state under the condition of the change of the control parameters. FIG. 10 shows the variation of the system loss in 3 scenarios before and after optimization
As can be seen from fig. 10, when the system in the scene i operates stably, the optimization effect is obvious, when the system in the scene ii operates, the load of the system increases, the converter station 4 injects active power deviating from the reference value, and the operation parameters are updated by the optimization algorithm after being uploaded by the acquisition device, so that each converter station operates near a new reference point. As the total load of the system is increased, the network loss is increased, and the optimization effect is still not obvious at the moment; and the active power output of the scene III system is reduced, the converter station 3 injects active power deviating from the reference value, and similarly, the operation parameters of the converter station are updated through an optimization algorithm after the operation parameters are uploaded by the acquisition device, so that each converter station operates near a new reference point, the network loss is reduced, and the optimization effect is obvious. In general, under the scene of system load and active output fluctuation, the optimization method provided by the embodiment can reduce the network loss on the basis of maintaining the stable operation of the converter station.
Fig. 11 shows the voltage variation of the converter station during the optimization, and the voltage fluctuation of the dc node is not obvious when the system load fluctuates because the test system used in this embodiment has a simple structure and the parameter updating speed is fast. The optimized direct-current voltage of each converter station is within the constraint range, and the deviation from the rated value is not large, which indicates that the optimized direct-current voltage of the flexible direct-current power grid meets the normal operation requirement.
4. Conclusion
(1) The method is characterized in that the minimum network loss is taken as a target, the influence of the new energy power generation output or the load fluctuation on the constraint condition is considered, an optimal power flow mathematical model is constructed, the active power reference value in the droop control mode is optimized by using an interior point method, and simulation proves that the network loss can be effectively reduced and the optimal distribution of the power flow of the flexible direct-current power grid can be realized by optimizing the droop coefficient and the active power reference value.
(2) The embodiment also considers the applicability of the optimization method in the situations of load fluctuation and active power output change, and simulation results show that the optimization effect is different according to the time when the fluctuation occurs, but generally, the optimization method can reduce network loss to a certain extent, and has great promotion effect on the optimization effect of the method along with the development of a short-term or ultra-short-term prediction method and theory of new energy.
The two sets of simulation data verify the correctness and the effectiveness of the optimization method provided by the embodiment, provide references for system scheduling and setting of droop coefficients and active power reference values in the background of the existing high-permeability renewable energy sources, and have certain theoretical and practical significance. If an ultra-short-term load prediction technology is combined, the optimization efficiency is effectively improved, and the power regulation effect of the flexible direct-current power grid is further enhanced.
The present invention and its embodiments have been described above schematically, without limitation, and what is shown in the drawings is only one of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, if the person skilled in the art receives the teaching, without departing from the spirit of the invention, the person skilled in the art shall not inventively design the similar structural modes and embodiments to the technical solution, but shall fall within the scope of the invention.
Claims (4)
1. A method for optimizing a collaborative power flow between flexible direct current power grid stations is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the steps that firstly, control parameters of the flexible direct-current power grid are brought into an optimization category, the control parameters comprise an active power reference value and a droop coefficient, and a power flow optimization mathematical model of the flexible direct-current power grid is established by taking the minimum network loss as a target;
and solving the mathematical model for the power flow optimization of the flexible direct-current power grid based on an interior point method to realize the power flow optimization of the flexible direct-current power grid.
2. The method for optimizing the coordinated power flow between the flexible direct-current power grid stations according to claim 1, wherein the method comprises the following steps: the power flow optimization mathematical model of the flexible direct-current power grid is as follows:
the optimal power flow problem of the flexible direct current power grid is to solve a nonlinear optimization problem, and the nonlinear optimization problem is represented by a mathematical model containing an objective function and constraint conditions, namely:
wherein x represents a decision variable; (x) represents an objective function; h (x) represents an equality constraint; g (x) represents an inequality constraint;
and (3) incorporating the converter station control strategy and the corresponding control variable reference value into the load flow optimization calculation, and expressing the state variable as follows:
x T ＝[U dc ,U dcref ,P ref ,K] (2)
wherein U is dc Indicating the direct current bus voltage of the converter station; p ref And represents an active power reference value; k represents the droop coefficient, and the number of the converter stations is set to be N VSC ，U dcref Has a dimension of N u ，P ref Has a dimension of N P Dimension of K is N droop Then, the above dimensions satisfy:
N VSC ＝N u +N P +N droop (3)
the method comprises the following steps of selecting a single target of network loss to optimize the power flow of the flexible direct-current power grid, wherein the system network loss is expressed as:
wherein U is i And U j Representing a direct voltage, G ij Represents the conductance between nodes i and j;
the stable operation point of the flexible direct current power grid is related to the direct current bus voltage and the injected active power of the converter station, and a power flow constraint equation is written according to the four-end direct current power grid topology column:
wherein P is Gi Representing active power, P, injected into the converter station i Di Representing a load directly connected with a converter station i, and U represents a converter station direct current bus voltage;
the objects controlled by different control modes of the converter station are different, and the active equation is expressed as follows:
P ref -P＝K(U-U dcref ) (6)
P i ＝P ref (7)
wherein K represents the sag factor, P ref Representing an active power reference value;
the converter station adopts a droop control mode, and the direct-current voltage and the injected active power of the converter station meet the formula (6); the converter station adopting a fixed active power control mode satisfies the formula (7);
and (3) taking the power variation of the two sampling points into consideration, linearizing the new energy output curve according to the sampling points, and expressing the power variation as follows:
P'(t+t c )＝P(t)+ΔP(t) (8)
wherein P (t) represents the active power injected by the converter station accessed to the new energy at the time t, and P' (t + t) c ) The active power injection amount after a sampling period is represented, and delta P represents the active power fluctuation amount at the beginning and the end of the period;
active power reference value Pref and actual power P' (t + t) of converter station c ) Unbalance, not satisfying equation (7), thus introducing a new active power reference value P' ref And satisfies the following conditions:
P' ref ＝P'(t+t c ) (9)
the flexible direct-current power grid power flow optimization inequality constraint condition is expressed as follows:
U dcmin ≤U dc ≤U dcmax (10)
P min ≤P ref ≤P max (11)
Q min ≤Q ref ≤Q max (12)
K min ≤K≤K max (13)
wherein U is dcmin And U dcmax Respectively representing the upper limit and the lower limit of the direct current bus voltage, considering the capacity margin of the converter station, and if the capacity of the converter station is S, the upper limit P of the active power reference value and the upper limit P of the reactive power reference value max 、Q max All take 0.8S, lower limit P min 、Q min All take-0.8S, the lower limit K of the droop coefficient K min An upper limit of K of 0 max The derivation formula of (d) is taken as:
3. the method for optimizing the coordinated power flow between the flexible direct-current power grid stations according to claim 2, wherein the method comprises the following steps: the method for solving the problem of power flow optimization of the flexible direct-current power grid by adopting the interior point method comprises the following steps:
s1, introducing a relaxation variable and a penalty function, and converting the original problem into an optimization problem only containing equality constraint;
s2, initializing each variable; taking the result of load flow calculation as direct current voltage U dc The droop coefficient K is selected according to the capacity proportion of each converter station;
s3, eliminating equality constraint by utilizing a Lagrange multiplier method, and converting the equality constraint into an unconstrained optimization problem;
s4, making the partial derivative of each variable be 0 according to the unconditional extremum solving method, to obtain a series of nonlinear equations where f (x) is 0, that is, a correction equation set in the newton method; finally, solving a correction equation set by using a Newton method to obtain a correction quantity delta X;
s5, judging whether a convergence condition delta X is met and is less than an allowable error epsilon, if so, correcting the variable and outputting data; if not, the variables are corrected and the process returns to S4.
4. The method for optimizing the coordinated power flow between the flexible direct-current power grid stations according to claim 3, wherein the method comprises the following steps: introducing a relaxation variable and a penalty function, and converting the equation (1) into an optimization problem only containing equality constraint, wherein the mathematical model is represented as:
wherein u and l are relaxation variables, mu is a barrier constant, and mu is more than 0;
inequality constraints are bound to occur when the optimal power flow of the flexible direct-current power grid is solved, and the inner point method is to always keep the iteration process in a feasible domain, so that the problem of out-of-range control variable or function inequality needs to be processed;
because the upper limit and the lower limit of the control variable are clear, when the out-of-range condition occurs, the control variable is directly taken as the upper limit or the lower limit to continue iteration, namely:
the function inequality constraint is different from the control variable constraint, the function value is jointly determined by a plurality of variables, and the boundary can not be directly selected to continue iteration like the border crossing of the processing control variable; introducing a penalty function to avoid the condition that the function inequality is out of bounds in the iteration process, and expanding a penalty term of the target function in the equation (15) as follows:
the subscript i denotes the order of the inequality constraint, and as the function h (x) approaches the boundary, the penalty function approaches infinity, which forces the control variable to iterate in the direction of decreasing penalty function, thus ensuring that the iterative process is always within the feasible region.
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