CN109802399B - Dynamic reactive power optimization method for extra-high voltage direct current converter station - Google Patents

Dynamic reactive power optimization method for extra-high voltage direct current converter station Download PDF

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CN109802399B
CN109802399B CN201910067450.5A CN201910067450A CN109802399B CN 109802399 B CN109802399 B CN 109802399B CN 201910067450 A CN201910067450 A CN 201910067450A CN 109802399 B CN109802399 B CN 109802399B
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reactive power
converter station
formula
converter
direct current
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CN109802399A (en
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颜伟
莫静山
钱威
田其生
肖繁
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Chongqing University
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
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Chongqing University
State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
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Abstract

The invention discloses a dynamic reactive power optimization method for an extra-high voltage direct current converter station, which mainly comprises the following steps: 1) and establishing a dynamic reactive power optimization model M of the extra-high voltage direct current converter station. 2) And calculating a dynamic reactive power optimization model M of the extra-high voltage direct current converter station by using a hybrid solving algorithm of dynamic reactive power optimization, thereby optimizing the extra-high voltage direct current converter station. According to the direct current transmission power plan and the dynamic reactive power reserve requirement of the system, the invention uses the residual capacity of the phase modulator to participate in the steady-state reactive voltage regulation of the converter station, and simultaneously considers that the phase modulator has higher up and down regulation margins, thereby realizing the coordination and coordination of the phase modulator and the direct current system and fully playing the performance of the phase modulator.

Description

Dynamic reactive power optimization method for extra-high voltage direct current converter station
Technical Field
The invention relates to the field of optimization of converter stations, in particular to a dynamic reactive power optimization method for an extra-high voltage direct current converter station.
Background
The direct current converter station is accompanied with a large amount of reactive power consumption while transmitting active power, the requirement of self balance is met by arranging an alternating current filter and a parallel capacitor under the normal condition, the direct current system changes phases by depending on alternating current voltage of a current conversion bus, and the reduction of the large-amplitude change of the voltage of the current conversion bus has important significance for preventing the direct current system from failing in phase change. With the large amount of grid connection of an extra-high voltage direct current transmission system, the problem of strong direct current and weak alternating current of a power grid is obvious, a national power grid company plans and constructs 47 large phase modulators to mainly solve the voltage stability problem caused by the grid connection of a large amount of direct current projects, however, the phase modulators which are put into operation at present mainly provide dynamic reactive power support after faults for the system, the steady state reactive power compensation function is withdrawn, meanwhile, the phase modulators and the direct current transmission system have respective control modes and control targets, the two systems are mutually independent, and effective coordination and coordination are not achieved. On the other hand, in the power market environment, frequent changes in the dc transmission power also increase the number of operations of discrete control devices such as a converter station static var compensator and a converter transformer.
The dynamic reactive power optimization method plays an important role in realizing the coordination of the reactive power of a generator (phase modulator), the tap gear of the on-load tap changing transformer and the capacitance reactor group switch and reducing the action times of discrete equipment. However, the existing research focuses on the reactive power optimization of an alternating current-direct current hybrid system, and takes a power transmission network and a power distribution network comprising a power plant, an alternating current transformer substation and a direct current converter station as objects, and the optimization calculation of the objects needs the source load power information of nodes of the whole network, so that the coordination and the coordination of the reactive power of a generator (phase modulator) of the whole network, a tap of an on-load tap-changing transformer and a capacitor-reactor group switch are realized, but the existing research is not suitable for the local optimization requirements of a single converter station and the phase; meanwhile, the above research does not consider the filtering requirement of the converter station, and the optimization result may not meet the switching requirement of the ac filter. Therefore, a new dynamic reactive power optimization model of the extra-high voltage direct current converter station needs to be researched, and the coordination of the phase modulator and the direct current transmission system and the filtering requirement of the system are considered.
Disclosure of Invention
The present invention is directed to solving the problems of the prior art.
The technical scheme adopted for achieving the purpose of the invention is that the dynamic reactive power optimization method of the extra-high voltage direct current converter station mainly comprises the following steps:
1) and establishing a dynamic reactive power optimization model M of the extra-high voltage direct current converter station.
The method mainly comprises the following steps of establishing a dynamic reactive power optimization model of the extra-high voltage direct current converter station:
1.1) setting an optimization objective function min f, namely:
Figure GDA0002460916220000021
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000022
and respectively representing the number of tap positions, the number of groups of input alternating current filters and the number of groups of input high-voltage parallel capacitors of the converter transformer of the direct current system in the time period t.
Figure GDA0002460916220000023
Figure GDA0002460916220000024
Respectively representing the ideal values of the reactive power of the phase modifier and the reactive power of the phase modifier in the time period t.
Figure GDA0002460916220000025
Respectively representing the commutation bus voltage amplitude and the commutation bus voltage amplitude control target in a time period t. a is1And the weight coefficient is the target of the number of times of tap position actions of the converter transformer of the direct current system. a is2And the weight coefficient is the target of the switch action times of the alternating current filter bank. a is3And the weight coefficient is the target of the switching action times of the high-voltage parallel capacitor bank. a is4And the weight coefficient is the target weight coefficient of the deviation of the reactive output of the phase modulator and the ideal value of the reactive output of the phase modulator. a is5And the weight coefficient is the deviation target of the amplitude value of the commutation bus voltage and the ideal control value of the commutation bus voltage. And n is 96.
Wherein, the time period t phase modulator has ideal reactive power output value
Figure GDA0002460916220000026
As follows:
Figure GDA0002460916220000027
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000028
and
Figure GDA0002460916220000029
respectively representing the upper limit and the lower limit of the allowable steady-state reactive power output of the phase modulator during the time period t.
1.2) setting constraint conditions, which mainly comprise alternating current-direct current system tidal current equation constraint, converter characteristic equation constraint, converter station and alternating current system coupling state variable constraint, converter station control variable constraint, system filtering requirement constraint and phase modulator dynamic reactive power reserve constraint.
1.2.1) the current equation constraints of the alternating current and direct current system are shown in formula 3 and formula 4.
The active power constraints are as follows:
Figure GDA00024609162200000210
in the formula (I), the compound is shown in the specification,
Figure GDA00024609162200000211
respectively representing the active power of the generator and/or phase modulator, the load, the inverter connected to node i during time period t. When the inverter is a rectifier, the inverter is,
Figure GDA00024609162200000212
when the converter is an inverter, the inverter is,
Figure GDA00024609162200000213
when the node i is a pure ac node,
Figure GDA00024609162200000214
SSLACKrepresenting a set of balanced nodes.
Figure GDA0002460916220000031
The active injection power equation for node i in time period t.
The reactive power constraints are as follows:
Figure GDA0002460916220000032
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000033
respectively representing the reactive power of the generator and/or phase modulator, the static reactive power compensation device, the load and the converter connected with the node i in the time period t. When node i is connected to the converter station sQi1, otherwise sQi＝0。SPQA set of PQ nodes is represented.
Figure GDA00024609162200000315
The reactive injection power equation for node i over time period t.
1.2.2) converter characteristic equation constraints are shown in equations 5 through 7.
Figure GDA0002460916220000034
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000035
respectively representing the pole-to-ground dc voltage, dc current of time period t.
Figure GDA0002460916220000036
Figure GDA0002460916220000037
And respectively representing the transformation ratio of the converter transformer and the triggering angle of the converter in the time period t, wherein the rectifying station is the triggering angle, and the inverting station is the turn-off angle. XcRepresenting the commutation reactance. k is a radical ofbRepresenting the number of pulsating converters per pole 6. k is a radical ofdTNRepresenting the rated ratio of the converter transformer valve side to the network side.
Figure GDA0002460916220000038
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000039
representing the total apparent power of the converter station during time period t. k is a radical ofpIndicating the number of converter station operating poles η indicates the factor to account for the introduction of commutation overlap phenomenon T is the period.
Figure GDA00024609162200000310
In the formula (I), the compound is shown in the specification,
Figure GDA00024609162200000311
and
Figure GDA00024609162200000312
respectively representing the active transmission power and the reactive power of the converter station in a time period t.
1.2.3) converter station to ac system coupling state variable constraints are as shown in equations 8 to 9.
The commutation bus voltage amplitude constraints are as follows:
Figure GDA00024609162200000313
in the formula of UH,maxAnd UH,minRespectively representing the upper limit and the lower limit of the amplitude of the commutation bus voltage.
The system reactive exchange constraints are as follows:
Figure GDA00024609162200000314
in the formula, Qexc,maxAnd Qexc,minRespectively representing the upper limit and the lower limit of the reactive exchange of the system.
Wherein, the time period t system reactive power exchange
Figure GDA0002460916220000041
As follows:
Figure GDA0002460916220000042
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000043
the period t is represented by the reactive compensation capacity of the ac filter/parallel capacitor of the converter station. The subscripts f, c denote the ac filter and the shunt capacitor, respectively, collectively (·). U shapeN(·)、QN(·)Respectively representing the ac filter or parallel capacitor voltage rating and the single set of rated capacities.
Reactive compensation capacity of alternating current filter/parallel capacitor of time interval t converter station
Figure GDA0002460916220000044
As follows:
Figure GDA0002460916220000045
in the formula, subscripts f and c respectively represent an alternating current filter and a parallel capacitor, and are collectively represented by (·); u shapeN(·)And QN(·)The converter station ac voltage ac filter and parallel capacitor voltage ratings and the single set of rated capacities are shown separately.
1.2.4) converter station control variable constraints are shown in equations 12 to 17. The discrete control variables of the converter station comprise tap positions of a converter transformer, an alternating current filter bank switch and a parallel capacitor bank switch. The converter station continuous control variables comprise phase modulator reactive power and converter control angle.
Figure GDA0002460916220000046
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000047
and
Figure GDA0002460916220000048
respectively representing the maximum lag phase and phase advance capability of the phase modulator.
Figure GDA0002460916220000049
The above formula represents the inequality of the cosine value of the control angle of the current converterThe formula constraint is that the control angle of the transmitting and receiving end converter stations is stabilized within a certain operation range in normal operation, and for the receiving end converter station, in order to prevent commutation failure, strategies such as minimum turn-off angle control are configured, so the control angle is uniformly expressed as about
Figure GDA00024609162200000410
Is constrained by the inequality of (a).
Figure GDA00024609162200000411
In the formula, TapdT,maxAnd TapdT,minRespectively representing the upper limit and the lower limit of the gear number of the tap of the converter transformer.
Figure GDA00024609162200000412
In the formula, Nf，maxThe upper limit of the number of ac filter banks to be applied.
Figure GDA00024609162200000413
Transformation ratio of converter transformer
Figure GDA00024609162200000414
As follows:
Figure GDA0002460916220000051
in the formula, Δ U represents a tap gear voltage regulation step of the converter transformer.
1.2.5) system filtering requirement constraints are shown in equations 18 and 19.
Figure GDA0002460916220000052
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000053
representing the minimum number of filter banks devoted to time period t.
Figure GDA0002460916220000054
Indicating the minimum number of filter banks to be devoted to the time period t by the system filtering requirements, i.e. with respect to the dc transmission power
Figure GDA0002460916220000055
As a function of (c).
The number of groups of the converter station participating in reactive compensation parallel capacitors is as follows:
Figure GDA0002460916220000056
in the formula, Nc,maxThe upper limit of the number of high-voltage parallel capacitor banks to be charged.
1.2.6) phase modulator dynamic var reserve constraints are as follows:
Figure GDA0002460916220000057
wherein, the phase modifier has an upper limit of steady-state reactive power output
Figure GDA0002460916220000058
And lower limit
Figure GDA0002460916220000059
Respectively as follows:
Figure GDA00024609162200000510
wherein, systemACtFor the time t, the operating state of the alternating current system, the above expression shows that the allowable steady-state reactive power output range of the phase modulator is closely related to the direct current transmission power, the operating state of the alternating current system and other factors.
1.3) establishing a dynamic reactive power optimization model M of the extra-high voltage direct current converter station based on the current equation constraint of the alternating current-direct current system, the characteristic equation constraint of the converter, the coupling state variable constraint of the converter station and the alternating current system, the control variable constraint of the converter station, the system filtering requirement constraint/phase modulator dynamic reactive power reserve constraint and an objective function minf.
2) And calculating a dynamic reactive power optimization model M of the extra-high voltage direct current converter station by using a hybrid solving algorithm of dynamic reactive power optimization, thereby optimizing the extra-high voltage direct current converter station.
The method comprises the following main steps of calculating a dynamic reactive power optimization model M of the extra-high voltage direct current converter station:
2.1) carrying out equivalent transformation on an absolute value target in the dynamic reactive power optimization model M objective function 1 of the extra-high voltage direct current converter station by using a formula 22, and converting the absolute value target into a nonlinear mixed integer programming model M 'containing a balance equation'
Figure GDA0002460916220000061
In the formula, XtJoint tap gear of converter transformer with unified representation time period t
Figure GDA0002460916220000062
Number of AC filter sets
Figure GDA0002460916220000063
Or number of parallel capacitor banks
Figure GDA0002460916220000064
The auxiliary variables introduced by the converter transformer/ac filter/parallel capacitor are collectively denoted.
2.2) carrying out equivalent transformation on the constraint conditions 19 in the dynamic reactive power optimization model M of the extra-high voltage direct current converter station by using a formula 23, and converting the constraint conditions into a nonlinear mixed integer programming model M' containing a balance equation.
Figure GDA0002460916220000065
In the formula, λ and μ represent a shape coefficient and a translation amount, respectively.
2.3) calculating a nonlinear mixed integer programming model M' so as to optimize the extra-high voltage direct current converter station, wherein the method mainly comprises the following steps:
2.2.1) discrete control variables and balance conditions in the relaxation model M ', and solving the relaxation solution of the nonlinear mixed integer programming model M' through iteration.
2.2.2) maintaining the continuous control variable of the converter station unchanged, and solving the optimal solution of the discrete control variable by adopting a dynamic programming method in the neighborhood of the relaxed solution of the discrete control variable under the condition of meeting the control variable constraint and the system filtering constraint of the converter station.
2.2.3) maintaining the discrete control variable unchanged, solving the optimal solution of the continuous control variable in each time period by a nonlinear interior point method, and if the convergence condition is met, taking the calculation result as the optimal solution of the dynamic reactive power optimization model M of the extra-high voltage direct current converter station. Otherwise, the continuous control variable is kept unchanged, the relaxation solution of the discrete control variable is solved by a nonlinear inner point method, and the step 2.2.2 is returned.
The technical effect of the present invention is undoubted. According to the direct current transmission power plan and the absolute minimum filter table of the converter station, the switching of the static reactive power compensation device of the converter station is subjected to modeling constraint, so that the optimization result meets the engineering requirement. Aiming at the problems that the efficiency of a phase modulator in engineering is not fully exerted and the coordination function of the phase modulator is not considered in the existing research, the invention uses the residual capacity of the phase modulator to participate in the steady-state reactive voltage regulation of a converter station according to a direct current transmission power plan and the dynamic reactive standby requirement of the system, and simultaneously considers that the phase modulator has higher up and down regulation margins, thereby realizing the coordination and the coordination of the phase modulator and a direct current system and fully exerting the performance of the phase modulator.
Drawings
FIG. 1 is an overall flow diagram;
FIG. 2 is an equivalent model of an extra-high voltage DC converter station;
FIG. 3 shows f (N)f) An image;
FIG. 4 is a commutation bus voltage deviation curve;
FIG. 5 is a system reactive exchange deviation curve;
fig. 6 is a phase modulator reactive power curve.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1 to 6, the method for dynamic reactive power optimization of an extra-high voltage direct current converter station considering the coordination of a phase modulator and the requirements of system filtering mainly comprises the following steps:
1) and establishing a dynamic reactive power optimization model M of the extra-high voltage direct current converter station.
The method mainly comprises the following steps of establishing a dynamic reactive power optimization model of the extra-high voltage direct current converter station:
1.1) setting an optimization objective function min f, aiming at the reduction of tap position of a converter transformer of a direct current system and the switching action times of static reactive compensation equipment, and simultaneously considering that the voltage fluctuation of a converter bus is small and a phase modulator has higher reactive power regulation capability. The optimization objective function min f is as follows:
Figure GDA0002460916220000071
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000072
and respectively representing the number of tap positions, the number of groups of input alternating current filters and the number of groups of input high-voltage parallel capacitors of the converter transformer of the direct current system in the time period t.
Figure GDA0002460916220000073
Figure GDA0002460916220000074
Respectively representing the ideal values of the reactive power of the phase modifier and the reactive power of the phase modifier in the time period t.
Figure GDA0002460916220000081
Respectively representing time interval t commutation bus voltage amplitudeValue and commutation bus voltage amplitude control target. a is1And the weight coefficient is the target of the number of times of tap position actions of the converter transformer of the direct current system. a is2And the weight coefficient is the target of the switch action times of the alternating current filter bank. a is3And the weight coefficient is the target of the switching action times of the high-voltage parallel capacitor bank. a is4And the weight coefficient is the target weight coefficient of the deviation of the reactive output of the phase modulator and the ideal value of the reactive output of the phase modulator. a is5And the weight coefficient is the deviation target of the amplitude value of the commutation bus voltage and the ideal control value of the commutation bus voltage. n is 96, i.e. optimized according to a 15min power transmission plan, with the number of time segments being 96.
In order to enable the phase modulator to have higher adjusting capacity under the conditions of overhigh voltage and overlow voltage of the current conversion bus, the ideal reactive power output value of the phase modulator is taken as a middle value of upper and lower limits of allowable steady-state reactive power output of the phase modulator in a time period t, and therefore the ideal reactive power output value of the phase modulator in the time period t
Figure GDA00024609162200000813
As follows:
Figure GDA0002460916220000082
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000083
and
Figure GDA0002460916220000084
respectively representing the upper limit and the lower limit of the allowable steady-state reactive power output of the phase modulator during the time period t.
1.2) setting constraint conditions, which mainly comprise alternating current-direct current system tidal current equation constraint, converter characteristic equation constraint, converter station and alternating current system coupling state variable constraint, converter station control variable constraint, system filtering requirement constraint and phase modulator dynamic reactive power reserve constraint. The constraint conditions not only comprise the operation constraint in the reactive power optimization of the conventional alternating current and direct current system, but also comprise special constraint conditions such as dynamic reactive power reserve of a phase modulator, system filtering requirements and the like.
1.2.1) the current equation constraints of the alternating current and direct current system are shown in formula 3 and formula 4.
The active power constraints are as follows:
Figure GDA0002460916220000085
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000086
respectively representing the active power of a generator and/or a phase modifier, a load and a current converter connected with the node i in a time period t; when the inverter is a rectifier, the inverter is,
Figure GDA0002460916220000087
when the converter is an inverter, the inverter is,
Figure GDA0002460916220000088
when the node i is a pure ac node,
Figure GDA0002460916220000089
SSLACKrepresenting a set of balancing nodes;
Figure GDA00024609162200000810
an active injection power equation of the node i in the time period t;
the reactive power constraints are as follows:
Figure GDA00024609162200000811
in the formula (I), the compound is shown in the specification,
Figure GDA00024609162200000812
respectively representing the reactive power of a generator and/or a phase modulator, a static reactive power compensation device, a load and a current converter which are connected with the node i in a time period t; when node i is connected to the converter station sQi1, otherwise sQi＝0；SPQRepresents a set of PQ nodes;
Figure GDA0002460916220000091
for node i inReactive injection power equation for time period t.
1.2.2) converter characteristic equation constraints are shown in equations 5 through 7.
Figure GDA0002460916220000092
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000093
respectively representing the pole-to-ground dc voltage, dc current of time period t.
Figure GDA0002460916220000094
Figure GDA0002460916220000095
And respectively representing the transformation ratio of the converter transformer and the triggering angle of the converter in the time period t, wherein the rectifying station is the triggering angle, and the inverting station is the turn-off angle. XcRepresenting the commutation reactance. k is a radical ofbRepresenting the number of pulsating converters per pole 6. k is a radical ofdTNRepresenting the rated ratio of the converter transformer valve side to the network side. The 6 pulsating converter consists of 6 converter valves. T is a period;
Figure GDA0002460916220000096
in the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000097
representing the total apparent power of the converter station during time period t. k is a radical ofpThe number of the operating poles of the converter station is shown, η shows a coefficient for taking account of the introduction of the commutation overlapping phenomenon, η is 0.995.
Figure GDA0002460916220000098
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000099
and
Figure GDA00024609162200000910
respectively representing the active transmission power and the reactive power of the converter station in a time period t.
1.2.3) converter station to ac system coupling state variable constraints are as shown in equations 8 to 9.
The commutation bus voltage amplitude constraints are as follows:
Figure GDA00024609162200000911
in the formula of UH,maxAnd UH,minRespectively representing the upper limit and the lower limit of the amplitude of the commutation bus voltage.
The system reactive exchange constraints are as follows:
Figure GDA00024609162200000912
in the formula, Qexc,maxAnd Qexc,minRespectively representing the upper limit and the lower limit of the reactive exchange of the system.
Wherein, the time period t system reactive power exchange
Figure GDA00024609162200000913
As follows:
Figure GDA00024609162200000914
in the formula (I), the compound is shown in the specification,
Figure GDA00024609162200000915
the period t is represented by the reactive compensation capacity of the ac filter/parallel capacitor of the converter station. The subscripts f, c denote the ac filter and the shunt capacitor, respectively, collectively (·). U shapeN(·)、QN(·)Respectively representing the ac filter or parallel capacitor voltage rating and the single set of rated capacities.
Reactive compensation capacity of alternating current filter/parallel capacitor of time interval t converter station
Figure GDA0002460916220000101
As follows:
Figure GDA0002460916220000102
in the formula, subscripts f and c respectively represent an alternating current filter and a parallel capacitor, and are collectively represented by (·); u shapeN(·)And QN(·)The converter station ac voltage ac filter and parallel capacitor voltage ratings and the single set of rated capacities are shown separately.
1.2.4) converter station control variable constraints are shown in equations 12 to 17. The discrete control variables of the converter station comprise tap positions of a converter transformer, an alternating current filter bank switch and a parallel capacitor bank switch. The converter station continuous control variables comprise phase modulator reactive power and converter control angle.
Figure GDA0002460916220000103
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000104
and
Figure GDA0002460916220000105
respectively representing the maximum lag phase and phase advance capability of the phase modulator.
Converter control angle cosine value constraint
Figure GDA0002460916220000106
The following were used:
Figure GDA0002460916220000107
the above equation represents the inequality constraint of the converter control angle cosine value. In normal operation, the control angle of the transmitting and receiving end converter station is stabilized within a certain range, and for the receiving end converter station, in order to prevent commutation failure and have control strategies such as minimum turn-off angle, the control strategies are uniformly expressed in the text as about
Figure GDA0002460916220000108
Is constrained by the inequality of (a).
Figure GDA0002460916220000109
In the formula, TapdT,maxAnd TapdT,minRespectively representing the upper limit and the lower limit of the gear number of the tap of the converter transformer.
Figure GDA00024609162200001010
In the formula, Nf，maxThe upper limit of the number of ac filter banks to be applied.
Figure GDA00024609162200001011
Transformation ratio of converter transformer
Figure GDA00024609162200001012
As follows:
Figure GDA00024609162200001013
in the formula, Δ U represents a tap gear voltage regulation step of the converter transformer.
1.2.5) system filtering requirement constraints are shown in equations 18 and 19.
In practical engineering, the switching of the ac filter bank is limited by the system filtering requirement, which is related to various factors such as the operation mode of the dc system and the dc transmission power, in addition to the requirement for self reactive power balance, and each dc converter station has a minimum filter and an absolute minimum filter configuration table. Since the capacity of a single set of different ac filters in a converter station is the same and the dc system is usually operated in a bipolar symmetrical manner, the absolute minimum filter set number requirement can be simply expressed as a function of the dc transmission power.
Figure GDA0002460916220000111
In the formula (I), the compound is shown in the specification,
Figure GDA0002460916220000112
representing the minimum number of filter banks devoted to time period t.
Figure GDA0002460916220000113
Indicating the minimum number of filter banks to be devoted to the time period t by the system filtering requirements, i.e. with respect to the dc transmission power
Figure GDA0002460916220000114
As a function of (c).
In addition, the parallel capacitor bank is usually put into use after the ac filter is completely put into operation, and the number of the parallel capacitor banks participating in reactive compensation in the converter station is as follows:
Figure GDA0002460916220000115
in the formula, Nc,maxThe upper limit of the number of high-voltage parallel capacitor banks to be charged.
1.2.6) the dynamic reactive power reserve of the phase modulator is related to a plurality of factors such as a transmitting end alternating current system, a receiving end alternating current system, direct current transmission power and the like, and the steady-state reactive power output of the phase modulator meets the requirement of the dynamic reactive power reserve of the system. The phase modulator dynamic reactive reserve constraints are as follows:
Figure GDA0002460916220000116
wherein, the phase modifier has an upper limit of steady-state reactive power output
Figure GDA0002460916220000117
And lower limit
Figure GDA0002460916220000118
Respectively as follows:
Figure GDA0002460916220000119
wherein, systemACtFor the time t, the operating state of the alternating current system, the above expression shows that the allowable steady-state reactive power output range of the phase modulator is closely related to the direct current transmission power, the operating state of the alternating current system and other factors.
Figure GDA00024609162200001110
To relate to direct current transmission power
Figure GDA00024609162200001111
And time period t communicates the system operating conditions.
Figure GDA00024609162200001112
To relate to direct current transmission power
Figure GDA00024609162200001113
And time period t communicates the system operating conditions.
1.3) establishing a dynamic reactive power optimization model M of the extra-high voltage direct current converter station based on the current equation constraint of the alternating current-direct current system, the characteristic equation constraint of the converter, the coupling state variable constraint of the converter station and the alternating current system, the control variable constraint of the converter station, the system filtering requirement constraint/phase modulator dynamic reactive power reserve constraint and an objective function min f.
2) And calculating a dynamic reactive power optimization model M of the extra-high voltage direct current converter station by using a hybrid solving algorithm of dynamic reactive power optimization, thereby optimizing the extra-high voltage direct current converter station.
The model M is a nonlinear mixed integer programming problem containing special function types such as a piecewise function, an absolute value function and the like. Considering the characteristic that the number of discrete control variables of the converter station is limited, all possible combination states in a relaxation solution neighborhood of the discrete control variables can be enumerated, and a dynamic planning method is adopted to obtain an optimal solution. Compared with a hybrid intelligent algorithm, the dynamic programming method has the characteristics of high solving efficiency and stable calculation result.
The method comprises the following main steps of calculating a dynamic reactive power optimization model M of the extra-high voltage direct current converter station:
2.1) carrying out equivalent transformation on an absolute value target in the dynamic reactive power optimization model M objective function 1 of the extra-high voltage direct current converter station by using a formula 22, and converting the absolute value target into a nonlinear mixed integer programming model M 'containing a balance equation'
Figure GDA0002460916220000121
In the formula, XtJoint tap gear of converter transformer with unified representation time period t
Figure GDA0002460916220000122
Number of AC filter sets
Figure GDA0002460916220000123
Or number of parallel capacitor banks
Figure GDA0002460916220000124
The auxiliary variables introduced by the converter transformer/ac filter/parallel capacitor are collectively denoted.
2.2) carrying out equivalent transformation on the constraint conditions 19 in the dynamic reactive power optimization model M of the extra-high voltage direct current converter station by using a formula 22, and converting the constraint conditions into a nonlinear mixed integer programming model M' containing a balance equation.
Figure GDA0002460916220000125
In the formula, λ and μ represent a shape coefficient and a translation amount, respectively.
2.3) calculating a nonlinear mixed integer programming model M' so as to optimize the extra-high voltage direct current converter station, wherein the method mainly comprises the following steps:
2.3.1) discrete control variables and balance conditions in the relaxation model M ', and solving the relaxation solution of the nonlinear mixed integer programming model M' through iteration.
2.3.2) maintaining the continuous control variables of the converter station unchanged, namely maintaining the continuous control variables such as reactive power of a phase modulator, a converter control angle and the like unchanged, satisfying formulas 14 to 19 under the condition of satisfying the control variable constraint of the converter station and the system filter variable constraint, respectively taking the nearest 1 integer solution from top to bottom in the neighborhood of the discrete control variable relaxation solution of the converter station, and solving the optimal solution by adopting a dynamic programming method.
2.3.3) maintaining the discrete control variable unchanged, solving the optimal solution of the continuous control variable in each time period by a nonlinear interior point method, and if the convergence condition is met, taking the calculation result as the optimal solution of the dynamic reactive power optimization model M of the extra-high voltage direct current converter station. Otherwise, the continuous control variable is kept unchanged, the relaxation solution of the discrete control variable is solved by a nonlinear inner point method, and the step 2.3.2 is returned.
Example 2:
an experiment for verifying a dynamic reactive power optimization method of an extra-high voltage direct current converter station considering the coordination function of a phase modulator and the system filtering requirement mainly comprises the following steps:
1) and selecting an extra-high voltage direct current sending end converter station, and carrying out dynamic reactive power optimization on the basis of a typical daily direct current transmission power plan curve of a certain domestic extra-high voltage direct current sending end converter station. The equivalent model of the extra-high voltage direct current transmitting end converter station is shown in figure 2, equivalent modeling is carried out on the converter station alternating current power grid based on a PSASP national dispatching data packet, and a converter station typical day direct current transmission power plan curve and an equivalent power source prediction curve are selected. In fig. 2, Zeq is the equivalent impedance and Beq is the equivalent admittance.
2) And (3) constructing a dynamic reactive power optimization model of the extra-high voltage direct current converter station considering the phase modulator coordination action and the system filtering requirement as shown in formulas (1) to (21), and solving by adopting the hybrid algorithm.
3) Multi-objective weight coefficient selection
Reasonable selection of the weight coefficient plays a key role in obtaining effective optimization results, and the weight coefficient a is given by qualitatively analyzing the result characteristics of each sub-target in the formula (1) and the requirements of the sub-target in actual operation1～a5The selection scheme of (1).
The numerical results of the tap gear of the converter transformer and the switch action times of the AC filter/parallel capacitor are a series of discrete integers, and a is taken in consideration of the influence of the equipment action times on the performances such as the service life and the like of the equipment1＝1，a2＝a310 and analysis based thereon a4And a5The value of (a).
The rated capacity of the phase modulator is approximately equal to that of a single group of static reactive power compensation devices, the dynamic reactive power standby requirement of a system and the steady-state regulation capacity of the phase modulator are considered, 2 phase modulators can replace one group of alternating current filters to compensate reactive power at most, and the order of magnitude of the deviation target of the reactive power output of the phase modulator and an ideal value in 96 time periods of a whole day under per unit system is 0-102Taking its weight coefficient a4＝10-2。
Compared with the first 4 targets, the importance degree of reducing the fluctuation target of the converter bus voltage within the allowable variation range is far less than that of the former target, and the magnitude of the deviation target of the converter bus voltage from the ideal value is 0-10 in 96 time periods per unit-3Taking its weight coefficient a5＝102。
2) Algorithmic effect analysis
And in the discrete control variable optimization stage, the nearest integer solution is respectively taken up and down in the neighborhood of the discrete control variable relaxation solution to calculate the optimal solution, so that the calculation speed is improved, the search space is reduced, and in order to verify the effectiveness of the scheme, the objective function values and the solution time when the values of the integer solutions are respectively 1-3 are compared.
The calculation results are shown in table 1:
TABLE 1 simulation calculation results for different values
Figure GDA0002460916220000141
In the above table, f1～f5Respectively representing 5 sub-target values of the action times of a converter transformer tap, the switch action times of an alternating current filter bank, the switch action times of a parallel capacitor bank, the reactive power deviation of a phase modulator and the voltage deviation of a converter bus, wherein f represents an optimization target value, namely the sum of the weighted values of the sub-target values.
And comparing the calculation time and the optimized target value when the values are different, wherein the calculation time when the value is 2 and the calculation time when the value is 3 are respectively 3.78 times and 9.99 times of the calculation time when the value is 1. The optimal target values are approximately equal when the number of values is 1 and 2, which can be ignored, and the optimal target values can be further reduced when the number of values is 3, but the optimal target values are obtained at the cost of greatly sacrificing the regulation capability of the phase modulator and increasing the number of times of the tap action of the converter transformer, which means that different sub-target values can be mutually converted with the increase of the search space, and although the target function value can be reduced, the unreasonable calculation result can be caused by the overlarge sub-target, and meanwhile, the influence of the weight coefficient of each sub-target on the optimal result can be reflected.
Therefore, a method of performing discrete control variable optimization by respectively taking 1 integer solution from top to bottom on the basis of reasonably selecting the weight coefficient by comprehensively considering the calculation speed, the optimization target value and each sub-target value is feasible.
3) Analysis of effect of phase modifier coordination
The coordination function of the phase modulator is mainly embodied in the aspects of the action times of discrete control equipment of a converter station, the voltage of a converter bus, the reactive power exchange fluctuation of a system, the reactive power regulation capability of the phase modulator and the like, and in order to verify the effectiveness of the model M, the following comparative test is designed:
s1: model M of the invention.
S2: on the basis of the model M of the invention, the dynamic reactive standby requirement of the phase modulator is not considered, namely the constraint condition does not comprise the expressions (21) and (22), and the weight coefficient a is set4＝0。
S3: and based on the actual control strategy of the system, the steady-state reactive voltage regulation function of the phase modulator is not considered.
I) Discrete control of device action times
The number of actions of the 3 schemes discrete control device is shown in table 2. Comparing S1 and S3, compared with the actual control strategy of the system, the number of the tap actions of the model converter transformer provided by the invention is reduced from 16 times to 10 times, and is reduced by 37.5%. The action times of the alternating current filter are reduced from 18 times to 16 times, and are reduced by 11.11 percent. Simulation results show that the steady-state reactive power output of the phase modulator is reasonably arranged, and the action times of discrete control equipment such as a converter transformer, an alternating current filter and the like can be effectively reduced.
TABLE 2 number of discrete control device actions
Figure GDA0002460916220000151
II) conversion of the bus voltage and reactive power exchange of the system
The expected (E) and standard deviation (σ) of the commutation bus voltage and system reactive power interchange from the respective ideal values were calculated and the results are shown in tables 3 and 4, respectively.
TABLE 3 commutation bus Voltage calculation results
Figure GDA0002460916220000152
TABLE 4 reactive exchange calculation results for the system
Figure GDA0002460916220000161
Comparing S1 and S3, the expectation and standard deviation of the model converter bus voltage and the system reactive power exchange from their respective ideal values are smaller than the actual control strategy of the system, and the simulation result shows that the phase modulator participating in the steady-state reactive voltage regulation can effectively reduce the converter bus voltage and the system reactive power exchange fluctuation, as shown in fig. 4 and 5.
III) dynamic reactive reserve for phase modulators
The phase modifier reactive power curve and the calculation result of the deviation of the phase modifier reactive power curve from the ideal value are respectively shown in fig. 6 and table 5, and S1 and S2 are compared, when the dynamic reactive power standby requirement of the system and the phase modifier adjusting capacity are not considered, in order to reduce the action times of discrete control equipment and the voltage fluctuation of a converter bus to the maximum extent, the phase modifier output is close to the limit of the capacity, so that the dynamic reactive power reserve of the system is insufficient, and the safety level of the transient voltage is reduced.
TABLE 5 phase Modulator reactive Power calculation results
Figure GDA0002460916220000162
4) System filtering requirement impact analysis
In order to verify the influence of the system filtering requirement on the optimization result, the following comparative experiment is designed:
s1: model M of the invention.
S4: on the basis of the model M of the invention, the system filtering requirement is not considered.
The calculation results of the sub-standard values of the two simulation schemes are shown in Table 6, f1～f5The meanings are the same as in Table 1. Simulation results show that when the system filtering requirement is not considered, S4 preferentially switches the parallel capacitors to meet the reactive power requirement of the converter station. The capacity of a single group of parallel capacitors of the system of the calculation example is larger than the capacity of the alternating current filter, and on the premise of meeting dynamic reactive power storage of the system and the allowable change range of the voltage of the converter bus, the static reactive power compensation device with larger capacity of the single group is preferentially switched to adapt to the change of direct current transmission power by properly sacrificing the steady-state regulation capability of the phase modulator and increasing the voltage fluctuation of the converter bus so as to further reduce the action times of discrete control equipment.
TABLE 6 sub-target calculation results of schemes S1 and S4
Figure GDA0002460916220000171

Claims (3)

1. The dynamic reactive power optimization method of the extra-high voltage direct current converter station considering the coordination function of a phase modulator and the system filtering requirement is characterized by comprising the following steps of:
1) establishing a dynamic reactive power optimization model M of the extra-high voltage direct current converter station, comprising the following steps of:
1.1) setting an optimization objective function min f, namely:
Figure FDA0002475898650000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000012
respectively representing the number of tap positions of a converter transformer of the direct current system, the number of input alternating current filter sets and the number of input high-voltage parallel capacitor sets in a time period t;
Figure FDA0002475898650000013
Figure FDA0002475898650000014
respectively representing ideal values of reactive power output of a phase modifier and reactive power output of the phase modifier in a time period t;
Figure FDA0002475898650000015
respectively representing a commutation bus voltage amplitude value and a commutation bus voltage amplitude value control target in a time period t; a is1Weighting coefficients of the frequency target of tap position actions of the converter transformer of the direct current system; a is2Weighting coefficients of the alternating current filter bank switch action frequency target; a is3A weight coefficient which is the target of the switching action times of the high-voltage parallel capacitor bank; a is4The weight coefficient is the deviation target of the reactive power output of the phase modulator and the ideal value of the reactive power output of the phase modulator; a is5The weight coefficient is the deviation target of the voltage amplitude of the commutation bus and the voltage amplitude ideal control value of the commutation bus;
wherein, the time period t phase modulator has ideal reactive power output value
Figure FDA0002475898650000016
As follows:
Figure FDA0002475898650000017
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000018
and
Figure FDA0002475898650000019
respectively representing the upper limit and the lower limit of allowable steady-state reactive power output of the phase modulator in the time period t;
1.2) setting constraint conditions, including AC/DC system tidal current equation constraint, converter characteristic equation constraint, converter station and AC system coupling state variable constraint, converter station control variable constraint, system filtering requirement constraint and phase modulator dynamic reactive power reserve constraint;
the current equation constraint of the alternating current-direct current system is shown as a formula (3) and a formula (4);
the active power constraints are as follows:
Figure FDA00024758986500000110
in the formula (I), the compound is shown in the specification,
Figure FDA00024758986500000111
respectively representing the active power of a generator and/or a phase modifier, a load and a current converter connected with the node i in a time period t; when the inverter is a rectifier, sPi1 is ═ 1; when the converter is an inverter, sPi-1; when node i is a pure AC node, sPi＝0；SSLACKRepresenting a set of balancing nodes; pi tAn active injection power equation of the node i in the time period t;
the reactive power constraints are as follows:
Figure FDA0002475898650000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000022
respectively representing the reactive power of a generator and/or a phase modulator, a static reactive power compensation device, a load and a current converter which are connected with the node i in a time period t; when node i is connected to the converter station sQi1, otherwise sQi＝0；SPQRepresents a set of PQ nodes;
Figure FDA00024758986500000213
reactive injection power for node i during time period tAn equation;
the current converter characteristic equation constraint is shown in an equation (5) to an equation (7);
Figure FDA0002475898650000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000024
a pole-to-ground direct current voltage and a direct current which respectively represent a time period t;
Figure FDA0002475898650000025
Figure FDA0002475898650000026
respectively representing the transformation ratio of the converter transformer and the control angle of the converter in the time period t; the control angle of the rectifier station is a trigger angle, and the control angle of the inverter station is a turn-off angle; xcRepresenting a commutation reactance; k is a radical ofbRepresenting the number of pulsating converters per pole 6; k is a radical ofdTNRepresenting the rated transformation ratio of the valve side of the converter transformer relative to the network side;
Figure FDA0002475898650000027
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000028
representing the apparent power of the converter station in time period tmotal; k is a radical ofpRepresenting the number of the operation poles of the converter station, η representing a coefficient introduced by a commutation overlapping phenomenon, T being a period;
Figure FDA0002475898650000029
in the formula (I), the compound is shown in the specification,
Figure FDA00024758986500000210
and
Figure FDA00024758986500000211
respectively representing active transmission power and reactive power of the converter station in a time period t;
the state variable constraint of the converter station and the alternating current system is shown in a formula (8) to a formula (9);
the commutation bus voltage amplitude constraints are as follows:
Figure FDA00024758986500000212
in the formula of UH,maxAnd UH,minRespectively representing the upper limit and the lower limit of the voltage amplitude of the commutation bus;
the system reactive exchange constraints are as follows:
Figure FDA0002475898650000031
in the formula, Qexc,maxAnd Qexc,minRespectively representing the upper limit and the lower limit of the reactive exchange of the system;
wherein, the time period t system reactive power exchange
Figure FDA0002475898650000032
As follows:
Figure FDA0002475898650000033
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000034
representing the reactive compensation capacity of an alternating current filter/parallel capacitor of the converter station in a time period t;
reactive compensation capacity of alternating current filter/parallel capacitor of time interval t converter station
Figure FDA0002475898650000035
As follows:
Figure FDA0002475898650000036
in the formula, subscripts f and c respectively represent an alternating current filter and a parallel capacitor, and are collectively represented by (·); u shapeN(·)And QN(·)Respectively representing rated voltage and single group rated capacity of an alternating voltage alternating current filter or a parallel capacitor of the converter station;
the constraint of the control variable of the converter station is shown in a formula (12) to a formula (17); the discrete control variables of the converter station comprise tap positions of a converter transformer, an alternating current filter bank switch and a parallel capacitor bank switch; the continuous control variables of the converter station comprise reactive power of a phase modulator and a converter control angle;
Figure FDA0002475898650000037
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000038
and
Figure FDA0002475898650000039
respectively representing the maximum lag phase and phase advance capacity of the phase modulator;
Figure FDA00024758986500000310
the above formula represents the inequality constraint of the cosine value of the control angle of the converter, because the control angle of the transmitting and receiving end converter stations is stable in a certain operation range in normal operation, and for the receiving end converter station, in order to prevent commutation failure, a minimum cut-off angle control strategy is configured, so that the control angle is uniformly expressed as about
Figure FDA00024758986500000311
Is constrained by an inequality of;
Figure FDA00024758986500000312
in the formula, TapdT,maxAnd TapdT,minRespectively representing the upper limit and the lower limit of the gear number of the tap of the converter transformer;
Figure FDA00024758986500000313
in the formula, Nf，maxThe upper limit of the number of the AC filter sets is input;
Figure FDA0002475898650000041
in the formula, Nc,maxThe upper limit of the number of high-voltage parallel capacitor groups is input;
transformation ratio of converter transformer
Figure FDA0002475898650000042
As follows:
Figure FDA0002475898650000043
in the formula, delta U represents the tap gear voltage regulating step length of the converter transformer;
the system filtering requirement constraints are shown in equation (18) and equation (19);
Figure FDA0002475898650000044
in the formula (I), the compound is shown in the specification,
Figure FDA0002475898650000045
represents the minimum filter bank number invested in the time period t;
Figure FDA0002475898650000046
indicating the minimum number of filter banks to be devoted to the time period t by the system filtering requirements, i.e. with respect to the dc transmission power
Figure FDA0002475898650000047
A function of (a);
the number of groups of the converter station participating in reactive compensation parallel capacitors is as follows:
Figure FDA0002475898650000048
in the formula, Nc,maxThe upper limit of the number of high-voltage parallel capacitor groups is input; n is a radical off，maxThe upper limit of the number of the AC filter sets is input;
the phase modulator dynamic reactive reserve constraints are as follows:
Figure FDA0002475898650000049
wherein, the phase modifier has an upper limit of steady-state reactive power output
Figure FDA00024758986500000410
And lower limit
Figure FDA00024758986500000411
Respectively as follows:
Figure FDA00024758986500000412
in the formula, SystemACtThe running state of the alternating current system is set; the expression shows that the allowable steady-state reactive power output range of the phase modulator is closely related to the running state of the direct current transmission power and the alternating current system;
Figure FDA00024758986500000413
for active transmission of power in time period t with respect to the converter station
Figure FDA00024758986500000414
Exchanging the function of the running state of the system with the time t;
Figure FDA00024758986500000415
for active transmission of power in time period t with respect to the converter station
Figure FDA00024758986500000416
Exchanging the function of the running state of the system with the time t;
1.3) establishing a dynamic reactive power optimization model M of the extra-high voltage direct current converter station based on the current equation constraint of the alternating current-direct current system, the characteristic equation constraint of the converter, the coupling state variable constraint of the converter station and the alternating current system, the control variable constraint of the converter station, the system filtering requirement constraint, the dynamic reactive power reserve constraint of the phase modulator and an objective function min f;
2) and calculating a dynamic reactive power optimization model M of the extra-high voltage direct current converter station by using a hybrid solving algorithm of dynamic reactive power optimization, thereby optimizing the extra-high voltage direct current converter station.
2. The extra-high voltage direct current converter station dynamic reactive power optimization method according to claim 1, wherein n is 96.
3. The method for dynamically reactive power optimization of the extra-high voltage direct current converter station according to claim 1, wherein the step of calculating the dynamic reactive power optimization model M of the extra-high voltage direct current converter station is as follows:
1) performing equivalent transformation on an absolute value target in a dynamic reactive power optimization model M objective function (1) of the extra-high voltage direct current converter station by using a formula (22), and converting the absolute value target into a nonlinear mixed integer programming model M' containing a balance equation;
Figure FDA0002475898650000051
in the formula, XtJoint tap gear of converter transformer with unified representation time period t
Figure FDA0002475898650000052
Number of AC filter sets
Figure FDA0002475898650000053
Or number of parallel capacitor banks
Figure FDA0002475898650000054
Figure FDA0002475898650000055
Auxiliary variables introduced by a converter transformer, an alternating current filter or a parallel capacitor are uniformly expressed;
2) carrying out equivalent transformation on constraint conditions (19) in the dynamic reactive power optimization model M of the extra-high voltage direct current converter station by using a formula (23), and converting the constraint conditions into a nonlinear mixed integer programming model M' containing a balance equation;
Figure FDA0002475898650000056
in the formula, λ and μ represent a shape coefficient and a translation amount, respectively; n is a radical off，maxThe upper limit of the number of the AC filter sets is input; n is a radical ofc,maxThe upper limit of the number of high-voltage parallel capacitor groups is input;
3) calculating a nonlinear mixed integer programming model M' so as to optimize the extra-high voltage direct current converter station, wherein the steps are as follows:
3.1) discrete control variables and balance conditions in the relaxation model M 'and solving a nonlinear mixed integer programming model M' through iteration; the discrete control variables of the converter station comprise tap positions of a converter transformer, an alternating current filter bank switch and a parallel capacitor bank switch; the continuous control variables of the converter station comprise reactive power of a phase modulator and a converter control angle;
3.2) maintaining the continuous control variable of the converter station unchanged, and solving the optimal solution of the discrete control variable by adopting a dynamic programming method in the neighborhood of the relaxed solution of the discrete control variable under the condition of meeting the control variable constraint and the system filtering constraint of the converter station;
3.3) maintaining the discrete control variable unchanged, solving the optimal solution of the continuous control variable in each time period by a nonlinear interior point method, and if the convergence condition is met, taking the calculation result as the optimal solution of the dynamic reactive power optimization model M of the extra-high voltage direct current converter station; otherwise, the continuous control variable is kept unchanged, the relaxation solution of the discrete control variable is solved by a nonlinear interior point method, and the step 3.2 is returned.
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