CN112670978B - Power grid operation optimization method and system - Google Patents
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Abstract
The invention discloses a power grid operation optimization method, which comprises the following steps: establishing an energy-saving economic optimization model of the power grid; acquiring calculation parameters required by an optimization model and active output adjustment measures of a candidate unit; correcting an adjustable space of an active output adjustment measure of the candidate unit; the method comprises the steps of adjusting the adjustable space of a generator according to various proportions to generate a space scheme with adjustable proportions; carrying out economic operation optimization on the space schemes with adjustable proportions; carrying out safety check under expected faults on each optimized scheme; the scheme with the biggest benefit is selected from the schemes passing through the safety check to serve as a final scheme, and decision support can be provided for power grid energy-saving economic operation optimization.
Description
Technical Field
The invention belongs to the technical field of power system automation, and particularly relates to a power grid operation optimization method and system.
Background
The invention belongs to the technical field of power system automation, and particularly relates to a power grid operation mode optimization adjustment method considering generation benefits and safety constraints.
The power grid reforms and requires an optimized energy supply and demand structure, enhances the development and utilization of renewable energy sources, cultures a batch of clean energy bases, accelerates the on-site digestion of wind power and photovoltaic power generation, enhances the construction of peak regulation capacity of the power grid, and effectively solves the problems of wind discarding, light discarding and water discarding. The aim of the power grid is to achieve reliable, safe, economical, efficient, environmentally friendly and safe use of the power grid operation. Meanwhile, the optimal power flow theory considering the base state and the expected fault safety constraint can effectively guarantee the safety of the power grid, but the expected faults of the power grid are numerous, and the process memory consumption is large and the calculation time is long when the mathematical programming method is directly adopted for solving, so that the practical application is difficult to realize.
And (3) sequencing candidate control measures according to the control performance indexes to sequentially participate in control based on the heuristic method of the control performance indexes, gradually adjusting until a final scheme is found, and combining an enumeration parallel mode to improve the calculation efficiency. Compared with a mathematical programming method, the heuristic method based on the control performance index is faster in calculation speed and easier to practically apply, but cannot guarantee to obtain an optimal solution.
Disclosure of Invention
The invention aims to provide a power grid operation optimization method which can maximize benefits under the condition of ensuring the operation safety of a power grid.
In order to achieve the above purpose, the present invention provides the following technical solutions:
in a first aspect, a power grid operation optimization method is provided, including:
establishing an energy-saving economic optimization model of the power grid;
acquiring calculation parameters required by an optimization model and active output adjustment measures of a candidate unit;
correcting an adjustable space of an active output adjustment measure of the candidate unit;
the method comprises the steps of adjusting the adjustable space of a generator according to various proportions to generate a space scheme with adjustable proportions;
carrying out economic operation optimization on the space schemes with adjustable proportions;
carrying out safety check under expected faults on each optimized scheme;
and selecting the scheme with the biggest profit from the schemes passing the security check as a final scheme.
With reference to the first aspect, further, the power grid energy-saving economic optimization model is shown as follows:
wherein N is t C is the number of thermal power units t For the market price of coal, P ti Is the active output of the ti-th thermal power unit, a 0,ti 、a 1,ti 、a 2,ti The coal consumption coefficients of the zero-order item, the primary item and the secondary item of the ti-th thermal power unit are respectively, and deltat is a control period; n (N) g Is the number of natural gas sets, C gas Is the market price of natural gas, P gk Is the active output of the gk-th natural gas engine set, a 0,gk 、a 1,gk 、a 2,gk The zero-order term, the primary term and the secondary term gas consumption coefficient of the gk-th natural gas unit; n (N) l For the number of loads, C d,l For the electricity price of the first load, P d,l Active power for the first load;
constraints of the model include:
constraint of a tide equation:
voltage safety constraints:
branch current constraint:
section active power constraint:
active output constraint of the unit:
standby constraint:
wherein P is Gi 、Q Gi 、P Di 、Q Di Active power supply power, reactive power supply power, active load, reactive load, V of the ith node respectively i 、δ i Voltage amplitude and phase angle of the ith node, Y ij 、α ij Admittance magnitude and phase angle, k, between the i-th node and the j-th node, respectively ij For the tap position of the transformer between the ith node and the jth node, S Kij Is a transformer set, S' Kij To condition the transformer set S' Kij For the adjustable non-ideal transformer side collection, Y' ii To disregard the self-admittance magnitude, Y ', of the ith node in the transformer branch' ij For the unit admittance amplitude of the adjustable transformer between the ith node and the jth node, Y' mj The unit admittance amplitude, Y 'of the adjustable non-ideal transformer between the mth node and the jth node' ll To be out of capacitor admittanceThe first node self-admittance magnitude, Y' l Admittance magnitude, k, for capacitor unit xl For the first node parallel capacitor/reactor tap to strain ratio, S X A set of parallel capacitor/reactor tap pair strain ratios; V i respectively the upper limit and the lower limit of the voltage of the ith node, S N Is a system node set; i ij For the line current amplitude between the i-th node and the j-th node,/and> I ij respectively the upper limit and the lower limit of the amplitude of the line current between the ith node and the jth node, S L Is a line set;active power for kth transmission section, < -> ij ΣPRespectively the upper limit and the lower limit of the active power of the kth transmission section, S ∑ Is a power transmission section set; /> P Gi S is the upper limit and the lower limit of the active output of the Gi table unit G Is an adjustable unit set; /> P ti The upper limit and the lower limit of the active output of the ti-th thermal power generating unit are respectively +.> P hj The upper limit and the lower limit of the active force of the hj-th hydroelectric generating set are respectively> P gk The upper limit and the lower limit of the active output of the gk-th natural gas engine set are respectively,P wm is the lower limit of the active output of the wm wind turbine,P pn is the lower limit of the active output of the pn-stage photovoltaic unit, R l 、R′ l Positive and negative capacity percentages, respectively.
With reference to the first aspect, further, the calculation parameters required by the optimization model include: control period, upper reserve coefficient, lower reserve coefficient, coal price, natural gas price, electrical parameters of lines and transformers, active output of a generator and limit value thereof, power generation flow and operating water head limit value of a hydropower station, consumption coefficient of the generator and active power of load.
With reference to the first aspect, further, the following adjustable space is adopted to correct the active output adjustment measures of the candidate unit;
wherein, P tgi the upper limit and the lower limit of the corrected active output of the tgi thermal power unit or the natural gas unit respectively, the upper limit and the lower limit of the original active power output of the tgi thermal power unit or the natural gas unit respectively are ++>Is the original active power output of tgi thermal power or natural gas unit, R tgi,down 、R tgi,up The downward slope climbing rate and the upward slope climbing rate of the tgi thermal power unit or the natural gas unit respectively; /> P hj The upper limit and the lower limit of the corrected active force of the hj-th hydroelectric generating set and the +.>The upper limit and the lower limit of the original power output of the hj-th hydroelectric generating set are respectively +.>For the original power output of the hj-th hydroelectric generating set, R hj,down 、R hj,up The downward slope climbing rate and the upward slope climbing rate, eta of the hj-th hydroelectric generating set are respectively hj For the efficiency of the hj-th hydroelectric generating set, < >> Q hj The upper limit and the lower limit of the power generation flow of the hj-th hydroelectric generating set are respectively +.> H hj The upper limit and the lower limit of the running water head of the hj-th hydroelectric generating set are respectively set;the upper limit and the lower limit of the corrected active output of the wpn wind power or photovoltaic unit are +.>The predicted active output of the wpn wind power or photovoltaic unit in the next calculation period is obtained.
With reference to the first aspect, further, the adjustable spatial schemes are generated by adopting the following formula:
wherein,the upper limit and the lower limit of the active output of the Gi unit under the mth scheme; p (P) Gi Active output of the Gi th unit; ρ m An adjustable space reduction ratio for the mth scheme; /> P Gi The upper limit and the lower limit of the corrected active output of the Gi table set are respectively set.
With reference to the first aspect, further, the performing safety check under the expected failure on each optimized solution includes: checking whether static overload, voltage and section safety problems exist or not through static safety analysis; and checking whether transient power angles, voltages, frequencies and dynamic damping safety problems exist through time domain simulation.
In a second aspect, there is provided a grid operation optimization system comprising:
modeling module: the method is used for establishing an energy-saving economic optimization model of the power grid;
the scheme generation module: the method comprises the steps of obtaining calculation parameters required by an optimization model and active output adjustment measures of a candidate unit;
correcting an adjustable space of an active output adjustment measure of the candidate unit;
the method comprises the steps of adjusting the adjustable space of a generator according to various proportions to generate a space scheme with adjustable proportions;
scheme optimizing module: the system is used for carrying out economic operation optimization on the adjustable space schemes of all the proportions;
carrying out safety check under expected faults on each optimized scheme;
and selecting the scheme with the biggest profit from the schemes passing the security check as a final scheme.
The beneficial technical effects are as follows: the invention establishes the power grid energy-saving economic operation optimization model taking the maximum power grid benefit as a target and taking the power flow equation, the voltage safety constraint, the line current constraint, the transformer power constraint, the section active power constraint, the unit active output constraint and the standby constraint into consideration. And decomposing the solving process into two stages of optimal power flow parallel calculation and expected fault safety check calculation which take the ground state safety constraint into consideration. Slicing the adjustable space of the active power output adjustment measures of the candidate unit according to different proportions, and solving the optimal power flow considering the ground state safety constraint by adopting an interior point method with strong robustness and good convergence based on the adjustable space after each slice. And carrying out safety check under expected faults on each optimized mode, and selecting a scheme with the biggest income from schemes passing through the safety check. The invention provides decision support for optimizing the energy-saving economic operation of the power grid on the premise of ensuring the safe and stable operation of the power grid under the condition of ground state and expected faults.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
As shown in fig. 1, the invention provides a power grid operation optimization method, which comprises the following steps:
s1, establishing a power grid energy-saving economic optimization model, and acquiring calculation parameters required by the optimization model and candidate unit active output adjustment measures;
the established power grid energy-saving economic optimization model is shown as a formula (1):
wherein N is t C is the number of thermal power units t For the market price of coal, P ti Is the active output of the ti-th thermal power unit, a 0,ti 、a 1,ti 、a 2,ti The coal consumption coefficients of the zero-order item, the primary item and the secondary item of the ti-th thermal power unit are respectively, and deltat is a control period; n (N) g Is the number of natural gas sets, C gas Is the market price of natural gas, P gk Is the active output of the gk-th natural gas engine set, a 0,gk 、a 1,gk 、a 2,gk The zero-order term, the primary term and the secondary term gas consumption coefficient of the gk-th natural gas unit; n (N) l For the number of loads, C d,l For the electricity price of the first load, P d,l Active power for the first load;
and the generating cost of hydroelectric, wind power and photovoltaic units is not considered.
Constraints of the model include:
constraint of a tide equation:
voltage safety constraints:
branch current constraint:
section active power constraint:
active output constraint of the unit:
standby constraint:
wherein P is Gi 、Q Gi 、P Di 、Q Di Active power supply power, reactive power supply power, active load, reactive load, V of the ith node respectively i 、δ i Voltage amplitude and phase angle of the ith node, Y ij 、α ij Admittance magnitude and phase angle, k, between the i-th node and the j-th node, respectively ij For the tap position of the transformer between the ith node and the jth node, S Kij Is a transformer set, S' Kij To condition the transformer set S' Kij For the adjustable non-ideal transformer side collection, Y' ii To disregard the self-admittance magnitude, Y ', of the ith node in the transformer branch' ij For the unit admittance amplitude of the adjustable transformer between the ith node and the jth node, Y' mj The unit admittance amplitude, Y 'of the adjustable non-ideal transformer between the mth node and the jth node' ll The first node self-admittance magnitude, Y 'at the time of capacitor admittance is not considered' l Admittance magnitude, k, for capacitor unit xl For the first node parallel capacitor/reactor tap to strain ratio, S X A set of parallel capacitor/reactor tap pair strain ratios; V i respectively the upper limit and the lower limit of the voltage of the ith node, S N Is a system node set; i ij For the line current amplitude between the i-th node and the j-th node,/and> I ij respectively the upper limit and the lower limit of the amplitude of the line current between the ith node and the jth node, S L Is a line set;active power for kth transmission section, < -> ij ΣPRespectively the upper limit and the lower limit of the active power of the kth transmission section, S ∑ Is a power transmission section set; /> P Gi S is the upper limit and the lower limit of the active output of the Gi table unit G Is an adjustable unit set; /> P ti The upper limit and the lower limit of the active output of the ti-th thermal power generating unit are respectively +.> P hj The upper limit and the lower limit of the active force of the hj-th hydroelectric generating set are respectively> P gk The upper limit and the lower limit of the active output of the gk-th natural gas engine set are respectively,P wm is the lower limit of the active output of the wm wind turbine,P pn is the lower limit of the active output of the pn-stage photovoltaic unit, R l 、R′ l Positive and negative capacity percentages (default 5%) respectively.
The calculation parameters required by the optimization model comprise: control period, upper reserve coefficient, lower reserve coefficient, coal price, natural gas price, electrical parameters of lines and transformers, active output of a generator and limit value thereof, power generation flow and operating water head limit value of a hydropower station, consumption coefficient of the generator and active power of load.
S2, correcting the adjustable space of the active power output adjustment measure of the candidate unit, and specifically correcting the adjustable space by adopting formulas (8) - (10).
Wherein, P tgi the upper limit and the lower limit of the corrected active output of the tgi thermal power unit or the natural gas unit respectively, the upper limit and the lower limit of the original active power output of the tgi thermal power unit or the natural gas unit respectively are ++>Is the original active power output of tgi thermal power or natural gas unit, R tgi,down 、R tgi,up The downward slope climbing rate and the upward slope climbing rate of the tgi thermal power unit or the natural gas unit respectively; /> P hj The upper limit and the lower limit of the corrected active force of the hj-th hydroelectric generating set and the +.>The upper limit and the lower limit of the original power output of the hj-th hydroelectric generating set are respectively +.>For hj-th hydropower stationOriginal active output of unit, R hj,down 、R hj,up The downward slope climbing rate and the upward slope climbing rate, eta of the hj-th hydroelectric generating set are respectively hj For the efficiency of the hj-th hydroelectric generating set, < >> Q hj The upper limit and the lower limit of the power generation flow of the hj-th hydroelectric generating set are respectively +.> H hj The upper limit and the lower limit of the running water head of the hj-th hydroelectric generating set are respectively set;the upper limit and the lower limit of the corrected active output of the wpn wind power or photovoltaic unit are +.>The predicted active output of the wpn wind power or photovoltaic unit in the next calculation period is obtained.
S3, adjusting the variable space of the generator according to various proportions to generate each proportion-adjustable space scheme, wherein the scheme is specifically shown in a formula (11):
wherein,the upper limit and the lower limit of the active output of the Gi unit under the mth scheme; p (P) Gi Active output of the Gi th unit; ρ m An adjustable space reduction ratio for the mth scheme; /> P Gi The upper limit and the lower limit of the corrected active force of the Gi table set are respectively (each scheme corresponds to a group of upper limit and lower limit).
S4, optimizing economic operation of the adjustable space schemes of each proportion by adopting an interior point method;
s5, carrying out safety check under expected faults on each optimized scheme, wherein the method specifically comprises the following steps:
checking whether static overload, voltage and section safety problems (voltage out-of-limit, section out-of-limit and the like) exist or not through static safety analysis; and checking whether transient power angles, voltages, frequencies and dynamic damping safety problems exist through time domain simulation.
S6, selecting a scheme with the biggest benefit from the schemes passing the security check as a final scheme.
Example 2
There is provided a grid operation optimization system comprising:
modeling module: the method is used for establishing an energy-saving economic optimization model of the power grid;
the scheme generation module: the method comprises the steps of obtaining calculation parameters required by an optimization model and active output adjustment measures of a candidate unit;
correcting an adjustable space of an active output adjustment measure of the candidate unit;
the method comprises the steps of adjusting the adjustable space of a generator according to various proportions to generate a space scheme with adjustable proportions;
scheme optimizing module: the system is used for carrying out economic operation optimization on the adjustable space schemes of all the proportions;
carrying out safety check under expected faults on each optimized scheme;
and selecting the scheme with the biggest profit from the schemes passing the security check as a final scheme.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (6)
1. A method for optimizing operation of a power grid, comprising:
establishing an energy-saving economic optimization model of the power grid;
acquiring calculation parameters required by an optimization model and active output adjustment measures of a candidate unit;
correcting an adjustable space of an active output adjustment measure of the candidate unit;
the method comprises the steps of adjusting the adjustable space of a generator according to various proportions to generate a space scheme with adjustable proportions;
carrying out economic operation optimization on the space schemes with adjustable proportions;
carrying out safety check under expected faults on each optimized scheme;
selecting a scheme with the biggest profit from the schemes passing the security check as a final scheme;
the energy-saving economic optimization model of the power grid is shown as follows:
wherein N is t C is the number of thermal power units t For the market price of coal, P ti Is the active output of the ti-th thermal power unit, a 0,ti 、a 1,ti 、a 2,ti The coal consumption coefficients of the zero-order item, the primary item and the secondary item of the ti-th thermal power unit are respectively, and deltat is a control period; n (N) g Is the number of natural gas sets, C gas Is the market price of natural gas, P gk Is the active output of the gk-th natural gas engine set, a 0,gk 、a 1,gk 、a 2,gk The zero-order term, the primary term and the secondary term gas consumption coefficient of the gk-th natural gas unit; n (N) l For the number of loads, C d,l For the electricity price of the first load, P d,l Active power for the first load;
constraints of the model include:
constraint of a tide equation:
voltage safety constraints:
branch current constraint:
section active power constraint:
active output constraint of the unit:
standby constraint:
wherein P is Gi 、Q Gi 、P Di 、Q Di Active power supply power, reactive power supply power, active load, reactive load, V of the ith node respectively i 、δ i Voltage amplitude and phase angle of the ith node, Y ij 、α ij Admittance magnitude and phase angle, k, between the i-th node and the j-th node, respectively ij For the tap position of the transformer between the ith node and the jth node, S Kij Is a transformer set, S' Kij To condition the transformer set S' Kij For the adjustable non-ideal transformer side collection, Y' ii To disregard the self-admittance magnitude, Y ', of the ith node in the transformer branch' ij For the unit admittance amplitude of the adjustable transformer between the ith node and the jth node, Y' mj For the mth node and the jth nodeUnit admittance amplitude, Y 'of adjustable non-ideal transformer between nodes' ll The first node self-admittance magnitude, Y 'at the time of capacitor admittance is not considered' l Admittance magnitude, k, for capacitor unit xl For the first node parallel capacitor/reactor tap to strain ratio, S X A set of parallel capacitor/reactor tap pair strain ratios; V i respectively the upper limit and the lower limit of the voltage of the ith node, S N Is a system node set; i ij For the line current amplitude between the i-th node and the j-th node,/and> I ij respectively the upper limit and the lower limit of the amplitude of the line current between the ith node and the jth node, S L Is a line set;active power for kth transmission section, < -> ij ΣPRespectively the upper limit and the lower limit of the active power of the kth transmission section, S ∑ Is a power transmission section set; /> P Gi S is the upper limit and the lower limit of the active output of the Gi table unit G Is an adjustable unit set; /> P ti The upper limit and the lower limit of the active output of the ti-th thermal power generating unit are respectively +.> P hj The upper limit and the lower limit of the active force of the hj-th hydroelectric generating set are respectively> P gk The upper limit and the lower limit of the active output of the gk-th natural gas engine set are respectively,P wm is the lower limit of the active output of the wm wind turbine,P pn is the lower limit of the active output of the pn-stage photovoltaic unit, R l 、R′ l Positive and negative capacity percentages, respectively.
2. The grid operation optimization method according to claim 1, wherein: the calculation parameters required by the optimization model comprise: control period, upper reserve coefficient, lower reserve coefficient, coal price, natural gas price, electrical parameters of lines and transformers, active output of a generator and limit value thereof, power generation flow and operating water head limit value of a hydropower station, consumption coefficient of the generator and active power of load.
3. The grid operation optimization method according to claim 1, wherein the following is adopted to correct the adjustable space of the candidate unit active output adjustment measures;
wherein, P tgi is tgi th station of thermal power respectivelyOr upper and lower limits of the corrected active output of the natural gas unit, < >> The upper limit and the lower limit of the original active power output of the tgi thermal power unit or the natural gas unit respectively are ++>Is the original active power output of tgi thermal power or natural gas unit, R tgi,down 、R tgi,up The downward slope climbing rate and the upward slope climbing rate of the tgi thermal power unit or the natural gas unit respectively; /> P hj The upper limit and the lower limit of the corrected active force of the hj-th hydroelectric generating set and the +.>The upper limit and the lower limit of the original power output of the hj-th hydroelectric generating set are respectively +.>For the original power output of the hj-th hydroelectric generating set, R hj,down 、R hj,up The downward slope climbing rate and the upward slope climbing rate, eta of the hj-th hydroelectric generating set are respectively hj For the efficiency of the hj-th hydroelectric generating set, < >> Q hj The upper limit and the lower limit of the power generation flow of the hj-th hydroelectric generating set are respectively +.> H hj The upper limit and the lower limit of the running water head of the hj-th hydroelectric generating set are respectively set; />The upper limit and the lower limit of the corrected active output of the wpn wind power or photovoltaic unit are +.>The predicted active output of the wpn wind power or photovoltaic unit in the next calculation period is obtained.
4. The grid operation optimization method according to claim 1, wherein the ratio-adjustable spatial schemes are generated by adopting the following formula:
wherein,the upper limit and the lower limit of the active output of the Gi unit under the mth scheme; p (P) Gi Active output of the Gi th unit; ρ m An adjustable space reduction ratio for the mth scheme; /> P Gi The upper limit and the lower limit of the corrected active output of the Gi table set are respectively set.
5. The grid operation optimization method according to claim 1, wherein the performing safety check on each optimized scheme under the expected failure includes: checking whether static overload, voltage and section safety problems exist or not through static safety analysis; and checking whether transient power angles, voltages, frequencies and dynamic damping safety problems exist through time domain simulation.
6. A grid operation optimization system, comprising:
modeling module: the method is used for establishing an energy-saving economic optimization model of the power grid;
the scheme generation module: the method comprises the steps of obtaining calculation parameters required by an optimization model and active output adjustment measures of a candidate unit;
correcting an adjustable space of an active output adjustment measure of the candidate unit;
the method comprises the steps of adjusting the adjustable space of a generator according to various proportions to generate a space scheme with adjustable proportions;
scheme optimizing module: the system is used for carrying out economic operation optimization on the adjustable space schemes of all the proportions;
carrying out safety check under expected faults on each optimized scheme;
selecting a scheme with the biggest profit from the schemes passing the security check as a final scheme;
the energy-saving economic optimization model of the power grid is shown as follows:
wherein N is t C is the number of thermal power units t For the market price of coal, P ti Is the active output of the ti-th thermal power unit, a 0,ti 、a 1,ti 、a 2,ti The coal consumption coefficients of the zero-order item, the primary item and the secondary item of the ti-th thermal power unit are respectively, and deltat is a control period; n (N) g Is the number of natural gas sets, C gas Is the market price of natural gas, P gk Is the active output of the gk-th natural gas engine set, a 0,gk 、a 1,gk 、a 2,gk The zero-order term, the primary term and the secondary term gas consumption coefficient of the gk-th natural gas unit; n (N) l For the number of loads, C d,l For the electricity price of the first load, P d,l Active power for the first load;
constraints of the model include:
constraint of a tide equation:
voltage safety constraints:
branch current constraint:
section active power constraint:
active output constraint of the unit:
standby constraint:
wherein P is Gi 、Q Gi 、P Di 、Q Di Active power supply power, reactive power supply power, active load, reactive load, V of the ith node respectively i 、δ i Voltage amplitude and phase angle of the ith node, Y ij 、α ij Admittance magnitude and phase angle, k, between the i-th node and the j-th node, respectively ij For the tap position of the transformer between the ith node and the jth node, S Kij Is a transformer set, S' Kij To condition the transformer set S' Kij For the adjustable non-ideal transformer side collection, Y' ii To disregard the self-admittance magnitude, Y ', of the ith node in the transformer branch' ij Is the ithThe unit admittance amplitude of the transformer can be adjusted between the node and the j node, Y' mj The unit admittance amplitude, Y 'of the adjustable non-ideal transformer between the mth node and the jth node' ll To the first node self-admittance magnitude at the time of capacitor admittance, Y l ' admittance magnitude in capacitor units, k xl For the first node parallel capacitor/reactor tap to strain ratio, S X A set of parallel capacitor/reactor tap pair strain ratios; V i respectively the upper limit and the lower limit of the voltage of the ith node, S N Is a system node set; i ij For the line current amplitude between the i-th node and the j-th node,/and> I ij respectively the upper limit and the lower limit of the amplitude of the line current between the ith node and the jth node, S L Is a line set; />Active power for kth transmission section, < -> ij ΣPRespectively the upper limit and the lower limit of the active power of the kth transmission section, S ∑ Is a power transmission section set; /> P Gi S is the upper limit and the lower limit of the active output of the Gi table unit G Is an adjustable unit set; /> P ti The upper limit and the lower limit of the active output of the ti-th thermal power generating unit are respectively +.> P hj The upper limit and the lower limit of the active output of the hj-th hydroelectric generating set are respectively, P gk the upper limit and the lower limit of the active output of the gk-th natural gas engine set are respectively,P wm is the lower limit of the active output of the wm wind turbine,P pn is the lower limit of the active output of the pn-stage photovoltaic unit, R l 、R′ l Positive and negative capacity percentages, respectively.
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