CN106058887A - Reactive optimization method for improving qualified rate of power distribution network comprising distributed photovoltaic power sources - Google Patents
Reactive optimization method for improving qualified rate of power distribution network comprising distributed photovoltaic power sources Download PDFInfo
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- 238000005457 optimization Methods 0.000 title claims abstract description 46
- 238000000034 method Methods 0.000 title claims abstract description 24
- 239000002245 particle Substances 0.000 claims abstract description 9
- 239000003990 capacitor Substances 0.000 claims description 38
- 238000012797 qualification Methods 0.000 claims description 11
- 230000004308 accommodation Effects 0.000 claims description 7
- 238000004364 calculation method Methods 0.000 claims description 5
- 230000008569 process Effects 0.000 claims description 5
- 238000002347 injection Methods 0.000 claims description 3
- 239000007924 injection Substances 0.000 claims description 3
- 230000005611 electricity Effects 0.000 claims description 2
- 238000005304 joining Methods 0.000 claims description 2
- 238000012913 prioritisation Methods 0.000 claims description 2
- 230000008901 benefit Effects 0.000 abstract description 2
- 230000008859 change Effects 0.000 description 3
- 230000006872 improvement Effects 0.000 description 2
- FGUUSXIOTUKUDN-IBGZPJMESA-N C1(=CC=CC=C1)N1C2=C(NC([C@H](C1)NC=1OC(=NN=1)C1=CC=CC=C1)=O)C=CC=C2 Chemical compound C1(=CC=CC=C1)N1C2=C(NC([C@H](C1)NC=1OC(=NN=1)C1=CC=CC=C1)=O)C=CC=C2 FGUUSXIOTUKUDN-IBGZPJMESA-N 0.000 description 1
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Classifications
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
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- H02J3/383—
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/50—Photovoltaic [PV] energy
- Y02E10/56—Power conversion systems, e.g. maximum power point trackers
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/30—Reactive power compensation
Abstract
The invention discloses a reactive optimization method for improving a qualified rate of a power distribution network comprising distributed photovoltaic power sources. The method mainly comprises the following steps: when the photovoltaic power sources work in an MPPT mode, by taking minimization of whole-network voltage deviations as a target, performing reactive optimization on residual capacities of photovoltaic inverters by use of a particle swarm algorithm; if an optimization result still comprises a node voltage off-limit condition, employing an improved optimization scheme: first of all, under the condition that it is ensured that whole-network voltages are qualified, by taking maximization of total active output of the photovoltaic power sources as a target, obtaining an optimal active value of each photovoltaic power source; and then by taking the result as an active output value of each photovoltaic power source and by taking the minimization of the whole-network deviations as the target, performing the reactive optimization on the residual capacities of the photovoltaic inverters again. According to the invention, operation economic benefits and reliability of the power distribution network are taken into integrated consideration, distribution of active and reactive output of the photovoltaic inverters is optimized, and the voltage qualified rate of the power distribution network comprising the photovoltaic power sources is effectively improved.
Description
Technical field
The present invention relates to GA for reactive power optimization technical field, particularly relate to a kind of raising distribution Han distributed photovoltaic power
The idle work optimization method of net rate of qualified voltage.
Background technology
Along with becoming increasingly conspicuous of problem of energy crisis, regenerative resource is more favored by people, especially cleaning, nothing dirt
Contaminate, resource distribution is wide, exploit convenient solar energy.Photovoltaic generation efficiently utilizes the form of solar energy in the world as a kind of
Inside increase rapidly.Photo-voltaic power supply makes original single supply radial structure become many power supply architectures after being incorporated to power distribution network, change
Original direction of tide and size, along with the raising of photovoltaic permeability, the grid-connected impact on distribution network voltage is increasingly
Greatly.At present some scholars propose photovoltaic DC-to-AC converter while active power of output, also can export certain reactive power, permissible
The spare capacity of photovoltaic DC-to-AC converter is participated in the middle of the idle work optimization of power distribution network as continuously adjustable reactive power source.It addition,
Owing to inverter active output and idle output have coupling on capacity, when photovoltaic is meritorious exert oneself take capacity excessive time,
It is possible that call all residual capacities carry out reactive-load compensation cannot be by the situation in Voltage Cortrol to prescribed limit.
But, in prior art, meritorious output and idle output to photovoltaic DC-to-AC converter lack optimization method of completing the square, nothing
Method realizes photo-voltaic power supply and gains merit the target that output is maximum, the whole network voltage deviation is minimum.
Summary of the invention
Present invention aim at providing a kind of can the meritorious output of optimum distribution photovoltaic DC-to-AC converter and idle output, reality
Existing photo-voltaic power supply is gained merit and is exported raising distribution network voltage qualification rate Han distributed photovoltaic power maximum, that the whole network voltage deviation is minimum
Idle work optimization method.
For achieving the above object, have employed techniques below scheme: the method for the invention is by utilizing Particle Swarm Optimization
Method is optimized computing, solve photovoltaic DC-to-AC converter active reactive output optimal value, on-load transformer tap changer gear and
Compensation capacitors number so that power distribution network each node voltage deviation is minimum, improves distribution network voltage qualification rate;Concrete steps
As follows:
Step 1, on the premise of photo-voltaic power supply exports with MPPT, sets up the object function making the whole network voltage deviation minimum;
Step 2, carries out Load flow calculation according to distribution net work structure parameter, sets up the GA for reactive power optimization etc. containing photo-voltaic power supply
Formula retrains;
Step 3, with residual capacity, on-load transformer tap changer gear and the reactive-load compensation capacitor of photovoltaic DC-to-AC converter
Group is control variable, and each node voltage of power distribution network is state variable, sets up the GA for reactive power optimization inequality containing photo-voltaic power supply
Constraint;
Step 4, according to the object function set up, equality constraint and inequality constraints, utilizes particle cluster algorithm to carry out excellent
Change computing, solve the idle output valve of each inverter, load tap changer gear and Capacitor banks input group number;
Step 5,
5.1, in the optimum results obtained in each control variable range of accommodation, if occurring without the out-of-limit situation of node voltage,
It is now optimal case, terminates optimization process
5.2, in the optimum results obtained in each control variable range of accommodation, if still there being the out-of-limit situation of node voltage to go out
Existing, then proceed prioritization scheme;The first step optimizes, it is ensured that under the most qualified premise of the whole network voltage, with all photovoltaic electrics of power distribution network
The meritorious sum of exerting oneself in source is target to the maximum, with each control variable range of accommodation in the current photovoltaic meritorious output upper limit and step 3 is
Inequality constraints, solves each inverter active output optimal value;Second step optimizes, and each photo-voltaic power supply is in meritorious output optimal value
Under premise, return step 1, with the minimum target of the whole network voltage deviation, and carry out step 2,3,4 operations successively, finally solve
Output valve that each inverter active is idle, load tap changer gear and Capacitor banks input group number.
Further, the object function making the whole network voltage deviation minimum is set up in step 1, as shown in formula (1)
Wherein
In formula, UiFor the voltage of each node of power distribution network in addition to balance node,For each node voltage expected value, λ is
The out-of-limit penalty coefficient of node voltage, Uimax、UiminBeing respectively the bound value of node voltage, n is except balance node external system
Nodes.
Further, the GA for reactive power optimization equality constraint containing photo-voltaic power supply is set up in step 2, as shown in formula (2)
In formula, Gij、BijAnd θijIt is respectively conductance, susceptance and the phase difference of voltage between node i, j, PZi、QZiIt is respectively
The injection active power of node i and reactive power, PPVi、QPViIt is respectively node i and accesses the active power of photo-voltaic power supply and idle
Power, PLi、QLiIt is respectively active power and reactive power, the Q of load at node iCiIdle by the connect Capacitor banks of node i
Go out force value.
Further, the GA for reactive power optimization inequality constraints containing photo-voltaic power supply is set up in step 3, such as formula (3) institute
Show
In formula, QPViThe reactive power sent for i-th photo-voltaic power supply, QPVi.maxCan send for i-th photo-voltaic power supply
Reactive power maximum and meetNPVFor the quantity of photo-voltaic power supply, QCjElectric capacity is compensated for jth platform
The capacity that device puts into, LjCapacitor maximum group number, Q is compensated for jth platformCj0The appearance of capacitor list group capacitor is compensated for jth platform
Amount, NCCompensate the number of units of Capacitor banks, TtkFor the tap joint position of kth platform ULTC, Ttk.min、Ttk.maxIt is respectively
The tap joint position upper lower limit value of kth platform ULTC, NTThe quantity of ULTC, N is system node number,
Ui.min、Ui.maxIt is respectively the voltage upper lower limit value of i-th node.
Further, the first step optimization concrete grammar described in step 5.2 is as follows:
Under ensureing the most qualified premise of the whole network voltage, it is target to the maximum with the meritorious sum of exerting oneself of all photo-voltaic power supplies of power distribution network
Set up object function,
Wherein
In formula, PPViFor the active power of i-th photo-voltaic power supply output, UiFor each node of power distribution network in addition to balance node
Voltage, λ is the out-of-limit penalty coefficient of node voltage (for negative value), Uimax、UiminIt is respectively the bound value of node voltage, NPV
By the number of the photo-voltaic power supply that power distribution network is accessed, n is except the nodes of balance node external system;
Carry out successively step 2,3,4, solve each photo-voltaic power supply meritorious output optimal value.
Compared with prior art, present invention have the advantage that and considering power distribution network performance driving economy and reliability
On the basis of, the meritorious output of optimum distribution photovoltaic DC-to-AC converter and idle output, on the premise of ensureing that the whole network voltage is the most qualified,
Realize photo-voltaic power supply to gain merit the target that output is maximum, the whole network voltage deviation is minimum, be effectively improved the electricity containing photo-voltaic power supply power distribution network
Pressure qualification rate.
Accompanying drawing explanation
Fig. 1 is the flow chart of the inventive method.
Drawing reference numeral: 1 be first step optimization in step 5.2,2 be the second step optimization in step 5.2.
Detailed description of the invention
The present invention will be further described below in conjunction with the accompanying drawings:
As it is shown in figure 1, the method for the invention is by utilizing particle swarm optimization algorithm to be optimized computing, solve photovoltaic
Output optimal value that inverter active is idle, on-load transformer tap changer gear and compensation capacitors number so that join
Electrical network each node voltage deviation is minimum, improves distribution network voltage qualification rate;Specifically comprise the following steps that
A, on the premise of photo-voltaic power supply exports with MPPT, sets up the object function making the whole network voltage deviation minimum;Such as formula
(1) shown in
Wherein
In formula, UiFor the voltage of each node of power distribution network in addition to balance node,For each node voltage expected value, λ is
The out-of-limit penalty coefficient of node voltage, Uimax、UiminBeing respectively the bound value of node voltage, n is except balance node external system
Nodes.
B, carries out Load flow calculation according to distribution net work structure parameter, sets up the GA for reactive power optimization equation containing photo-voltaic power supply about
Bundle;As shown in formula (2)
In formula, Gij、BijAnd θijIt is respectively conductance, susceptance and the phase difference of voltage between node i, j, PZi、QZiIt is respectively
The injection active power of node i and reactive power, PPVi、QPViIt is respectively node i and accesses the active power of photo-voltaic power supply and idle
Power, PLi、QLiIt is respectively active power and reactive power, the Q of load at node iCiIdle by the connect Capacitor banks of node i
Go out force value.
C, with residual capacity, on-load transformer tap changer gear and the compensation capacitors of photovoltaic DC-to-AC converter be
Control variable, each node voltage of power distribution network is state variable, sets up the GA for reactive power optimization inequality constraints containing photo-voltaic power supply;
As shown in formula (3)
In formula, QPViThe reactive power sent for i-th photo-voltaic power supply, QPVi.maxCan send for i-th photo-voltaic power supply
Reactive power maximum and meetNPVFor the quantity of photo-voltaic power supply, QCjElectric capacity is compensated for jth platform
The capacity that device puts into, LjCapacitor maximum group number, Q is compensated for jth platformCj0The appearance of capacitor list group capacitor is compensated for jth platform
Amount, NCCompensate the number of units of Capacitor banks, TtkFor the tap joint position of kth platform ULTC, Ttk.min、Ttk.maxIt is respectively
The tap joint position upper lower limit value of kth platform ULTC, NTThe quantity of ULTC, N is system node number,
Ui.min、Ui.maxIt is respectively the voltage upper lower limit value of i-th node.
D, according to the object function set up, equality constraint and inequality constraints, utilizes particle cluster algorithm to be optimized fortune
Calculate, solve the idle output valve of each inverter, load tap changer gear and Capacitor banks input group number;
E, it is judged that the optimum results obtained in each control variable range of accommodation the most still has the out-of-limit situation of node voltage to occur,
If the out-of-limit situation of no-voltage, terminate optimization process;If still there being node that voltage out-of-limit situation occurs, the scheme of improving and optimizating is utilized to enter
Row optimizes, and improves and optimizates scheme optimization process and is divided into two steps, and in Fig. 1, in the dotted line frame of label 1 indication, step f, g, h are that improvement is excellent
The change scheme first step optimize, in Fig. 1 in the dotted line frame 2 of label 2 indication step i, j, k for improving and optimizating scheme second step optimization.
Improve and optimizate scheme first step optimization:
F, under ensureing the most qualified premise of the whole network voltage, is mesh to the maximum with the meritorious sum of exerting oneself of all photo-voltaic power supplies of power distribution network
Mark sets up object function, as shown in formula (4)
Wherein
In formula, PPViFor the active power of i-th photo-voltaic power supply output, UiFor each node of power distribution network in addition to balance node
Voltage, λ is the out-of-limit penalty coefficient of node voltage (for negative value), Uimax、UiminIt is respectively the bound value of node voltage, NPV
By the number of the photo-voltaic power supply that power distribution network is accessed, n is except the nodes of balance node external system;
G, carries out Load flow calculation according to the structural parameters of power distribution network, the foundation GA for reactive power optimization containing photo-voltaic power supply etc.
Formula retrains, as shown in formula (2).
With photovoltaic DC-to-AC converter meritorious output higher limit, photovoltaic DC-to-AC converter residual capacity, on-load transformer tap changer shelves
Position and compensation capacitors are control variable, and each node voltage of power distribution network is state variable, set up joining containing photo-voltaic power supply
Reactive power optimization inequality constraints, as shown in formula (5)
In formula, PPViFor photovoltaic active power output valve, PPVi.maxFor i-th photo-voltaic power supply in current time active power
Can be output by maximum, NPVFor the quantity of photo-voltaic power supply, QPViThe reactive power sent for i-th photo-voltaic power supply, QPVi.maxIt is
Reactive power maximum that i photo-voltaic power supply can send and meetingQCjElectricity is compensated for jth platform
The capacity that container puts into, LjCapacitor maximum group number, Q is compensated for jth platformCj0The appearance of capacitor list group capacitor is compensated for jth platform
Amount, NCCompensate the number of units of Capacitor banks, Ttk.min、Ttk.maxThe tap joint position being respectively kth platform ULTC is upper and lower
Limit value, NTThe quantity of ULTC, N is system node number, Ui.min、Ui.maxThe voltage being respectively i-th node is upper and lower
Limit value;
H, utilizes particle cluster algorithm to be optimized computing, solves each inverter active output optimal value.
Improve and optimizate scheme second step optimization:
I, in the first step optimizes under each photo-voltaic power supply of gained meritorious output optimal value premise, minimum with the whole network voltage deviation
Set up shown in object function such as formula (1) for target;
G, carries out Load flow calculation according to the structural parameters of power distribution network, the foundation GA for reactive power optimization containing photo-voltaic power supply etc.
Formula retrains, as shown in formula (2);
With photovoltaic DC-to-AC converter residual capacity, on-load transformer tap changer gear and compensation capacitors for controlling
Variable, each node voltage of power distribution network is state variable, sets up the GA for reactive power optimization inequality constraints containing photo-voltaic power supply, such as formula
(6) shown in
In formula, QPViThe reactive power sent for i-th photo-voltaic power supply, QPVi.maxCan send for i-th photo-voltaic power supply
Reactive power maximum and meetNPVFor the quantity of photo-voltaic power supply, QCjElectric capacity is compensated for jth platform
The capacity that device puts into, LjCapacitor maximum group number, Q is compensated for jth platformCj0The appearance of capacitor list group capacitor is compensated for jth platform
Amount, NCCompensate the number of units of Capacitor banks, Ttk.min、Ttk.maxThe tap joint position being respectively kth platform ULTC is upper and lower
Limit value, NTThe quantity of ULTC, N is system node number, Ui.min、Ui.maxThe voltage being respectively i-th node is upper and lower
Limit value;
K, uses particle cluster algorithm to carry out optimizing according to the described GA for reactive power optimization mathematical model containing photo-voltaic power supply
Solving-optimizing computing, finally solves the idle output valve of each inverter active, load tap changer gear and Capacitor banks and puts into
Group number, terminates optimization process.
Embodiment described above is only to be described the preferred embodiment of the present invention, the not model to the present invention
Enclose and be defined, on the premise of designing spirit without departing from the present invention, the those of ordinary skill in the art technical side to the present invention
Various deformation that case is made and improvement, all should fall in the protection domain that claims of the present invention determines.
Claims (5)
1. the idle work optimization method improved containing distributed photovoltaic power distribution network voltage qualification rate, it is characterised in that described
Method, by utilizing particle swarm optimization algorithm to be optimized computing, solves photovoltaic DC-to-AC converter active reactive output optimal value, has
Voltage adjustment of on-load load tap changer gear and compensation capacitors number so that power distribution network each node voltage deviation is minimum, improve
Distribution network voltage qualification rate;Specifically comprise the following steps that
Step 1, on the premise of photo-voltaic power supply exports with MPPT, sets up the object function making the whole network voltage deviation minimum;
Step 2, carries out Load flow calculation according to distribution net work structure parameter, sets up the GA for reactive power optimization equation containing photo-voltaic power supply about
Bundle;
Step 3, with residual capacity, on-load transformer tap changer gear and the compensation capacitors of photovoltaic DC-to-AC converter be
Control variable, each node voltage of power distribution network is state variable, sets up the GA for reactive power optimization inequality constraints containing photo-voltaic power supply;
Step 4, according to the object function set up, equality constraint and inequality constraints, utilizes particle cluster algorithm to be optimized fortune
Calculate, solve the idle output valve of each inverter, load tap changer gear and Capacitor banks input group number;
Step 5,
5.1, in the optimum results obtained in each control variable range of accommodation, if occurring without the out-of-limit situation of node voltage, now
For optimal case, terminate optimization process
5.2, in the optimum results obtained in each control variable range of accommodation, if still there being the out-of-limit situation of node voltage to occur, then
Proceed prioritization scheme;The first step optimizes, it is ensured that under the most qualified premise of the whole network voltage, gains merit with all photo-voltaic power supplies of power distribution network
Sum of exerting oneself is target to the maximum, and in the current photovoltaic meritorious output upper limit and step 3, each control variable range of accommodation is as inequality
Constraint, solves each inverter active output optimal value;Second step optimizes, and each photo-voltaic power supply is in meritorious output optimal value premise
Under, return step 1, with the minimum target of the whole network voltage deviation, and carry out step 2,3,4 operations successively, finally solve each inverse
Become device active reactive output valve, load tap changer gear and Capacitor banks input group number.
The raising the most according to claim 1 idle work optimization method containing distributed photovoltaic power distribution network voltage qualification rate,
It is characterized in that: set up the object function making the whole network voltage deviation minimum in step 1, as shown in formula (1)
Wherein
In formula, UiFor the voltage of each node of power distribution network in addition to balance node,For each node voltage expected value, λ is node
Voltage out-of-limit penalty coefficient, Uimax、UiminBeing respectively the bound value of node voltage, n is except the node of balance node external system
Number.
The raising the most according to claim 1 idle work optimization method containing distributed photovoltaic power distribution network voltage qualification rate,
It is characterized in that: set up the GA for reactive power optimization equality constraint containing photo-voltaic power supply in step 2, as shown in formula (2)
In formula, Gij、BijAnd θijIt is respectively conductance, susceptance and the phase difference of voltage between node i, j, PZi、QZiIt is respectively node i
Injection active power and reactive power, PPVi、QPViIt is respectively node i and accesses active power and the reactive power of photo-voltaic power supply,
PLi、QLiIt is respectively active power and reactive power, the Q of load at node iCiIdle exerting oneself by the connect Capacitor banks of node i
Value.
The raising the most according to claim 1 idle work optimization method containing distributed photovoltaic power distribution network voltage qualification rate,
It is characterized in that: set up the GA for reactive power optimization inequality constraints containing photo-voltaic power supply in step 3, as shown in formula (3)
In formula, QPViThe reactive power sent for i-th photo-voltaic power supply, QPVi.maxFor i-th photo-voltaic power supply can send idle
Power maximum and meetNPVFor the quantity of photo-voltaic power supply, QCjCompensate capacitor for jth platform to throw
The capacity entered, LjCapacitor maximum group number, Q is compensated for jth platformCj0The capacity of capacitor list group capacitor, N is compensated for jth platformCMend
Repay the number of units of Capacitor banks, TtkFor the tap joint position of kth platform ULTC, Ttk.min、Ttk.maxIt is respectively kth platform to have
The tap joint position upper lower limit value of voltage adjustment of on-load transformator, NTThe quantity of ULTC, N is system node number, Ui.min、
Ui.maxIt is respectively the voltage upper lower limit value of i-th node.
The raising the most according to claim 1 idle work optimization method containing distributed photovoltaic power distribution network voltage qualification rate,
It is characterized in that, it is as follows that the first step described in step 5.2 optimizes concrete grammar:
Under ensureing the most qualified premise of the whole network voltage, it is target to the maximum with the meritorious sum of exerting oneself of all photo-voltaic power supplies of power distribution network and sets up
Object function,
Wherein
In formula, PPViFor the active power of i-th photo-voltaic power supply output, UiFor the electricity of each node of power distribution network in addition to balance node
Pressure, λ is the out-of-limit penalty coefficient of node voltage (for negative value), Uimax、UiminIt is respectively the bound value of node voltage, NPVFor joining
The number of the photo-voltaic power supply that electrical network is accessed, n is except the nodes of balance node external system;
Carry out successively step 2,3,4, solve each photo-voltaic power supply meritorious output optimal value.
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