CN107546743B - Distributed power flow optimization method for radial power distribution network - Google Patents
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Abstract
The invention discloses a distributed power flow optimization method for a radial power distribution network, which comprises the following steps: connecting photovoltaic power generation and battery energy storage devices into a power distribution network in a distributed manner, and constructing an optimized power flow model of the power distribution network; the method comprises the steps of dividing an original problem of power distribution network optimized power flow into a plurality of subproblems by constructing an augmented Lagrange function, and solving the original problem by adopting an asynchronous iteration mode among the subproblems; and decomposing the optimized power flow model into an upper layer and a lower layer, and realizing distributed solution on the optimized power flow problem by adopting an alternating direction multiplier algorithm to obtain the final optimal output of each distributed unit and the electricity price of each node. The distributed method designed by the invention can be realized only by exchanging upper and lower layers of limited boundary information, and node shadow prices related to internal constraint of the power distribution network and the power price of the root node of the power distribution network are mutually independent, so that the distributed method can be used as a coordination strategy of a power distribution system operator to an aggregation in a power market environment.
Description
Technical Field
The invention relates to the field of electrical engineering, in particular to a distributed power flow optimization method for a radial power distribution network, which is used for solving the problem of regulation and control of the power distribution network containing distributed power supplies.
Background
At present, a large amount of renewable energy power generation is merged into a power distribution network in a distributed mode, so that the traditional power distribution network mainly powered on gradually shows the active characteristic, and the difficulty of power balance and voltage support regulation is increased. In addition, small power sources are often merged into the power distribution network in a distributed mode, and meanwhile the potential of active regulation and control participated by a user is gradually paid attention to, so that the voltage problem caused by the fact that distributed renewable energy sources are connected to the power distribution network can be effectively relieved or solved through reasonable regulation and control of active quantities distributed in the power distribution network, the local problem is locally solved, the power distribution network can be matched with a conventional unit for regulation and control, and the economical efficiency of the overall operation of the system is improved. At the moment, the power distribution network is changed from the traditional passive mode to the active mode, and regulation and control of the power distribution network are also changed from the pure reactive power optimization to the active and reactive power combined optimization. However, the active regulation and control unit (such as an energy storage battery) has the characteristics of small monomer capacity, large quantity, dispersion in a low-voltage distribution network and the like, and the traditional centralized regulation and control mode is difficult to achieve. Therefore, related researches try to regulate and control distributed power generation in a layered and distributed mode, a series of defects existing in a centralized regulation and control mode are overcome, and the problem that the regulation and control of distributed power generation units in a power distribution network is a distributed dynamic optimization trend is solved.
The prior art discloses a power distribution network optimal power flow solving method, which divides an active power distribution network optimal power flow scheduling period into a plurality of sections which are connected in series, and forms an optimal power flow scheduling strategy of the whole scheduling period by constructing a state transition equation of the sections and combining optimal decisions of the sections. The method realizes the lowest operation cost in a complete scheduling period on the basis of meeting various network operation constraints and ensuring the maximum utilization of renewable energy sources.
The method determines the operation peak-valley time period of the distribution network according to the characteristic analysis and load prediction results of the accessed distributed power supply, the micro-grid and the load, determines the daily output curve of the distributed power supply and the micro-grid and the power plan of the adjustable load, and uniformly allocates the power supply-distribution network-load operation state. The method can maximally consume the proportion of renewable energy sources on the basis of ensuring the safe and reliable power supply of the intelligent power distribution network, improve the economical efficiency of the power distribution network, realize short-term energy balance,
however, the above-mentioned methods are all in order to implement centralized scheduling, and need to transmit a large amount of information of the power distribution units, which is not favorable for the confidentiality of the operation information of each power distribution unit.
The prior art discloses a power distribution network economic dispatching method, which is characterized in that a power distribution network economic dispatching model which comprises a plurality of control areas and takes network loss into consideration is established, and the active power output by a local generator with optimal global economic benefit is obtained by adopting an alternative direction multiplier method. Although the method realizes the distribution calculation formula of the power distribution network optimization power flow, the method is too simple for processing the voltage problem in the power distribution network, does not relate to detailed modeling in a power distribution unit or a polymer, and has certain limitation.
Disclosure of Invention
The invention provides a distributed power flow optimization method for a radial power distribution network, aiming at solving the problems, the method can be realized only by exchanging limited boundary information of an upper layer and a lower layer, and node shadow prices related to internal constraints of the power distribution network and power prices of root nodes of the power distribution network are independent from each other and can be used as a coordination strategy of power distribution system operators to aggregates in a power market environment.
In order to achieve the purpose, the invention adopts the following technical scheme:
a distributed power flow optimization method for a radial power distribution network comprises the following steps:
(1) aiming at a radial topological structure of a power distribution network, connecting photovoltaic power generation and battery energy storage devices into the power distribution network in a distributed manner;
(2) constructing a power distribution network optimization power flow model, wherein the model takes the minimum overall operation cost of the power distribution network as a target and comprises a plurality of constraint conditions: the power flow equation constraint of the node j, the voltage equation constraint, the voltage constraint, the current constraint and the additional constraint of the branch ij;
(3) constructing an augmented Lagrange function, dividing the original problem of the power distribution network optimized power flow into a plurality of sub-problems, and solving the original problem by adopting an asynchronous iteration mode among the sub-problems;
(4) and decomposing the power distribution network optimized power flow model into an upper layer and a lower layer, and realizing distributed solution of the optimized power flow problem by adopting an alternating direction multiplier algorithm to obtain the final optimal output of each distributed unit and the electricity price of each node.
Further, the constructed power distribution network optimization power flow model specifically comprises the following steps:
wherein the content of the first and second substances,
representing the set of numbers of all battery energy storage units, NbRepresenting the number of all battery energy storage units;
representing a set of all node numbers;
represents a set of all time segments, T represents the number of time segments; f. ofb.k(t) represents the operating cost of the kth battery energy storage device during the t period; piP(t)、πQ(t) respectively representing the price of buying unit active and reactive power from the outside of the power distribution network in the period t; pi(t)、Qi(t) respectively representing active power and reactive power exchanged between the node i and the outside in the period t; ploss(t)、QlossAnd (t) represents the active and reactive losses of the power distribution network in the period of t.
Further, the power flow equation constraint of the node j specifically includes:
wherein, (i, j) represents a line number connecting the node i and the node j;
represents a set of all line numbers;
＝{1,…,Hidenotes a set of node numbers, H, connected to and downstream of node iiRepresenting the number of nodes connected with and downstream of the node i; sij(t)、lij(t) represents the square of the terminal complex power flowing from node i to node j in line (i, j) and the line current respectively during period t; sj(t) represents the complex power exchanged between the node j and the outside in the period t, and the inflow node is positive; s0(t) power injected into a root node of the power distribution network from the outside in a period t; z is a radical ofijRepresenting the impedance of the line (i, j).
Further, the voltage equation constraint of the branch ij specifically includes:
putting the t period on the line(in i, j), the product of the terminal complex power flowing from the node i to the node j and the absolute value of the impedance of the line (i, j) is a real number part, and then a value which is 2 times is obtained;
adding the value obtained by the operation and the square of the voltage flowing from the node i to the node j in the line (i, j) in the period t;
the summed value is equal to the difference of the squares of the voltage amplitudes of the node i and the node j during the period t.
Further, the voltage constraint specifically includes: the square of the voltage amplitude of the node i in the period t is not less than the lower limit of the square of the voltage amplitude of the node i.
Further, the current constraint specifically includes: the square of the line current flowing from the node i to the node j in the line (i, j) in the t period is not less than the ratio of the square of the terminal complex power flowing from the node i to the node j in the line (i, j) in the t period to the square of the voltage amplitude of the node j in the t period.
Further, the additional constraint is specifically:
on the line during the period t(i, j) end complex power flowing from node i to node j is equal to t period in line(j, h), the summation of the terminal complex power flowing from the node j to all nodes connected with and downstream from the node j and the complex power exchanged with the outside by the node i in the period t;
and the power injected into the root node of the power distribution network from the outside in the period t is equal to the power on the line in the period t(0, h), the cumulative sum of the terminal complex powers of all nodes connected to and downstream from the root node flows from the root node of the distribution network to the root node;
and the difference of the square of the voltage amplitudes of the node i and the node j in the period t is equal to the difference of the voltage amplitudes of the node i and the node j in the period t on the line(in i, j), the product of the terminal complex power flowing from the node i to the node j and the absolute value of the impedance of the line (i, j) is a real number part, and then a value which is 2 times is obtained;
and the square of the voltage amplitude of the node i in the period t is not more than the upper limit of the square of the voltage amplitude of the node i.
Further, the power S flowing out of each nodeiAnd (3) satisfying the constraint:
the complex power exchanged between the node i and the outside in the t period is equal to the difference value between the load of the ith node in the t period and the complex power accumulated sum of each photovoltaic power generation unit under the node i in the t period in turn and the complex power accumulated sum of each battery energy storage unit under the node i in the t period.
Furthermore, the operation cost of the photovoltaic power generation unit of the access node i is neglected, and the photovoltaic power generation unit model of the access node i is specifically as follows:
the apparent power of the photovoltaic power generation unit in the t period is equal to the sum of the actual active power and the reactive power of the photovoltaic power generation unit in the t period;
in addition, the sum of squares of the actual active power and the reactive power of the photovoltaic power generation unit in the period t is not more than the rated apparent power of the photovoltaic power generation unit;
and the actual active power of the photovoltaic power generation unit in the period t is not greater than the predicted output of the photovoltaic power generation unit in the period t.
Further, the battery energy storage unit model for the access node i is specifically as follows:
the operation cost of the battery energy storage unit is equal to the product of the operation cost coefficient and the sum of the discharge power and the charging power of the energy storage battery in the period t.
Further, the constraint conditions of the battery energy storage unit model comprise: charge and discharge power constraints and energy constraints.
Further, in the step (3), the original problem of the power distribution network optimization trend with the objective of minimizing the overall operation cost of the power distribution network is equivalent to:
an optimization sub-problem targeting minimization of local energy storage operating costs and electricity purchase costs and an optimization sub-problem targeting minimization of overall operating costs of the distribution network.
Further, the specific method of the step (4) is as follows:
each node of the lower layer aggregates local photovoltaic power generation and energy storage, and the electricity price pi is given in the power gridP(t)、πQ(t) and λ last optimization iteration by the distribution system operatorP.i(t)、λQ.i(t)、Pi(t)、Qi(t) to minimize local energy storage operating costs and electricity purchase costsOptimizing for the target; wherein, Pi(t)、Qi(t) respectively representing active power and reactive power exchanged between the node i and the outside in the period t; lambda [ alpha ]P.i(t)、λQ.i(t) Lagrange multipliers corresponding to an active power balance equation and a reactive power balance equation respectively;
the upper-layer power distribution system operator returns according to each aggregate of the lower layer, and optimization is carried out with the aim of minimizing the overall operation cost of the power distribution network;
and obtaining the optimal output of each distributed unit through continuous iteration between the distribution system operator and the aggregation until the convergence criterion is met.
Furthermore, in the optimization process, the operator of the power distribution system does not need to know the conventional load inside the polymer, the output of each distributed unit and specific operation parameters, and can realize the regulation and control of the distributed units by only acquiring the total output of the conventional load and the distributed units.
Further, the electricity price of each node in the power distribution network is related to P through the Lagrange function which is used for amplifying the structureL.i(t)，QL.i(t) obtaining a partial derivative.
The invention has the beneficial effects that:
the power flow model adopted by the invention is strictly equivalent to the original branch power flow model in most cases and is a convex optimization problem, the designed distributed method can be realized only by exchanging upper and lower layers of limited boundary information, and node shadow prices related to internal constraints of the power distribution network and the power price of a root node of the power distribution network are mutually independent and can be used as a coordination strategy of a power distribution system operator to an aggregation in an electric power market environment.
Because the shadow price related to the internal constraint of the power distribution network and the power price of the root node of the power distribution network are independent, the method can be completely used as a coordination method for the output of the aggregate in the power market environment, and a power distribution system operator forms the shadow price and the coordination amount related to the power flow constraint of the power distribution network according to the power flow distribution of the power distribution network, so that the output of each aggregate is coordinated, and the bidding of each aggregate in the power market can be smoothly realized.
Drawings
Fig. 1 is a schematic diagram of a distributed optimization power flow of a power distribution network according to the invention.
The specific implementation mode is as follows:
the invention is further described with reference to the following figures and examples.
The invention discloses a distributed power flow optimization method for a radial power distribution network, which comprises the following steps:
(1) aiming at a radial topological structure of a power distribution network, photovoltaic power generation and battery energy storage devices are connected into the power distribution network in a distributed mode;
for the photovoltaic power generation unit of the access node i, neglecting the operation cost, the photovoltaic power generation unit model of the access node i can be expressed as:
the apparent power of the photovoltaic power generation unit in the t period is equal to the sum of the actual active power and the reactive power of the photovoltaic power generation unit in the t period;
in addition, the sum of squares of the actual active power and the reactive power of the photovoltaic power generation unit in the period t is not more than the square of the rated apparent power of the photovoltaic power generation unit;
and the actual active power of the photovoltaic power generation unit in the period t is not greater than the predicted output of the photovoltaic power generation unit in the period t.
Expressed in the form of an equation:
equations (12) to (14):
in the formula (12), Sw.j(t) represents the apparent power of the photovoltaic power generation unit during a period t; pw.j(t)、Qw.j(t) each represents tAnd actual active and reactive power output of the photovoltaic power generation unit in time intervals. In the formula (13), the reaction mixture is,
representing the rated apparent power of the photovoltaic power generating unit. In the formula (14), the compound represented by the formula (I),
and the predicted output of the photovoltaic power generation unit in the t period is shown.
The battery energy storage unit model of the access node i is specifically as follows:
the operation cost of the battery energy storage unit is equal to the product of the operation cost coefficient and the sum of the discharge power and the charging power of the energy storage battery in the period t.
Expressed in the form of an equation:
the operation cost is as follows:
in the formula (15), the reaction mixture is,
set representing the number of battery storage units of an access node, Nb.iRepresenting the number of battery energy storage units of the access node; k is a radical ofjRepresenting an operating cost coefficient of the energy storage unit; pd.j(t)、Pc.jAnd (t) respectively represents the discharge power and the charge power of the energy storage battery in the period of t.
The battery energy storage unit model comprises a charge and discharge power constraint condition and an energy constraint condition, and the battery energy storage unit model specifically comprises the following components:
1) charge and discharge power constraint:
in the formula (16), Sb.j(t) apparent power of the battery energy storage unit inverter for a period of t; pb.j(t) and Qb.j(t) is the fact that the time period t is the battery energy storage unitAnd active and reactive power output.
In the formula (17), the compound represented by the formula (I),
the rated apparent power of the battery energy storage unit inverter.
In the formula (18), the reaction mixture,
the rated power of the battery energy storage unit is obtained.
In formulae (19) to (21), Pd.j(t)、Pc.j(t) the discharging power and the charging power of the energy storage battery are respectively in the period of t, when the running cost coefficient of the energy storage battery is larger than zero and the charging and discharging efficiency is smaller than 1, and when the optimized tide problem is optimal, Pd.j(t)、Pc.j(t) at least one is equal to 0, which satisfies the actual operating conditions of the battery for energy storage.
(2) Constructing a power distribution network optimization power flow model, wherein the model aims at minimizing the overall operation cost of the power distribution network and comprises a plurality of constraints;
the goal in the optimization model can be expressed as:
in the formula (1), the reaction mixture is,
representing the set of numbers of all battery energy storage units, NbRepresenting the number of all battery energy storage units;
representing a set of all node numbers;
represents a set of all time segments, T represents the number of time segments; f. ofb.k(t) represents the operating cost of the kth battery energy storage device during the t period; piP(t)、πQ(t) respectively representing the price of buying unit active and reactive power from the outside of the power distribution network in the period t; pi(t)、Qi(t) respectively representing active power and reactive power exchanged between the node i and the outside in the period t; ploss(t)、QlossAnd (t) represents the active and reactive losses of the power distribution network in the period of t.
The optimization model comprises the following nine power flow constraints:
1) power flow equation constraint for node j
In the formulas (2) and (3), (i, j) represents a line number connecting the node i and the node j;
represents a set of all line numbers;
represents a set of node numbers, H, connected to and downstream of node iiRepresenting the number of nodes connected with and downstream of the node i; sij(t)、lij(t) represents the square of the terminal complex power flowing from node i to node j in line (i, j) and the line current respectively during period t; sj(t) represents the complex power exchanged by the node j with the outside in the time period t, and the inflow node is positive; s0(t) power injected into a root node of the power distribution network from the outside in a period t; z is a radical ofijRepresenting the impedance of the line (i, j).
2) Voltage equation constraints for branch ij
The method specifically comprises the following steps:
putting the t period on the line(in i, j), the product of the terminal complex power flowing from the node i to the node j and the absolute value of the impedance of the line (i, j) is a real number part, and then a value which is 2 times is obtained;
adding the value obtained by the operation and the square of the voltage flowing from the node i to the node j in the line (i, j) in the period t;
the summed value is equal to the difference of the squares of the voltage amplitudes of the node i and the node j during the period t.
It can also be expressed in the form of the following formula:
in the formula (4), vi(t)、vj(t) represents the square of the voltage amplitude of the node i, j during the period t; z is a radical ofijRepresenting the impedance of the line (i, j); sij(t)、lij(t) represents the square of the line current, the terminal complex power flowing from node i to node j in line (i, j) for period t, respectively.
3) Voltage confinement
The method specifically comprises the following steps:
the square of the voltage amplitude of the node i in the period t is not less than the lower limit of the square of the voltage amplitude of the node i.
It can also be expressed in the form of the following formula:
in the formula (5), vi(t) represents the square of the voltage magnitude at node i; ivrepresenting the lower limit of the squared voltage magnitude at node i.
4) Current confinement
The method specifically comprises the following steps:
the square of the line current flowing from the node i to the node j in the line (i, j) in the t period is not less than the ratio of the square of the terminal complex power flowing from the node i to the node j in the line (i, j) in the t period to the square of the voltage amplitude of the node j in the t period.
It can also be expressed in the form of the following formula:
in the formula (6), vj(t) represents the square of the voltage magnitude at node j during t; sij(t)、lij(t) represents the square of the line current, the terminal complex power flowing from node i to node j in line (i, j) for period t, respectively.
5) Additional constraints
The method specifically comprises the following steps:
on the line during the period t(i, j) end complex power flowing from node i to node j is equal to t period in line(j, h), the summation of the terminal complex power flowing from the node j to all nodes connected with and downstream from the node j and the complex power exchanged with the outside by the node i in the period t;
and the power injected into the root node of the power distribution network from the outside in the period t is equal to the power on the line in the period t(0, h), the cumulative sum of the terminal complex powers of all nodes connected to and downstream from the root node flows from the root node of the distribution network to the root node;
and the difference of the square of the voltage amplitudes of the node i and the node j in the period t is equal to the difference of the voltage amplitudes of the node i and the node j in the period t on the line(i, j) product of the terminal complex power flowing from node i to node j and the absolute value of the impedance of line (i, j)Taking the real number part, and then taking the value of 2 times;
and the square of the voltage amplitude of the node i in the period t is not more than the upper limit of the square of the voltage amplitude of the node i.
It can also be expressed in the form of the following formula:
equations (7) to (10) represent additional constraints added to make the model equivalent to the original branch power flow model, Sij(t) represents the terminal complex power in line (i, j) flowing from node i to node j during the period t in the additional constraint; si(t) represents the complex power exchanged by node i with the outside during the period t in the additional constraint; s0(t) power injected into the root node of the distribution network from the outside during the period t in the additional constraint; v. ofi(t)、vj(t) represents the square of the voltage amplitude at node i, j during period t in the additional constraint; z is a radical ofijRepresenting the impedance of the line (i, j). In the formula (10), the compound represented by the formula (10),
representing a set formed by the numbers of other nodes except the root node;
representing the upper limit of the squared voltage magnitude at node i.
The above model adopts
Replacing in the original branched flow model
And introducing constraint conditional expressions (7) - (10), and performing convex relaxation on the optimization problem under the constraint of the original branch flow by adopting second-order cone programming.
Power S flowing out of each nodeiAnd (3) satisfying the constraint:
wherein the content of the first and second substances,
representing the set of all photovoltaic unit numbers under the ith node;
representing the set of the numbers of all battery energy storage devices under the ith node; sw.j(t) is the complex power of the jth photovoltaic power generation unit at the node i in the period t; sb.jAnd (t) is the complex power of the jth battery energy storage unit at the node i in the period t. SL.i(t) is the load of the ith node for a period t.
(3) The method comprises the steps of dividing an original problem of power distribution network optimized power flow into a plurality of subproblems by constructing an augmented Lagrange function, and solving the original problem by adopting an asynchronous iteration mode among the subproblems;
the power distribution network optimization power flow augmentation Lagrange function constructed is
In the formula, λP.i(t)、λQ.i(t) are Lagrange multipliers corresponding to the active power balance equation and the reactive power balance equation of the formula (11) respectively; alpha is alphai、βiLagrange expansion coefficients, respectively.
The original problem model is equivalent to the following problem:
the constraint conditions are equations (2) to (21).
Pw.j(t) the active power output of the jth photovoltaic unit connected to the ith node at the time period t; qw.j(t) is the reactive power output of the jth photovoltaic unit accessed to the ith node at the time period t; pd.z(t) the discharging power of the z-th energy storage unit accessed to the ith node is in a t period; pc.z(t) charging power of the z-th energy storage unit accessed to the ith node for a period t; qb.zAnd (t) the reactive power output of the z-th energy storage unit connected to the ith node in the t period.
(4) As shown in fig. 1, the optimized power flow model is decomposed into an upper layer and a lower layer, and the alternating direction multiplier algorithm is adopted to realize distributed solution of the optimized power flow problem, so as to obtain the final optimal output of each distributed unit and the electricity price of each node.
The optimized power flow model is decomposed into an upper layer and a lower layer, and the distributed solution of the optimized power flow problem is realized by adopting an alternating direction multiplier algorithm and is embodied in the following steps:
each node of the lower layer aggregates local photovoltaic power generation and energy storage, and the electricity price pi is given in the power gridP(t)、πQ(t) and λ last optimization iteration by the distribution system operatorP.i(t)、λQ.i(t)、Pi(t)、Qi(t), optimizing with the goal of minimizing local energy storage operating costs and electricity purchase costs:
the operator of the upper distribution system returns according to each polymer of the lower layer to optimize by taking the overall operation cost of the minimized distribution network as a target:
the optimal output of each distributed unit can be obtained through continuous iteration between the distribution system operator and the aggregation until convergence criteria are met.
In the implementation process of the method, the operator of the power distribution system does not need to know the conventional load in the polymer, the output of each distributed unit and specific operation parameters, and can realize the regulation and control of the distributed units by only acquiring the total output of the conventional load and the distributed units.
The electricity price of each node in the power distribution network is related to P through the Lagrange function which is enlarged to the structureL.i(t)，QL.i(t) obtaining a partial derivative:
πP.i(t)＝πP(t)+λP.i(t) (30)
πQ.i(t)＝πQ(t)+λQ.i(t) (31)
the node electricity price comprises two parts, wherein the first part is the electricity price of a root node of the power distribution network and is given by an upper-layer power grid; the second part is shadow prices related to network loss and constraints in the power distribution network and is formed according to the power flow distribution in the power distribution network. In the distributed method, the operator of the power distribution system guides the output of each polymer on the lower layer according to the adjustment of the price of the second part, so as to achieve the effect of distributed regulation and control. Therefore, the method can be understood in an economic mechanism that the power distribution system operator coordinates the output of each aggregate according to the network loss, the line capacity and the shadow price related to the voltage constraint, and finally the overall optimization of the power distribution network is realized.
Because the shadow price related to the internal constraint of the power distribution network and the power price of the root node of the power distribution network are independent, the method can be completely used as an on-line power supplyMethod for coordinating polymer forces in a force market environment, whereinP(t)、πQ(t) the active and reactive prices of the polymer buying/selling electricity from the electricity market, respectively, the distribution system operator forming a shadow price lambda related to the distribution network flow constraint according to the distribution network flow distributionP.i(t)、λQ.i(t) and the amount of coordination Pi(t)、QiAnd (t) coordinating the output of each aggregate to ensure that the bidding of each aggregate in the power market can be successfully realized.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (15)
1. A distributed power flow optimization method for a radial power distribution network is characterized by comprising the following steps:
(1) aiming at a radial topological structure of a power distribution network, connecting photovoltaic power generation and battery energy storage devices into the power distribution network in a distributed manner;
(2) constructing a power distribution network optimization power flow model, wherein the model takes the minimum overall operation cost of the power distribution network as a target and comprises a plurality of constraint conditions: the power flow equation constraint of the node j, the voltage equation constraint, the voltage constraint, the current constraint and the additional constraint of the branch ij;
(3) constructing an augmented Lagrange function, dividing the original problem of the power distribution network optimized power flow into a plurality of sub-problems, and solving the original problem by adopting an asynchronous iteration mode among the sub-problems;
(4) decomposing the power distribution network optimized power flow model into an upper layer and a lower layer, and realizing distributed solution of the optimized power flow problem by adopting an alternating direction multiplier algorithm to obtain the final optimal output of each distributed unit and the electricity price of each node;
the solution is embodied in:
local photovoltaic generator aggregated by nodes of lower layerElectric and energy storage, at a given electricity price of the grid, piP(t)、πQ(t) and λ last optimization iteration by the distribution system operatorP.i(t)、λQ.i(t)、Pi(t)、Qi(t), optimizing with the goal of minimizing local energy storage operating costs and electricity purchase costs:
the operator of the upper distribution system returns according to each polymer of the lower layer to optimize by taking the overall operation cost of the minimized distribution network as a target:
the optimal output of each distributed unit can be obtained through continuous iteration between the distribution system operator and the aggregation until convergence criterion is met;
πP(t)、πQ(t) respectively representing the price of buying unit active and reactive power from the outside of the power distribution network in the period t; pi(t)、Qi(t) respectively representing active power and reactive power exchanged between the node i and the outside in the period t; ploss(t)、Qloss(t) represents the active and reactive losses of the power distribution network in the period t; lambda [ alpha ]P.i(t)、λQ.i(t) Lagrange multipliers corresponding to an active power balance equation and a reactive power balance equation respectively; pd.j(t)、Pc.j(t) respectively representing the discharge power and the charge power of the energy storage battery in the period of t; qb.j(t) Battery energy storage for a time period tActual reactive power of the unit; pw.j(t) the active power output of the jth photovoltaic unit connected to the ith node at the time period t; qw.j(t) is the reactive power output of the jth photovoltaic unit accessed to the ith node at the time period t; pL.i(t)，QL.i(t) respectively representing the active load and the reactive load of the node i; pd.z(t) the discharging power of the z-th energy storage unit accessed to the ith node is in a t period; pc.z(t) charging power of the z-th energy storage unit accessed to the ith node for a period t; qb.z(t) reactive power output of the z-th energy storage unit accessed to the ith node in a t period; alpha is alphai、βiLagrange expansion coefficients are respectively;
representing the set of all photovoltaic unit numbers under the ith node;
representing the set of the numbers of all battery energy storage devices under the ith node; k. k-1 represents the kth iteration and the kth-1 iteration respectively; t represents the optimized total time period number; ppv.j(t)、Qpv.j(t) represents the active and reactive power output of the photovoltaic at the t node j in a time period; k is a radical ofjRepresenting the operating cost factor of the energy storage unit.
2. The distributed power flow optimization method for the radial power distribution network according to claim 1, wherein the power flow optimization model is specifically constructed by:
wherein the content of the first and second substances,
representing the set of numbers of all battery energy storage units, NbRepresenting the number of all battery energy storage units;
representing a set of all node numbers; t represents the number of time periods; f. ofb.k(t) represents the operating cost of the kth battery energy storage device during the t period.
3. The distributed power flow optimization method for the radial distribution network according to claim 1, wherein the power flow equation constraint of the node j is specifically as follows:
wherein, (i, j) represents a line number connecting the node i and the node j;
represents a set of all line numbers;
represents a set of node numbers, H, connected to and downstream of node iiRepresenting the number of nodes connected with and downstream of the node i; sij(t)、lij(t) represents the square of the terminal complex power flowing from node i to node j in line (i, j) and the line current respectively during period t; sj(t) represents the complex power exchanged between the node j and the outside in the period t, and the inflow node is positive; s0(t) power injected into a root node of the power distribution network from the outside in a period t; z is a radical ofijRepresenting the impedance of the line (i, j);
representing a set of node numbers connected to and downstream from the root node; z is a radical of0hRepresenting the impedance of the line (0, h);
represents a set of all time periods; subscript 0 represents the root node; h0Indicating the number of nodes connected to node 0 and downstream of node 0.
4. The distributed power flow optimization method for the radial distribution network according to claim 1, wherein the voltage equation constraints of the branches ij are specifically as follows:
putting the t period on the line(in i, j), the product of the terminal complex power flowing from the node i to the node j and the absolute value of the impedance of the line (i, j) is a real number part, and then a value which is 2 times is obtained;
adding the value obtained by the operation and the square of the voltage flowing from the node i to the node j in the line (i, j) in the period t;
the summed value is equal to the difference of the squares of the voltage amplitudes of the node i and the node j during the period t.
5. The distributed power flow optimization method for the radial distribution network according to claim 1, wherein the voltage constraints are specifically: the square of the voltage amplitude of the node i in the period t is not less than the lower limit of the square of the voltage amplitude of the node i.
6. The distributed power flow optimization method for the radial distribution network according to claim 1, wherein the current constraints are specifically: the square of the line current flowing from the node i to the node j in the line (i, j) in the t period is not less than the ratio of the square of the terminal complex power flowing from the node i to the node j in the line (i, j) in the t period to the square of the voltage amplitude of the node j in the t period.
7. The distributed power flow optimization method for the radial distribution network according to claim 1, wherein the additional constraints are specifically:
at time tThe end complex power of a segment flowing from node i to node j in line (i, j) is equal to t period(j, h), the summation of the terminal complex power flowing from the node j to all nodes connected with and downstream from the node j and the complex power exchanged with the outside by the node i in the period t;
and the power injected into the root node of the power distribution network from the outside in the period t is equal to the power on the line in the period t(0, h), the cumulative sum of the terminal complex powers of all nodes connected to and downstream from the root node flowing from the root node of the distribution network, wherein 0 represents the root node;
and the difference of the square of the voltage amplitude of the node i and the node j in the period t is equal to the product of the terminal complex power flowing from the node i to the node j in the line (i, j) in the period t and the absolute value of the impedance of the line (i, j) to obtain a real number part, and then obtain a value which is 2 times;
and the square of the voltage amplitude of the node i in the period t is not more than the upper limit of the square of the voltage amplitude of the node i.
8. The distributed power flow optimization method for radial distribution networks of claim 7, wherein the power S flowing out of each nodeiAnd (3) satisfying the constraint:
the complex power exchanged between the node i and the outside in the t period is equal to the difference value between the load of the ith node in the t period and the complex power accumulated sum of each photovoltaic power generation unit under the node i in the t period in turn and the complex power accumulated sum of each battery energy storage unit under the node i in the t period.
9. The distributed power flow optimization method for the radial power distribution network according to claim 1, wherein the operation cost of the photovoltaic power generation unit of the access node i is ignored, and the photovoltaic power generation unit model of the access node i specifically comprises:
the apparent power of the photovoltaic power generation unit in the t period is equal to the sum of the actual active power and the reactive power of the photovoltaic power generation unit in the t period;
in addition, the sum of squares of the actual active power and the reactive power of the photovoltaic power generation unit in the period t is not more than the square of the rated apparent power of the photovoltaic power generation unit;
and the actual active power of the photovoltaic power generation unit in the period t is not greater than the predicted output of the photovoltaic power generation unit in the period t.
10. The distributed power flow optimization method for the radial power distribution network according to claim 1, wherein the battery energy storage unit model for the access node i specifically comprises:
the operation cost of the battery energy storage unit is equal to the product of the operation cost coefficient and the sum of the discharge power and the charging power of the energy storage battery in the period t.
11. The distributed power flow optimization method for the radial power distribution network of claim 10, wherein the constraint conditions of the battery energy storage unit model comprise: charge and discharge power constraints and energy constraints.
12. The distributed power flow optimization method for the radial power distribution network according to claim 1, wherein in the step (3), the original problem of the power distribution network power flow optimization with the objective of minimizing the overall operation cost of the power distribution network is equivalent to:
and optimizing the subproblems with the aim of minimizing the local energy storage operation cost and the electricity purchasing cost.
13. The distributed power flow optimization method for the radial power distribution network according to claim 1, wherein the specific method in the step (4) is as follows:
each node of the lower layer aggregates local photovoltaic power generation and energy storage, and the active and reactive prices pi are given in the power gridP(t)、πQ(t) and λ last optimization iteration by the distribution system operatorP.i(t)、λQ.i(t)、Pi(t)、Qi(t) optimizing with the goal of minimizing local energy storage operating costs and electricity purchase costs; wherein, Pi(t)、Qi(t) respectively representing active power and reactive power exchanged between the node i and the outside in the period t; lambda [ alpha ]P.i(t)、λQ.i(t) is the active power balance equation and the reactive power balance equation pair respectivelyThe corresponding lagrange multiplier;
the upper-layer power distribution system operator returns according to each aggregate of the lower layer, and optimization is carried out with the aim of minimizing the overall operation cost of the power distribution network;
and obtaining the optimal output of each distributed unit through continuous iteration between the distribution system operator and the aggregation until the convergence criterion is met.
14. The distributed optimization power flow method for the radial distribution network according to claim 13, wherein in the optimization process, the operator of the distribution system does not need to know the normal load inside the aggregate, the output of each distributed unit and specific operation parameters, and can realize the control of the distributed units by only obtaining the total output of the normal load and the distributed units.
15. The distributed power flow optimization method for the radial power distribution network according to claim 13, wherein the electricity prices of nodes in the power distribution network are related to P through a Lagrangian function for structure augmentationL.i(t)，QL.i(t) obtaining a partial derivative.
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