CN110796291B - Multi-energy complementary micro-grid cluster distributed optimization scheduling based on Dantzig-Wolfe decomposition - Google Patents
Multi-energy complementary micro-grid cluster distributed optimization scheduling based on Dantzig-Wolfe decomposition Download PDFInfo
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Abstract
The invention discloses a distributed optimized scheduling method of a multi-energy complementary micro-grid cluster based on Dantzig-Wolfe decomposition, which relates to the field of regional comprehensive energy management of multi-energy flows, and comprises the following steps: step 1, establishing an optimized multi-energy complementary micro-grid cluster model; the multi-energy complementary micro-grid cluster model is a bus type and comprises a power distribution network and at least one micro-grid; the micro-grid is integrated into a node of the power distribution network through a cluster bus; step 2, decomposing the multi-energy complementary micro-grid cluster model into a main problem and a sub problem by applying a Dantzig-Wolfe decomposition method; and obtaining a global optimal solution by continuously generating columns and alternately solving the main problem and the sub problem. The invention has the advantages that the iteration times required for aggregation are less, the iteration times change little along with the increase of the scale of the micro-network, and the invention is suitable for information and calculation challenges brought by the future large-scale micro-network merging clusters.
Description
Technical Field
The invention relates to the field of regional comprehensive energy management of multi-energy flows, relates to a distributed optimal scheduling method of a multi-energy complementary micro-grid cluster, and particularly relates to a distributed optimal scheduling method of a multi-energy complementary micro-grid cluster based on Dantzig-Wolfe decomposition.
Background
The regional comprehensive energy system integrating multiple energy sources such as cold, heat, electricity and gas can realize the cascade utilization of energy, remarkably improves the economic benefit, is an important component in a modern energy supply system, and indicates the direction for future energy development. The regional type multifunctional complementary micro-grid is used as a specific implementation mode of the regional type comprehensive energy system, is a promising energy supply mode for future cells and regional type buildings, and provides a brand new view angle for comprehensive analysis and application of the multifunctional flow.
At present, a part of research on a regional comprehensive energy system with multiple energy flows is carried out, and the combination optimization of some energy flows in cold energy, heat energy, electric energy and gas energy is concentrated, and the combination optimization is concentrated on the comprehensive energy system or a multi-micro-grid system. However, since each micro-net in the multi-micro-net system may have different managers, the centralized optimization is no longer suitable for the development of future energy systems in view of the privacy of information and the independence of scheduling. At the same time, as more and more micro-networks are incorporated into clusters, the computational burden caused by centralized optimization will continue to grow, and distributed computing will be beneficial to address this challenge by decomposing the optimization problem into each micro-network.
At present, most of distributed scheduling uses a dual decomposition algorithm, such as a prediction correction near-end multiplier method and an auxiliary problem principle to process an integrated energy system, but due to the slow convergence speed of the dual decomposition algorithm, as the number of micro-networks incorporated into a cluster is gradually increased, the number of times and time required for iteration of the dual decomposition algorithm are also greatly increased, and the development of a future large-scale energy system is difficult to deal with. Unlike dual decomposition algorithm, the original decomposition algorithm can accelerate the aggregation speed of the distributed algorithm, and the iteration times do not obviously increase with the increase of the number of subsystems, so that the method is a more suitable choice for distributed optimization scheduling. The Dantzig-Wolfe decomposition algorithm is a column generation-based original decomposition algorithm, has the remarkable advantages of high convergence rate and small influence by subsystem scale, is already applied to the fields of demand response, electric vehicle charging and the like, but is not yet applied to a multi-micro-grid system.
Accordingly, those skilled in the art have been working to develop a multi-energy complementary micro-grid cluster distributed optimal scheduling method based on Dantzig-Wolfe decomposition, which solves the above-mentioned problems in the prior art.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, the present invention is to solve the technical problem of how to apply the Dantzig-Wolfe decomposition algorithm to the management of the multi-microgrid system, so as to solve the calculation challenges brought by information privacy and centralized optimization of different management subjects, and solve the problem that the convergence speed of the dual decomposition algorithm is slow and cannot cope with the development of the future large-scale energy system. The invention adopts the Dantzig-Wolfe decomposition algorithm, which is an original decomposition algorithm based on column generation, and has the remarkable advantages of high convergence rate and less influence by subsystem scale.
In order to achieve the above purpose, the invention provides a distributed optimized scheduling method of a multi-energy complementary micro-grid cluster based on Dantzig-Wolfe decomposition, which comprises the following steps:
Further, a virtual coordinator is introduced between the distribution network and the micro-grid of the step 1 to decouple the cluster bus.
Further, the main problem of step 2 is solved in the virtual coordinator, and the sub-problem is solved inside each micro grid.
Further, an objective function C of the micro-grid m Including the cost C of purchasing natural gas from the outside buy,t And the operation maintenance cost C of a gas turbine, a gas boiler, an absorption refrigerator, an electric gas conversion device, an electric heat conversion device, a photovoltaic power generation device and a wind power generation device om,t The following formulas (1) to (3):
C buy,t ＝F buy,t C fuel (2)
wherein:
t is the scheduling period, and Deltat is the 1h scheduling interval;
F buy,t is the consumption of natural gas purchased from the outside;
C fuel is the price of natural gas;
k m ,k gb ,k ac ,k ec ,k p2g ,k p2h ,k pv ,k wt ,k bt ,k tank is respectively with the gas turbine and the gas boilerThe absorption refrigerator, the electric gas conversion equipment, the electric heat conversion equipment, the photovoltaic power generation device, a storage battery and a heat storage box are related to the operation and maintenance cost;
P m,t is the power of the gas turbine;
Q gb,t is the heat power generated by the gas boiler;
Q ac,t is the refrigerating power of the absorption refrigerator;
Q ec,t is the refrigeration power of the electric refrigerator;
Q p2g,t is the gas power generated by the electric gas conversion equipment;
Q p2h,t is the thermal power generated by the electric heat transfer equipment;
P pv,t ,P wind,t the output force of the photovoltaic power generation device and the output force of the photovoltaic power generation device are respectively;
P c,t ,P d,t the charging and discharging efficiencies of the storage battery are respectively;
Q c,t ,Q d,t and the heat energy stored and released by the heat storage box respectively.
Further, the relevant constraints of each device of the micro-grid are as follows:
Q ac,t +Q ec,t ＝C load,t (6)
F m,t +F gb,t +Q cg,t ·Δt+G load,t ＝F buy,t +F p2g,t +Q dg,t ·Δt (7)
wherein:
equation (4) represents the power balance constraint of the microgrid;
equation (5) represents the thermal power balance constraint of the microgrid;
equation (6) represents the cold power balance constraint of the microgrid;
equation (7) represents the pneumatic power balance constraint of the microgrid;
equation (8) lists the gas consumption of the gas turbine, the thermal power recovered by the heat recovery system, the upper and lower limits of the gas turbine, and the climbing rate constraint, respectively;
equation (9) is the capacity constraint to be satisfied by the thermal power recovered by the heat recovery system and the constraint that the thermal power is used to provide cold and heat energy, respectively;
equation (10) lists the relation between the SOC of the storage battery at different moments, the upper limit constraint and the lower limit constraint of the SOC, the balance constraint between adjacent days of the SOC and the upper limit constraint and the lower limit constraint of the charge and discharge power of the storage battery respectively;
equation (11) lists the relation between the capacities of the heat storage tanks at different moments, the equation of the heat storage power of the heat storage tanks, the equation of the heat release power of the heat storage tanks, the upper and lower limit constraints of the capacities, the heat power constraint of the heat storage tanks for heating and cooling, and the charge and discharge power constraint of the heat storage tanks, respectively;
the formula (12) respectively lists the relation among different time capacities of the gas storage tank, the upper limit constraint and the lower limit constraint of the capacities, and the power constraint of the gas storage tank for storing gas energy and releasing gas energy;
equation (13) lists the relation between the absorption chiller and the heat energy provided by the heat recovery system, the gas boiler and the heat storage tank, and the cold power constraint provided by the absorption chiller, respectively;
equation (14) lists the relationship between the cold power provided by the electric refrigerator and the required electric power, and the cold power constraint provided by the electric refrigerator, respectively;
equation (15) lists a relational expression between the fuel gas consumption of the gas boiler and the heat power supplied by the gas boiler, and a relational expression between the heat power supplied by the gas boiler and the cooling power and heating power of the gas boiler, respectively; the upper limit constraint and the lower limit constraint of the thermal power provided by the gas-fired boiler are used for constraint of refrigerating power and heating power;
equation (16) describes the relationship between the thermal power provided by the electric heat transfer apparatus and the required electric power, and the upper and lower limit constraints of the thermal power provided by the electric heat transfer apparatus, respectively;
equation (17) describes the relation between the gas power provided by the electric conversion equipment and the required electric power, and the relation between the fuel gas consumption and the gas power of the electric conversion equipment and the upper limit constraint and the lower limit constraint of the provided gas power;
equation (18) gives the amount of fuel gas purchased from an external gas supply station;
equation (19) gives upper and lower limits constraints on power between the microgrid and the virtual coordinator;
wherein:
E load,t ,H load,t ,C load,t ,G load,t the electric load, the thermal load, the cold load and the air load values at time t;
P ec,t is the electric power required by the refrigeration of the electric refrigerator;
P p2g,t is the electric power required by the gas production of the electric gas conversion equipment;
P p2h,t is the electric power required by the electric heat transfer equipment for heating;
Q ac,t ,Q ec,t the refrigeration power of the absorption refrigerator and the electric refrigerator are respectively;
F m,t is the natural gas consumption of the gas turbine;
F gb,t is the natural gas consumption of the gas boiler;
Q cg,t ,Q dg,t the pneumatic power stored and released by the pneumatic storage box is respectively;
F p2g,t is the natural gas consumption of the electric gas conversion equipment;
η m is the power generation efficiency of the gas turbine;
Q rec,t is the thermal power recovered by the heat recovery system;
η rec is the recovery efficiency of the heat recovery system;
variables marked "min" and "max" represent the upper and lower limits of the relevant variable;
Δ rd and delta ru The upper limit value and the lower limit value of the climbing rate of the gas turbine are respectively;
SOC t the SOC value of the storage battery at the moment t;
delta is the self-discharge rate of the battery;
η c ,η d the charging and discharging efficiencies of the storage battery are respectively;
E s is the capacity of the battery;
W t is the available heat of the heat storage tank at time tCapacity;
u is the heat loss rate of the heat storage tank;
Q c,t ,Q d,t the thermal power stored and released by the thermal storage tank at the time t is respectively;
T c ,T d the efficiency of thermal power storage and release of the thermal storage tank is respectively;
W g,t the available air capacity of the air storage box at the moment t;
g is the gas loss rate of the gas storage tank;
G c ,G d the efficiency of storing and releasing the pneumatic power of the air storage box is respectively;
COP ac ,COP ec the energy efficiency ratio of the absorption refrigerator and the electric refrigerator is respectively;
Q gb,t is the thermal power provided by the gas boiler;
η gb is the conversion efficiency of the gas boiler;
C p2g ,C p2h and the conversion efficiency of the electric conversion equipment and the electric conversion heat equipment are respectively.
Further, the optimization model and related constraints of the virtual coordinator are as follows:
wherein:
C V is the total cost of the virtual coordinator;
C ex,t is the sum of transaction costs between the virtual coordinator and the large grid;
P ex,t the exchange power between the virtual coordinator and the large power grid is purchased positively and sold negatively;
E buy ,E sell the electricity purchase price between the virtual coordinator and the large power grid is respectively;
Φ V is the set of all micro-grids;
equation (21) describes the power balance constraint of the virtual coordinator, which is the coupling constraint of the virtual coordinator and all micro-grids, and is also the coupling constraint of the main problem;
equation (22) gives the upper and lower limit constraints of exchanging power between the virtual coordinator and the large grid.
Further, the objective function of the main problem is described as equation (23):
min τ v,k ＝C V,k +∑ m (∑ k λ m,k ·C m,k ) (23)
wherein:
τ v,k is an objective function of the main problem at the kth iteration;
C V,k is the running cost C of the virtual coordinator at the kth iteration V ；
C m,k Is the running cost C of the micro-grid m at the kth iteration m ，C m,k The value of (2) is transmitted to the virtual coordinator by the micro-grid m after k iterations;
λ m,k is the weight variable of the micro-grid m at the kth iteration, lambda m,k Is determined from a minimized objective function of the virtual coordinator.
Further, the formula (21) can be decomposed into the formula (24):
P ex,t +∑ m (∑ k λ m,k ·P m,t,k )＝0 (24)
wherein:
P m,t,k is the interaction power between the micro-grid m and the virtual coordinator at the time t after the kth iteration, P m,t,k To flow into the virtualThe coordinator is positive, and the outflow from the virtual coordinator is negative;
after several iterative convergence times, the actual exchange power between the micro-grid m and the virtual coordinator at time t
As shown in formula (25):
each iteration of the micro-grid m is newly added with a weight variable lambda m,k The weight variable represents a weight value occupied by each iteration in the optimal solution;
when lambda is m,k When the value is 0, the corresponding value under the corresponding iteration times is not part of the optimal solution;
when lambda is m,k When 1, the corresponding value under the corresponding iteration times is the optimal solution;
the weight variable lambda m,k The relevant constraints of (a) are shown in equations (26) and (27):
∑λ m,k ＝1 (26)
0≤λ m,k ≤1 (27)
π t is a dual variable corresponding to the equation constraint of equation (24) and can also be seen as a shadow price or marginal cost, i.e., if equation (24) is relaxed by one unit, it can bring pi t Is a benefit of (2);
aiming at Dantzig-Wolfe decomposition algorithm pi t The electricity clearing price between the micro-grid m and the virtual coordinator can be seen; sigma (sigma) m Is a dual variable (shadow price/marginal cost) constrained by a convex equation corresponding to equation (26), indicating whether subsequent iterations can continue to reduce the objective function value of the main problem, i.e., the total cost of the microgrid m must be less than or equal to σ m To ensure optimality; each iteration, the main problem solves for λ m,k 、π t And sigma (sigma) m The vector is sent to the child problem.
Further, the objective function v of the sub-problem m,k Is the objective function C of the micro-grid m,k Comprising a cost function C of said microgrid m m,k Cost of trading with the virtual coordinator and marginal cost sigma m The method comprises the steps of carrying out a first treatment on the surface of the At a known weight coefficient lambda m,k 、π t And sigma (sigma) m On the basis of the above, each micro-grid m minimizes and solves the expanded objective function v m,k (equation 28) to derive the actual cost C at the current iteration m,k With interaction power P m,t,k Uploading it to the master question;
if v m,k Less than or equal to 0, meaning that the optimal solution at the current iteration has the ability to further reduce the objective function value of the main question and is therefore valid to be added to the corresponding column of the main question; otherwise, the corresponding parameter is given as 0 and uploaded to the main problem, and the solution obtained in the current iteration is indicated to be invalid;
in the first few iterations of the beginning, even v m,k 0 is also allowed to add corresponding parameters to the main question until v begins to appear m,k When iteration is less than or equal to 0, removing or assigning the column parameters of the previous iterations to 0;
min v m,k ＝C m,k -∑ t P m,t,k ·π t -σ m (28)
when the objective function value tau of the main question v,k Equation (29) is satisfied and the iteration is stopped, and the iteration termination condition is determined by the main problem:
where ε is the polymerization tolerance, set to 0.001;
at the same time, add an additional iteration number limit k max =100, when the maximum number of iterations is reached, the procedure is forced to stop.
Further, the algorithm flow of the distributed optimal scheduling method of the multi-energy complementary micro-grid cluster is as follows:
firstly, initializing the main problem with an empty column set;
then, the weight coefficient lambda obtained by the main problem is calculated m,k 、π t And sigma (sigma) m Sending to the child questions;
thereafter, each micro-grid is at a known lambda m,k 、π t And sigma (sigma) m On the basis of (1) optimizing the respective sub-problems independently, and C after optimization m,k And P m,t,k Uploading parameter values to the master questions;
then, the main question starts the next iteration after adding a new column transmitted from the sub-question until the termination condition is met or the maximum iteration number is reached, the iteration of the main question is terminated, and lambda obtained by the last iteration is obtained m,k 、π t And sigma (sigma) m And sending the sub-problems to obtain the global optimal solution.
The distributed optimization scheduling method for the multi-energy complementary micro-grid cluster based on Dantzig-Wolfe decomposition provided by the invention considers the information privacy of different operation subjects and the calculation challenges brought by centralized optimization, and solves the problem of optimal scheduling of the cold-hot electric multi-energy complementary micro-grid by adopting a distributed algorithm. Meanwhile, in consideration of the fact that the convergence speed of the dual decomposition algorithm adopted by the distributed scheduling at present is low, the number of times and time required by iteration of the dual decomposition algorithm are greatly increased along with the gradual increase of the number of micro networks integrated into a cluster, and the development of a future large-scale energy system is difficult to deal with. The Dantzig-Wolfe decomposition algorithm adopted by the invention is an original decomposition algorithm based on column generation, and has the remarkable advantages of high convergence rate and small influence by subsystem scale.
The distributed optimal scheduling method for the cluster of the multi-energy complementary micro-network based on Dantzig-Wolfe decomposition provided by the invention has the advantages that the iteration number required for achieving aggregation is small, the iteration number changes little along with the increase of the micro-network scale, and the method is suitable for information and calculation challenges brought by the future large-scale micro-network integration cluster.
The conception, specific structure, and technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, features, and effects of the present invention.
Drawings
FIG. 1 is a schematic diagram of a topology architecture of a bus-type micro-grid cluster;
FIG. 2 is a schematic diagram of a topology equivalent architecture of a bus-type micro-grid cluster;
FIG. 3 is a schematic diagram of a typical topology of a micro-grid containing cold-hot-electricity-gas;
FIG. 4 is a flowchart of a distributed solution algorithm based on Dantzig-Wolfe.
Detailed Description
The following description of the preferred embodiments of the present invention refers to the accompanying drawings, which make the technical contents thereof more clear and easy to understand. The present invention may be embodied in many different forms of embodiments and the scope of the present invention is not limited to only the embodiments described herein.
Fig. 1 is a schematic diagram of a topology of a bus-type micro-grid cluster. Each microgrid (# 1 to #m, M is the total number of microgrids) is incorporated into node N of the distribution network via a cluster bus. To facilitate the application of the distributed algorithm, fig. 2 decouples the cluster bus by introducing a virtual coordinator between the micro-grid and the distribution network. Fig. 1 and 2 are multi-energy complementary microgrid cluster models, and then the microgrid and virtual coordinator in the multi-energy complementary microgrid cluster models are optimized.
Fig. 3 is a typical topology of a micro-grid containing cold-hot-electricity-gas, comprising a power supply loop, a heating loop, a cooling loop, and a gas supply loop.
Wherein:
the power supply loop comprises a gas Turbine (MT), a Photovoltaic power generation device (PV), a Wind Turbine (WT) and a storage battery;
the heating loop comprises a Heat recovery system, a gas boiler, a Heat storage box and electric Heat conversion equipment (p 2 h);
the cooling loop comprises an electric refrigerator and an absorption refrigerator;
the air supply loop comprises Power to Gas (p 2 g) and an air storage box.
Each microgrid contains an electrical load, a cold load, a hot load and a gas load inside.
The optimization model of the micro-grid is as follows:
objective function C of micro-grid m Including the cost C of purchasing natural gas from the outside buy,t And the operation maintenance cost C of a gas turbine, a gas boiler, an absorption refrigerator, an electric gas conversion device, an electric heat conversion device, a photovoltaic power generation device and a wind power generation device om,t The following formulas (1) to (3):
C buy,t ＝F buy,t C fuel (2)
wherein:
t is a scheduling period, which is set to 24h in the present invention;
Δt is a 1h scheduling interval;
F buy,t is the consumption of natural gas purchased from the outside;
C fuel is the price of natural gas;
k m ,k gb ,k ac ,k ec ,k p2g ,k p2h ,k pv ,k wt ,k bt ,k tank the system is respectively related to the operation and maintenance costs of a gas turbine, a gas boiler, an absorption refrigerator, an electric refrigerator, electric gas conversion equipment, electric heat conversion equipment, a photovoltaic power generation device, a storage battery and a heat storage box;
P m,t is the power of the gas turbine;
Q gb,t is the heat power generated by the gas boiler;
Q ac,t is the refrigerating power of the absorption refrigerator;
Q ec,t is the refrigeration of the electric refrigeratorA power;
Q p2g,t is the gas power generated by the electric gas conversion equipment;
Q p2h,t is the heat power generated by the electric heat conversion equipment;
P pv,t ,P wind,t the output force of the photovoltaic power generation device and the output force of the photovoltaic power generation device are respectively;
P c,t ,P d,t respectively the charge and discharge efficiency of the storage battery;
Q c,t ,Q d,t thermal energy stored and released by the thermal storage tank respectively.
Wherein, the relevant constraint of each device of the micro-grid is as follows (4) to (19):
Q ac,t +Q ec,t ＝C load,t (6)
F m,t +F gb,t +Q cg,t ·Δt+G load,t ＝F buy,t +F p2g,t +Q dg,t ·Δt (7)
wherein:
equation (4) represents the power balance constraint of the microgrid;
equation (5) represents the thermal power balance constraint of the microgrid;
equation (6) represents the cold power balance constraint of the microgrid;
equation (7) represents the pneumatic power balance constraint of the microgrid;
equation (8) lists the gas consumption of the gas turbine, the thermal power recovered by the heat recovery system, the upper and lower limits of the gas turbine, and the climbing rate constraint, respectively;
the equation (9) is the capacity constraint which needs to be satisfied by the heat power recovered by the heat recovery system and the constraint that the heat power is used for providing cold and heat energy;
the equation (10) respectively lists the relation between the SOC of the storage battery at different moments, the upper limit constraint and the lower limit constraint of the SOC, the balance constraint between adjacent SOC days and the upper limit constraint and the lower limit constraint of the charge and discharge power of the storage battery;
the formula (11) respectively lists the relation between the capacities of the heat storage boxes at different moments, the equation of the heat storage power of the heat storage boxes, the equation of the heat release power of the heat storage boxes, the upper limit constraint and the lower limit constraint of the capacities, the heat power constraint of the heat storage boxes for heating and cooling and the charge and discharge power constraint of the heat storage boxes;
the formula (12) respectively lists the relation among different time capacities of the gas storage tank, the upper limit constraint and the lower limit constraint of the capacities, and the power constraint of the gas storage tank for storing gas energy and releasing gas energy;
equation (13) lists the relation between the absorption refrigerator and the heat recovery system, the gas boiler and the heat energy provided by the heat storage box, and the cold power constraint provided by the absorption refrigerator;
equation (14) lists the relationship between the cold power provided by the electric refrigerator and the required electric power, and the cold power constraint provided by the electric refrigerator, respectively;
the equation (15) lists the relation between the fuel gas consumption of the gas boiler and the heat power provided by the gas boiler, and the relation between the heat power provided by the gas boiler and the refrigerating power and the heating power of the gas boiler; upper and lower limit constraints of heat power provided by the gas boiler and constraints for refrigeration power and heating power;
equation (16) describes the relationship between the thermal power provided by the electric heat transfer apparatus and the required electric power, and the upper and lower limit constraints of the thermal power provided by the electric heat transfer apparatus, respectively;
equation (17) describes the relation between the gas power provided by the electric conversion equipment and the required electric power, the relation between the fuel gas consumption and the gas power of the electric conversion equipment, and the upper limit constraint and the lower limit constraint of the provided gas power;
equation (18) gives the amount of fuel gas purchased from an external gas supply station;
equation (19) gives the upper and lower limits constraint of the power between the micro-grid and the virtual coordinator;
wherein:
E load,t ,H load,t ,C load,t ,G load,t the electric load, the thermal load, the cold load and the air load values at time t;
P ec,t is the electric power required by the refrigeration of the electric refrigerator;
P p2g,t is the electric power required by the gas production of the electric gas conversion equipment;
P p2h,t is the electric power required by the heating of the electric heat conversion equipment;
Q ac,t ,Q ec,t the refrigeration power of the absorption refrigerator and the electric refrigerator respectively;
F m,t is the natural gas consumption of the gas turbine;
F gb,t is the natural gas consumption of the gas boiler;
Q cg,t ,Q dg,t the pneumatic power stored and released by the pneumatic storage box is respectively;
F p2g,t is the natural gas consumption of the electric gas conversion equipment;
η m is the power generation efficiency of the gas turbine;
Q rec,t is the thermal power recovered by the heat recovery system;
η rec is the recovery efficiency of the heat recovery system;
variables marked "min" and "max" represent the upper and lower limits of the relevant variable;
Δ rd and delta ru The upper limit value and the lower limit value of the climbing rate of the gas turbine are respectively;
SOC t the SOC value of the storage battery at the moment t;
delta is the self-discharge rate of the battery;
η c ,η d the charging and discharging efficiencies of the storage battery are respectively;
E s is the capacity of the battery;
W t is the available heat capacity of the thermal storage tank at time t;
u is the heat loss rate of the heat storage tank;
Q c,t ,Q d,t the stored and released thermal power of the thermal storage tank at time t respectively;
T c ,T d efficiency of thermal power storage and release of the thermal storage tank, respectively;
W g,t the available air capacity of the air storage box at the moment t;
g is the gas loss rate of the gas storage tank;
G c ,G d the efficiency of storing and releasing the pneumatic power of the air storage box is respectively;
COP ac ,COP ec the energy efficiency ratio of the absorption refrigerator and the electric refrigerator respectively;
Q gb,t is the heat power provided by the gas boiler;
η gb is the conversion efficiency of the gas boiler;
C p2g ,C p2h respectively are provided withConversion efficiency of the electric conversion gas equipment and the electric conversion heat equipment.
The optimization model and related constraints of the virtual coordinator are as follows (20) - (22):
wherein:
C V is the total cost of the virtual coordinator;
C ex,t is the sum of transaction costs between the virtual coordinator and the large grid;
P ex,t the exchange power between the virtual coordinator and the large power grid is purchased positively and sold negatively;
E buy ,E sell the electricity purchase price between the virtual coordinator and the large power grid is respectively;
Φ V is a set of all micro-grids;
the expression (21) describes the power balance constraint of the virtual coordinator, which is the coupling constraint of the virtual coordinator and all micro-grids and is also the coupling constraint of the main problem;
equation (22) gives the upper and lower limit constraints for exchanging power between the virtual coordinator and the large grid.
After the optimization of the micro-grids and the virtual coordinator in the multi-energy complementary micro-grid cluster model is completed, the optimized micro-grids and the virtual coordinator model are solved in a distributed mode by using a Dantzig-Wolfe decomposition method based on column generation, wherein a formula (21) gives the coupling constraint of the virtual coordinator and all the micro-grids, and the coupling constraint limits the possibility of distributed solving. The Dantzig-Wolfe decomposition method decomposes a centralized optimization model into a main problem and a sub-problem, wherein the main problem is solved in a virtual coordinator, the sub-problem is solved inside each micro-grid, and a global optimal solution is obtained by continuously generating columns and alternately solving the main problem and the sub-problem.
The main problem represents the total running cost of the whole system at each iteration, and its objective function can be described as equation (23):
minτ v,k ＝C V,k +∑ m (∑ k λ m,k ·C m,k ) (23)
wherein:
τ v,k is the objective function of the main problem under the kth iteration;
C V,k is the running cost C of the virtual coordinator at the kth iteration V ；
C m,k Is the running cost C of the micro-grid m at the kth iteration m ，C m,k The value of (2) is transmitted to the virtual coordinator by the micro-grid m after k iterations;
λ m,k is the weight variable of the micro-grid m at the kth iteration, lambda m,k The value of (2) is found by the minimized objective function of the virtual coordinator.
Further, the formula (21) can be decomposed into the formula (24):
P ex,t +∑ m (∑ k λ m,k ·P m,t,k )＝0 (24)
wherein:
P m,t,k is the interaction power between the micro-grid m and the virtual coordinator at the time t after the kth iteration, P m,t,k Taking the inflow virtual coordinator as positive and the outflow virtual coordinator as negative;
after several iterative convergence, the actual exchange power between the micro-grid m and the virtual coordinator at time t
As shown in formula (25):
each iteration of the micro-grid m is added with a weight variable lambda m,k The weight variable represents the weight value occupied by each iteration in the optimal solution;
when lambda is m,k When the value is 0, the corresponding value under the corresponding iteration times is not part of the optimal solution;
when lambda is m,k When 1, the corresponding value under the corresponding iteration times is the optimal solution;
weight variable lambda m,k The relevant constraints of (a) are shown in equations (26) and (27):
∑λ m,k ＝1 (26)
0≤λ m,k ≤1 (27)
π t is a dual variable corresponding to the equation constraint of equation (24) and can also be seen as a shadow price or marginal cost, i.e., if equation (24) is relaxed by one unit, it can bring pi t Is a benefit of (2);
aiming at Dantzig-Wolfe decomposition algorithm pi t The electricity price of the micro-grid m and the virtual coordinator can be seen; sigma (sigma) m Is a dual variable (shadow price/marginal cost) constrained by the convex equation corresponding to equation (26), indicating whether subsequent iterations can continue to reduce the objective function value of the main problem, i.e., the total cost of the micro-grid m must be less than or equal to σ m To ensure optimality; each iteration, the main problem will solve for λ m,k 、π t And sigma (sigma) m The vector is sent to the child problem.
Objective function v of sub-problem m,k Is the objective function C of the micro-grid m,k Comprising a cost function C of a micro-grid m m,k Cost of trading with virtual coordinator and marginal cost sigma m The method comprises the steps of carrying out a first treatment on the surface of the At a known weight coefficient lambda m,k 、π t And sigma (sigma) m On the basis of (1) each micro-grid m minimisation solving the expanded objective function v m,k (equation 28) to derive the actual cost C at the current iteration m,k With interaction power P m,t,k Uploading it to the master question;
if v m,k Less than or equal to 0, thenMeaning that the optimal solution under the current iteration has the ability to further reduce the objective function value of the main problem and is therefore valid to be added to the corresponding column of the main problem; otherwise, the corresponding parameter is given as 0 and uploaded to the main problem, and the solution obtained by the current iteration is indicated to be invalid;
in the first few iterations of the beginning, even v m,k Gtoreq 0 is also allowed to add corresponding parameters to the main question until v begins to appear m,k When iteration is less than or equal to 0, removing or assigning the column parameters of the previous iterations to 0;
min v m,k ＝C m,k -∑ t P m,t,k ·π t -σ m (28)
when the objective function value tau of the main problem v,k Equation (29) is satisfied, the iteration is stopped, and the iteration termination condition is determined by the main problem:
where ε is the polymerization tolerance, set to 0.001;
at the same time, add an additional iteration number limit k max =100, when the maximum number of iterations is reached, the procedure is forced to stop.
The algorithm flow of the distributed optimal scheduling method of the multi-energy complementary micro-grid cluster based on Dantzig-Wolfe decomposition is as follows:
firstly, initializing a main problem with an empty column set;
then, the weight coefficient lambda obtained by the main problem is calculated m,k 、π t And sigma (sigma) m Send to the child problem;
thereafter, each micro-grid is at a known λ m,k 、π t And sigma (sigma) m On the basis of (1) independently optimizing the respective sub-problems, and optimizing the C m,k And P m,t,k Uploading the parameter values to the main problem;
then, after adding a new column transmitted by the slave sub-problem, the master problem starts the next iteration until the termination condition is met or the maximum iteration number is reached, and the master problemTerminating the iteration of (2) and determining lambda from the last iteration m,k 、π t And sigma (sigma) m And sending the solution to the sub-problem to obtain the global optimal solution. The number of iterations required does not substantially increase with the size of the microgrid, with about 20 iterations being sufficient to achieve adequate aggregation. A specific algorithm flow chart is shown in fig. 4.
The sub-problem of each micro-grid and the main problem of the virtual coordinator are independent, so that the sub-problem of each micro-grid and the main problem of the virtual coordinator can be solved in a distributed mode, and privacy of each micro-grid can be protected. In fact, each sub-problem is solved independently by the corresponding micro-grid, and the virtual coordinator knows only a small amount of data about the micro-grid operation. Moreover, distributed computing is more robust to communication failures, and if a certain micro-grid fails to communicate with a virtual coordinator, its computed local solution is always viable. In this case, the sub-problem may only consider the parameter values of the last column to find the optimal solution, and if the communication is resumed afterwards, the quality of its final solution is not affected, although the number of iterations required may increase significantly.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention without requiring creative effort by one of ordinary skill in the art. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (1)
1. A distributed optimal scheduling method for a multi-energy complementary micro-grid cluster based on Dantzig-Wolfe decomposition is characterized by comprising the following steps:
step 1, establishing an optimized multi-energy complementary micro-grid cluster model; the multi-energy complementary micro-grid cluster model is a bus type and comprises a power distribution network and at least one micro-grid; the micro-grid is integrated into a node of the power distribution network through a cluster bus;
step 2, decomposing the multi-energy complementary micro-grid cluster model into a main problem and a sub problem by applying a Dantzig-Wolfe decomposition method; obtaining a global optimal solution by continuously generating columns and alternately solving the main problem and the sub-problem;
introducing a virtual coordinator between the power distribution network and the micro-grid in the step 1 to decouple the cluster bus;
solving the main problem in the step 2 in the virtual coordinator, and solving the sub-problem in the interior of each micro-grid;
objective function C of the micro-grid m Including the cost C of purchasing natural gas from the outside buy，t And the operation maintenance cost C of a gas turbine, a gas boiler, an absorption refrigerator, an electric gas conversion device, an electric heat conversion device, a photovoltaic power generation device and a wind power generation device om，t The following formulas (1) to (3):
C buy，t ＝F buy，t C fuel (2)
wherein:
t is the scheduling period, and Deltat is the 1h scheduling interval;
F buy，t is the consumption of natural gas purchased from the outside;
C fuel is the price of natural gas;
k m ，k gb ，k ac ，k ec ，k p2g ，k p2h ，k pv ，k wt ，k bt ，k tank the coefficients are related to the operation and maintenance costs of the gas turbine, the gas boiler, the absorption refrigerator, the electric power conversion equipment, the photovoltaic power generation device, the storage battery and the heat storage box;
P m，t is the power of the gas turbine;
Q gb，t is the heat power generated by the gas boiler;
Q ac，t is the refrigerating power of the absorption refrigerator;
Q ec，t is the refrigeration power of the electric refrigerator;
Q p2g，t is the gas power generated by the electric gas conversion equipment;
Q p2h，t is the thermal power generated by the electric heat transfer equipment;
P pv，t ，P wind，t the output force of the photovoltaic power generation device and the output force of the photovoltaic power generation device are respectively;
P c，t ，P d，t the charging and discharging efficiencies of the storage battery are respectively;
Q c，t ，Q d，t the heat energy stored and released by the heat storage box is respectively;
the relevant constraints of each device of the micro-grid are as follows (4) to (19):
Q ac，t +Q ec，t ＝C load，t (6)
F m，t +F gb，t +Q cg，t ·Δt+G load，t ＝F buy，t +F p2g，t +Q dg，t ·Δt (7)
wherein:
equation (4) represents the power balance constraint of the microgrid;
equation (5) represents the thermal power balance constraint of the microgrid;
equation (6) represents the cold power balance constraint of the microgrid;
equation (7) represents the pneumatic power balance constraint of the microgrid;
equation (8) lists the gas consumption of the gas turbine, the thermal power recovered by the heat recovery system, the upper and lower limits of the gas turbine, and the climbing rate constraint, respectively;
equation (9) is the capacity constraint to be satisfied by the thermal power recovered by the heat recovery system and the constraint that the thermal power is used to provide cold and heat energy, respectively;
equation (10) lists the relation between the SOC of the storage battery at different moments, the upper limit constraint and the lower limit constraint of the SOC, the balance constraint between adjacent days of the SOC and the upper limit constraint and the lower limit constraint of the charge and discharge power of the storage battery respectively;
equation (11) lists the relation between the capacities of the heat storage tanks at different moments, the equation of the heat storage power of the heat storage tanks, the equation of the heat release power of the heat storage tanks, the upper and lower limit constraints of the capacities, the heat power constraint of the heat storage tanks for heating and cooling, and the charge and discharge power constraint of the heat storage tanks, respectively;
the formula (12) respectively lists the relation among different time capacities of the gas storage tank, the upper limit constraint and the lower limit constraint of the capacities, and the power constraint of the gas storage tank for storing gas energy and releasing gas energy;
equation (13) lists the relation between the absorption chiller and the heat energy provided by the heat recovery system, the gas boiler and the heat storage tank, and the cold power constraint provided by the absorption chiller, respectively;
equation (14) lists the relationship between the cold power provided by the electric refrigerator and the required electric power, and the cold power constraint provided by the electric refrigerator, respectively;
equation (15) lists a relational expression between the fuel gas consumption of the gas boiler and the heat power supplied by the gas boiler, and a relational expression between the heat power supplied by the gas boiler and the cooling power and heating power of the gas boiler, respectively; the upper limit constraint and the lower limit constraint of the thermal power provided by the gas-fired boiler are used for constraint of refrigerating power and heating power;
equation (16) describes the relationship between the thermal power provided by the electric heat transfer apparatus and the required electric power, and the upper and lower limit constraints of the thermal power provided by the electric heat transfer apparatus, respectively;
equation (17) describes the relation between the gas power provided by the electric conversion equipment and the required electric power, and the relation between the fuel gas consumption and the gas power of the electric conversion equipment and the upper limit constraint and the lower limit constraint of the provided gas power;
equation (18) gives the amount of fuel gas purchased from an external gas supply station;
equation (19) gives upper and lower limits constraints on power between the microgrid and the virtual coordinator;
wherein:
E load，t ，H load，t ，C load，t ，G load，t the electric load, the thermal load, the cold load and the air load values at time t;
P ec，t is the electric power required by the refrigeration of the electric refrigerator;
P p2g，t is the electric power required by the gas production of the electric gas conversion equipment;
P p2h，t is the electric power required by the electric heat transfer equipment for heating;
Q ac，t ，Q ec，t the refrigeration power of the absorption refrigerator and the electric refrigerator are respectively;
F m，t is the natural gas consumption of the gas turbine;
F gb，t is the natural gas consumption of the gas boiler;
Q cg，t ，Q dg，t the pneumatic power stored and released by the pneumatic storage box is respectively;
F p2g，t is the natural gas consumption of the electric gas conversion equipment;
η m is the power generation efficiency of the gas turbine;
Q rec，t is the thermal power recovered by the heat recovery system;
η rec is the recovery efficiency of the heat recovery system;
variables marked "min" and "max" represent the upper and lower limits of the relevant variable;
Δ rd and delta ru The upper limit value and the lower limit value of the climbing rate of the gas turbine are respectively;
SOC t the SOC value of the storage battery at the moment t;
delta is the self-discharge rate of the battery;
η c ，η d the charging and discharging efficiencies of the storage battery are respectively;
E s is the capacity of the battery;
W t is the available heat capacity of the thermal storage tank at time t;
u is the heat loss rate of the heat storage tank;
Q c，t ，Q d，t the thermal power stored and released by the thermal storage tank at the time t is respectively;
T c ，T d the efficiency of thermal power storage and release of the thermal storage tank is respectively;
W g，t the available air capacity of the air storage box at the moment t;
g is the gas loss rate of the gas storage tank;
G c ，G d the efficiency of storing and releasing the pneumatic power of the air storage box is respectively;
COP ac ，COP ec the energy efficiency ratio of the absorption refrigerator and the electric refrigerator is respectively;
Q gb，t is the thermal power provided by the gas boiler;
η gb is the conversion efficiency of the gas boiler;
C p2g ，C p2h conversion efficiencies of the electric conversion gas equipment and the electric conversion heat equipment are respectively;
the optimization model and related constraints of the virtual coordinator are as follows (20) - (22):
wherein:
C V is the total cost of the virtual coordinator;
C ex，t is the sum of transaction costs between the virtual coordinator and the large grid;
P ex，t the exchange power between the virtual coordinator and the large power grid is purchased positively and sold negatively;
E buy ，E sell the electricity purchase price between the virtual coordinator and the large power grid is respectively;
Φ V is the set of all micro-grids;
equation (21) describes the power balance constraint of the virtual coordinator, which is the coupling constraint of the virtual coordinator and all micro-grids, and is also the coupling constraint of the main problem;
equation (22) gives upper and lower limit constraints for exchanging power between the virtual coordinator and a large grid;
the objective function of the main problem is described as equation (23):
minτ v，k ＝C V，k +∑ m (∑ k λ m，k ·C m，k ) (23)
wherein:
τ v，k is an objective function of the main problem at the kth iteration;
C V，k is the running cost C of the virtual coordinator at the kth iteration V ；
C m，k Is the running cost C of the micro-grid m at the kth iteration m ，C m，k The value of (2) is transmitted to the virtual coordinator by the micro-grid m after k iterations;
λ m，k is the weight variable of the micro-grid m at the kth iteration, lambda m，k Is determined from a minimized objective function of the virtual coordinator;
equation (21) can be decomposed into equation (24):
P ex，t +∑ m (∑ k λ m，k ·P m，t，k )＝0 (24)
wherein:
P m，t，k is that the micro-grid m is transmitted to the virtual coordinator at two times t after the kth iterationInteraction power between the two, P m，t，k Taking the inflow of the virtual coordinator as positive and the outflow of the virtual coordinator as negative;
after several iterative convergence times, the actual exchange power between the micro-grid m and the virtual coordinator at time t
As shown in formula (25):
each iteration of the micro-grid m is newly added with a weight variable lambda m，k The weight variable represents a weight value occupied by each iteration in the optimal solution;
when lambda is m，k When the value is 0, the corresponding value under the corresponding iteration times is not part of the optimal solution;
when lambda is m，k When 1, the corresponding value under the corresponding iteration times is the optimal solution;
the weight variable lambda m，k The relevant constraints of (a) are shown in equations (26) and (27):
∑λ m，k ＝1 (26)
0≤λ m，k ≤1 (27)
π t is a dual variable corresponding to the equation constraint of equation (24) and can also be seen as a shadow price or marginal cost, i.e., if equation (24) is relaxed by one unit, it can bring pi t Is a benefit of (2);
aiming at Dantzig-Wolfe decomposition algorithm pi t The electricity clearing price between the micro-grid m and the virtual coordinator can be seen; sigma (sigma) m Is a dual variable (shadow price/marginal cost) constrained by a convex equation corresponding to equation (26), indicating whether subsequent iterations can continue to reduce the objective function value of the main problem, i.e., the total cost of the microgrid m must be less than or equal to σ m To ensure optimality; each iteration, the main problem solves for λ m，k 、π t And sigma (sigma) m The vector is sent to the sub-problem;
the objective function v of the sub-problem m，k Is the objective function C of the micro-grid m，k Comprising a cost function C of said microgrid m m，k Cost of trading with the virtual coordinator and marginal cost sigma m The method comprises the steps of carrying out a first treatment on the surface of the At a known weight coefficient lambda m，k 、π t And sigma (sigma) m On the basis of the above, each micro-grid m minimizes and solves the expanded objective function v m，k (equation 28) to derive the actual cost C at the current iteration m，k With interaction power P m，t，k Uploading it to the master question;
if v m，k Less than or equal to 0, meaning that the optimal solution at the current iteration has the ability to further reduce the objective function value of the main question and is therefore valid to be added to the corresponding column of the main question; otherwise, the corresponding parameter is given as 0 and uploaded to the main problem, and the solution obtained in the current iteration is indicated to be invalid;
in the first few iterations of the beginning, even v m，k 0 is also allowed to add corresponding parameters to the main question until v begins to appear m，k When iteration is less than or equal to 0, removing or assigning the column parameters of the previous iterations to 0;
min v m，k ＝C m，k -∑ t P m，t，k ·π t -σ m (28)
when the objective function value tau of the main question v，k Equation (29) is satisfied and the iteration is stopped, and the iteration termination condition is determined by the main problem:
where ε is the polymerization tolerance, set to 0.001;
at the same time, add an additional iteration number limit k max =100, when the maximum number of iterations is reached, the procedure is forced to stop;
the algorithm flow of the multi-energy complementary micro-grid cluster distributed optimization scheduling method is as follows:
firstly, initializing the main problem with an empty column set;
then, the weight coefficient lambda obtained by the main problem is calculated m，k 、π t And sigma (sigma) m Sending to the child questions;
thereafter, each micro-grid is at a known lambda m，k 、π t And sigma (sigma) m On the basis of (1) optimizing the respective sub-problems independently, and C after optimization m，k And P m，t，k Uploading parameter values to the master questions;
then, the main question starts the next iteration after adding a new column transmitted from the sub-question until the termination condition is met or the maximum iteration number is reached, the iteration of the main question is terminated, and lambda obtained by the last iteration is obtained m，k 、π t And sigma (sigma) m And sending the sub-problems to obtain the global optimal solution.
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