A distributed economic dispatch method for smart grid based on output feedback

Abstract

The present invention discloses a distributed economic dispatch method for a smart grid based on output feedback, specifically: establishing a mathematical model of economic dispatch under pollution emission constraints; using a distributed algorithm to obtain the optimal power generation, and updating the output variables, internal state variables and auxiliary variables of the economic dispatch algorithm; calculating whether the time has expired, and obtaining the optimal power generation of the power generation unit. The present invention can effectively reduce the computational burden of the economic dispatch algorithm; ensure that the balance constraints of power generation and load are met during the transient process of solving the problem, which is conducive to the plug-and-play and online application of the algorithm; limit the upper limit of pollutant emissions, which can meet the national regulations on environmental protection; and is more conducive to implementation on heterogeneous physical facilities.

Description

Technical Field

[0001] The present invention relates to energy management technology for smart grids, and in particular to a distributed economic dispatching method for smart grids based on output feedback. Background Art

[0002] With the organic integration and deep collaboration of information technologies such as communication, computing, sensing, and control with physical power systems, the smart grid will make the power system more reliable, safe, economical, efficient, and environmentally friendly. Energy management is an important part of the smart grid, which mainly includes economic dispatch, demand response, unit combination, and other issues. Economic dispatch is to minimize the total power generation cost of the power grid by coordinating the output power of multiple power generation units under the conditions of meeting the power generation and load balance of the power grid and other constraints.

[0003] Traditional economic dispatch methods require the smart grid to have a control center to collect information from the entire grid, solve economic dispatch problems, and send control instructions. This centralized economic dispatch has disadvantages such as single node failure, poor scalability, heavy communication and computing burden, and easy leakage of privacy information, which makes it difficult for centralized economic dispatch to meet the real-time, reliability, security, and plug-and-play requirements of smart grids. In order to overcome the shortcomings of centralized economic dispatch methods, some people have proposed distributed economic dispatch methods. For example, the document with application number 202211071171.4 [1], the invention name is a distributed economic dispatch optimization method based on constraint projection reinforcement learning; the document with application number 202010581637.X [2], the invention name is a distributed economic dispatch method for power systems based on dynamic event triggering; the document [3] published in the journal Automatica, the title is Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment; the document [4] published in the journal IEEE Transactions on Cybernetics, the title is A distributed optimization algorithm based on multiagent network for economic dispatch with region partitioning.

[0004] The existing distributed economic dispatch methods are based on the mechanism design of state feedback, which may have the following problems and defects. First, the existing distributed economic dispatch methods use projection technology (such as references [1,2,4]) or penalty technology (such as reference [3]) to deal with the upper and lower limits of power generation. The calculation of projection and the calculation of penalty coefficient range are usually complex and expensive. Second, although the existing distributed economic dispatch methods can achieve non-initialization operation, they cannot guarantee that the balance constraints of power generation and load are met in the transient process of solving economic dispatch. Third, the existing distributed economic dispatch methods consider the balance constraints between power generation and load and the upper and lower limits of power generation of power generation units, but ignore the pollution emission problems of power generation units. Summary of the invention

[0005] Aiming at the economic dispatch problem of smart grid under pollution emission constraints, the present invention provides a distributed economic dispatch method of smart grid based on output feedback. It aims to solve the economic dispatch problem of smart grid in a distributed manner without using projection technology or penalty technology, satisfying the system's non-initialized operation and solving the balance constraints of power generation and load in the transient process of economic dispatch.

[0006] The present invention provides a distributed economic dispatching method for a smart grid based on output feedback, specifically comprising:

[0007] Assume that the smart grid contains n power generation units, n is an integer greater than or equal to 2, and the total power generation cost function that needs to be optimized for economic dispatch is:

[0008]

[0009] Where f(p) represents the total power generation cost function, p = [p1, p2, …, p n ] T , f i (p i ) is the power generation cost function of the ith power generation unit, p i is the power generation of the ith power generation unit.

[0010] Optimizing the total power generation cost function (1) requires satisfying the following power generation and load balancing constraints:

[0011]

[0012] Among them, D i Represents the local active power demand in the area where the i-th generating unit is located.

[0013] Optimizing the total power generation cost function (1) requires satisfying the following pollution emission constraints:

[0014]

[0015] Among them, gi (p i ) represents the pollution emission function of the i-th power generation unit, E i It represents the virtual emission parameter of the area where the i-th power generation unit is located. The sum of all virtual emission parameters is the maximum pollution emission allowed by the smart grid.

[0016] Optimizing the total power generation cost function (1) requires satisfying the following upper and lower constraints on power generation:

[0017]

[0018] in, and are the lower and upper limits of the power generation of the ith power generation unit.

[0019] The following distributed algorithm is used to obtain the optimal power generation

[0020] The output variables of the economic dispatch algorithm for the i-th generation unit are updated as follows:

[0021]

[0022] Among them, N i represents the set of power generation units that communicate bidirectionally with the i-th power generation unit, a ij Represents the weight coefficient of communication. If there is a two-way communication connection between the i-th and j-th power generation units to obtain each other's information, then j∈N i And a ij =a ji >0, otherwise And a ij =a ji =0;x i and x j are the internal state variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively.

[0023] The internal state variables of the economic dispatch algorithm of the i-th generation unit are updated as follows:

[0024]

[0025] Among them, k i,x is the control gain parameter of the economic dispatch algorithm of the ith power generation unit, and its value is a positive constant, y i and j are the auxiliary variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, and x i The initial value of (0) is any bounded real value.

[0026] The auxiliary variables of the economic dispatch algorithm for the i-th generation unit are updated as follows:

[0027]

[0028] in, is the subgradient of the power generation cost function of the ith power generation unit, is the auxiliary variable for the lower limit constraint of the power generation of the i-th power generation unit economic dispatch algorithm, is the auxiliary variable for the upper limit constraint of the i-th generation unit economic dispatch algorithm, is the subgradient of the pollution emission function of the ith power generation unit, It is the pollution emission constraint auxiliary variable of the economic dispatch algorithm of the i-th power generation unit.

[0029] The auxiliary variable of the power generation lower limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows:

[0030]

[0031] Among them, max{s,0} means taking the maximum value of s and 0, γ i,1 is the multiplier variable for the lower limit constraint of the i-th generation unit economic dispatch algorithm, which is updated as follows:

[0032]

[0033] Among them, γ i,1 The initial value of (0) is any non-negative bounded real value, k i,1 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0034] The auxiliary variable of the power generation upper limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows:

[0035]

[0036] Among them, γ i,2 is the generation capacity upper limit constraint multiplier variable of the economic dispatch algorithm of the ith generation unit, which is updated as follows:

[0037]

[0038] Among them, γ i,2 The initial value of (0) is any non-negative bounded real value, k i,2 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0039] The pollution emission constraint auxiliary variables of the economic dispatch algorithm for the i-th power generation unit are updated as follows:

[0040]

[0041] Among them, γ i,3 and γ j,3 are the pollution emission constraint multiplier variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, i,3 and θ j,3 They are auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively.

[0042] The pollution emission constraint multiplier variable of the economic dispatch algorithm for the i-th generation unit is updated as follows:

[0043]

[0044] Among them, γ i,3 The initial value of (0) is any non-negative bounded real value, k i,3 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0045] The auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm of the i-th generation unit are updated as follows:

[0046]

[0047] Among them, θ i,3 The initial value of (0) is any bounded real value, k i,θ is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0048] Under the condition that the communication graph formed by the communication connections between all power generation units is connected, if the time set for calculation formulas (5) to (14) has not expired, the calculation continues; otherwise, the variable p in formula (5) i Converge to the optimal power generation

[0049] Optimal power generation The characteristics are as follows: If the power generation cost function f of the power generation unit i (p i ) or the pollution emission function g i (p i ) is at least one non-convex function, then the optimal power generation is a local optimal solution; if the power generation cost function f of the power generation unit i (p i ) and the pollution emission function g i (pi ) are all convex functions, then the optimal power generation is a global optimal solution; if the power generation cost function f i (p i ) is a strictly convex function and the pollution emission function g i (p i ) is a convex function, then the optimal power generation It is the only global optimal solution.

[0050] The beneficial technical effects of the present invention are:

[0051] The scheme of the present invention does not require the economic dispatch algorithm of the power generation unit to calculate the projection and penalty coefficients, which can effectively reduce the computational burden of the economic dispatch algorithm; the scheme of the present invention not only realizes the initialization-free operation of the economic dispatch algorithm, but also ensures that the balance constraints of power generation and load are met in the transient process of solving the problem, which is conducive to the plug-and-play and online application of the algorithm; the scheme of the present invention limits the upper limit of pollutant emissions while minimizing the power generation cost, which can meet the national regulations on environmental protection; the scheme of the present invention only requires the power generation unit to exchange composite information composed of the sum of multiple variables with the neighboring power generation units, and does not require the power generation units to exchange sensitive information such as sub-gradients and power generation, which is conducive to privacy protection; the scheme of the present invention allows different power generation units The economic dispatch algorithm adopts different control gain parameters, while the existing scheme requires the same control gain parameters, and the scheme of the present invention is more conducive to implementation on heterogeneous physical facilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of the distributed economic dispatching method of smart grid based on output feedback of the present invention.

[0053] Figure 2 It is a communication connection diagram between power generation units in an embodiment.

[0054] Figure 3 The cost coefficient, power demand, and upper and lower limit parameters of the power generation unit of the embodiment.

[0055] Figure 4 Pollution emission coefficient and virtual emission parameters of the power generation unit of the embodiment.

[0056] Figure 5 is the weight coefficient of the communication in the embodiment. DETAILED DESCRIPTION

[0057] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] The process of the distributed economic dispatching method of a smart grid based on output feedback of the present invention is as follows: Figure 1 As shown, specifically:

[0059] Assume that the smart grid contains n power generation units, n is an integer greater than or equal to 2, and the total power generation cost function that needs to be optimized for economic dispatch is:

[0060]

[0061] Where f(p) represents the total power generation cost function, p = [p1, p2, …, p n ] T , f i (p i ) is the power generation cost function of the ith power generation unit, p i is the power generation of the ith power generation unit.

[0062] Optimizing the total power generation cost function (1) requires satisfying the following power generation and load balancing constraints:

[0063]

[0064] Among them, D i Represents the local active power demand in the area where the i-th generating unit is located.

[0065] Optimizing the total power generation cost function (1) requires satisfying the following pollution emission constraints:

[0066]

[0067] Among them, g i (p i ) represents the pollution emission function of the i-th power generation unit, E i It represents the virtual emission parameter of the area where the i-th power generation unit is located. The sum of all virtual emission parameters is the maximum pollution emission allowed by the smart grid.

[0068] Optimizing the total power generation cost function (1) requires satisfying the following upper and lower constraints on power generation:

[0069]

[0070] in, and are the lower and upper limits of the power generation of the ith power generation unit.

[0071] The following distributed algorithm is used to obtain the optimal power generation

[0072] The output variables of the economic dispatch algorithm for the i-th generation unit are updated as follows:

[0073]

[0074] Among them, N irepresents the set of power generation units that communicate bidirectionally with the i-th power generation unit, a ij Represents the weight coefficient of communication. If there is a two-way communication connection between the i-th and j-th power generation units to obtain each other's information, then j∈N i And a ij =a ji >0, otherwise And a ij =a ji =0;x i and x j are the internal state variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively.

[0075] The internal state variables of the economic dispatch algorithm of the i-th generation unit are updated as follows:

[0076]

[0077] Among them, k i,x is the control gain parameter of the economic dispatch algorithm of the ith power generation unit, and its value is a positive constant, y i and j are the auxiliary variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, and x i The initial value of (0) is any bounded real value.

[0078] The auxiliary variables of the economic dispatch algorithm for the i-th generation unit are updated as follows:

[0079]

[0080] in, is the subgradient of the power generation cost function of the ith power generation unit, is the auxiliary variable for the lower limit constraint of the power generation of the i-th power generation unit economic dispatch algorithm, is the auxiliary variable for the upper limit constraint of the i-th generation unit economic dispatch algorithm, is the subgradient of the pollution emission function of the ith power generation unit, It is the pollution emission constraint auxiliary variable of the economic dispatch algorithm of the i-th power generation unit.

[0081] The auxiliary variable of the power generation lower limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows:

[0082]

[0083] Among them, max{s,0} means taking the maximum value of s and 0, γ i,1 is the multiplier variable for the lower limit constraint of the i-th generation unit economic dispatch algorithm, which is updated as follows:

[0084]

[0085] Among them, γ i,1 The initial value of (0) is any non-negative bounded real value, k i,1 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0086] The auxiliary variable of the power generation upper limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows:

[0087]

[0088] Among them, γ i,2 is the generation capacity upper limit constraint multiplier variable of the economic dispatch algorithm of the ith generation unit, which is updated as follows:

[0089]

[0090] Among them, γ i,2 The initial value of (0) is any non-negative bounded real value, k i,2 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0091] The pollution emission constraint auxiliary variables of the economic dispatch algorithm for the i-th power generation unit are updated as follows:

[0092]

[0093] Among them, γ i,3 and γ j,3 are the pollution emission constraint multiplier variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, i,3 and θ j,3 They are auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively.

[0094] The pollution emission constraint multiplier variable of the economic dispatch algorithm for the i-th generation unit is updated as follows:

[0095]

[0096] Among them, γ i,3 The initial value of (0) is any non-negative bounded real value, k i,3 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0097] The auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm of the i-th generation unit are updated as follows:

[0098]

[0099] Among them, θ i,3 The initial value of (0) is any bounded real value, k i,θ is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a normal number.

[0100] Under the condition that the communication graph formed by the communication connections between all power generation units is connected, if the time set for calculation formulas (5) to (14) has not expired, the calculation continues; otherwise, the variable p in formula (5) i Converge to the optimal power generation

[0101] Optimal power generation The characteristics are as follows: If the power generation cost function f of the power generation unit i (p i ) or the pollution emission function g i (p i ) is at least one non-convex function, then the optimal power generation is a local optimal solution; if the power generation cost function f of the power generation unit i (p i ) and the pollution emission function g i (p i ) are all convex functions, then the optimal power generation is a global optimal solution; if the power generation cost function f i (p i ) is a strictly convex function and the pollution emission function g i (p i ) is a convex function, then the optimal power generation It is the only global optimal solution.

[0102] Example:

[0103] Take a smart grid with five power generation units as an example. The communication connections between the power generation units are as follows: Figure 2 As shown. Economic dispatch needs to optimize the following total power generation cost function:

[0104]

[0105] Where f(p) represents the total power generation cost function of the five power generation units, p = [p1, p2,, p5] T , is the power generation cost function of the i-th (1≤i≤5) power generation unit, b i,1 、b i,2 、b i,3 、b i,4 、b i,5is the cost coefficient of the i-th power generation unit. These cost coefficients are Figure 3 Given, p i is the power generation of the ith power generation unit.

[0106] Optimizing the total power generation cost function (15) requires satisfying the following power generation and load balancing constraints:

[0107]

[0108] Among them, D i Represents the local active power demand of the area where the i-th power generation unit is located, and its parameter value is Figure 3 Given.

[0109] Optimizing the total power generation cost function (15) requires satisfying the following pollution emission constraints:

[0110]

[0111] in, represents the pollution emission function of the ith power generation unit, c i,1 、c i,2 、c i,3 、c i,4 、c i,5 is the pollution emission coefficient of the ith power generation unit, E i represents the virtual emission parameters of the region where the i-th power generation unit is located. These parameter values ​​are Figure 4 Given.

[0112] Optimizing the total power generation cost function (15) requires satisfying the following upper and lower constraints on power generation:

[0113]

[0114] in, and are the lower and upper limits of the power generation of the ith power generation unit, respectively. The parameter values ​​of these upper and lower limits are Figure 3 Given.

[0115] For the economic dispatch problem described by equations (15) to (18), the following distributed algorithm is used to obtain the optimal power generation: The output variables of the economic dispatch algorithm for the i-th generation unit are updated as follows:

[0116]

[0117] Among them, N i Represents the set of power generation units that communicate bidirectionally with the i-th power generation unit, and the communication weight coefficient a ij The value of Figure 5 Given: xi and x j are the internal state variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively.

[0118] The internal state variables of the economic dispatch algorithm of the i-th generation unit are updated as follows:

[0119]

[0120] Among them, k i,x is the control gain parameter of the economic dispatch algorithm for the i-th generation unit, and its values ​​are k 1,x =5, k 2,x =5, k 3,x =3, k 4,x =3, k 5,x =5,y i and j are the auxiliary variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, and x i The initial values ​​of (0) are x1(0)=10, x2(0)=0, x3(0)=10, x4(0)=0, and x5(0)=10 respectively.

[0121] The auxiliary variables of the economic dispatch algorithm for the i-th generation unit are updated as follows:

[0122]

[0123] in, is the subgradient of the power generation cost function of the ith power generation unit, is the auxiliary variable for the lower limit constraint of the power generation of the i-th power generation unit economic dispatch algorithm, is the auxiliary variable for the upper limit constraint of the i-th generation unit economic dispatch algorithm, is the subgradient of the pollution emission function of the ith power generation unit, It is the pollution emission constraint auxiliary variable of the economic dispatch algorithm of the i-th power generation unit.

[0124] The auxiliary variable of the power generation lower limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows:

[0125]

[0126] Among them, max{s,0} means taking the maximum value of s and 0, γ i,1 is the multiplier variable for the lower limit constraint of the i-th generation unit economic dispatch algorithm, which is updated as follows:

[0127]

[0128] Among them, γi,1 The initial values ​​of (0) are γ 1,1 (0) = 0, γ 2,1 (0) = 0, γ 3,1 (0) = 0, γ 4,1 (0) = 0, γ 5,1 (0) = 0, k i,1 is the control gain parameter of the economic dispatch algorithm for the i-th generation unit, and its values ​​are k 1,1 =4, k 2,1 =6, k 3,1 =4, k 4,1 =6, k 5,1 =4.

[0129] The auxiliary variable of the power generation upper limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows:

[0130]

[0131] Among them, γ i,2 is the generation capacity upper limit constraint multiplier variable of the economic dispatch algorithm of the ith generation unit, which is updated as follows:

[0132]

[0133] Among them, γ i,2 The initial values ​​of (0) are γ 1,2 (0) = 0, γ 2,2 (0) = 0, γ 3,2 (0) = 0, γ 4,2 (0) = 0, γ 5,2 (0) = 0, k i,2 is the control gain parameter of the economic dispatch algorithm for the i-th generation unit, and its values ​​are k 1,2 =4, k 2,2 =6, k 3,2 =4, k 4,2 =6, k 5,2 =4.

[0134] The pollution emission constraint auxiliary variables of the economic dispatch algorithm for the i-th power generation unit are updated as follows:

[0135]

[0136] Among them, γ i,3 and γ j,3 are the pollution emission constraint multiplier variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, i,3 and θ j,3are auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm of the i-th and j-th generation units, respectively. The pollution emission constraint multiplier variables of the economic dispatch algorithm of the i-th generation unit are updated as follows:

[0137]

[0138] Among them, γ i,3 The initial values ​​of (0) are γ 1,3 (0) = 0, γ 2,3 (0) = 0, γ 3,3 (0) = 0, γ 4,3 (0) = 0, γ 5,3 (0) = 0, k i,3 is the control gain parameter of the economic dispatch algorithm for the i-th generation unit, and its values ​​are k 1,3 =10, k 2,3 =10, k 3,3 =10, k 4,3 =10, k 5,3 = 10. The auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm of the i-th power generation unit are updated as follows:

[0139]

[0140] Among them, θ i,3 The initial values ​​of (0) are θ 1,3 (0) = 0, θ 2,3 (0) = 0, θ 3,3 (0) = 0, θ 4,3 (0) = 0, θ 5,3 (0) = 0, k i,θ is the control gain parameter of the economic dispatch algorithm for the i-th generation unit, and its values ​​are k 1,θ =10, k 2,θ =10, k 3,θ =10, k 4,θ =10, k 5,θ =10.

[0141] If the time set for calculating equations (19) to (28) is less than 100 seconds, the calculation continues; otherwise, the variable p in equation (19) i Converge to the only global optimal power generation

Claims

1. A distributed economic dispatching method for smart grid based on output feedback, characterized in that: Specifically: Assume that the smart grid contains n power generation units, n is an integer greater than or equal to 2, and the total power generation cost function that needs to be optimized for economic dispatch is: Where f(p) represents the total power generation cost function, p = [p1, p2, …, p n ] T , f i (p i ) is the power generation cost function of the ith power generation unit, p i is the power generation of the ith power generation unit; Optimizing the total power generation cost function requires satisfying the following power generation and load balancing constraints: Among them, D i represents the local active power demand in the area where the i-th generating unit is located; Optimizing the total power generation cost function needs to satisfy the following pollution emission constraints: Among them, g i (p i ) represents the pollution emission function of the i-th power generation unit, E i It represents the virtual emission parameter of the area where the i-th power generation unit is located. The sum of all virtual emission parameters is the maximum pollution emission allowed by the smart grid; Optimizing the total power generation cost function requires satisfying the following upper and lower constraints on power generation: in, and are the lower and upper limits of power generation of the ith power generation unit respectively; The following distributed algorithm is used to obtain the optimal power generation The output variables of the economic dispatch algorithm for the i-th generation unit are updated as follows: Among them, N i represents the set of power generation units that communicate bidirectionally with the i-th power generation unit, a ij Represents the weight coefficient of communication. If there is a two-way communication connection between the i-th and j-th power generation units to obtain each other's information, then j∈N i And a ij =a ji >0, otherwise And a ij =a ji =0;x i and x j are the internal state variables of the economic dispatch algorithm of the ith and jth generation units, respectively; The internal state variables of the economic dispatch algorithm of the i-th generation unit are updated as follows: Among them, k i,x is the control gain parameter of the economic dispatch algorithm of the ith power generation unit, and its value is a positive constant, y i and j are the auxiliary variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, and x i The initial value of (0) is any bounded real value; The auxiliary variables of the economic dispatch algorithm for the i-th generation unit are updated as follows: in, is the subgradient of the power generation cost function of the ith power generation unit, is the auxiliary variable for the lower limit constraint of the power generation of the i-th power generation unit economic dispatch algorithm, is the auxiliary variable for the upper limit constraint of the i-th generation unit economic dispatch algorithm, is the subgradient of the pollution emission function of the ith power generation unit, is the pollution emission constraint auxiliary variable of the economic dispatch algorithm of the i-th power generation unit; The auxiliary variable of the power generation lower limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows: Among them, max{s,0} means taking the maximum value of s and 0, γ i,1 is the multiplier variable for the lower limit constraint of the i-th generation unit economic dispatch algorithm, which is updated as follows: Among them, γ i,1 The initial value of (0) is any non-negative bounded real value, k i,1 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a positive constant; The auxiliary variable of the power generation upper limit constraint of the economic dispatch algorithm of the i-th power generation unit is updated as follows: Among them, γ i,2 is the generation capacity upper limit constraint multiplier variable of the economic dispatch algorithm of the ith generation unit, which is updated as follows: Among them, γ i,2 The initial value of (0) is any non-negative bounded real value, k i,2 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a positive constant; The pollution emission constraint auxiliary variables of the economic dispatch algorithm for the i-th power generation unit are updated as follows: Among them, γ i,3 and γ j,3 are the pollution emission constraint multiplier variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively, i,3 and θ j,3 are auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm for the i-th and j-th generation units, respectively; The pollution emission constraint multiplier variable of the economic dispatch algorithm for the i-th generation unit is updated as follows: Among them, γ i,3 The initial value of (0) is any non-negative bounded real value, k i,3 is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a positive constant; The auxiliary variables of the pollution emission constraint multiplier variables of the economic dispatch algorithm of the i-th generation unit are updated as follows: Among them, θ i,3 The initial value of (0) is any bounded real value, k i,θ is the control gain parameter of the economic dispatch algorithm of the ith generation unit, and its value is a positive constant; Under the condition that the communication graph formed by the communication connections between all power generation units is connected, if the time set for calculation formulas (5) to (14) has not expired, the calculation continues; otherwise, the variable p in formula (5) i Converge to the optimal power generation 2. A distributed economic dispatching method for smart grid based on output feedback according to claim 1, characterized in that: The optimal power generation The characteristics are as follows: If the power generation cost function f of the power generation unit i (p i ) or the pollution emission function g i (p i ) is at least one non-convex function, then the optimal power generation is a local optimal solution; if the power generation cost function f of the power generation unit i (p i ) and the pollution emission function g i (p i ) are all convex functions, then the optimal power generation is a global optimal solution; if the power generation cost function f i (p i ) is a strictly convex function and the pollution emission function g i (p i ) is a convex function, then the optimal power generation It is the only globally optimal solution.

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