Large power grid and micro power grid dispatching double-layer optimization method considering micro power grid active support

Abstract

The invention discloses a large power grid and micro power grid dispatching double-layer optimization method considering micro power grid active support. The large power grid and micro power grid dispatching double-layer optimization method considering micro power grid active support comprises the following steps: designing a day-ahead market interaction mechanism based on friendly interaction characteristics of a micro power grid and a large power grid and power support of the micro power grid to the large power grid; constructing a large power grid side objective function taking large power grid benefit maximization as an objective as an upper layer model; constructing a micro-grid side objective function taking micro-grid benefit maximization as an objective as a lower-layer model; a large power grid-micro power grid double-layer optimization model is constructed, and the double-layer model is converted into a single-layer optimization model. According to the method, the problem that in the prior art, cost and benefits generated during interaction of the large power grid and the micro power grid are difficult to share fairly is effectively solved by constructing the large power grid-micro power grid double-layer optimization model.

Description

Technical Field

[0001] The present invention relates to the technical field of dual-layer optimization of large power grid and microgrid dispatching, and in particular to a dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid. Background Art

[0002] With the continuous maturity of microgrid technology and the advancement of power market reform, microgrids have gradually become an important participant in the power market. Traditionally, microgrids operate in a "self-generation and self-use, surplus power connected to the grid" mode, and their main benefits depend on energy supply.

[0003] In the main energy market, microgrids can guide the operation of internal distributed energy with electricity prices by participating in power transactions, while in the auxiliary service market, microgrids integrate multiple distributed energy resources, such as photovoltaics, wind energy, and energy storage, which enables them to flexibly dispatch power supply and demand. The localized management and flexible operation mode of microgrids enable them to quickly respond to market changes, adjust power generation and consumption, and thus optimize economic benefits. Therefore, microgrids can also provide auxiliary services such as peak load regulation and frequency regulation, and have great potential.

[0004] In terms of microgrid market transactions that take into account the balance of interests of multiple entities, current research mainly focuses on cooperative and non-cooperative game models under the game theory framework. However, the cooperative and non-cooperative game models under the game theory framework only use the commonly used typical day or typical scenario equivalent method to evaluate the operating costs of microgrids. They cannot accurately simulate the actual operation of microgrids, cannot correctly evaluate the operating costs and benefits of microgrids, and the existing technology does not explore the problem of operating cost sharing caused by the interaction between large power grids and microgrids. Summary of the invention

[0005] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a two-layer optimization method for scheduling a large power grid and a microgrid taking into account the active support of the microgrid. By using a two-layer optimization method for scheduling a large power grid and a microgrid taking into account the active support of the microgrid, the problem in the prior art that the costs and benefits generated when the large power grid and the microgrid interact are difficult to be fairly shared is effectively solved.

[0006] To achieve the above object, the present invention provides the following technical solutions: A two-layer optimization method for large power grid and microgrid dispatching taking into account the active support of microgrids comprises the following steps: based on the friendly interaction characteristics of microgrids and large power grids and the power support of microgrids to large power grids, a day-ahead market interaction mechanism is designed, wherein the day-ahead market interaction mechanism includes a flexible electricity price mechanism and a deviation penalty mechanism; a large power grid side objective function with the goal of maximizing the benefits of the large power grid is constructed as an upper model; a microgrid side objective function with the goal of maximizing the benefits of the microgrid is constructed as a lower model; a large power grid-microgrid two-layer optimization model is constructed, and the two-layer model is converted into a single-layer optimization model.

[0007] In a preferred embodiment, the day-ahead market interaction mechanism is specifically as follows: the large power grid and the microgrid conduct cooperative bargaining through operating costs, quotations and interactive power; both parties evaluate their own resource allocation and market demand, and through continuous iteration and feedback, obtain the optimal interactive power level and the profit-maximizing trading electricity price; and calculate income and expenditure according to the profit-maximizing trading electricity price.

[0008] In a preferred embodiment, the deviation penalty mechanism is specifically: taking the peak-shaving deviation of the microgrid unit as an assessment indicator, and the peak-shaving deviation of the microgrid unit is the deviation between the actual output of the microgrid unit participating in peak-shaving and the required output.

[0009] In a preferred embodiment, the objective function on the large grid side aiming at maximizing the benefits of the large grid is constructed as an upper-level model, including decision variables and optimization objectives of the upper-level model; the decision variables of the upper-level model include the output of other resources purchased by the large grid and the price of the power for interaction between the microgrid and the large grid; the optimization objective is to minimize the cost of purchasing and selling electricity for the large grid, and the optimization objective includes the cost of the large grid purchasing other resources and the cost of interacting with the microgrid.

[0010] In a preferred embodiment, the microgrid-side objective function aimed at maximizing the benefits of the microgrid is constructed as a lower-level model, including decision variables and optimization objectives of the lower-level model; the decision variables of the lower-level model include the output of the microgrid, the peak-shaving deviation, and the interactive power provided by the microgrid to the large power grid; the optimization objective is to minimize the cost of the microgrid, and the optimization objectives include gas turbine costs, electricity purchase and sales costs, and deviation penalty costs.

[0011] In a preferred embodiment, the objective function on the large grid side includes constraints on the large grid side, and the constraints on the large grid side include power balance constraints, constraints on the price of electricity purchased and sold by the microgrid to the large grid, and upper and lower limit constraints on the output of other resources.

[0012] In a preferred embodiment, the microgrid side objective function includes microgrid side constraints, and the microgrid side constraints include power balance constraints, upper and lower limit constraints on the interaction power between the microgrid and the large grid, power deviation constraints, and gas turbine output constraints.

[0013] One or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages: 1. A two-layer optimization method for large power grid and microgrid dispatching taking into account the active support of microgrid is used to effectively solve the problem of fair sharing of costs and benefits generated by the interaction between large power grid and microgrid in the existing technology.

[0014] 2. Through flexible elastic electricity prices and peak-shaving deviation penalties, the interaction between microgrids and large power grids is effectively promoted, thereby ensuring the optimal allocation of resources and maximizing the economic benefits of both parties.

[0015] 3. By considering the friendly interaction characteristics between microgrids and large power grids, and taking into account the incentives for microgrids to respond to the peak-shaving needs of the large power grid, a large power grid-microgrid market interaction model based on flexible electricity prices and deviation penalties and a two-layer optimization model for participating in the day-ahead peak-shaving market are constructed, thereby solving the problem of fair sharing of costs and benefits generated when large power grids and microgrids interact.

[0016] 4. By converting the double-layer model into a single-layer model, the efficient solution of the double-layer model is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A flow chart of a dual-layer optimization method for large power grid and microgrid scheduling taking into account active support of microgrid provided in an embodiment of the present application; DETAILED DESCRIPTION The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "include..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0019] Embodiment 1, Figure 1 The present invention provides a dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid, comprising the following steps: S1 designs a day-ahead market interaction mechanism based on the friendly interaction characteristics between the microgrid and the large grid and the power support of the microgrid to the large grid. The day-ahead market interaction mechanism includes a flexible electricity price mechanism and a deviation penalty mechanism. The flexible electricity price mechanism clarifies the contribution of microgrids to the peak-shaving and valley-filling benefits of large power grids on the premise of incentivizing interaction between large power grids and microgrids. The scientifically and reasonably designed flexible electricity price mechanism achieves the effect of reasonably and fairly allocating costs and benefits to microgrids.

[0020] Considering the friendly interaction characteristics between microgrids and large power grids and the power support of microgrids to large power grids, a day-ahead market interaction mechanism based on the interaction mode of flexible electricity price and deviation penalty is designed. The core of the interaction mechanism is that the large power grid reasonably sets electricity prices to encourage microgrids to actively participate in peak load regulation services, while ensuring the operating efficiency and economic benefits of the large power grid.

[0021] The flexible electricity price mechanism is as follows: The large grid and microgrids engage in cooperative bargaining through operating costs, quotations, and interactive power; Both parties evaluate their own resource allocation and market demand, and through continuous iteration and feedback, obtain the optimal interactive power level and the transaction price that maximizes revenue; The income and expenditure are calculated according to the profit maximizing trading electricity price.

[0022] The deviation penalty mechanism is designed to enable microgrids to actively respond to the peak-shaving needs of large power grids under the market model. By increasing peak-shaving assessment and deviation penalty links and introducing competitive incentive mechanisms, the potential and willingness of market peak-shaving entities can be stimulated to a greater extent, thereby effectively ensuring the safe and stable operation of the power grid.

[0023] Compared with the settlement method of transaction electricity price, the incentive method is as follows: the large power grid and microgrid cooperate through operating costs, quotations and interactive power. In this process, each party evaluates its own resource allocation and market demand. Through continuous iteration and feedback, the two parties can determine the optimal interactive power level and the transaction electricity price that maximizes the benefits of both parties in the power transaction, so that the total cost of both parties is minimized. After the interaction process is over, the results of all entities participating in the day-ahead interaction are settled post-event, and the income and expenditure are calculated according to the electricity price generated by the real-time interaction.

[0024] The deviation penalty mechanism is as follows: The peak-shaving deviation of the microgrid unit is used as an assessment indicator. The peak-shaving deviation of the microgrid unit refers to the deviation between the actual output of the microgrid unit participating in peak-shaving and the required output. The calculation formula is as follows:

[0025] Where: is the peak load deviation of the microgrid unit, To provide actual peak load regulation for microgrids, Peak load regulation demand released by large power grid.

[0026] It should be noted that the peak-shaving deviation of the microgrid unit refers to the output deviation of the microgrid unit during the peak-shaving process. When the peak-shaving deviation of the microgrid unit is positive, it means that the actual output is higher than the demanded output. When the peak-shaving deviation of the microgrid unit is negative, it means that the actual output is lower than the demanded output.

[0027] It should be noted that the actual peak load output of a microgrid is the actual power generation capacity of the microgrid in a specific time period, which may be affected by factors such as unit performance, equipment failure, and fuel supply, and is usually expressed in kilowatts (kW) or megawatts (MW). The peak load demand released by the large power grid represents the power demand required by users in the same time period, also in kilowatts (kW) or megawatts (MW). The demand output is usually calculated based on factors such as load forecasting, user demand, and electricity usage habits.

[0028] The peak-shaving indicators of microgrids are assessed, and deviation penalties are imposed on the peak-shaving process. The size of the penalty fee depends on the degree to which the peak-shaving process of the unit responds to the peak-shaving demand of the large power grid. The penalty function is as follows:

[0029] Where: Penalty costs for peak load ancillary services, is the microgrid penalty coefficient, is the peak load deviation of the microgrid unit.

[0030] Combining the above two mechanisms, when the microgrid interacts with the large grid in response to the demand, the power of the microgrid and the large grid is regarded as the output of the peak-shaving market. The large grid should give a reasonable purchase and sale price to encourage the microgrid to participate in the peak-shaving auxiliary service while ensuring its own interests. The large grid should also punish the deviation between the response power of the microgrid and the published demand to reduce the uncertainty of the transaction power.

[0031] In addition, the microgrid mainly achieves peak load regulation by agreeing on peak load regulation with the large power grid. Agreed demand means that the large power grid and the microgrid agree on a certain amount of peak load regulation output in advance, and the large power grid directly invites the demand, and the microgrid provides feedback and responds according to the specified requirements. Finally, the electricity price and operation strategy that maximize the interests of both parties are obtained by solving the double-layer optimization model, and a rapid response to peak load regulation is achieved.

[0032] S2 constructs a large grid side objective function with the goal of maximizing the benefits of the large grid as the upper model. The decision variables of the upper model include the output of other resources purchased by the large grid and the price of the power of the interaction between the microgrid and the large grid. The optimization goal is to minimize the cost of purchasing and selling electricity for the large grid. The optimization goal includes the cost of the large grid purchasing other resources and the cost of interacting with the microgrid. The objective function of the large power grid side with the goal of maximizing the benefits of the large power grid is constructed as the upper model, and the specific calculation formula is as follows:

[0033] Where: is the objective function of the large power grid side, For quotes on other resources, Contribute to other resources purchased by the large power grid, The price of power provided by the microgrid to the main grid, is the price of power absorbed by the microgrid from the large grid, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid, is the deviation penalty coefficient, It is the positive deviation of the peak load of the microgrid. It is the negative deviation of the peak load output of the microgrid.

[0034] The objective function with the goal of maximizing the benefits of the large power grid includes the constraints on the large power grid side. The constraints on the large power grid side include power balance constraints, power purchase and sales price constraints of the microgrid to the large power grid, and upper and lower limits of other resource output, as follows: The power balance constraint is specifically:

[0035] Where: The peak load demand released by the large power grid, Contribute to other resources purchased by the large power grid, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid.

[0036] The price constraints for the microgrid to purchase and sell electricity from the large grid are specifically:

[0037] The upper and lower limits of other resource output constraints are specifically:

[0038] Where: The maximum amount of other resources that the large power grid can purchase. Contribute to other resources purchased by the large power grid.

[0039] S3 constructs a microgrid-side objective function with the goal of maximizing the benefits of the microgrid as the lower-level model. The decision variables of the lower-level model include the output of the microgrid, the peak-shaving deviation, and the interactive power provided by the microgrid to the large grid. The optimization goal is to minimize the cost of the microgrid, which includes the gas turbine cost, the cost of purchasing and selling electricity, and the deviation penalty cost. The microgrid side objective function is specifically:

[0040] Where: is the objective function of the microgrid side, N is the number of gas turbines, is the output of the i-th gas turbine, a, b, c are the cost coefficients of the gas turbine, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid, is the deviation penalty coefficient, It is the positive deviation of the peak load of the microgrid. is the negative deviation of the microgrid peak load output. The price of power provided by the microgrid to the main grid, The price of power absorbed by the microgrid from the large grid.

[0041] It should be noted that the objective function on the microgrid side approximates the microgrid operating cost as the gas turbine cost and calculates it using a quadratic function.

[0042] The objective function of the microgrid side with the goal of maximizing the benefits of the microgrid includes microgrid side constraints, which include power balance constraints, upper and lower limit constraints of the interactive power between the microgrid and the large grid, power deviation constraints, and gas turbine output constraints, as follows: The power balance constraint is specifically:

[0043] Where: is the total power generation of the microgrid, is the load demand of the microgrid, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid, It is the positive deviation of the peak load of the microgrid. It is the negative deviation of the peak load output of the microgrid.

[0044] The upper and lower limits of the interaction power between the microgrid and the large grid are specifically:

[0045] Where: is the maximum power provided by the microgrid to the large grid, is the maximum power absorbed by the microgrid from the large grid, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid.

[0046] The power deviation constraint is specifically:

[0047] Where: Provide the maximum positive deviation output for the microgrid to provide peak load regulation to the large grid. Provides the maximum reverse deviation output for the microgrid to provide peak load regulation to the large grid. It is the positive deviation of the peak load of the microgrid. It is the negative deviation of the peak load output of the microgrid.

[0048] The gas turbine output constraint is specifically:

[0049] Where: is the maximum output of the ith gas turbine.

[0050] S4 combines the upper model and the lower model to construct the Lagrangian function, uses the strong duality theorem to obtain the optimal KKT condition and complementary condition, and uses the bigM method to transform the complementary condition into cutting plane constraints to obtain a single-layer optimization model.

[0051] The single-layer optimization model is specifically:

[0052] Where: is the objective function of the large power grid side, x is the decision variable of the upper model, y is the decision variable of the lower model, , v represents the dual variable corresponding to the constraint condition in the market clearing problem, Represents the set of KKT conditions in the market clearing problem.

[0053] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0054] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product.

[0055] Those of ordinary skill in the art will appreciate that the modules and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0056] In addition, each functional module in each embodiment of the present application may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0057] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0058] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid, characterized in that: The following steps are involved: Based on the friendly interaction characteristics between microgrid and large power grid and the power support of microgrid to large power grid, a day-ahead market interaction mechanism is designed, which includes a flexible electricity price mechanism and a deviation penalty mechanism. Construct the large power grid side objective function with the goal of maximizing the benefits of the large power grid as the upper model; Construct a microgrid-side objective function that aims to maximize the benefits of the microgrid as the lower-level model; A two-layer optimization model of large power grid and microgrid is constructed, and the two-layer model is converted into a single-layer optimization model.

2. A dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid as claimed in claim 1, characterized in that: The day-ahead market interaction mechanism is specifically as follows: The large grid and microgrids engage in cooperative bargaining through operating costs, quotations, and interactive power; Both parties evaluate their own resource allocation and market demand, and through continuous iteration and feedback, obtain the optimal interactive power level and the transaction price that maximizes revenue; The income and expenditure are calculated according to the profit maximizing trading electricity price.

3. The dual-layer optimization method for large power grid and microgrid dispatching taking into account the active support of microgrid as claimed in claim 2 is characterized in that: The deviation penalty mechanism is specifically as follows: The peak-shaving deviation of the microgrid unit is used as an assessment indicator. The peak-shaving deviation of the microgrid unit is the deviation between the actual output of the microgrid unit participating in peak-shaving and the required output. The calculation formula is as follows: Where: is the peak load deviation of the microgrid unit, To provide actual peak load regulation for microgrids, Peak load regulation demand released by large power grid.

4. The dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid as claimed in claim 3 is characterized in that: The objective function of the large power grid side aiming at maximizing the benefits of the large power grid is constructed as an upper model, including decision variables and optimization objectives of the upper model; The decision variables of the upper model include the power output of other resources purchased by the large grid and the price of the power exchanged between the microgrid and the large grid; The optimization goal is to minimize the cost of purchasing and selling electricity for the large power grid, and the optimization goal includes the cost of purchasing other resources for the large power grid and the cost of interacting with the microgrid.

5. The dual-layer optimization method for large power grid and microgrid dispatching taking into account the active support of microgrid as claimed in claim 4 is characterized in that: The microgrid side objective function aiming at maximizing the benefits of the microgrid is constructed as a lower-level model, including decision variables and optimization objectives of the lower-level model; The decision variables of the lower model include the output of the microgrid, the peak load deviation, and the interactive power provided by the microgrid to the large grid; The optimization goal is to minimize the cost of the microgrid, and the optimization goal includes the gas turbine cost, the electricity purchase and sales cost, and the deviation penalty cost.

6. The dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid as claimed in claim 5, characterized in that: The calculation formula of the large power grid side objective function is as follows: Where: is the objective function of the large power grid, For quotes on other resources, Contribute to other resources purchased by the large power grid, The price of power provided by the microgrid to the main grid, is the price of power absorbed by the microgrid from the large grid, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid, is the deviation penalty coefficient, It is the positive deviation of the peak load of the microgrid. It is the negative deviation of the peak load output of the microgrid.

7. The dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid as claimed in claim 6, characterized in that: The objective function on the large grid side includes the constraints on the large grid side. The constraints on the large grid side include power balance constraints, power purchase and sales price constraints of the microgrid to the large grid, and upper and lower limits of other resource output constraints, which are as follows: The power balance constraint is specifically: Where: The peak load demand released by the large power grid, Contribute to other resources purchased by the large power grid, The power provided by the microgrid to the large grid, It is the power absorbed by the microgrid from the large grid. The price constraints for the microgrid to purchase and sell electricity from the large grid are specifically: The upper and lower limits of other resource output constraints are specifically: Where: The maximum amount of other resources that the large power grid can purchase. Contribute to other resources purchased by the large power grid.

8. The dual-layer optimization method for large power grid and microgrid dispatching taking into account the active support of microgrid as claimed in claim 7, characterized in that: The microgrid side objective function is calculated as follows: Where: is the objective function of the microgrid side, N is the number of gas turbines, is the output of the i-th gas turbine, a, b, c are the cost coefficients of the gas turbine, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid, is the deviation penalty coefficient, It is the positive deviation of the peak load of the microgrid. is the negative deviation of the microgrid peak load output. The price of power provided by the microgrid to the main grid, is the electricity price of the power absorbed by the microgrid from the large grid, and E is an intermediate variable.

9. The dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid as claimed in claim 8, characterized in that: The microgrid side objective function includes microgrid side constraints, and the microgrid side constraints include power balance constraints, upper and lower limit constraints of the interactive power between the microgrid and the large grid, power deviation constraints, and gas turbine output constraints, which are specifically as follows: The power balance constraint is specifically: Where: is the total power generation of the microgrid, is the load demand of the microgrid, The power provided by the microgrid to the large grid, is the power absorbed by the microgrid from the large grid, It is the positive deviation of the peak load of the microgrid. It is the negative deviation of the peak load output of the microgrid. The upper and lower limits of the interaction power between the microgrid and the large grid are specifically: Where: is the maximum power provided by the microgrid to the large grid, is the maximum power absorbed by the microgrid from the large grid, The power provided by the microgrid to the large grid, It is the power absorbed by the microgrid from the large grid. The power deviation constraint is specifically: Where: Provide the maximum positive deviation output for the microgrid to provide peak load regulation to the large grid. Provides the maximum reverse deviation output for the microgrid to provide peak load regulation to the large grid. It is the positive deviation of the peak load of the microgrid. It is the negative deviation of the peak load output of the microgrid. The gas turbine output constraint is specifically: Where: is the maximum output of the ith gas turbine.

10. The dual-layer optimization method for large power grid and microgrid dispatching taking into account active support of microgrid as claimed in claim 9, characterized in that: The single-layer optimization model is specifically: Where: is the objective function of the large power grid side, x is the decision variable of the upper model, y is the decision variable of the lower model, , v represents the dual variable corresponding to the constraint condition in the market clearing problem, Represents the set of KKT conditions in the market clearing problem.

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