JP2024503999A - Power grid resource allocation - Google Patents

Abstract

A method of operating a power grid includes: generating, by a power management system of a power grid, an intermediate resource allocation schedule that provides a tentative schedule of resource allocation for power grid resources operating in the power grid; The power management system determines whether the intermediate resource allocation schedule is executable by combining the combined constraints of the power grid resource allocation profile of the power grid that directs the operation of the power grid constrained by the power grid operation information with the intermediate resource allocation. determining, by checking whether the schedule satisfies, and generating, by the power management system, a feasible resource allocation schedule in response to determining that the intermediate resource allocation schedule is infeasible; repairing the intermediate resource allocation schedule, the repairing determining whether a first dispatch solution obtained by solving the dispatch problem with fixed integer decisions from the intermediate resource allocation schedule is feasible. including determining.

Description

TECHNICAL FIELD This disclosure relates generally to power grids and power grid operation, and in certain embodiments to power grid resource allocation.

BACKGROUND Independent system operators (ISOs) use unit commitments (UCs) to obtain generation resource and demand commitments and dispatch in power grids. Unit commitment establishes the commitment state and generation levels of all generators, energy storage systems, and price-dependent loads over a scheduling horizon to ensure load balance and spinning reserve requirements, transmission network constraints, and individual unit Minimize total power generation costs while meeting all system and area constraints, including operating constraints. Unit commitment is often formulated as a mixed integer linear programming (MILP) problem.

Since a typical power grid is being driven to operate closer and closer to its security margins, security-related transmission constraints are included to constrain unit commitments. Thus, typical power system resource scheduling involves security constrained unit commitments (SCUC), where security constraints include, for example, transmission line thermal capacity constraints for base case operating conditions and contingent operating conditions. There may be. SCUC is used in day-ahead, intra-day, and real-time power grid scheduling. In solving for security constraint unit commitments, a minimum cost operating schedule for a generator (also referred to as a power plant) is determined over a scheduling horizon. For example, a minimum cost operating schedule is identified that satisfies the operating constraints of each generator unit, the electrical network constraints in the base case network topology, and various operator specified contingency scenarios.

SUMMARY In some embodiments, a method of operating a power grid includes generating an intermediate resource allocation schedule by a power management system of the power grid, the intermediate resource allocation schedule operating within the power grid. The power management system determines whether the intermediate resource allocation schedule is feasible by providing a preliminary schedule of resource allocation for the power grid resources in the power grid, and determining whether the intermediate resource allocation schedule is feasible. determining, by checking whether an allocation schedule is met, that the power grid resource allocation profile directs operation of the power grid constrained by power grid operating information; Responsive to determining that the schedule is infeasible, by the power management system, repairing the intermediate resource allocation schedule to generate a feasible resource allocation schedule, the resource allocation schedule comprising: Providing a final schedule of resource allocation for power grid resources operating in a power grid and repairing intermediate resource allocation schedules is obtained by solving a dispatch problem with fixed integer decisions from intermediate resource allocation schedules. and determining whether the first dispatch solution to be executed is feasible.

In some embodiments, a power management system for a power grid includes one or more processors and a memory storing a program executed within the processor, the program comprising instructions, the instructions comprising one or more generating an intermediate resource allocation schedule for one or more processors when executed within a processor of the power grid, the intermediate resource allocation schedule comprising: generating a resource allocation schedule for power grid resources operating within the power grid; providing a tentative schedule and determining whether the intermediate resource allocation schedule is feasible by checking whether the intermediate resource allocation schedule satisfies a binding constraint of a power grid resource allocation profile of the power grid; in response to determining that the power grid resource allocation profile directs operation of the power grid that is constrained by the power grid operating information and that the intermediate resource allocation schedule is infeasible; repairing the intermediate resource allocation schedule to generate a workable resource allocation schedule, the resource allocation schedule being a final schedule of resource allocation for power grid resources operating in the power grid; and repairing the intermediate resource allocation schedule includes determining whether a first dispatch solution obtained by solving the dispatch problem with fixed integer decisions from the intermediate resource allocation schedule is feasible. and a memory.

In some embodiments, a system of a power grid is a power management system that generates an intermediate resource allocation schedule, the intermediate resource allocation schedule comprising: a power grid resource operating within the power grid; providing a tentative schedule of resource allocation for and checking whether the intermediate resource allocation schedule is feasible and whether the intermediate resource allocation schedule satisfies the joint constraints of the power grid resource allocation profile of the power grid; determining that the power grid resource allocation profile directs power grid operation that is constrained by the power grid operational information and that the intermediate resource allocation schedule is infeasible; generating an executable resource allocation schedule by repairing an intermediate resource allocation schedule in response to a power grid resource operating in the power grid; Providing the final schedule of resource allocation and repairing the intermediate resource allocation schedule determines whether the first dispatch solution obtained by solving the dispatch problem with fixed integer decisions from the intermediate resource allocation schedule is feasible. a power management system configured to determine, and a power grid resource configured to be controlled according to a resource allocation schedule, and a resource allocation schedule from the power management system to the power grid resource. a transmitter configured to transmit.

BRIEF DESCRIPTION OF THE DRAWINGS The details of one or more embodiments of the disclosure are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the disclosure will be apparent from the description and drawings, and from the claims. In the figures, the same reference numerals generally indicate the same component parts throughout the various views, which are generally not redescribed in the interest of brevity. For a more complete understanding of the disclosure, reference is now made to the following description in conjunction with the accompanying drawings.

1 illustrates a block diagram of a power grid having a power management system (PMS) within a control loop of the power grid in some embodiments; FIG. 1 is a functional block diagram of a power management system (PMS) in some embodiments. 1 is a functional block diagram of a security constraint unit commitment (SCUC) solver in some embodiments. FIG. 2 illustrates a flowchart of a method for solving the Lagrangian-relaxed (LR) duality of a security constraint unit commitment (SCUC) system in an embodiment. FIG. 3 illustrates a flowchart of a method for repairing infeasibility of a power resource allocation profile in an embodiment. 1 is a block diagram of a processing system for performing power management system processing in some embodiments. 2 is a flowchart of a method of operating a power grid in some embodiments.

Detailed Description of Exemplary Embodiments The making and use of the preferred embodiments is discussed in detail below. However, it should be appreciated that this disclosure provides many applicable inventive concepts that can be embodied in a wide variety of specific situations. The specific embodiments discussed are merely illustrative of specific ways to make and use the disclosure and do not limit the scope of the disclosure.

Solving a large-scale security constraint unit commitment (SCUC) can require significant time and computing resources due to its huge dimension and complexity. Embodiments of the present disclosure describe a SCUC solver that efficiently solves large-scale SCUC. The exemplary SCUC solver first finds a tentative power resource allocation schedule by solving the Lagrangian relaxation (LR) dual of the power grid resource allocation profile. The SCUC solver then checks whether the tentative resource allocation schedule is feasible. If the tentative resource allocation schedule is infeasible, the SCUC solver repairs the infeasibility of the tentative resource allocation schedule to achieve a feasible resource allocation schedule.

FIG. 1 illustrates a block diagram of a power grid 100 in some embodiments. Power grid 100 (which may also be referred to as a power system) includes a plurality of power resources 101 (eg, power generators or energy storage systems). Power resources 101 may be of different types, such as thermal power plants (e.g., coal, natural gas, nuclear plants), hydropower plants, renewable resource power plants (e.g., wind farms, solar plants), energy storage systems, and demand response programs. It may be of. Depending on the power plant type, each of the power resources 101 may have minimum up/down times, ramp up/down rates, regulation/stability (e.g., if a unit changes its production level too many times) ), and startup/shutdown ramp rates (e.g., when starting/stopping, the unit follows a specific power curve, which depends on how long the plant is offline/online) may be subject to complex technical and business constraints, such as

Power grid 100 also includes transmission grid 103, which is an electrical grid that supplies electricity produced by power resource 101 (eg, a power plant) to consumers. Transmission grid 103 is an interconnected network that may span a large geographic area (eg, a country). Resource response rates, along with complex characteristics of the transmission grid 103, such as network topology, equipment equipment parameters, and line flow limitations, may need to be considered in solving the security constraint unit commitment system.

As illustrated in FIG. 1, power grid 100 further includes a power management system (PMS) 105, which may be a market management system (MMS) or an emergency management system (EMS). PMS 105 may include various functional blocks to implement various functions, such as functional blocks 200 and 300 of FIG. 3. For example, the PMS 105 runs market scheduling applications to clear markets, establish market clearing prices for energy and ancillary services (such as various reserves and responses), and schedule commitments and dispatches for reliability. It may also include a clearing engine.

In some embodiments, the clearing engine solves the security constraint unit commitment system to provide a resource allocation schedule for the power grid 100. Resource allocation schedules include commitment decisions (e.g., whether a power plant is online and capable of producing energy at any given time), production (also known as dispatch) decisions (e.g., how much energy to produce at any given time), controllable network element determination (e.g., power flow on HVDC transmission lines and AC transmission lines with phase angle regulators). The resource allocation schedule may also be referred to as the operating schedule of power grid 100. In some embodiments, once generated, the resource allocation schedule is configured such that the power resource 101 is operated on, for example by a transmitter (which may be part of the power management system 105), such that the power resource 101 is operated according to the resource allocation schedule. 101.

In some embodiments, the resource allocation schedule includes power resource 101 constraints (e.g., generation capacity and operating margins, including safe operating ranges), transmission grid 103 constraints, market information (e.g., bidding information, cost information). The security constraint unit commitment system is generated by solving the security constraint unit commitment system while taking into account operating information (e.g., various constraints) of the power grid 100, such as , predicted demand information, regulatory requirements such as emissions targets). The goal of a resource allocation schedule is to clear market offers and bids while maximizing total welfare or minimizing total cost. In one exemplary embodiment, the goal may be to meet energy demands while minimizing energy production costs while being subject to reliability and emissions constraints. In another exemplary embodiment, the goal may be to maximize energy production profits, eg, the difference between revenue (from selling electricity) and cost (from producing electricity).

FIG. 2 is a functional block diagram of the power management system (PMS) 105 in an embodiment. PMS 105 in FIG. 2 may be used in power management system 105 of FIG. 1, as an example. For simplicity, not all functional blocks of PMS 105 are illustrated in FIG. 2.

As illustrated in FIG. 2, PMS 105 formulates the SCUC problem as a mixed integer programming (MIP) representation 133 by using SCUC model 131 and applying market and grid data 132 to SCUC model 131. . Thus, MIP representation 133 is, in some embodiments, a mathematical model (eg, 131) with constraints. Details of the SCUC model and the formulation of MIP representation 133 are described below. In the discussion herein, the term mixed integer programming (MIP) may be used interchangeably with mixed integer linear programming (MILP).

PMS 105 further includes a SCUC solver 134 configured to generate a SCUC solution 135 (eg, a resource allocation schedule). In some embodiments, SCUC solver 134 is configured to implement functional blocks 200 and 300 of FIG. 3 and is described in further detail below.

In embodiments, the SCUC model 131 for a Security Constraint Unit Commitment (SCUC) system has the following optimization problem:

This is formulated as

and

, where N is the number of power grid resources (e.g., the number of power plants and loads in the power grid), j is the resource index, x _j is the decision vector for resource j, and c _j is the cost coefficient vector for resource j, A _j is the constraint matrix for resource j, A _c,j is the joint constraint matrix for resource j, and b _j is the constraint boundary vector for resource j. , and b _c is the constraint boundary vector of the joint constraint. The constraints in equation (1.2) may be referred to as constraints on each of the power grid resources, and the constraints in equation (1.3) may be referred to as the coupling constraints of the SCUC system. In the discussion herein, the SCUC system (also referred to as the SCUC problem) of equations (1.1)-(1.3) may also be referred to as a power grid resource allocation function, or a power grid resource allocation profile. Note that in equation (1.1), vector x is used to represent all of the decision vectors x _j , j=1, 2,...,N. Throughout the discussion herein, unless specified otherwise, the same mathematical symbols in different mathematical formulas (e.g., x _j , c _j , A _j , A _c,j ) refer to the same or similar entities.

Therefore, solving the security-constrained unit commitment system minimizes the loss function (or cost function) shown in equation (1.1) while satisfying the various constraints in equations (1.2) and (1.3). is equivalent to finding a decision vector x _j , j=1,2,...,N, where the decision vector x _j contains information about the resource allocation schedule for the jth power grid resource. For example, each decision vector x _j includes binary information about the jth power resource (eg, a commitment decision to turn the jth power resource on or off in a particular scheduled time slot). In addition, each decision vector x _j includes non-binary (eg, continuous-valued) information about the jth power resource, such as production information (eg, how much energy to produce). The decision vector x _j , j = 1, 2, ..., N, is the schedule of resource allocation for the power grid resources operating in the power grid (e.g., turning on or off a power station in a particular time slot). used to form power resource allocation schedules, such as whether to generate power and how much power to generate.

In some embodiments, various constraints of the power grid 100 discussed above (eg, market and grid data 132) may be included in the constraint matrix A _j and/or the combined constraint matrix A _c,j . The cost coefficient vector c _j may include information such as energy production cost information. In various embodiments, the security constraint unit commitment system is a large-scale mixed integer linear non-convex optimization problem. Security constraint unit commitment systems are non-deterministic polynomial-time hardness (NP hard) and scale poorly with parallel MIP solvers using traditional methods. .

As illustrated in the example of FIG. 2, a security constraint unit commitment (SCUC) system may be expressed as a mixed integer planning (MIP) representation 133. Traditionally, MIP solvers are used to solve SCUC problems. A MIP solver may be a software package that runs on a processor (eg, a computer) to solve MIP problems (eg, a Security Constraint Unit Commitment System). Commercially available general purpose MIP solvers, such as CPLEX or Gurobi, may be used to solve the security constraint unit commitment system. Open source MIP solvers such as CBC may also be used as MIP solvers.

Typically, a MIP solver solves a vector of decision vectors through a series of branch-and-bound (B&B) operations and/or a series of branch-and-cut (B&C) operations. Search through space to find integer feasible solutions with progressively smaller loss functions for the SCUC system, thereby leading to the optimal solution (e.g., the set of decision vectors x _i corresponding to the minimum loss function for the SCUC system). gradually approaching. The MIP solver changes the values for the decision vector in multiple iterations such that the loss function decreases over time until the MIP solver reaches a final solution that is the optimal solution for the SCUC system or is sufficiently close to the optimal solution. Compute and update in steps. The path from the initial (e.g., interim) solution to the final solution (e.g., the vector space traversed by the MIP solver) is said to be the convergence path of the MIP solver (or of the SCUC system), and the MIP solver It is said to converge to a final solution along the path.

For example, a larger number of variables (e.g., hundreds, thousands, or millions) in the decision vector and the factor that the decision vector contains both integer-valued and real-valued variables (e.g., with continuous values) Due to this, it may take a long time and intensive computing resources for the MIP solver to find a feasible solution to the SCUC system. This disclosure describes an SCUC solver that uses a two-step process to efficiently find a feasible solution with good optimality (typically with a duality gap <0.5%) for an SCUC system. .

FIG. 3 illustrates a functional block diagram of a security constraint unit commitment (SCUC) solver 134 in some embodiments. SCUC solver 134 may be used in SCUC solver 134 of FIG. SCUC solver 134 includes two functional blocks 200 and 300 for a two-step process to find a feasible solution to the SCUC system.

As illustrated in FIG. 3, in functional block 200, the SCUC solver 134 optimizes the Lagrangian relaxation (LR) duality (also referred to as the LR duality problem) of the SCUC problem in Equations (1.1) to (1.3). , generate an intermediate (eg, tentative) resource allocation schedule. However, the intermediate resource allocation schedule may not satisfy all coupling constraints of the SCUC system. SCUC solver 134 then checks whether the tentative resource allocation schedule is feasible (eg, satisfies all constraints of the SCUC system). If the tentative resource allocation schedule is infeasible, the SCUC solver 134 repairs the infeasibility of the tentative resource allocation schedule to achieve a feasible resource allocation schedule at function block 300. Details of functional blocks 200 and 300 are discussed below.

FIG. 4 illustrates a flowchart of a method 250 for optimizing the Lagrangian relaxation (LR) duality of a security constraint unit commitment (SCUC) system, in an embodiment. The process illustrated in FIG. 4 is used to implement functional block 200 of FIG. 3 in the illustrated embodiment.

In block 201 of FIG. 4, the LR duality of the SCUC system is set up. In an exemplary embodiment, optimizing the LR dual of the SCUC problem is the following optimization problem:

This is formulated as

, where λ is a Lagrangian multiplier vector (e.g., a vector containing multiple Lagrangian multipliers), and Φ (λ) is

is the LR dual of SCUC defined as , which has the following constraints

receive.
By rewriting (2.3) to (2.4), the LR dual problem of formulas (2.3) and (2.5) can be transformed into multiple LR dual subproblems.

Note that this is subject to the constraints of equation (2.5) (e.g., A _j x _j >_b _j , j=1,2,...,N.). Each of the LR dual subproblems in (2.6) contains only the jth decision vector x _j and the jth joint constraint matrix A _c,j . Therefore, the number of variables in each of the LR dual subproblems is much smaller than the number of variables in the original SCUC problem, and therefore can be solved much faster. In addition, each of the LR dual subproblems may be solved by a different solver (e.g., a MIP solver), and therefore all of the LR dual subproblems can reduce the amount of time required to solve the LR dual subproblem. may be solved in parallel by multiple solvers (eg, N MIP solvers) to reduce In other words, solving the LR duality problem can be accomplished by solving multiple LR duality subproblems in parallel. In the discussion herein, a solver for solving an LR dual subproblem may also be referred to as an LR dual subproblem solver. As described in more detail below, optimizing the LR duality of the SCUC problem is accomplished by solving the LR duality problem and updating the Lagrangian multiplier vector λ alternately in multiple iterations.

Next, in block 203, the LR duality of the SCUC system solves the LR duality subproblems of equation (2.6) using, for example, LR duality subproblem solvers (e.g., MIP solvers). This will solve the problem. When solving the LR dual subproblem of equation (2.6), the variable to be solved (e.g., to be optimized) is the decision vector x _j and the Lagrangian multiplier vector λ has a fixed value (e.g., treated as a constant vector). Please note, in particular. In the first iteration, the Lagrangian multiplier vector λ is assigned an appropriate initial value (eg, a zero vector). The Lagrangian multiplier vector λ is subsequently updated at each iteration (see blocks 205 and 207). Therefore, in subsequent iterations, for the processing of block 203, Lagrangian multiplier vector λ uses the updated value of Lagrangian multiplier vector λ obtained from the previous iteration.

Next, at block 205, the partial slope of the Lagrangian multiplier vector λ is determined by the following formula:

where the decision vector x _j in equation (2.7) is the decision vector x _j obtained from solving the LR dual problem in block 203.

Next, in block 207, the Lagrangian multiplier vector λ is updated using the calculated partial slope sg from block 205. Those skilled in the art will readily appreciate that different methods for updating the Lagrangian multiplier vector λ are available, and that any suitable updating method may be used to update the Lagrangian multiplier vector λ. . As a non-limiting example, the Lagrangian multiplier vector λ is

where Δ is the step size used in updating the Lagrangian multiplier vector λ and k is the iteration index.

Next, in block 209, convergence of the optimization of the LR dual problem is checked, for example by checking the difference between the values of Φ(λ) achieved in the current iteration and the last iteration. For example, if the difference between Φ(λ) in the current iteration and the last iteration is less than a predetermined threshold, it is determined that convergence of the optimization of the LR duality problem is achieved and processing proceeds to block 211 . Another criterion for stopping iterative processing may be reaching a predetermined maximum number of iterations. If convergence of the LR dual problem optimization has not been achieved and the maximum number of iterations has not been reached, processing returns to block 203 for the next iteration.

At block 211, an intermediate resource allocation schedule is formed based on the decision vector x _j of the solution to the LR dual problem (or LR dual problem solution for short). Since the LR dual problem solution may not be a feasible solution with respect to the relaxed constraints, the intermediate resource allocation schedule provides a tentative resource allocation schedule. Next, check the feasibility of solving the LR dual problem. If the decision vector x _j of the LR dual problem solution satisfies all the constraints in equations (1.2) and (1.3), then the LR dual problem solution is said to be feasible and the intermediate resource allocation schedule is , is output by SCUC solver 134 as a resource allocation schedule, and the processing in function block 300 is skipped.

On the other hand, if the decision vector x _j does not satisfy all the constraints in equations (1.2) and (1.3), the LR dual problem solution is infeasible or has residual infeasibility. Then it is said. In the illustrated embodiment, the solution to the LR dual subproblem (2.6) must satisfy the constraints in equation (2.5), which are the same as the constraints in equation (1.2). Note that, therefore, in order to determine the feasibility of the LR dual problem solution, only the associative constraints in equation (1.3) need to be checked. When any of the associative constraints in equation (1.2) is not satisfied, the LR dual problem solution is said to have residual infeasibility due to the associative constraints.

When the LR dual problem solution is determined to be infeasible, the intermediate resource allocation schedule is repaired by function block 300 (see FIG. 3) to obtain a feasible resource allocation schedule. Accordingly, the processing of function block 300 may include repairing (residual) infeasibility of an intermediate resource allocation schedule, repairing (residual) infeasibility of an LR dual problem solution, or repairing (residual) infeasibility of a joint constraint. It may also be referred to as repairing infeasibility.

FIG. 5 illustrates a flowchart of a method 350 for repairing infeasibility of a power resource allocation profile, in an embodiment. The process illustrated in FIG. 5 is used to implement functional block 300 of FIG. 3 in the illustrated embodiment.

The process illustrated in FIG. 5 is iterative, and therefore the index k is used to indicate the number of iterations of the iterative process. In block 301, index k is assigned an initial value of zero. Next, at block 303, the dispatch problem (also referred to as the economic dispatch problem) is solved. For the first iteration (eg, when k=0), the dispatch problem is solved with fixed integer decisions from the LR dual problem solution (obtained in function block 200 of FIG. 3). For subsequent iterations (eg, when k>0), the dispatch problem is solved with fixed integer decisions from the extended subproblem solution (obtained in block 309 of the last iteration). For ease of discussion, it is assumed that the dispatch problem is solved with fixed integer decisions, without identifying the source of the fixed integer decisions (e.g., from the LR dual problem solution or from the extended subproblem solution). May be called. The dispatch problem is

This is formulated as

and

receive.
The dispatch problem in (3.1)-(3.3) is similar to the original SCUC problem in (1.1)-(1.3), but (involving multiple real-valued slack variables) A slack variable vector S is added. In other words, the dispatch problem is obtained by modifying the SCUC problem with slack variables. The dispatch problem also includes a penalty vector M for the slack variable vector S. The dispatch problem is solved by fixed integer decisions, which means that when solving the optimization problems (3.1) to (3.3 ₎ , the integer variables in the decision vector or the decision to turn off, and other variables with integer values, if any) provided by the LR dual problem solution (when k=0) or by the extended subproblem solution (when k>0) Note that this means fixed to the value given. In other words, optimization of the dispatch problem is performed only on non-integer variables in the decision vector x _j , and integer variables in the decision vector x _j are treated as constants. Because the number of variables to solve in the dispatch problem is smaller than that in the original SCUC system, and because the variables to be optimized are all real-valued (and therefore may have continuous gradients), the dispatch Problems are easier to solve. A MIP solver may be used to solve the dispatch problem, but in this case the MIP solver only needs to solve for non-integer variables, which reduces the time required to solve the dispatch problem. This is the result. Alternatively, a simpler solver than the MIP solver, for example one that only optimizes non-integer variables, may be used to solve the dispatch problem.

A slack variable vector S is added to the dispatch problem to ensure technical feasibility, so that the solver for the dispatch problem solves (e.g., decision vector x _j and slack variable vector S). In particular, slack variables help satisfy the join constraint in (3.3). Without the slack variable vector S, the dispatch problem may not have a feasible solution, because the integer variables in the decision _vector or because it is fixed to the value provided by the extended subproblem solution. Since the optimization process is likely to avoid the high costs associated with slack variables, the elements in the penalty vector M are assigned sufficiently large values (e.g., high costs for slack variables) such that (3 .3) Prevents the solver from relying on the slack variable vector S to satisfy the coupling constraints.

Next, in block 305, the feasibility of the solution to the dispatch problem (also referred to as the dispatch solution) is checked. The dispatch solution is feasible when the coupling constraint in (3.3) is satisfied with a zero-valued slack variable vector S, which is equivalent to satisfying the coupling constraint (1.3) of the original SCUC system. It is. Therefore, a dispatch solution is considered viable when the slack variables in the slack variable vector S are zero. A nonzero-valued slack variable vector S means that the dispatch solution is technically feasible (e.g., satisfies (3.3)) relying on the slack variables, but does not satisfy the coupling constraint (1.3) of the SCUC system. , which means that it is therefore not executable. If the dispatch solution is feasible, processing proceeds to block 306 where SCUC solver 134 generates a resource allocation schedule based on the decision vector x _j of the feasible dispatch solution and processing stops.

If the dispatch solution is infeasible, method 350 solves the infeasible problem by solving multiple augmented subproblems in one or more iterations and solving the dispatch problem with a fixed integer decision from the solution to the augmented subproblem. The details are discussed below. For ease of discussion, checking whether a dispatch solution is infeasible may also be referred to as checking the joint constraint infeasibility of a dispatch solution.

To repair the infeasibility of the dispatch solution, processing of method 350 proceeds to block 307 for a first iteration (e.g., k=0), where multiple augmented subproblems are set up and expanded The joint constraint boundaries for the subproblems are initialized. The extended part problem is

is defined as , which is

and

, where k is the iteration index, λ ^(k) is the multiplier vector (e.g., containing multiple multipliers) at the kth iteration, and s _j ^(k) is the jth multiplier vector at the kth iteration. is the slack variable vector for the extended subproblem of , and y _j ^(k) is the joint constraint bond vector (e.g., of joint constraints, including multiple boundaries) for the jth extended subproblem at the kth iteration. , ρ is the penalty coefficient for the quadratic term in (4.1). The multiplier vector λ ^(k) may also be referred to as the Lagrangian multiplier vector of the extended subproblem, and the multipliers in the multiplier vector λ ^(k) may also be referred to as Lagrangian multipliers.

The multiplier vector λ ^(k) is initialized to the final value obtained from block 200 of FIG. In subsequent iterations (k>0), the multiplier vector λ ^(k) is updated at each iteration. The penalty coefficient ρ is an input parameter for the extended subproblem and therefore has a fixed value during optimization. The associative constraint bond vector y _j ^(k) is initialized at the first iteration (when k = 0) with the assigned infeasibility, if any, plus the value from the dispatch solution. be done. Details are discussed below.

Once the extended subproblems are set up and the joint constraint bond vectors y _j ⁽⁰⁾ are initialized, a suitable solver, such as a MIP solver, is used to solve each of the extended subproblems, as illustrated at block 309. Good too. To reduce the time required to find a solution to an extended subproblem, multiple solvers may be used to solve the extended subproblem in parallel. In the discussion herein, a solution to an extended subproblem (eg, decision vector x _j , j=1, 2, . . . N) is also referred to as an extended subproblem solution.

Next, at block 310, the iteration index k is incremented by one. Processing returns to block 303 for the next iteration of processing.

Next, in block 303, the dispatch problem is solved again with fixed integer decisions from the expanded subproblem solution. The details are the same or similar to those discussed above and are therefore not repeated here.

Next, at block 305, the feasibility of the dispatch solution is checked using the same or similar processing as discussed above. If the dispatch solution is feasible, processing proceeds to block 306 where SCUC solver 134 generates a resource allocation schedule based on the decision vector x _j of the feasible dispatch solution and processing stops. If the dispatch solution is infeasible, processing proceeds to blocks 311 and 313, where the multiplier vector λ ^(k) and the joint constraint boundary vector y _j ^(k) are updated, as discussed below.

Next, at block 311, updates are computed for the multiplier vector λ ^(k) and the joint constraint boundary vector y _j ^(k) . In particular, the update Δλ ^(k) (i) for the i-th element of the multiplier vector λ ^(k) at the k-th iteration is

Calculated by
The update Δy j ^(k) (i) for the i-th element of the j-th joint constraint boundary vector y _j ⁽ k) in the k- _th iteration is

Next, in block 313, the multiplier vector λ ^(k) and the joint constraint boundary vector y _j ^(k) are updated using the updates computed in block 311. In particular, the multiplier vector λ ^(k) is

The joint constraint boundary vector y _j ^(k) is updated by

updated by.
Next, at block 309, the expanded subproblem is computed using the same or similar processing as discussed above with the updated multiplier vector λ ^(k) and the updated joint constraint boundary vector y _j ^(k) , so the details are not repeated.

Next, at block 310, the iteration index k is incremented by 1 and processing returns to block 303 for the next iteration of the process.

Next, in block 303, the dispatch problem is solved with fixed integer decisions from the extended subproblem solution obtained with the updated multiplier vector λ ^(k) and the updated joint constraint boundary vector y _j ^(k). It will be destroyed. The iterative process continues until a feasible solution is achieved. Note that the processing in block 307 is performed only once at the beginning, when k=0. In subsequent iterations (k>0), processing of method 350 takes a path along blocks 311 and 313. By updating the multiplier vector λ ^(k) and the joint constraint boundary vector y _j ^(k) at each iteration, the processing of method 350 reduces the residual infeasibility of the joint constraints and eventually produces a feasible dispatch solution. find.

FIG. 6 is a block diagram of a processing system 900 for performing power management system processing in some embodiments. For example, processing system 900 may be used to implement PMS 105 of FIG.

As shown in FIG. 6, processing system 900 includes a processor 902, memory 904, and interfaces 906-910, which may (or may not) be arranged as shown in FIG. Processor 902 may be any component or collection of components adapted to perform computing and/or other processing related tasks, and memory 904 may store programming for execution by processor 902. and/or any component or collection of components adapted to store instructions. In embodiments, memory 904 includes non-transitory computer-readable media. Interfaces 906, 908, 910 may be any component or collection of components that allow processing system 900 to communicate with other devices/components. For example, one or more of interfaces 906, 908, 910 may be adapted to communicate data, control, or management messages from processor 902 to an application installed on a host device and/or a remote device. good. As another example, one or more of interfaces 906, 908, 910 may be configured to allow a device (e.g., a personal computer (PC), etc.) to interact/communicate with processing system 900. may be adapted. Processing system 900 may include additional components not depicted in FIG. 6, such as long-term storage (eg, non-volatile memory, etc.).

FIG. 7 illustrates a flowchart of a method 1000 of operating a power grid, according to some embodiments. It should be understood that the embodiment method shown in FIG. 7 is merely an example of many possible embodiment methods. Those skilled in the art will recognize many variations, substitutions, and modifications. For example, various steps may be added, removed, substituted, rearranged, or repeated as illustrated in FIG.

Referring to FIG. 7, at block 1010, a power grid resource allocation profile is generated by the power management system of the power grid, the power grid resource allocation profile directing operation of the power grid constrained by operating information of the power grid. ing. At block 1020, an intermediate resource allocation schedule is generated by the power management system, the intermediate resource allocation schedule providing a tentative schedule of resource allocations for power grid resources operating within the power grid. At block 1030, the power management system determines whether the intermediate resource allocation schedule is executable by checking whether the intermediate resource allocation schedule satisfies the binding constraints of the power grid resource allocation profile. At block 1040, in response to determining that the intermediate resource allocation schedule is infeasible, the power management system repairs the intermediate resource allocation schedule to generate a feasible resource allocation schedule and The schedule provides a final schedule of resource allocation for power grid resources operating within the power grid.

Embodiments may achieve advantages. For example, due to the larger number of variables to optimize, the types of variables to optimize (e.g., integer-valued and real-valued variables), and the NP-hardness of SCUC systems, the MIP solver may It may take a long time to find out. The present disclosure provides a computationally efficient way to solve the SCUC problem in two steps. In the first step, the SCUC solver solves the Lagrangian relaxation (LR) duality of the SCUC problem. The LR dual problem includes multiple LR subproblems that have lower dimensions (eg, fewer variables) and are suitable for parallel processing. The feasibility of the LR dual problem solution is checked. If the LR dual problem solution is feasible, a resource allocation schedule is generated from the decision vector of the LR dual problem solution. If the LR dual problem solution is infeasible, the infeasibility of the LR dual problem solution is repaired to achieve a feasible solution. The repair process involves solving the dispatch problem with fixed integer decisions and solving multiple extended subproblems with lower dimensions and suitable for parallel processing. Dispatch problems and extended subproblems allow finding feasible solutions quickly and efficiently.

Variations and modifications to the disclosed embodiments are possible and are fully intended to fall within the scope of this disclosure. For example, although the disclosed method is described within the framework of solving SCUC problems, the disclosed method may readily be applied to other MIP problems. As another example, the processing for updating the multiplier vector λ ^(k) (e.g., blocks 311 and 313 of FIG. 5) may be performed only for join constraints with infeasibility from the dispatch solution. good. As yet another example, whereas in FIG. 5 the feasibility test is performed on the dispatch solution, it is possible to test the feasibility directly on the extended subproblem solution.

Exemplary embodiments of the disclosure are now summarized. Other embodiments can be understood from the full scope of this specification and the claims filed herein.

Example 1. In embodiments, a method of operating a power grid is to generate an optimizer that addresses an optimization problem related to power grid resource allocation by a power management system of the power grid, the optimizer having an objective, constraints, and a computational an optimization model, the coupling is between at least two of the constraints, and generating a solution to the optimization problem as an intermediate resource allocation schedule by the optimizer's computing model, wherein the intermediate resource allocation schedule is , by providing a tentative schedule of resource allocation for power grid resources operating in the power grid, and by checking whether the solution satisfies the optimizer's coupling constraints by the optimizer's computing model. , in response to determining whether the intermediate resource allocation schedule is feasible, and in response to determining that the intermediate resource allocation schedule is infeasible, the optimizer's computing model determines a feasible resource allocation schedule. repairing an intermediate resource allocation schedule to generate an intermediate resource allocation schedule, the resource allocation schedule providing a final schedule of resource allocations for power grid resources operating in the power grid; repairing includes determining whether a first dispatch solution obtained by solving the dispatch problem with fixed integer decisions from the intermediate resource allocation schedule is feasible.

Example 2. 2. The method of example 1, further comprising transmitting a resource allocation schedule to power grid resources by a power management system.

Example 3. 2. The method of example 1, wherein the optimizer constraints include information for constraining operation of a power grid and include security-related transmission constraint information and cost information.

Example 4. The method of example 1, wherein generating the optimizer includes formulating the optimization problem as a security constraint unit commitment (SCUC) system based on a mixed integer program.

Example 5. An intermediate resource allocation schedule is generated by solving the Lagrangian relaxation (LR) dual of the optimization problem, where the LR dual of the optimization problem includes the Lagrangian multipliers and coupling constraints of the optimization problem, and the LR dual of the optimization problem includes multiple LR subproblems, and generating the intermediate resource allocation schedule includes solving the multiple LR subproblems in parallel using multiple mixed integer programming (MIP) solvers as described in Example 1. the method of.

Example 6. 6. The method of example 5, wherein generating the intermediate resource allocation schedule further includes calculating partial slopes for Lagrangian multipliers and updating the Lagrangian multipliers using the calculated partial slopes.

Example 7. Determining whether the first dispatch solution is feasible includes forming the dispatch problem by modifying the optimization problem with a slack variable and using intermediate resources to obtain the first dispatch solution. The method of Example 1, comprising solving a dispatch problem with a fixed integer decision from an allocation schedule and determining whether there is a non-zero slack variable in the first dispatch solution.

Example 8. Restoring the intermediate resource allocation schedule includes generating a resource allocation schedule from the commitment decisions of the first dispatch solution in response to determining that there is no non-zero slack variable in the first dispatch solution. The method of Example 7, further comprising.

Example 9. 9. The method of Example 8, wherein the first dispatch solution is determined to be infeasible in response to determining that there is a non-zero slack variable in the first dispatch solution.

Example 10. solving the plurality of expanded subproblems to generate a first expanded subproblem solution in response to repairing the intermediate resource allocation schedule determining that the first dispatch solution is infeasible; and generating a second dispatch solution by solving the dispatch problem with fixed integer decisions from the first extended subproblem solution, and determining whether the second dispatch solution is feasible. 10. The method of Example 9, further comprising: generating a resource allocation schedule from the commitment determination of the second dispatch solution if the second dispatch solution is feasible.

Example 11. Repairing the intermediate resource allocation schedule includes setting up a plurality of extended subproblems before solving the plurality of extended subproblems, the plurality of extended subproblems including a Lagrangian multiplier for the plurality of extended subproblems. and initializing the joint constraint boundaries for the plurality of extended subproblems.

Example 12. repairing the intermediate resource allocation schedule includes updating Lagrangian multipliers and joint constraint boundaries of the plurality of extended subproblems in response to determining that the second dispatch solution is infeasible; Solving multiple extended subproblems with updated Lagrangian multipliers and updated joint constraint boundaries to generate extended subproblem solutions of 2 and dispatching with fixed integer decisions from the second extended subproblem solution. generating a third dispatch solution by solving the problem; determining whether the third dispatch solution is feasible; and determining the third dispatch solution if the third dispatch solution is feasible; 12. The method of Example 11, further comprising: generating a resource allocation schedule from the solution commitment decisions.

Example 13. In embodiments, a power management system for a power grid includes one or more processors and a memory storing a program executed in the processor, the program including instructions, and the instructions executing in the one or more processors. generating an intermediate resource allocation schedule in one or more processors when executed on the power grid, wherein the intermediate resource allocation schedule is a tentative schedule of resource allocation for power grid resources operating in the power grid; and determining whether an intermediate resource allocation schedule is feasible by checking whether the intermediate resource allocation schedule satisfies a joint constraint of a power grid resource allocation profile of a power grid. in response to determining that the power grid resource allocation profile directs operation of the power grid that is constrained by the power grid operating information and that the intermediate resource allocation schedule is infeasible; repairing the intermediate resource allocation schedule to generate a possible resource allocation schedule, the resource allocation schedule providing a final schedule of resource allocation for power grid resources operating in the power grid; , repairing the intermediate resource allocation schedule includes determining whether a first dispatch solution obtained by solving the dispatch problem with fixed integer decisions from the intermediate resource allocation schedule is feasible; and a memory for performing the operation.

Example 14. The power management system of Example 13, further comprising a transmitter configured to transmit a resource allocation schedule to a power grid resource, the power grid resource being configured to be controlled according to the resource allocation schedule.

Example 15. an intermediate resource allocation schedule is generated by solving a Lagrangian relaxation (LR) dual of a power grid resource allocation profile, the LR dual of the power grid resource allocation profile includes a plurality of LR subproblems, the program includes instructions; 14. The power management system of example 13, wherein the instructions cause the one or more processors to generate an intermediate resource allocation schedule by solving multiple LR subproblems in parallel using multiple solvers.

Example 16. Determining whether the first dispatch solution is feasible includes forming a dispatch problem by modifying the power grid resource allocation profile with a slack variable and obtaining the first dispatch solution. repairing the intermediate resource allocation profile, the method comprising: solving a dispatch problem with a fixed integer solution from the intermediate resource allocation schedule; and determining whether there is a non-zero slack variable in the first dispatch solution. as in Example 13, further comprising generating a resource allocation schedule from a commitment decision of the first dispatch solution in response to determining that there is no non-zero slack variable in the first dispatch solution. Power management system.

Example 17. Solving multiple extended subproblems to generate a first extended subproblem solution in response to determining that a first dispatched solution is infeasible to one or more processors , the plurality of extended subproblems include Lagrangian multipliers and joint constraint boundaries for the plurality of extended subproblems, and the first extended subproblem is solved by solving the dispatch problem with fixed integer decisions from the first extended subproblem solution. generating a second dispatch solution; determining whether the second dispatch solution is feasible; and in response to determining that the second dispatch solution is feasible; 17. The power management system of example 16, wherein the program includes further instructions for repairing an intermediate resource allocation schedule by causing: generating a resource allocation schedule from a commitment decision of a dispatch solution.

Example 18. Updating Lagrangian multipliers and joint constraint boundaries of multiple extended subproblems in response to determining that a second dispatch solution is infeasible to one or more processors; and Solving multiple extended subproblems with updated Lagrangian multipliers and updated joint constraint boundaries to generate extended subproblem solutions of 2 and dispatching with fixed integer decisions from the second extended subproblem solution. 18. The power management system of example 17, wherein the program includes instructions for repairing an intermediate resource allocation schedule by solving a problem to generate a third dispatch solution.

Example 9. In an embodiment, a system of a power grid is a power management system that generates an intermediate resource allocation schedule, the intermediate resource allocation schedule comprising resource allocation for power grid resources operating within the power grid. providing a tentative schedule of allocation and checking whether the intermediate resource allocation schedule is feasible by checking whether the intermediate resource allocation schedule satisfies the joint constraints of the power grid resource allocation profile of the power grid; determining that the power grid resource allocation profile directs power grid operation that is constrained by power grid operational information; and determining that the intermediate resource allocation schedule is infeasible. In response, generating a feasible resource allocation schedule by repairing the intermediate resource allocation schedule, the resource allocation schedule comprising: providing a final schedule and repairing the intermediate resource allocation schedule determines whether a first dispatch solution obtained by solving the dispatch problem with fixed integer decisions from the intermediate resource allocation schedule is feasible; a power management system configured to: and a power grid resource configured to be controlled according to a resource allocation schedule, and transmitting a resource allocation schedule from the power management system to the power grid resource. A transmitter configured as follows.

Example 20. Determining whether the first dispatch solution is feasible includes forming a dispatch problem by modifying the power grid resource allocation profile with a slack variable and obtaining the first dispatch solution. repairing the intermediate resource allocation schedule, the method comprising: solving a dispatch problem with fixed integer decisions from the intermediate resource allocation schedule; and determining whether there is a non-zero slack variable in the first dispatch solution; as in Example 19, further comprising generating a resource allocation schedule from the commitment decision of the first dispatch solution in response to determining that there is no non-zero slack variable in the first dispatch solution. system.

Although this disclosure has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments, as well as other embodiments of the disclosure, will be apparent to those skilled in the art upon reference to the description. Accordingly, the appended claims are intended to cover any such modifications or embodiments.

Claims (20)

A method of operating a power grid, the method comprising:
generating an intermediate resource allocation schedule by a power management system of the power grid, the intermediate resource allocation schedule generating a tentative schedule of resource allocation for power grid resources operating in the power grid; to provide and
The power management system determines whether the intermediate resource allocation schedule is executable by checking whether the intermediate resource allocation schedule satisfies a binding constraint of a power grid resource allocation profile of the power grid. the power grid resource allocation profile directs operation of the power grid constrained by operational information of the power grid;
Responsive to determining that the intermediate resource allocation schedule is infeasible, repairing the intermediate resource allocation schedule by the power management system to generate a feasible resource allocation schedule; , wherein the resource allocation schedule provides a final schedule of resource allocation for the power grid resources operating in the power grid, and repairing the intermediate resource allocation schedule comprises: determining whether a first dispatch solution obtained by solving a dispatch problem with a fixed integer decision is feasible. The method of claim 1, further comprising transmitting the resource allocation schedule to the power grid resources by the power management system. 3. The method of claim 1 or 2, wherein the operational information includes information for constraining the operation of the power grid and includes security-related transmission constraint information and cost information. Any one of claims 1 to 3, wherein generating the power grid resource allocation profile comprises formulating the power grid resource allocation profile as a security constrained unit commitment (SCUC) system based on mixed integer planning. The method described in section. The intermediate resource allocation schedule is generated by solving a Lagrangian relaxation (LR) dual of the power grid resource allocation profile, and the LR dual of the power grid resource allocation profile is determined by the Lagrangian multiplier and the LR dual of the power grid resource allocation profile includes a combination constraint, the LR dual of the power grid resource allocation profile includes a plurality of LR subproblems, and generating the intermediate resource allocation schedule is performed using a plurality of mixed integer programming (MIP) solvers. A method according to any one of claims 1 to 4, comprising solving multiple LR subproblems in parallel. generating the intermediate resource allocation schedule;
calculating partial slopes for the Lagrangian multipliers;
6. The method of claim 5, further comprising: updating the Lagrangian multiplier using the calculated partial slope. Determining whether the first dispatch solution is feasible,
forming the dispatch problem by adding a slack variable to the combination constraints of the power grid resource allocation profile and to an objective function of the power grid resource allocation profile;
solving the dispatch problem with the fixed integer decision from the intermediate resource allocation schedule to obtain the first dispatch solution;
7. A method according to any preceding claim, comprising: determining whether there is a non-zero slack variable in the first dispatch solution. Restoring the intermediate resource allocation schedule includes, in response to determining that there is no non-zero slack variable in the first dispatch solution, repairing the resource allocation schedule from a commitment decision of the first dispatch solution. 8. The method of claim 7, further comprising generating. 9. The method of claim 8, wherein the first dispatch solution is determined to be infeasible in response to determining that there is a non-zero slack variable in the first dispatch solution. restoring the intermediate resource allocation schedule;
In response to determining that the first dispatch solution is infeasible;
solving a plurality of extended subproblems to generate a first extended subproblem solution;
generating a second dispatch solution by solving the dispatch problem with fixed integer decisions from the first extended subproblem solution;
determining whether the second dispatch solution is feasible;
10. The method of claim 9, further comprising: generating the resource allocation schedule from a commitment decision of the second dispatch solution if the second dispatch solution is viable. repairing the intermediate resource allocation schedule before solving the plurality of extended subproblems;
setting up the plurality of extended subproblems, the plurality of extended subproblems including Lagrangian multipliers and coupling constraint boundaries for the plurality of extended subproblems;
11. The method of claim 10, further comprising initializing the joint constraint boundaries for the plurality of extended subproblems. restoring the intermediate resource allocation schedule;
In response to determining that the second dispatch solution is infeasible;
updating the Lagrangian multipliers and the joint constraint boundaries of the plurality of extended subproblems;
solving the plurality of extended subproblems with updated Lagrangian multipliers and updated joint constraint boundaries to generate a second extended subproblem solution;
generating a third dispatch solution by solving the dispatch problem with fixed integer decisions from the second extended subproblem solution;
determining whether the third dispatch solution is feasible;
12. The method of claim 11, further comprising: generating the resource allocation schedule from a commitment decision of the third dispatch solution if the third dispatch solution is viable. A power management system for a power grid, comprising:
one or more processors;
a memory for storing a program executed within the processor, the program including instructions, and when the instructions are executed within the one or more processors, the one or more processors;
generating an intermediate resource allocation schedule, the intermediate resource allocation schedule providing a tentative schedule of resource allocation for power grid resources operating within the power grid;
determining whether the intermediate resource allocation schedule is executable by checking whether the intermediate resource allocation schedule satisfies a binding constraint of a power grid resource allocation profile of the power grid; a power grid resource allocation profile directs operation of the power grid constrained by operational information of the power grid;
Responsive to determining that the intermediate resource allocation schedule is infeasible, repairing the intermediate resource allocation schedule to generate a feasible resource allocation schedule, the resource allocation schedule comprising: , providing a final schedule of resource allocation for the power grid resources operating in the power grid, and repairing the intermediate resource allocation schedule is a dispatch problem with fixed integer decisions from the intermediate resource allocation schedule. A power management system comprising: determining whether a first dispatch solution obtained by solving a first dispatch solution is feasible; further comprising a transmitter configured to transmit the resource allocation schedule to the power grid resource, the power grid resource configured to be controlled according to the resource allocation schedule;
The power management system according to claim 13. the intermediate resource allocation schedule is generated by solving a Lagrangian relaxation (LR) dual of the power grid resource allocation profile, the LR dual of the power grid resource allocation profile includes a plurality of LR subproblems; , instructions that cause the one or more processors to generate the intermediate resource allocation schedule by solving the plurality of LR subproblems in parallel using a plurality of solvers; The power management system according to claim 13 or 14. Determining whether the first dispatch solution is feasible,
forming the dispatch problem by modifying the power grid resource allocation profile with a slack variable;
solving the dispatch problem with a fixed integer solution from the intermediate resource allocation schedule to obtain the first dispatch solution;
determining whether there is a non-zero slack variable in the first dispatch solution;
repairing an intermediate resource allocation profile generates the resource allocation schedule from a commitment decision of the first dispatch solution in response to determining that there is no non-zero slack variable in the first dispatch solution; The power management system according to any one of claims 13 to 15, further comprising: the one or more processors;
In response to determining that the first dispatch solution is infeasible;
solving a plurality of extended subproblems to generate a first extended subproblem solution, the plurality of extended subproblems including Lagrangian multipliers and joint constraint boundaries for the plurality of extended subproblems; and,
generating a second dispatch solution by solving the dispatch problem with fixed integer decisions from the first extended subproblem solution;
determining whether the second dispatch solution is feasible;
and generating the resource allocation schedule from the commitment decisions of the second dispatch solution in response to determining that the second dispatch solution is feasible. 17. The power management system of claim 16, wherein the program includes further instructions for repairing a schedule. the one or more processors;
In response to determining that the second dispatch solution is infeasible;
updating the Lagrangian multipliers and the joint constraint boundaries of the plurality of extended subproblems;
solving the plurality of expanded subproblems with updated Lagrangian multipliers and updated joint constraint boundaries to generate a second expanded subproblem solution;
generating a third dispatch solution by solving the dispatch problem with fixed integer decisions from the second extended subproblem solution; The power management system according to claim 17, wherein the program includes: A power grid system,
A power management system,
generating an intermediate resource allocation schedule, the intermediate resource allocation schedule providing a tentative schedule of resource allocation for power grid resources operating within the power grid;
determining whether the intermediate resource allocation schedule is executable by checking whether the intermediate resource allocation schedule satisfies a binding constraint of a power grid resource allocation profile of the power grid; a power grid resource allocation profile directs operation of the power grid constrained by operational information of the power grid;
generating a feasible resource allocation schedule by repairing the intermediate resource allocation schedule in response to determining that the intermediate resource allocation schedule is infeasible, wherein the resource allocation schedule is , providing a final schedule of resource allocation for the power grid resources operating in the power grid, and repairing the intermediate resource allocation schedule is a dispatch problem with fixed integer decisions from the intermediate resource allocation schedule. determining whether a first dispatch solution obtained by solving is feasible;
a power grid resource configured to be controlled according to the resource allocation schedule;
a transmitter configured to transmit the resource allocation schedule from the power management system to the power grid resources. Determining whether the first dispatch solution is feasible,
forming the dispatch problem by modifying the power grid resource allocation profile with a slack variable;
solving the dispatch problem with the fixed integer decision from the intermediate resource allocation schedule to obtain the first dispatch solution;
determining whether there is a non-zero slack variable in the first dispatch solution;
Restoring the intermediate resource allocation schedule includes, in response to determining that there is no non-zero slack variable in the first dispatch solution, repairing the resource allocation schedule from a commitment decision of the first dispatch solution. 20. The system of claim 19, further comprising: generating.

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