Generator Scheduling Using Decision Diagrams and Mixed-Integer Programming
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Solution Overview
Problem
The existing methods for scheduling electric generators struggle to efficiently minimize the total cost of producing electrical energy while meeting target power demands and adhering to operational constraints, especially with the integration of renewable energy sources and uncertainty in power demand.
Innovation Solution
A novel formulation of the unit commitment problem using decision diagrams and mixed-integer programming, which incorporates state-space representations and network flow constraints to tighten the feasible operations of generators, allowing for improved computational performance and handling of uncertainty in power demand.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional combinatorial optimization methods are used to solve the unit commitment problem, then the scheduling can meet operational constraints, but the computational complexity increases significantly and solution time becomes excessive
Solution Approach 1:
The patent segments the complex unit commitment problem into smaller subproblems by introducing state variables that track generator status (on/off) and operational history (hours on/off) at each time period. This segmentation allows the use of dynamic programming with manageable state spaces, breaking down the combinatorial explosion into tractable sequential decisions.
Solution Approach 2:
The patent performs preliminary action by pre-defining the state space structure and transition rules before solving the optimization problem. The state variables and constraints are established in advance, allowing the solver to navigate a predetermined feasible space rather than searching the entire combinatorial space, thus reducing solution time.
2Productivity
If the feasible set of generator operations is relaxed for computational ease, then solution speed improves, but the solution quality and cost minimization accuracy deteriorates
Solution Approach 1:
The patent changes the parameter representation from simple on/off binary variables to state variables that encode operational history (hours on, hours off). This parameter transformation tightens the feasible set by incorporating minimum up-time and down-time constraints directly into the state definitions, improving solution accuracy without sacrificing computational tractability through dynamic programming.
Solution Approach 2:
The patent introduces state variables as intermediaries between the generator control decisions and the operational constraints. These state variables mediate the relationship by capturing the essential historical information needed to enforce minimum up/down time requirements, allowing the solver to work with tighter constraints while maintaining computational efficiency.
3Reliability
If minimum up-time and down-time constraints are incorporated into the optimization model, then operational reliability improves, but the complexity of the optimization problem increases
Solution Approach 1:
The patent applies dynamics by making the feasible set of actions dependent on the current state. The minimum up-time and down-time constraints are enforced dynamically through state transitions: a generator that is ON must remain ON for a specified number of periods, and similarly for OFF states. This dynamic constraint enforcement is naturally handled by the state variable definitions in the dynamic programming formulation, avoiding the need for complex static constraint matrices.
Data Source
AI summary
A power generation planning system for controlling on/off sequence of generators according to operational parameters includes an interface to receive the operational parameters including a power demand, state-data of the generators and operational histories of the generators from a power control system, a memory to store an objective function, a mixed-integer programming solver, generator parameters of each the generators and planning modules including a state-space representation module, a variable assignment module, a network flow module and a tight constraint module, a processor to perform the planning modules based on the operational parameters received by the interface. The processor is configured to construct decision diagrams for each of the generators by using the state-space representation module, generate arc-variables representing state-transformations of the generators by assigning binary variables to arcs of the decision, generate network flow constraints to represent feasible operations of each of the generators, generate tight constraints of each of the generators by using the tight constraint module and formulate a mixed-integer problem, solve the mixed-integer problem, by using the mixed-integer programming solver, based on the states-data of the generators, the network flow constraints and the tight constraints, and transmit on/off sequence data of each of the generators obtained from the solved mixed-integer problem to a power control system via the interface.