Mixed-Integer Linear Programming (MILP) Dispatch

MILP is uniquely capable of modeling binary commitment decisions (e.g., generator on/off, breaker open/closed) alongside continuous variables like power output setpoints. This is essential for DER fleets where assets like backup generators cannot be partially committed.

• Models start-up costs and minimum up/down time constraints
• Handles integer states for battery charging/discharging modes
• Enforces logical constraints (e.g., if generator A is on, generator B must be off)

Unlike heuristic or greedy algorithms, MILP solvers use branch-and-bound and cutting-plane methods to mathematically prove that the found solution is the global optimum within a specified tolerance gap. This is critical for financial settlement in wholesale energy markets.

• Provides a provable optimality gap (e.g., 0.01%)
• Eliminates the risk of leaving revenue on the table from suboptimal dispatch
• Essential for auditability in regulated utility environments

MILP frameworks can encode virtually any linear operational constraint, making them ideal for the IEEE 1547-2018 and UL 1741 SB compliance landscape. Constraints are expressed as linear equalities and inequalities.

• Ramp rate limits: Maximum change in output per minute
• State of charge (SOC) boundaries: Battery minimum and maximum energy levels
• Export limits: Dynamic operating envelopes enforced as hard constraints
• Reserve requirements: Headroom allocation for frequency response

The objective function can be tailored to any linear combination of cost or value drivers, enabling multi-objective optimization through weighted-sum methods or lexicographic goal programming.

• Economic dispatch: Minimize fuel cost, grid import cost, or levelized cost of energy
• Self-consumption: Maximize behind-the-meter solar utilization
• Peak shaving: Minimize the maximum demand charge over a billing period
• Emissions minimization: Dispatch to minimize carbon intensity using locational marginal emissions signals

MILP dispatch is typically deployed in a Model Predictive Control (MPC) framework, where the optimization is solved repeatedly over a rolling time window. Only the first timestep's decisions are executed before the problem is re-solved with updated forecasts.

• Incorporates updated load and solar forecasts at each step
• Provides inherent feedback correction against forecast errors
• The look-ahead horizon (e.g., 24-48 hours) ensures decisions account for future expected events like peak pricing periods

Commercial solvers like Gurobi and IBM CPLEX, along with open-source alternatives like HiGHS, have achieved dramatic performance improvements. Modern MILP solvers can handle problems with millions of variables and constraints in minutes.

• Presolve routines automatically simplify the problem before solving
• Parallel branch-and-bound exploits multi-core processors
• Warm-starting from a previous solution accelerates convergence
• Solver-as-a-service APIs enable cloud-native dispatch engines

The combinatorial optimization of deciding which generators or DERs to turn on/off over a multi-period horizon. MILP solves this by modeling each unit's status as a binary decision variable (0=off, 1=on), while respecting minimum up/down time constraints, startup costs, and ramping limits. The solver simultaneously determines commitment schedules and dispatch levels to minimize total operational cost.

The foundational exact solution method used by MILP solvers. The algorithm systematically partitions the feasible region by branching on fractional integer variables, then prunes suboptimal branches using linear programming relaxations. Key components include:

• Presolve: Simplifies the problem before branching
• Cut generation: Adds valid inequalities to tighten the LP relaxation
• Heuristics: Finds feasible integer solutions quickly to improve pruning

Variables restricted to values of 0 or 1 that encode discrete yes/no decisions in the optimization model. In DER dispatch, binary variables represent:

• Unit commitment status: Is battery $i$ discharging at time $t$?
• Mode selection: Is the EV charger in V2G export mode?
• Logical constraints: Mutual exclusivity (can't simultaneously charge and discharge)

These variables are what distinguish MILP from simpler linear programming formulations.

Special Ordered Sets are constraint structures that improve solver efficiency for piecewise-linear approximations common in DER modeling:

• SOS1: At most one variable in the set can be non-zero (mutual exclusivity)
• SOS2: At most two adjacent variables can be non-zero (convex combination)

SOS2 constraints efficiently model non-linear efficiency curves of inverters and batteries without introducing non-convexity, keeping the problem within MILP's tractable framework.

A decomposition technique that dualizes coupling constraints (such as system-wide power balance) into the objective function using Lagrange multipliers. This decomposes a large MILP into independent subproblems per DER, each solvable in parallel. The multipliers are iteratively updated via subgradient optimization to converge toward a feasible, near-optimal solution. Particularly valuable when dispatching geographically dispersed DER fleets with local constraints.