**4.1.2 Hierarchical Planning in Power Management**

** **The control of markets and electricity grids requires coordinated decision-making across five decision domains. The scopes of these domains are identified below.

• Capacity planning: installed generation capacity, grid configuration, market regulations

• Power flow planning: bi-lateral contracts, wholesale bids & offers, unit availability

• Power flow scheduling: unit commitment, ancillary services contracts, reserve requirements

• Power dispatching: unit dispatch, demand management, regulation

• Power system controlling : voltage control, frequency control, circuit protection

The determination of the optimal power flow in a grid over a sequence of time periods requires the simultaneous optimization of all of the decisions listed above - a feat made impossible by the large number of variables that these decisions encompass. Consequently, power grid and market management is carried out through the application of a conventional hierarchical approach.

The conventional hierarchy of decision making conforms to the ordered list of decisions show above. Every decision is characterized by three elements: decision variables, which specify the alternatives available to the decision maker; performance measures, which specify the basis for evaluating the feasibility and objectives of a decision; parameters, which specify the given, uncontrollable factors that, together with the decision variables, determine the values of the performance measures The basic idea behind ** hierarchical planning ** is that the solution to a rough-cut representation of a decision in terms of aggregated decision variables can serve as a set of guidelines and constraints for a refined decision in terms of detailed decision variables. For example, the problems of determining the unit availability, unit commitment and unit dispatch are all related through performance measures such as profit for asset owners, service level to loads and total cost of power throughout a grid. Rather than attempt to find solutions to all three decisions simultaneously so that a globally optimal solution is obtained, a hierarchical planning approach would solve three separate decisions in stages. Specifically, the determination of unit availability is based on approximate forecasts of total demand over the upcoming week. The unit availability decision provides capacity constraints on the commitment and dispatching decisions. The commitment decision, in turn, is based on a forecast of load variations over the next 36 hours and consumes the bulk of the generation capacity, leaving a judicious amount of capacity for support of the regulation dispatching decisions, which cure any imbalances between loads and committed generation.

In order to implement a hierarchical planning scheme, each level of planning must approximate the effects of the lower-level decision variables on the current stage's constraints and performance measures. Furthermore, the solutions to higher-level decisions impose constraints on the lower-level decisions.

Using the "hat" notation to indicate approximations, the hierarchical planning approach is described as follows:

Suppose we have three sets of decision variables y_{1}, y_{2}, y_{3} for the following decision model,

subject to:

By approximating the effects of variables y_{2}, y_{3} we construct the following aggregate planning problem.

for *j=1, ...,n*

The first optimization in the hierarchy is,

subject to:

Resulting in a solution, y_{1}*^{}, which becomes a parameter in for all of the succeeding problems. The second approximate decision model is,

subject to:

The remaining optimization problems are formulated in a similar manner.