1 What is the scheduling problem with energy storage?
Energy storage is an important part of the smart grid. The introduction of energy storage into economic dispatch can achieve peak-shaving and new energy access. Scheduling problems with energy storage can usually be described by the mathematical model of Figure 1 (assuming that the energy storage and discharge price is an input parameter): under the constraints of energy storage operation constraints, unit operation constraints and network constraints, strive to achieve minimum Total operating costs of the power grid. Due to the addition of energy storage, two points must be considered in the total operating cost of the grid: the charging cost of energy storage and the discharge cost of energy storage.
For the charging cost of energy storage, if the charging price is positive, the charging cost is considered to be paid by the energy storage to the grid; if the charging price is negative, the charging cost is considered to be paid by the grid to the energy storage.
For the discharge cost of energy storage, if the discharge price is positive, the discharge cost is considered to be paid by the grid to the energy storage; if the discharge price is negative, the discharge cost is considered to be paid by the energy storage to the grid.
If the energy storage and the power grid have signed a long-term contract, the operation cost of the energy storage is not considered during the dispatch. At this time, the charge and discharge price can be set to zero.
2 What are the challenges of the energy storage scheduling problem?
Compared with the scheduling problem without energy storage, all the storage problems with energy storage face a common challenge - the energy storage cannot be both charged and discharged at the same time, so this characteristic must be considered in the constraints. An intuitive idea is to use the power exchanged between the energy storage and the grid as the only optimization variable. It is positive when charging and negative when discharging, but this method is not feasible because the efficiency of charge and discharge of energy storage is different, and the price at the time of charge and discharge. It is also different from the cash flow (such as the storage of energy to the grid when charging, the grid to pay for energy storage during discharge), can not be modeled with only one continuous variable in the optimization model. Therefore, in the related research, two independent optimization variables (charging power and discharge power) are generally used to model the energy storage, which inevitably requires the introduction of “complementary constraints†in the optimization model, that is, any time. The charging power of any energy storage & TImes; discharge power = 0 (as shown in Figure 1). Obviously, the introduction of such a nonlinear constraint makes the optimization problem non-convex strong and difficult to solve. Although the optimization problem with complementary constraints can be transformed into a general problem solution by introducing a penalty function, a smooth function or a discrete variable, it is necessary to solve the sub-problems of the same scale multiple times, so the calculation time of such methods is usually long. Efficiency needs to be improved.
3 How to deal with this challenge? - strict relaxation method
It is not difficult to find that the key to the whole problem lies in this complementary constraint. If it does not exist, it can be transformed into a conventional convex programming problem. There is a mature method to solve it, and the efficiency is also very high. So, can we deliberately "ignore" this complementary constraint in the solution process? That is, this constraint is directly relaxed in the scheduling model. The question that this article wants to answer is: Is this slack “strict†when certain conditions are met? That is, the optimal solution obtained by using the simplified model after relaxation will "naturally" satisfy the complementary constraint of "charge power & TImes; discharge power = 0". If such a condition can be found, and such a condition can be established under normal circumstances, it means that in many cases we can significantly simplify a complex optimization problem with energy storage, which greatly improves the efficiency of the solution.
4 What conditions can make relaxation “strict�
It can be known from the mathematical counter-evidence that this slack is "strict" as long as the following two conditions are met at the same time.
Condition 1: For any energy storage, the discharge price is greater than (or not less than) the charge price at any scheduled time.
Condition 2: For any energy storage, the charging price is not greater than (or less than) the node price at any scheduling time.
The physical meaning of these two conditions is clear. From the perspective of economics, an intuitive explanation of “strict†relaxation can be given: if both conditions 1 and 2 can be satisfied, then from the perspective of grid economic operation, simultaneous storage and discharge of energy storage is a suboptimal solution, while the optimal solution is It is the relaxation problem that can satisfy the complementary constraints "naturally".
5 How can I determine if these specific conditions can be established?
First, look at Condition 1. Since the charge/discharge price (or predicted value) is an input parameter of the model, it is easy to check, and it is proved that Condition 1 is established. For condition 2, it is necessary to predict the node price in the scheduling period by historical data, and then determine whether condition 2 can be satisfied. Since condition 2 only needs to compare the charging price and the node price, if it is found that the charging price is lower than the lower bound of the section where the node price is predicted, then it can be determined that condition 2 is established.
6 Can these specific conditions be generally established in general?
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