Evaluation of Wind Energy Accommodation Based on Two-Stage Robust Optimization

Large-scale renewable energy integration brings unprecedented challenges to electric power system planning and operation. The paper aims at economic dispatch and the safe operation of high penetration renewable energy power systems. According to the principle of power system dispatchability, the assessment of wind energy accommodation is formulated into a two-stage robust optimization problem with a min-max-min structure. Based on the benders algorithm, the intractable robust optimization problem is transformed into the form of sub-problem and master problem. Strong duality theory and big-M method are used to recast the sub problem into a mixed integer linear programming. The envelope of wind energy accommodation can be obtained by using commercial software to solve the master problem and sub problem alternately. For the realization of arbitrary wind power within the envelope, the amount of wind energy leakage and load shedding in power system operation are acceptable. An example of modified IEEE 39-bus test systems is used to verify the effectiveness and practicability of the evaluation method.

(a) (b) Fig. 3. Hourly power production for all generators. All TG are involved in the daily dispatch. TG located on nodes 30, 33, 34, and 35 are always in the turned-on state, and the other units have start-up and shut-down actions. Due to the limitation of the ramping capacity of TG, the excessive prediction deviation of wind power will lead to wind energy curtailment and load shedding. Applying the framework to assess the largest wind power interval that the power system can accommodate, the results are given in Section V-B.

B. Assessment of Wind Energy Accommodation
In this section, the output deviation range of all WT nodes is calculated through the solution strategy in Section IV, which is the envelope band of wind power accommodation. To verify the influence of wind energy leakage and load shedding on wind power envelope that electric power system can be accommodated, we designed the following four cases: The hourly allowable wind power deviation in different cases is given in Fig. 5.
The data in Fig. 5 shows that there are some time periods with allowable wind power deviation of 0 in all four cases. The results mean that the ability of power system to deal with wind power fluctuations is different in temporal. Wind power continuously ramping-up or ramping-down will cause wind power leakage and load shedding, which will greatly consume the dispatchability resources of power system. Besides, the mathematical statistics indexes are used to evaluate the allowable deviation of wind power in each period of four cases, and the results are given in Table II.  Note that the maximum adjusted output of all TG within the response time is 246 MW. Therefore, there is wind spillage and load curtailment in Case 2, Case 3, and Case 4. As the load demand is far greater than the installed capacity of WT, the allowable wind power deviation of Case 2 is greater than Case 3. Both wind power leakage and load shedding are allowed in Case 4, which makes the maximum allowable wind power deviation. The envelope band is given in Fig. 6. The envelope band in Fig. 6 has such properties: for the realization of arbitrary wind power within the envelope, the amount of wind leakage or load shedding in the re-dispatch stage is acceptable through correcting the pre-dispatch scheme. Once the prediction deviation of wind power exceeds the range of wind accommodation envelope, wind leakage or load shedding will run out of predetermined constraints. The envelope band is similar to a metric and can provide early warning information. Furthermore, the hourly wind leakage or load shedding in Case 4 are given in Fig 7(a) and Fig. 7(b). The total amount of wind spillage and load curtailments are 1316 MWh and 6223 MWh, respectively. Wind spillage occurs in 2 nd , 5 th , 13 th , 15 th , and 23 th periods, while the amount of load curtailment is zero. Note that the amount of load curtailment is both zero in 4 th , 9 th , 11 th , 17 th , and 21 th periods. Reasonable wind power leakage and load shedding can significantly improve the ability of the system to withstand net load fluctuations.

VI. CONCLUSIONS
Based on the pre-dispatch and re-dispatch theory, the dispatchability of the power system is introduced, and the evaluation framework of wind energy accommodation is proposed. The results of numerical studies show that: 1. It is feasible to counterweight the deviation of wind power by correcting the pre-dispatch scheme. The effect of this method is related to the dispatchability resource of the electric power system. 2. Allowing certain wind spillage and load curtailment can greatly improve the ability of the grid to cope with wind power deviation. The results show that the reasonable wind spillage or load curtailment is beneficial to power system scheduling operation. 3. The envelope band of wind power accommodation represents the maximum range of wind power deviation for the power system, which can provide warning information (wind curtailment or load shedding) for decision-makers. The envelope of wind power accommodation is affected by the electric power system pre-dispatching scheme. Therefore, the problem of co-optimization of the pre-dispatch scheme and envelope band of wind energy accommodation is worthy of attention in the future work. Besides, the deployment of energy storage to improve the envelope band of wind power accommodation is concerned.

CONFLICTS OF INTEREST
The authors declare that they have no conflicts of interest.