A Method for Estimating the System’s Maximum Effective Reserve under the Electricity Market

System’s reserve is one of the important security constrains when conducting the day-ahead clearing calculation. Usually, the reserve requirement is determined by the local dispatching center based on their experience. However, this experience-based threshold may lead to two issues, i.e., the invalid reserve and the slow calculation speed under the electricity market condition. Based on the concept of effective reserve, a method for estimating the system’s maximum effective reserve is proposed in this paper. The main idea is to design an optimization algorithm to determine the operating unit set with the goal of maximizing the system’s effective reserve. The maximum value obtained can help the dispatching center to design the system’s reserve threshold, which is of great engineering significance. Simulation analysis verified the correctness and rationality of the proposed model through comparative analysis of multiple scenarios.


Introduction
When conducting the clearing calculation for the day-ahead electricity market, it is important for the power grid dispatching centre to ensure that the calculation result obtained satisfies the operation safety constrains.This means that making sure that the power grid can operate safely is the first task [1].To achieve this goal, a few safety constrains are added into the optimization calculation problem, the balancing constrain between the unit output and the load in the system.Besides this balancing equation, a certain amount of reserve capacity should also be taken into account to respond to the system's real-time changes [2].Usually, the requirement for the reserve capacity is decided by the local dispatching centre based on their operating experience.Although this experience-based guidance is meaningful, it is likely that the goal made is quite different from the real reserve capacity that the system can provide.On the one hand, under the electricity market situations, the power resources are distributed according to the minimum cost of the power generation, the operating condition of the system may lead to an increasing trend of the network congestion [3,4].This would result in an emergency that part of the pre-reserved unit capacity cannot be utilized, which means that this part of capacity is invalid.In such a situation, even if a high threshold is planned for the reserve capacity, it is still possible that the valid part is unable to meet the real-time requirement [5].On the other hand, considering the constrain for the system reserve request when conducting the clearing calculation, the value of the capacity threshold designed will directly influence the solving speed of the optimization calculation.Extremely, if the threshold is set unreasonably, for example, it is set too high, this will lead to no feasible solution to the problem and the failure of the clearing calculation.Based on the above considerations, if the range of effective reserve capacity that the system can provide can be obtained before the day-ahead clearing calculation, it is of great significance for the dispatching centre to design the system reserve on the basis of this reference.Also, it is beneficial to mitigate the two problems mentioned before, the invalid reserve and the calculation speed.
Due to the rapid increase of the renewable resources, a large amount of research is conducted considering the influence of the uncertainty of the power generation on the reserve capacity calculation [6][7][8][9].On the other hand, there is a little research on the consideration of the effective reserve and the setting of the reserve threshold from the engineering perspective [10].A real-time estimation method for reserve deduction is proposed in [10].Based on the determined network operating status, a deduction algorithm is designed to calculate the corresponding system's reserve capacity.Although the method can be used to calculate the real-time reserve, it is not appliable under the electricity market mechanism.A novel reserve allocation method is proposed by Z. Ren et al. [11].The concept of unit availability, which is a probability value, is considered in the reserve allocation mission to enhance the description of the unit reserve, but how to determine this value reasonably can be a problem.The concept of effective reserve is used in [12] to help to mitigate the congestion impact brought by the electricity market on the operation safety.Corresponding constrains are added into the day-ahead clearing calculation to determine the operating unit set.
To solve this problem, this paper proposes a method for estimating the system's maximum effective reserve under the electricity market.If we want to get the relatively accurate value for the system's valid reserve at a certain moment, the system operating conditions should be provided, including the network topology, the set of the operating units and the load capacity.However, under the electricity market, the operating unit set is determined by the day-ahead clearing calculation, this set cannot be obtained in advance.In addition, the system's reserve requirement is included in the clearing calculation, meaning that the threshold set for this requirement is also one of the influencing factors for the operating unit set.Therefore, to some extent, it is impossible to get the accurate effective reserve at a certain moment.However, if the status of the unit is determined with the goal of maximizing the system's effective reserve capacity, the maximum value obtained can be one of the references for the design of the system's reserve when doing the clearing calculation.Based on the calculation method for the effective reserve proposed in [12], an optimization methodology for the calculation of the maximum reserve capacity is proposed in this paper.
The rest of the paper is organized as follows.The security constrained unit commitment (SCUC) [13] model is briefly introduced in Section 2. The optimization model for calculating the system's maximum effective reserve capacity is explained in Section 3. Section 4 exhibits some studied cases to verify the effectiveness of the proposed method and the conclusions are drawn in Section 5.

Common SCUC model
The common SCUC model used for the day-ahead clearing calculation is described in the following.The object function is to minimize the system operation cost: Formula ( 1) is the objective function, where , , ( ) C denote the unit output cost and the startup cost of a single unit respectively; s SL and s SL represent the slack variables of the branches and the cross-sections, and SE is the set of these branches and cross-sections; M is the penalty factor, which is usually a large positive integer; G and T are the total unit number and the total number of the time period considered respectively.The safety constrains considered are listed as follows: , , , , , , , , .
Equation ( 2) is the balance equation between the total unit output and the load in a certain period, where , l t D is the load demand in that period and Tj,t is the power transferred from the tie-line.K and NT are the sets for them respectively.The system's reserve capacity constrains are shown in (3) and (4), where max , i t P and min , i t P denote the maximum and minimum output of a unit respectively.Also, , i t D is the 0-1 variable for a single unit, where 0 and 1 stands for shutting down and turning on respectively.Here, U t R and D i R are the positive and negative thresholds set for the system's reserve requirement.Equations ( 6) and ( 7) represent the ramp constrains for a single unit, where are the ramp speeds.The unit segment output constrains are presented in (8), and the startup cost can be calculated as shown in (9), where U i C is the cost required for one startup and , i t K is a binary variable denoting the operating status of the unit.The safety constrains for the branches or the cross-section are shown in (10).s i G is the power transfer distribution factor from node i to transmission lines, and SE is the collection of these lines.max s P and min s P are the upper and lower limits of that line respectively.Note that the unit reserve capacity considered in the common SCUC model is the difference between the maximum output and the current output, max , , i t i t P P .In such a condition, it is believed that all the reserved power can be utilized to fulfil the real-time power gap.

SCUC model considering the system's effective reserve
Two calculation methods for the system's effective reserve are proposed in [12], which are briefly summarized below.
The main idea for the effective reserve calculation is to introduce the corresponding variables , i t PR for a single unit.The following constrains (11) and ( 12) are used to replace (3) to (7) where UD is the lasting duration of the startup process, calculated to the unit minimum output; DD is the lasting duration of the shutdown process, calculated from the unit minimum output.E and J are the binary variables denoting the operating status of the units.Pi,U and Pi,D represent the points on the power output curve of the startup and shutdown, respectively.The effective reserve variable , i t PR should be equal to zero if its corresponding s i G and the power of the branches are out of limit as shown below: 0 and Threshold 0 0 and < -Threshold 0 Formula ( 13) represents this part of the unit reserve is considered invalid.Instead of adding too many extra binary variables, increasing the pressure of problem solving, an approximate modelling method is considered.When the system reserve is sufficient, equation ( 12) can be replaced by the following constrains (14-15): denotes the current power flow of the cross-section.If the correlation between reserve variables is considered, equation ( 12) can be replaced by ( 16): , the positive and negative influence of the effective reserve variables on the power flow of the crosssection can offset each other.Details of the above two modelling methods can be seen in [12].

Method for Estimating the System's Maximum Effective Reserve
It can be seen in Section II that whether the concept of the effective system's reserve is adopted or not, the threshold of the reserve capacity U t R should be determined in advance.Usually, it is experiencebased value decided by the dispatching center.Here, a novel idea is proposed to estimate the system's maximum effective reserve capacity, which can be used as the reference for U t R .As mentioned before, it is less likely to obtain the accurate value of the effective reserve at a certain moment due to the lack of the operating unit set under the electricity market mechanism.In other words, the effective reserve capacity and the system operating status are corresponding to each other.Therefore, among these possible operating conditions, there exists a situation when the system's effective reserve is maximum.This maximum value is the one that is desired to help to determine the reserve threshold.The above idea can be realized by the optimization methodology below.Based on the effective reserve variables, the objective function can be designed as follows (17): The system's effective reserve at a certain moment is desired to be maximum.The constrains considered here can also be divided into two situations based on whether the coupling relationship between the effective reserve variables is considered or not.
If the coupling is disregarded, constrains (2), ( 5), ( 14) and ( 15) should be added into the optimization problem.On the contrary, constrains (2), ( 5), ( 10) and ( 16) should be taken into account if the coupling is considered.In essence, in this optimization calculation, the operating status of the units are decided by its effective contributing to the whole system.Figure 1 shows the flamework of the proposed methodology and its relationship with the day-head clearing calculation.2. After calculating the effective reserves, the existing reserve demand value is corrected to the original model, the reserve demand is corrected, and the calculation efficiency is compared 3.After correcting the values of positive and standby for different models, compare the situation of cross section exceeding the limit, unit startup and shutdown, and cross section exceeding the limit.

Comparison of maximum effective reserve and other results among different models
This section compares the maximum effective reserve of different models under different sensitivity thresholds, and the results are as follows: Figures 2 and 3 respectively illustrate the maximum effective forward reserve of the system under different sensitivity thresholds.It can be seen that when the sensitivity threshold is 0.2, there is a significant improvement in the system's effective forward and reserve.However, it is still unable to meet the system's maximum active reserve.
Among them, the effective reserve value of reserve calculation mode 2 is slightly higher than that of reserve calculation mode 1, which is also in line with our initial expectations The table 1 lists the comparison results of different models when the sensitivity threshold is 0.2.It can be seen that Mode 2 has fewer cross section violations and fewer unit starts and stops.

Comparison of calculation efficiency before and after modifying reserve requirements
In order to compare the computational efficiency of different models, we will use half of the calculated maximum effective reserve value as a new reserve requirement for calculation.We selected five typical scenarios, randomly generating 5 cases for each scenario, and calculated the average clearance time of cases under different models.The specific results are as follows: From the table 2, it can be seen that the cases with improved reserve requirements have shown some improvement in computational efficiency.

Comparison of rationality of results before and after modifying reserve requirements
In order to compare the clearance status of the model, the average node electricity price of the modified system was compared, and the specific results are as follows: From the figure 4, it can be seen that the average price of the system has decreased, with Model 2 showing a more significant decrease.This is because Model 2 has a larger feasible region and can find better unit combinations, resulting in a decrease in the average node electricity price of the entire network.

Conclusions
In order to help the dispatching center to set the threshold for the system's reserve capacity reasonably and effectively, an optimization methodology is proposed to obtain the system's maximum effective reserve.The maximum value obtained corresponding to a certain operating unit set without considering their operating cost.In other words, this value is only determined by the physical feature of the power grid.Note that the proposed method is conducted before the day-ahead clearing calculation, and the result plays an assisting role.

Fig. 1
Fig. 1 Flamework of the proposed methodology and its relationship with the day-ahead clearing calculation

Fig. 2 Fig. 3
Fig. 2 Comparative Analysis of Maximum Effective Reserve of Different Models in Scenario 1

Fig. 4
Fig. 4 Comparison of electricity price results for different models ,

Table 1 .
Comparison of clearance status of different models