Abstract
To secure power system operations, practical dispatches in industries place a steady power transfer limit on critical inter-corridors, rather than high-dimensional and strong nonlinear stability constraints. However, computational complexities lead to over-conservative pre-settings of transfer limit, which further induce undesirable and non-technical congestion of power transfer. To conquer this barrier, a scenario-classification hybrid-based banding method is proposed. A cluster technique is adopted to separate similarities from historical and generated operating condition dataset. With a practical rule, transfer limits are approximated for each operating cluster. Then, toward an interpretable online transfer limit decision, cost-sensitive learning is applied to identify cluster affiliation to assign a transfer limit for a given operation. In this stage, critical variables that affect the transfer limit are also picked out via mean impact value. This enables us to construct low-complexity and dispatcher-friendly rules for fast determination of transfer limit. The numerical case studies on the IEEE 39-bus system and a real-world regional power system in China illustrate the effectiveness and conservativeness of the proposed method.
RENEWABLE energy penetrated power systems are principal energy carriers under low-carbon concerns. However, the volatility and uncertainty of renewable energy make power system operating conditions more complex and bring tremendous challenges to efficient operation in critical inter-corridors [
Thus far, the analysis of critical interconnected power transfer capacity has become a popular research topic. Various algorithms have been presented, and typical physics-based methods can be classified into four broad categories: repeated power flow (RPF) [
Ahead of online dispatch, dispatchers typically consider the most conservative among a gathered scenario set of transfer capacities as a fixed transfer limit. However, end-to-end computations from operating conditions/scenarios to transfer capabilities are computationally intensive even though the entire process is executed offline.
Reference [
Inspired by the analysis, this paper develops a scenario-classification hybrid-based banding method for power transfer limits. Notably, this paper does not deal with end-to-end computations from operating conditions to transfer capabilities; instead, a pragmatic way to determine the transfer limit is studied. Our method clusters numerous historical and generated operating data points to finely partition power systems into multiple typical scenarios or subspaces, each of which has a conservativeness-dominated transfer limit. Then, a cost-sensitive classifier is used to bridge the transfer limit and operating conditions and enable real-time and direct online optimization of the transfer limit. The main advantages of the proposed method are as follows.
1) It fixes the poor convergence and computationally cumbersome nature of traditional impractical methods, but still provides a global search method. Compared with the expertise-based method used in power industries, it enables more precise decisions.
2) By customizing the cluster number, the proposed method enables a degree of freedom that compromises the conservativeness and economy of inter-corridor operations. In addition, to assign transfer limits to each cluster, we bridge the transfer limits and operating conditions such that the transfer limits become controllable and can be optimized to release the power transfer potential of the inter-corridors.
3) By incorporating a classification method with clustering, real-time and direct decisions regarding the transfer limit can be made. This can provide efficient control information for flexibly regulating the transfer limit. Interestingly, no sample imbalance issues exist, because the decision model is built on balanced clustering labels.
For better readability, the key ideas of the traditional and proposed methods for deciding and operating power transfers are compared, as shown in

Fig. 1 Intuitive illustrations of contributions of proposed method. (a) Comparisons among ideal method, current method, and proposed method. (b) Key ideas of traditional and proposed methods.
Transfer capabilities of inter-corridors are constrained by transient stability, security, voltage security, etc. These constraints place a heavy computational burden on the determination of the transfer capability.
However, transfer capabilities are time-varying and operation-dependent indices, and they must be updated along with operations such that a precise security situation and a latent increase in power transfers can be realized.
The current research implies a key compromise between precise awareness and fast calculation of transfer capabilities. To solve this issue, dispatchers prefer to conduct fixed transfer limits that come from a conservative operation-mode analysis a year ahead.

Fig. 2 Sketch map of traditional transfer-limit decision method.
Remark: although the concept of transfer limit appears to be similar to that of transfer capability, there is still a difference. Transfer capability is a dependent variable on operating conditions; thus, it is not pragmatic in a realistic online dispatch because of its time-consuming computation. Instead, dispatchers compute transfer capabilities offline over several empirical extreme scenarios and deploy the most conservative scenario to set a fixed transfer limit on a critical inter-corridor. This process is offline, and in an online dispatch, the security constraints on the inter-corridors are reduced to steady transmission power constraints whose bounds are the determined transfer limits. Therefore, to prevent confusion, we distinguish between the transfer capability and transfer limit, i.e., the transfer capability refers to the true varying power transfer constraint of an inter-corridor, whereas the transfer limit is a constant limit that is set in advance. The latter is a major concern.
As shown in
(1a) |
(1b) |
(1c) |
(1d) |
(1e) |
(1f) |
where overline and underline denote power transfer with positive and negative directions, respectively. The security verification, i.e., , should embody static, dynamic, and securities. Although our method is compatible with all security validation, only static security, security, and transient angular stability are considered for the sake of simplicity. This enables us to focus on the innovative design of the proposed model. The security verification models are as follows.
(2a) |
(2b) |
(2c) |
where , , and represent the power flow equations, differential algebraic equations (DAEs) during and after fault occurrence, respectively. The security criterion is a practical engineering index. It constrains the angle difference between any two generators to be below a predefined threshold, which is typically set to be 180° or 360°. Here we use the 180° criterion. Because massive temporal intermediate variables are introduced, (1) is highly complex. This supports the argument that transfer-limit computation is time-consuming.
After solving (1), we can use (3) to constrain the online dispatches.
(3) |
However, applying the transfer limits determined by conventional method (1) may result in the discarding of some security conditions with high-power transfers. Many security conditions are screened out of the security domain because a nonlinear correlation between power transfers and security conditions jumbles security and insecurity operations near the security boundary. Only sufficiently conservative transfer limits can be determined, which triggers a significant waste of secure operations.
In conclusion, traditional engineering methods undoubtedly lead to overconservative transfer limits such that unnecessary obstruction of power transfer is induced. However, it still offers the advantages of fast online decisions and security guarantees. This paper intends to exploit both traditional engineering methods and existing data-driven methods to meet the demands of practicality and higher availability of inter-corridors.
Over-conservative transfer limits are derived from the elimination of operating domains where security and insecurity conditions coexist. To address this issue, we intend to utilize the unavailable security conditions. Specifically, the proposed solution is to divide the operating scenario set into several clusters, followed by the same determination methodology as in (1) to set the transfer limits for each cluster. To produce these clusters, we introduce unsupervised learning (UL). The UL can assemble quantities of similar operating conditions into one cluster and divide the original strong nonlinearity into pieces of linearity or poor nonlinearity, such that there can be a straightforward relationship between power transfers and security in the operating space created by a cluster. In other words, in one cluster, we can approximate a security boundary in the power transfer coordinates. This allows us to determine the transfer limits for each cluster. The specific formulation is given in (4).
(4a) |
(4b) |
(4c) |
(4d) |
(4e) |
(4f) |
The remaining symbols are the same as those in (1).
We can then provide the inter-corridor transfer constraints in an online dispatch, as shown in (5).
(5) |
Constraint (5) intuitively shows that the proposed method transforms the old single limit in (3) into a finer transfer limit rule with bands. Comparing the proposed model (4) with model (1), this idea permits a wider exploitation of security operations near the security boundary to maximize the use of inter-corridors.
Operational data should be prepared prior to transfer-limit banding. This can be achieved by using good point-set sampling (GPS) over a parametric space and by collecting historical data. Specifically, we utilize existing operating limits to establish such a space, and the GPS is deployed in this space. Therefore, the input features are defined as: {active/reactive outputs of generators including synchronous generators and wind generators, active/reactive loads, terminal voltages, overall active loads}. Note that the on/off conditions of the generators are implicit in the power outputs (i.e., 0 denotes an off condition), and all inputs can be directly obtained. To simplify, the inputs are denoted by and outputs by . In addition, the overall transfer-limit decision task for all inter-corridors is separated into subtasks whose output is , and in the subsequent description, represents . Here, a subtask refers to the determination of the transfer limit for a specified inter-corridor. We deploy our method on each inter-corridor. Therewith, .
Following the above idea, the UL was first introduced to produce several operating scenario clusters. The database for learning originates from historical operations and generates unseen unstable or extreme operating conditions (i.e., set ), which are composed of critical operating variables formed as:
(6a) |
(6b) |
(6c) |
The collected data were subjected to unsupervised learning. This paper uses the K-means++ algorithm to produce clusters to band-transfer limits, as K-means++ improves clustering accuracy and convergence compared with practical K-means. K-means++ executes the following process.
1) k centers are arbitrarily initialized, where the second subscript denotes the number of iterations.
2) Starting from the
3) For each cluster , the center is set as , where is the number of points in the cluster.
4) Iterations are counted, and 2) and 3) are repeated until remains unchanged.
The proposed framework aims to identify the cluster to which an unseen operation belongs. Therefore, the clustering result is a target for real-time classifiers. For a given operating scenario, the cluster assignment is set as the classification label. We can obtain:
(7) |
Remark: in future, we will combine classification methods to enable real-time cluster attribution identification. Once the cluster to which an online operating condition belongs is determined, the transfer limit for the condition can be obtained by matching the associated transfer limit value of the cluster.
It is computationally inapplicable to involve all the parameters or variables in transfer-limit banding. Therefore, the critical variables must be identified. The mean impact value (MIV) method is used to determine barriers. The MIV first uses data to train neural networks (NNs). The responses of the NNs resulting from the perturbations of each input are then used as indices to determine the significance of the inputs. Therefore, a strong and robust NN structure is required. Thus, a multi-layer NN is used in this paper. As multi-label classifiers generally use Softmax layers to provide the probability of each label, which is a regression task, MIV method is available.
The mathematical model is given as:
(8) |
(9) |
(10) |
where and are the affine function and activation function of the neural network, respectively; is the output of the
(11) |
(12) |
where the subscript indicates the two adjoining layers, and the superscript denotes the locations of specified neurons in the two layers. and are the calculation functions of covariance and variance, respectively.
In the deployment feedforward process of (13), the influence of the
(13) |
By integrating (10) and (13), the importance of the
(14) |
where denotes the elementwise multiplication.
By considering variables whose MIVs are above a given threshold, the critical variables that impact the transfer-limit banding are filtered. A compressed feature group can accurately and efficiently represent the operating patterns. Moreover, it is much easier to know the control variables to be regulated and the extent to which they must be. For simplification, we continue to use to denote the compressed input features.
After identifying the critical decision variables, unseen operations are categorized into clusters, with only the principal features informed. Thus, the inputs for online transfer-limit decisions are prescribed as variables screened by the MIV, and the output is the cluster numbers. Each cluster corresponds to a single transfer-limit banding level. To ensure the conservativeness of the banding, we determine the banding level according to (15).
(15a) |
(15b) |
Here is introduced to simplify the later model illustration, and it is the same as the above transfer limit symbol in (1), (3), (4), and (5). is the trained classifier and calculates probabilities that operation may locate in a cluster. Using the argmax operator, (15a) finally determines to which cluster pertains. Here, m is a cluster. Subsequently, (15b) assigns the corresponding transfer limit to . For a better understanding, the traditional method and proposed method of calculating the online transfer limit are visualized in

Fig. 3 Comparative diagram of traditional method and proposed method.
Equations (
Several methods have been developed to achieve this goal. Because data are prepared offline, which means that efficiency is not demanding, precision is valued more than speed at this stage. Therefore, we conduct a time-domain simulation (TDS) to infer the transient stability. TDS applies numerical computation to capture the trajectories of DAEs instead of finding an analytical solution [
In practice, a critical demand is that the decision must be sufficiently conservative to ensure secure operation. This is also the pivot point that a classifier for transfer-limit banding should follow. Therefore, we introduce a cost-sensitive learning technique. The cost-sensitive learning in [
(16a) |
(16b) |
(16c) |
where the columns and rows correspond to the predicted and true labels, respectively. Equations (
To highlight the essence of this paper, details of the cost-sensitive learning process are ignored.
It is expected that the over-conservativeness issue is fixed to some extent because a finer transfer-limit banding rule activates more security operating modes that are discarded in the previous single-transfer limit. The next step is to flexibly tune the operation such that the transfer potential of the critical inter-corridors can be used. Classification-based decisions provide a straightforward and fast way to determine how the transfer limit varies with operations as well as control information, but no nonlinear operation is required. This is useful for dispatching tasks. In this paper, we instantiate an optimization-based showcase to justify the entire workflow.
An economic dispatch model is then devised, where the intention is to optimize power system operations under strict power transfer security constraints. This model is given by (17).
(17a) |
(17b) |
(17c) |
In (17b), is also a variable which is decided by operations. Back to Sections III-A and III-B, we know that once the cluster to which current operation belongs is found, can be identified via (4) and (15).
Because this paper demonstrates the effectiveness of enhancing the utilization of power inter-corridors via the proposed data-driven banding method for power transfer limit, we do not focus on a detailed optimization algorithm design. Here, a distributed genetic algorithm (DGA) is proposed to solve model (17). Using simplified model (17) as (18), the DGA-solving model can be denoted as (19).
(18) |
(19a) |
(19b) |
where , , and are the compact forms of the objective, equality, and inequality constraints in (18); is the transformed optimization objective with penalties. is a function of accumulating inequality constraint violations, i.e., for the constraints , the portion that exceeds 0 is included in penalty function .
The implementation process of the proposed method is illustrated in

Fig. 4 Implementation process of proposed method.
The proposed method is tested using a modified IEEE 39-bus system [
To visualize the banding process for power transfer limit, we provided five different scenarios, including deciding the transfer limit via the most conservative criterion and banding limit by 3, 5, 10, and 20 levels, respectively. The results are shown in

Fig. 5 Outcomes of proposed cluster-based banding method. (a) 3-cluster banding. (b) Transfer-limit decision with 3 bands. (c) 5-cluster banding. (d) Transfer-limit decision with 5 bands. (e) 10-cluster banding. (f) Transfer-limit decision with 10 bands.
As shown in
Clustering condition | Transfer-limit banding (from low to high) (p.u.) |
---|---|
Conservative | 12.62 |
3-cluster | 12.62, 12.94, 13.60 |
5-cluster | 12.62, 12.94, ..., 14.35 |
10-cluster | 12.62, 12.94, ..., 15.22 |
20-cluster | 12.62, 12.94, ..., 16.30 |

Fig. 6 Stacked bar chart of transfer-limit banding level under different clustering conditions.
As listed in
In the online dispatch stage, straightforward rules are preferred to tune the power transfers for more efficient and economical operations. In this subsection, we do not care about the structure of such rules, but intend to provide cautious decision-making to ensure that power transfer operates securely. Cost-sensitive neural networks (CSNNs) are adopted. To illustrate the conservativeness via the CSNN, we provide the confusion matrix outcomes tested on the testing dataset, as shown in Tables II-V. Additionally, comparative studies are conducted using non-cost-sensitive NNs, as given in Tables
Transfer-limit banding level | Prediction, 1/12.62 p.u. | Prediction, 2/13.60 p.u. | Prediction, 3/12.94 p.u. |
---|---|---|---|
True label, 1/12.62 p.u. | 2885 | 0 | 24 |
True label, 2/13.60 p.u. | 0 | 2783 | 15 |
True label, 3/12.94 p.u. | 17 | 18 | 4608 |
Transfer-limit banding level | Prediction, 1/12.95 p.u. | Prediction, 2/13.58 p.u. | Prediction, 3/12.94 p.u. | Prediction, 4/12.62 p.u. | Prediction, 5/14.35 p.u. |
---|---|---|---|---|---|
True label, 1/12.95 p.u. | 2973 | 11 | 13 | 0 | 0 |
True label, 2/13.58 p.u. | 10 | 2431 | 0 | 0 | 4 |
True label, 3/12.94 p.u. | 10 | 0 | 2482 | 14 | 0 |
True label, 4/12.62 p.u. | 0 | 0 | 18 | 1235 | 0 |
True label, 5/14.35 p.u. | 0 | 8 | 0 | 0 | 1141 |
Recall the conservativeness demand mentioned in Section III-C, i.e., which strictly prohibits the classifier from overestimating the true transfer limit. We begin the analysis by comparing the data in Tables
Transfer-limit banding level | Prediction, 1/12.62 p.u. | Prediction, 2/13.60 p.u. | Prediction, 3/12.94 p.u. |
---|---|---|---|
True label, 1/12.62 p.u. | 2909 | 0 | 0 |
True label, 2/13.60 p.u. | 0 | 2706 | 92 |
True label, 3/12.94 p.u. | 90 | 0 | 4553 |
Transfer-limit banding level | Prediction, 1/12.95 p.u. | Prediction, 2/13.58 p.u. | Prediction, 3/12.94 p.u. | Prediction, 4/12.62 p.u. | Prediction, 5/14.35 p.u. |
---|---|---|---|---|---|
True label, 1/12.95 p.u. | 2940 | 1 | 56 | 0 | 0 |
True label, 2/13.58 p.u. | 33 | 2411 | 0 | 0 | 1 |
True label, 3/12.94 p.u. | 0 | 0 | 2456 | 50 | 0 |
True label, 4/12.62 p.u. | 0 | 0 | 1 | 1252 | 0 |
True label, 5/14.35 p.u. | 0 | 39 | 0 | 0 | 1110 |
Moreover, misclassifications are transferred to the conservative cases. This result is due to the fact that cost-sensitive classifiers are more likely to identify a true transfer limit to a lower value. For instance, as for the 5-band classifiers, a conservative identification of transfer limit is to decide true transfer limit of 13.58 p.u. (label 2) to 12.95 p.u. (label 1). The corresponding data in the confusion matrices are shown in Tables
Combined with the conclusions presented in Section IV-B, a worthy concern emerges: how does the performance of the classifier vary with finer transfer-limit banding and more banding levels? Thus, the online transfer-limit decision precision trends along with the number of bands are given in

Fig. 7 Online transfer-limit decision precision trends along with number of bands.
As shown in
In addition, the transfer-limit decision elapsed time of the well-built classifiers is less than 1 s on average. This supports the online application of the transfer-limit banding rule.
To justify the proposed transfer-limit banding rules for online dispatch, the outcomes of a showcase are presented. We report 5 transfer-limit banding conditions to highlight superiority of our method, i.e., rule 1 (the most conservative rule), rule 2 (transfer-limit rule with 3 bands), rule 3 (transfer-limit rule with 5 bands), rule 4 (transfer-limit rule with 10 bands), and rule 5 (transfer-limit rule with 20 bands). A 24-hour economic dispatch instance with a timescale of 1 hour is designed and tested.

Fig. 8 Operating conditions of inter-corridors before and after economic dispatch. (a) Power using rule 1 before economic dispatch. (b) Power using rule 1 after economic dispatch. (c) Power using rule 2 before economic dispatch. (d) Power using rule 2 after economic dispatch. (e) Power using rule 3 before economic dispatch. (f) Power using rule 3 after economic dispatch. (g) Power using rule 4 before economic dispatch. (h) Power using rule 4 after economic dispatch. (i) Power using rule 5 before economic dispatch. (j) Power using rule 5 after economic dispatch.
It can be observed from the data in
To demonstrate the positive influence of the finer transfer limit rule on wind power consumption, the wind curtailment profiles incurred by the testing rules are presented in

Fig. 9 Wind curtailment profiles incurred by testing rules. (a) Rule 1. (b) Rule 2. (c) Rule 3. (d) Rule 4. (e) Rule 5.
The results, as shown in
The proposed method is verified using a real-world power system in China. The applied regional power system is located in Northwest China and comprises five provincial grids (Gansu, Shaanxi, Qinghai, Ningxia, and Xinjiang). The northwestern power system of China has over 7500 dispatchable generators including thermal units, hydropower units, wind power generators, and photovoltaic plants. There are more than 4000 transmission lines in the transmission-level system, of which four critical power transfer inter-corridors that affect system security are selected for the numerical study. The abbreviations used are GN, GX, GQ, and GS. and short-circuit faults on the critical inter-corridors as well as a few severe faults set from the dispatcher experience, are considered in the contingency.
We test the proposed method under two operating conditions, i.e., OC1 and OC2:
1) OC1: with a total load of MW and total renewable power generation of MW.
2) OC2: with a total load of MW and a total renewable power generation of MW.
The outcomes of tuning transfer limits by the proposed method under OC1 and OC2 are listed in Tables
Inter-corridor | Power flow before tuning | Transfer limit before tuning | Power flow after tuning | Transfer limit after tuning | Transfer limit increase on average (%) |
---|---|---|---|---|---|
GN | 67.45 | 56.98 | 64.02 | 65.27 | 10.42 |
GX | -29.86 | -20.48 | -20.21 | -21.50 | |
GQ | -13.07 | -2.21 | -6.37 | -6.44 | |
GS | 49.94 | 34.94 | 31.79 | 33.65 |
Inter-corridor | Power flow before tuning | Transfer limit before tuning | Power flow after tuning | Transfer limit after tuning | Transfer limit increase on average (%) |
---|---|---|---|---|---|
GN | 30.03 | 21.40 | 22.98 | 24.97 | 20.40 |
GX | -29.84 | -14.88 | -14.62 | -15.35 | |
GQ | -18.09 | -7.63 | -8.04 | -19.38 | |
GS | 49.98 | 34.97 | 34.52 | 35.26 |
As observed from Tables
To further compare the proposed method with the traditional dispatch-experience-based method, we provide the testing outcomes of the GX, as shown in

Fig. 10 Comparative outcomes of GX by proposed method and traditional method. (a) Before tuning. (b) After tuning.
In
In this paper, a new pragmatic data-driven method that enables fine and conservative transfer-limit control is proposed. The key is to use unsupervised cluster learning to identify typical operating patterns and determine the band-conservativeness-dominated transfer limit for each cluster. Subsequently, a cost-sensitive classifier is used to produce a fast and reliable rule for flexibly controlling the transfer limit. Finally, an optimization-based showcase is provided to justify the proposed method. The numerical results on the modified IEEE benchmark and a real-world power system in China show that compared with the current research, the proposed method enables a more practical implementation in engineering, as no intricate transfer-limit modeling is needed. However, in comparison with the traditional empirical method, the proposed method renders better utilization of power transfer inter-corridors while guaranteeing security. In future work, a faster deep-learning-aided sensitivity-based method will be studied to enhance transfer limit control with respect to efficiency and engineering practicability.
Nomenclature
Symbol | —— | Definition |
---|---|---|
A. | —— | Sets |
—— | Set of buses | |
—— | Set of contingencies | |
—— | Set of clustering centers | |
—— | Set of loads | |
—— | Set of historical operations and empirical extreme operations | |
—— | Operation set belonging to the | |
—— | Set of synchronous machines | |
—— | Set of operation clusters (or set of transfer limit bands) | |
—— | Set of power transfer inter-corridors | |
—— | Set of lines | |
—— | Set of dispatch time | |
—— | Set of renewable power plants | |
B. | —— | Parameters/Indices |
—— | Vector containing power angle and speed of generators | |
—— | Vector containing bus voltage and phase | |
—— | Time before and at fault clearance | |
, , | —— | Transient period, start time of transient process, and end time of transient process |
—— | A security upper bound for absolute values of generator angular differences, which is usually set to be 180° or 360° in practice | |
—— | Structural parameters of neural network applied in mean impact value technique | |
—— | Transfer limit of the | |
—— | Security margin of the th power transfer inter-corridor | |
—— | A set threshold to ensure safe operation of power transfer inter-corridor | |
—— | Penalty weights on equality and inequality constraints of economic dispatch model | |
, | —— | Conductance and susceptance between bus i and bus j |
—— | Number of clusters | |
—— | Number of neurons in the th layer | |
—— | Number of collected operations/scenarios used for cluster analysis | |
—— | Dimension of input, which is formed by power system operating variables | |
—— | Active and reactive loads of the | |
—— | Transfer limit of the | |
, | —— | Lower and upper bounds of active generation of the th generator |
, | —— | Net active and reactive injections at bus i |
, | —— | Lower and upper bounds of ramp rate of the th generator |
, | —— | Lower and upper bounds of active power flow from bus i to bus j corresponding to branch l |
—— | Forecasted active output of the | |
—— | The minimum and maximum power generations of the | |
, | —— | Lower and upper bounds of reactive generation of the th generator |
—— | Dimension of output (note that it is also the number of inter-corridors, i.e., ) | |
—— | Quantity of effect of the | |
—— | Mean impact value (MIV) quantity of effect of the | |
—— | Endogenous quantity of effect of the | |
—— | Element in row i and column j of the cost-sensitive matrix | |
—— | A normalization factor | |
C. | —— | Variables of Transfer-limit Decision |
—— | Vector of power angle of each synchronous generator | |
—— | Vector of speed of each synchronous generator | |
—— | Vector of nodal voltages | |
—— | Vector of nodal phase angles | |
—— | Power angle of the | |
—— | The minimum and maximum values of power transfer of the | |
—— | The minimum and maximum values of power transfer of the | |
—— | Lower and upper transfer limits of the | |
—— | The minimum and maximum values of power transfer of the | |
—— | The minimum and maximum values of power transfer of the | |
—— | Transmission power in the th scenario through the | |
—— | Post-fault security state under contingency c of the | |
D. | —— | Variables of Economic Dispatch |
—— | Transfer limit of the | |
—— | Power generation of the th generator at dispatch timestamp | |
—— | Power generation of the th renewable power plant at dispatch timestamp | |
—— | Power curtailment of the th renewable power plant at dispatch timestamp | |
—— | Power flow through the |
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