Abstract
This paper develops a segmented real-time dispatch model for power-gas integrated systems (PGISs), where power-to-gas (P2G) devices and traditional automatic generation control units are cooperated to manage wind power uncertainty. To improve the economics of the real-time dispatch in regard to the current high operation cost of P2Gs, the wind power uncertainty set is divided into several segments, and a segmented linear decision rule is developed, which assigns adjustment tasks differently when wind power uncertainty falls into different segments. Thus, the P2G operation with high costs can be reduced in real-time adjustment. Besides, a novel segmented stochastic robust optimization is proposed to improve the efficiency and robustness of PGIS dispatch under wind power uncertainty, which minimizes the expected cost under the empirical wind power distribution and builds up the security constraints based on the robust optimization. The expected cost is formulated using a Nataf conversion-based multi-point estimate method, and the optimal number of estimate points is determined through sensitivity analysis. Furthermore, a difference-of-convex optimization with a partial relaxation rule is developed to solve the non-convex dispatch problem in a sequential optimization framework. Numerical simulations in two testing cases validate the effectiveness of the proposed model and solving method.
POWER-GAS integrated system (PGIS) can utilize the electricity and natural gas energy synergistically and interactively, which improves the energy efficiency and operation flexibility of the total system [
Currently, massive studies have been conducted on PGIS operations with wind power uncertainty. From the perspective of optimization models, mainstream methods can be classified into scenario-based optimization (SO) [
Besides the problem regarding the optimization methods to deal with the uncertainty problems, another critical issue is how to coordinate P2Gs with traditional units in the PGIS. In day-ahead scheduling, the P2Gs are often optimized together with other resources [
While many publications have studied either the PGIS operation optimizations with wind power uncertainty or PGIS real-time dispatch, much less attention has been directed to coordinating P2Gs and traditional AGC resources with wind power uncertainty in the real-time dispatch. Specifically, in the existing real-time dispatch models [
Moreover, it is noticed that most of the existing real-time dispatch methods of PGIS are based on IO, CRO, and DRO methods. In order to combine the benefits of stochastic and robust optimizations, we introduce stochastic robust optimization (SRO) [
In this paper, we propose a segmented stochastic robust optimization (SSRO) method to better coordinate P2Gs and traditional AGC resources in the real-time dispatch of PGIS. The segmented linear decision rule actually upgrades parameterized wind uncertainty set into a variable-involved segmented uncertainty set. However, such a modification will make the security constraints in the power system non-convex and the gas flow transmission constraints are also intrinsically non-convex. To solve the real-time dispatch of PGIS with complex non-convex constraints, we design an effective convexified solution. To sum up, the main contributions of this paper are as follows.
1) A segmented real-time dispatch model of the PGIS is constructed to cooperate the traditional AGC units and P2Gs together to cope with the wind power uncertainty. With consideration of the high operation cost of P2Gs, a new segmented linear decision rule is proposed to assign the adjustment task differently when wind power uncertainty falls into different segments, leading to a lower total cost of the PGIS.
2) An SSRO is proposed to address the dispatch of PGIS under wind power uncertainty. With SSRO, the security constraints are built up with robust optimization to increase the system safety, while the expected cost under the empirical distribution is optimized based on stochastic optimization to reach economical efficiency. A multi-point estimate method is developed for the expected cost formulation.
3) A partial relaxation-based difference-of-convex optimization (DCO) is developed to solve the non-convex dispatch problem. To be specific, the bilinear constraints converted from the uncertain constraints from the power system and the non-convex constraints from the gas system are equivalently transformed to difference-of-convex (DC) constraints with the tight and relaxed rule, respectively, and then solved by DCO method. Besides, a sequential optimization procedure is developed to correct the initialization of convexification.
As stated in the introduction, typical methods for optimizing the PGIS operation with wind power uncertainties include SO, IO, CRO, and DRO. The common thread of the SO, IO, CRO, and DRO methods is to minimize the operating cost with sufficient resources to accommodate real-time uncertainty, but they differ in uncertainty representations and mathematical formulations. In specific, [
To combine the advantages of the above-mentioned methods, some hybrid optimization methods, e.g., stochastic interval optimization (SIO) [
To meet the timeliness requirement of real-time dispatch, linear decision-based optimization methods are proposed, in which the baseline power and the participation factors are determined. References [
To cope with the wind power uncertainty, real-time dispatch optimizes the baseline state of generation units, wind power and gas sources as well as the participation factors of AGC resources. When wind power deviates from the baseline state, AGC resources regulate to neutralize the power imbalance, while non-AGC resources will operate at the baseline state. In general, when wind power fluctuates upward, the generation-side AGC units need to decrease the output power while the load-side AGC resources need to increase the power consumption. In contrast, when wind power fluctuates downward, the generation-side AGC units need to increase the output power while the load-side AGC resources need to decrease the power consumption.
In this paper, the AGC resources mainly include the AGC units and P2Gs. With regard to the current inadequate conversion efficiency and high cost of P2Gs (water electrolysis and methanation) [

Fig. 1 Illustration of segmented real-time dispatch at different uncertainty levels.
For each wind farm, is represented as the summation of and , i.e.,
(1) |
and are assumed to be in the forecast intervals:
(2) |
(3) |
In the real-time dispatch, the forecasted available wind power within cannot be fully integrated into the PGIS when it exceeds its adjustment capability, and then the excessive power will be curtailed. The wind power curtailment strategy can be described as:
(4) |
is smaller than the forecast upper bound:
(5) |
When taking the the allowable upward wind power fluctuation into consideration, the uncertainty set of the allowable wind power can be described as:
(6) |
In the dispatch mode, the traditional linear decision rule is upgraded to the segmented linear decision rule. The wind power uncertainty, i.e., the total wind power fluctuation, is first divided into four segments.
(7) |
where , and they satisfy:
(8) |
The adjustment task is assigned to resources by different decision rules when wind power uncertainty falls into different segments.
1) When the wind power uncertainty falls into segment ② in
(9) |
2) When the wind power uncertainty falls into segment ① in
(10) |
3) When the wind power uncertainty falls into segment ③ in
(11) |
4) When the wind power uncertainty falls into segment ④ in
(12) |
In the above four situations, constraints (13) and (14) need to be satisfied.
(13) |
(14) |
The above segmented decision rule can be described in a compact form as
(15) |
The constraints of the PGIS mainly include the power system constraints [
In the following context, and represent the baseline and the actual value of the decision variables, respectively; represent the possible extreme boundaries at the adjustment stage; and and represent the actual minimum and maximum limits, respectively.
(16) |
(17) |
(18) |
(19) |
(20) |
(21) |
(22) |
(23) |
(24) |
(25) |
Note that the extreme adjustment of AGC units and P2Gs is caused by extreme total wind power fluctuations. Therefore, power output/input limits of AGC units and P2Gs are established by extreme scenarios, as shown in (18) and (22). However, the power flow in transmission lines depends on the actual power output of each wind farm and cannot be described by extreme scenarios. To address this problem, the uncertain variable is introduced into the power flow constraints as:
(26) |
To sum up, the security constraints of the power system can be described in the following unified form.
(27) |
(28) |
Note that (28) contains the uncertain variables, and it can be transferred into the deterministic constraints using dual theory as:
(29) |
In the natural gas system, natural gas loads are supplied by natural gas sources through pipelines and compressor stations [
(30) |
(31) |
(32) |
(33) |
(34) |
(35) |
(36) |
(37) |
(38) |
(39) |
For the P2Gs and natural gas turbines which participate in the AGC service, they need to respond to the uncertain wind power, and further bring the uncertainty and fluctuations to the gas output (P2Gs) or input (gas turbine) of the natural gas system. In practice, the above gas uncertainty will be mainly balanced by the line pack in the pipeline, which leads to pressure fluctuations in the pipeline. Extreme fluctuations of the gas pressure will possibly bring about low-pressure or high-pressure events [
(40) |
The segmented real-time dispatch model optimizes the baseline cost in the first stage and the expected adjustment cost in the second stage, as shown in (43). The baseline cost includes the fuel cost of generation units, the cost of gas sources, and the operation cost of P2Gs.
(43) |
Note that the operation cost of P2Gs is mainly associated with the cost of electric power and the cost of materials, i.e., H2O in the water electrolysis and CO2 in the methanation and other catalysts. The electric power cost of P2Gs has already been included in the generation cost of units, and hence the operation cost coefficient of P2Gs actually indicates the material cost.
The generation costs of coal-fired generation units are quadratic functions associated with their outputs as:
(44) |
Traditionally, the expected value is modeled by the random sampling method. However, the results of random samplings depend on the sampled points, and an accurate estimation usually requires sampling a large number of points. Thus, this paper conducts the multi-point estimate method, which is indeed a deterministic estimate method and can uniformly cover the uncertain wind power fluctuation with fewer estimate points [
(45) |
(46) |
The number of estimate points () is usually an odd number for reaching a certain accuracy [
(47) |
(48) |
(49) |
The nonlinear constraints in this model include the bilinear constraints (18), (22), (29) of the power system and the gas flow transmission constraint (36) of the natural gas system. This paper adopts DCO to deal with nonlinear constraints. One of the features of DCO is that the constraints of the optimization problem are convex or can be expressed as the difference between two convex functions. For example, can be expressed as . In view of this, the bilinear constraints (18), (22), (29) expressed in the compact form as (50) are transformed to DC constraint as (51).
(50) |
(51) |
Then, gas flow transmission constraint (36) is replaced by two inequations (
(52) |
(53) |
Thus, the real-time dispatch of PGIS with nonlinear constraints is converted to the below compact form with DC constraints.
(54) |
Furthermore, the DCO is introduced to optimize the problem (53). The problem is convexified as:
(55) |
DCO iteratively updates the linearized base point and solves the updated problem to look for a high-quality solution. The algorithm converges when the optimization results of the two steps are close enough [
Algorithm 1 : DCO for the non-convex problem |
---|
Step 1: initialization: given an initial solution , let the iteration step |
Step 2: convexification: convexify the nonlinear constraint by (54), and solve the convex problem |
Step 3: stop when the following conditions (56) and (57) hold or the maximum iteration step limit is reached; otherwise, update , , and go to Step 2. |
(56) |
(57) |
Partial relaxation rule: in this paper, a partial relaxation rule is incorporated into the DCO to accelerate the convergence of the algorithm. To be specific, it is found that the decision variables in nonlinear constraints in the power system () have large impacts on the objective function. As a result, it usually requires many iterations in DCO for the relaxed variables to converge to 0. Therefore, we let the relaxed variables in nonlinear power flow constraints to be strictly equal to 0, and these constraints hold strictly during the iteration process to speed up the convergence. As for the nonlinear gas flow constraints (), the decision variables have minor impacts on the objective function, and meanwhile, it is difficult to find an initial feasible solution. Thus, there is no need to let the relaxed variable to be 0 for nonlinear gas flow constraints.
For the nonlinear constraints in the power system (), the initial point must be a feasible solution. Note that if the initial solution is feasible, the iteration will also be feasible for the convexification when letting the relaxed variable be 0 [
Firstly, the nonlinear constraints (18), (22), and (29) are linearized using the extreme scenarios as:
(58) |
(59) |
(60) |
(61) |
Secondly, we ignore the non-convex constraint (52) of the natural gas system and optimize the baseline cost and the allowable upward wind power fluctuations, as shown in (61), such that the problem to obtain the initial values of the variables involved in DC constraints is convex.
(62) |
The sign variables in the objective function of the SSRO also bring challenges for solving the problem and need to be determined in advance. In order to deal with the non-convex constraints and the sign variables together, we propose a two-step sequential optimization framework for real-time dispatch, as shown in

Fig. 2 Two-step sequential optimization framework for real-time dispatch.
Step 1: ignore the P2G adjustment for the wind power fluctuations and solve the stochastic robust dispatch model to obtain the sign variables . The process is divided into two sub-steps. In each sub-step, let .
1) Solve the traditional real-time robust dispatch without the P2G adjustment. To be specific, optimize the objective function (61) with system constraints, where nonlinear constraints (18), (22), (29) are replaced by (57)-(60) for the initial solution (denoted as Problem ). Then, use the results of Problem as the initial solution, and optimize the objective function (61) with the original DC constraints (18), (22), (29) (denoted as Problem ) to obtain the approximated allowable upward wind power fluctuations .
2) Solve the stochastic robust dispatch model without the P2G adjustment. Here, the uncertainty set is divided into two segments, i.e., and . Compare in Problem with the estimate points , and the sign variables of each estimate point can be obtained. Then, with the solution from Problem as the initial point, solve the SSRO without the P2G adjustment (denoted as Problem ).
Step 2: solve the stochastic robust dispatch model with the P2G adjustment (denoted as Problem 2). Based on the results of Problem , the approximated allowable wind power boundaries can be calculated by , , . Compare these boundary values with the estimate points (), and the final signal variable of each estimate point can be obtained. Then, with the solution from Problem as the initial point, solve the SSRO with adjustment of AGC units and P2Gs for wind power fluctuations.
It should be noted that since constraint (52) only changes the gas flow distribution in the natural gas system, while has minor impacts on the power outputs of units and power input of P2Gs in the power system. Thus, the constraint (52) can be ignored in Step 1 to accelerate the solving process. In addition, when obtained in Problem is less than 0, the wind uncertainty set is divided into two segments, i.e., , and the objective function and constraints in the SSRO need to be updated accordingly.
This section conducts the simulation studies on a PGIS, which combines an IEEE 39-bus system and a Belgian 20-bus natural gas system, as shown in

Fig. 3 Diagram of PGIS.
Unit | AGC | ($/(MWh)) | ($/MWh) | ($) | (MW) | (MW) | (MW per 5 min) |
---|---|---|---|---|---|---|---|
C | No | 0.0069 | 30.915 | 1352 | 455.2 | 135.7 | 45.5 |
C | Yes | 0.0098 | 32.342 | 1519 | 507.5 | 152.3 | 50.8 |
C | No | 0.0055 | 30.070 | 1353 | 480.9 | 144.3 | 48.1 |
C | Yes | 0.0062 | 32.100 | 1984 | 605.5 | 181.7 | 60.6 |
C | No | 0.0074 | 32.271 | 2224 | 770.0 | 231.0 | 77.0 |
Unit | AGC | (%) | (MW) | (MW) | (MW per 5 min) |
---|---|---|---|---|---|
G | Yes | 40 | 509.6 | 135.6 | 152.8 |
G | Yes | 40 | 284.2 | 231.0 | 85.2 |
G | Yes | 40 | 276.3 | 118.4 | 82.9 |
P2G | (MW) | (%) | ($/m) |
---|---|---|---|
P2G | 50 | 60 | 0.03 |
P2G | 50 | 60 | 0.03 |
Gas source | (m/s) | (m/s) | ($/m) |
---|---|---|---|
S | 30.79 | 133.29 | 0.3 |
S | 35.90 | 104.23 | 0.3 |
Figures

Fig. 4 Baseline power and wind power fluctuations undertaken by gas turbines among AGC units.

Fig. 5 Baseline power and wind power fluctuations undertaken by P2Gs.
As a result, they only undertake the DF adjustment since there is no room for a downward adjustment of the gas turbines. The baseline power of P2Gs is zero in this case because their operation costs are comparatively high, and the wind power is not redundant during this time period. Meanwhile, P2Gs undertake a large amount of UF adjustment tasks since the adjustment capability from AGC units is insufficient in this case. The results also verify the necessity to involve the gas uncertainty issues in the security constraints of PGIS due to their highly volatile and uncertain operations caused by the wind power uncertainty.
System | Optimized result | MCS result | |||
---|---|---|---|---|---|
(MW) | Objective ($) | Wind curtailment cost ($) | Adjustment cost ($) | Total cost ($) | |
Without P2G | 1274.82 | 229363 | 52.000 | 378 | 229389 |
With P2G | 1918.70 | 229281 | 0.449 | 355 | 229309 |
Method | Optimized result ($) | MCS result | |||
---|---|---|---|---|---|
Wind curtailment cost ($) | P2G input (MW) | Adjustment cost ($) | Total cost ($) | ||
Non-segmented | 229399 | 2.22 | 71.82 | 472 | 229432 |
Segmented | 229281 | 4.49 | 13.97 | 355 | 229309 |

Fig. 6 Adjustment tasks undertaken by different AGC resources in SSRO.
To verify the effectiveness of the proposed SSRO method, this subsection compares SSRO with CRO [
Capacity | Strategy | Optimization result | MCS result | |||
---|---|---|---|---|---|---|
Cost ($) | Time (s) | Wind curtailment cost ($) | Adjustment cost ($) | Total cost ($) | ||
1.00 | SCRO | 230875 | 75 | 0 | 190 | 231065 |
SDRO | 230718 | 88 | 0.211 | 258 | 230586 | |
SSRO | 229281 | 46 | 0.449 | 355 | 229309 | |
0.75 | SCRO | 232185 | 161 | 0.680 | -197 | 231989 |
SDRO | 230510 | 94 | 2.360 | 346 | 230055 | |
SSRO | 229304 | 34 | 3.200 | 404 | 229362 |
In the multi-point estimate method, the number of estimate points directly affects the optimization results and the computation time. Therefore, this subsection compares the results of different numbers of estimate point. The number of the estimate points is usually selected as an odd number such as 3, 5, and 7 ().

Fig. 7 Allowable upper bound of wind power fluctuation with different numbers of estimate points.
Optimization result | MCS result | ||||
---|---|---|---|---|---|
Objective ($) | Time (s) | Wind curtailment cost ($) | Adjustment cost ($) | Total cost ($) | |
3 | 229218 | 39 | 41.000 | 365 | 229359 |
5 | 229246 | 39 | 0.953 | 352 | 229307 |
7 | 229281 | 46 | 0.449 | 355 | 229309 |
Overall, the MCS costs of 5-point and 7-point estimate are closer to the optimized results, showing that more estimate points will lead to a more precise estimation. Note that the computation time increases along with the increase of the estimate numbers, but such an increase is acceptable. Therefore, we select 7-point estimate to formulate the expected cost objective in this paper.
In this subsection, the partial relaxation-based DCO is compared with the original complete relaxation-based method. We also compare the results with some other methods, including the piecewise linearization method [
Capacity | Method | Optimized objective ($) | Iteration | Time (s) |
---|---|---|---|---|
1.00 | MIQCP | Non-convergence | Non-convergence | Non-convergence |
NLP | 231261 | 1 | 319 | |
DCO (complete) | 232791 | 50 | 213 | |
DCO (partial) | 229281 | 11 | 31 | |
0.75 | MIQCP | Non-convergence | Non-convergence | Non-convergence |
NLP | 231314 | 1 | 416 | |
DCO (complete) | 232578 | 50 | 208 | |
DCO (partial) | 229304 | 7 | 17 |
Compared with the DCOs, the optimal cost of the direct NLP is larger, and the computation time is much longer. By comparing the partial and complete relaxation-based DCO methods, it can be observed that the partial relaxation-based DCO method significantly saves computation time and iterative times. The reason is that the non-convex constraints in the power system have large influences on the objective values. When completely relaxing the non-convex constraints, the algorithm needs to search outside the feasible region for many times to enter the feasible region. To sum up, the partial relaxation-based DCO illustrates the the best performance among the four methods.
To further verify the effectiveness of the proposed model, we conduct a simulation on a large-scale PGIS, which combines the IEEE 118-bus power system [
Capacity | Strategy | Optimization result | MCS result | ||||
---|---|---|---|---|---|---|---|
Cost ($) | Time (s) | Wind curtailment cost ($) | Adjustment cost ($) | Total cost ($) | |||
1.00 | SCRO | 354139 | 35 | 0 | 248.00 | 354387 | |
SDRO | 354247 | 106 | 0.511000 | -6.45 | 354170 | ||
SSRO | 352586 | 240 | 0.912000 | 191.00 | 352621 | ||
0.75 | SCRO | 354660 | 90 | 0.000134 | 104.00 | 354763 | |
SDRO | 354364 | 107 | 0.477000 | -4.66 | 354208 | ||
SSRO | 352701 | 223 | 11.000000 | 249.00 | 352723 |
This paper proposes a segmented real-time dispatch model for PGIS to cooperate the traditional AGC units and P2Gs based on the segmented linear decision rule. Meanwhile, SSRO is proposed to address the wind power uncertainty in real-time dispatch, and a partial relaxation-based DCO method is developed to solve the proposed model. The participation of the P2Gs in the AGC service enhances the system capability to address the wind power uncertainty and increases wind power integration. The segmented linear decision rule assigns the adjustment task differently when wind power uncertainty falls into different segments, which reduces the total cost through better cooperation between traditional AGC units and P2Gs. Out-of-sample analysis in a testing system verifies the higher cost efficiency and better computation performance of the proposed SSRO compared to the conventional robust methods. Besides, the developed partial relaxation-based DCO illustrates faster convergence compared with other methods.
It should be noted that the proposed SSRO is based on the empirical distribution, which is a fitting distribution developed from historical data. When sufficient historical data are available and a well-done fitting method is applied, the fitted empirical distribution could probably be very close to the actual probability distribution. In such cases, SSRO will illustrate superior performance. However, SSRO can hardly guarantee good performance when the fitted empirical distribution is far away from the actual distribution. A promising way to address this problem may be to combine the empirical distribution in SSRO and the extreme distribution in SDRO to balance the economic efficiency and robustness of the real-time dispatch, which will be conducted in our future work.
Nomenclature
Symbol | —— | Definition |
---|---|---|
A. | —— | Indices and Sets |
—— | Wind uncertainty set | |
—— | Wind uncertainty subset | |
—— | Set of coal-fired generation units | |
—— | Pipeline with and without a compressor | |
—— | Index of gas sources | |
—— | Index of automatic generation control (AGC) units | |
—— | Index of power-to-gas (P2G) devices | |
—— | Index of wind farms | |
—— | Index of uncertainty subsets | |
—— | Index of dispatch periods | |
—— | Index of iteration steps in convexification of nonlinear constraints | |
—— | Index of estimate points | |
B. | —— | Parameters and Functions |
—— | Participation factors | |
—— | Forecasted lower and upper bounds of total uncertain wind power | |
—— | Normalized lower and upper bounds of total uncertain wind power | |
—— | Consumed gas flow of compressor | |
—— | Conversion efficiencies of gas turbine and P2G device | |
—— | Adjustment cost coefficients of AGC unit and P2G | |
—— | Penalty factor of wind curtailment | |
—— | Penalty factor of relax variables | |
—— | Weight of the | |
—— | Cumulative distribution function (CDF) of the standard Gaussian distribution | |
—— | Positive constants of convexification of nonlinear constraints | |
—— | Constant matrices of security constraints of power system | |
—— | Convex function associated with decision variables | |
—— | Bilinear function concerning , and | |
—— | Gas flow transmission coefficient of pipe | |
—— | Quadratic function of generation costs | |
, | —— | Constant vectors of security constraints of power system |
—— | Bilinear function concerning , , and | |
e | —— | Column vector whose cell values are 1 |
—— | Calorific value of natural gas | |
—— | Expected adjustment cost under empirical distribution | |
—— | Inverse of CDF of total available wind power fluctuation | |
—— | Shift factors of AGC unit i, non-AGC unit m, wind farm k, P2G device j, and load n to line | |
—— | Bilinear function of decision variables | |
—— | The minimum and maximum pressurizations of compressor | |
—— | Required line pack in gas network after dispatch | |
—— | Number of estimate points | |
—— | Empirical distribution | |
—— | Forecast expectation of wind farm | |
—— | The minimum and maximum power outputs of AGC unit | |
—— | The minimum and maximum power outputs of non-AGC unit | |
—— | The maximum power input of P2G | |
—— | Power demand at node n in power network | |
—— | The minimum and maximum gas pressures of node n in gas network | |
—— | Gas purchase price of gas source | |
—— | Operation cost coefficient of P2G | |
—— | The minimum and maximum gas flow outputs of gas source | |
—— | Gas demand of node | |
—— | The maximum ramp down and ramp up of non-AGC unit | |
—— | Line pack coefficient of pipe | |
—— | The minimum and maximum limits of power line | |
—— | Forecasted lower and upper bounds of uncertain wind power fluctuation of wind farm | |
—— | Quadratic penalty function for wind curtailment | |
—— | The th estimate point of standard Gaussian distribution | |
C. | —— | Decision Variables |
—— | Participation factors of AGC unit for downward and upward wind power fluctuations | |
—— | Participation factors of P2G for downward and upward wind power fluctuations | |
—— | Allowable downward wind power fluctuation undertaken by P2Gs | |
—— | Allowable upward wind power fluctuation undertaken by traditional AGC units | |
—— | Total allowable upward wind power fluctuation | |
—— | Endpoints of wind uncertainty subsets | |
—— | Relax variable to convexify DC constraints | |
—— | Dual variables of corresponding boundary constraints | |
—— | Power flow of line at time | |
—— | Line pack in pipe | |
—— | Baseline power output of wind farm | |
—— | Baseline power output of AGC unit | |
—— | Baseline power input of P2G | |
—— | Baseline power output of non-AGC unit | |
—— | Gas pressure of node in gas network | |
—— | Adjustment cost in the second stage | |
—— | Baseline gas flow output of gas source | |
—— | Gas inflow and outflow of pipe | |
—— | Average gas flow of pipe | |
—— | The minimum and maximum gas flow consumptions of gas turbine | |
—— | The minimum and maximum gas flow outputs of P2G | |
—— | Reserve down and up provided by AGC unit | |
—— | Reserve down and up provided by P2G | |
—— | Decision variables of convexification of nonlinear constraints | |
D. | —— | Uncertain Variables |
—— | Total available wind power fluctuation of all wind farms | |
—— | Total allowable power fluctuation of all wind farms | |
—— | Available wind power of wind farm | |
—— | Actual power output of wind farm | |
—— | Actual power output of AGC unit | |
—— | Actual power input of P2G | |
—— | Actual gas flow consumption of gas turbine | |
—— | Actual gas flow output of P2G | |
—— | Available wind power fluctuation of wind farm | |
—— | Allowable power fluctuation of wind farm |
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