A Smart Power System Operation Using Sympathetic Impact of IGDT and Smart Demand Response With the High Penetration of RES

The enhanced penetration of available renewable energy sources (RES) is preferred over-utilizing the maximum cost budget for the conventional power system operation. Severe uncertainty and power generation and load demand balance are the pre and post-challenges of RES penetration respectively. Penetration of RES can be made effective by modeling the RES uncertainty with a computationally efficient technique and controlling the load demand smartly. In this paper for the smooth and stable penetration of RES, the uncertainty of RES is modeled using the sympathetic impact of information gap decision theory (SI-IGDT) to deal with minimum possible uncertainty. Smart demand response (SDR) is modeled using a virtual layer as a smart demand response operator (SDO) between the main grid and consumers for the post-challenge of RES penetration. The SDO categorizes consumers into virtual prosumer (VP), real prosumer seller (RPS), and real prosumer buyer (RPB) using a power flow conditional algorithm (PFCA). The uncertainty of RES is subsequently optimized and implemented using the firefly optimization algorithm (FOA) and the power flow algorithm (PFA). To achieve technical and economic benefits for the main grid and all consumers, a Stackelberg game is formulated using PFCA and multi-objective FOA (MFOA). MATLAB is used for the implementation of the algorithms and the test system. Simulation results show that the maximum available RES power is penetrated up to 300 %, and load demand reduction is observed up to 62% which ultimately reduces the power flow loss by 70%.


RES
Climate change has a perceptible effect on the forecasting 30 of RES. Because of the COVID-19 pandemic, the global 31 weather showed diverted behavior from its normal data. 32 In such situations, the forecasting of RES has become 33 extremely challenging. The World Meteorological Organi-34 zation has released a report that the COVID-19 pandemic 35 has negatively affected the quantity and quality of weather 36 forecasts, and climate monitoring [1]. Consequently, the level 37 of uncertainty has increased. In this paper, uncertainty is 38 defined as the actual information gap between forecasted 39 data and real-time data. Thus, the integration of RES with 40 the running stable system demands dealing with the level of 41 uncertainty. In the past, stochastic and probabilistic methods 42 were used to deal with uncertainty. However, this could only 43 be achieved with essential historical data, probability density 44 functions, and a high computational burden. IGDT is an 45 alternative method that is considered to be better equipped 46 to deal with uncertainty. After the integration of RES two 47 possible situations must be considered: 48 1) Power supplied from the RES is less, or 49 2) Greater than the demand at the point of common cou-50 pling of the RES.

51
In the first case, an incentive-based SDR is a remedial 52 solution, while an ESS can be used to reserve the surplus 53 power from the MG in the second case. The second case can 54 also be handled through the local energy trade between real 55 prosumers.

57
The motivation of this study is to model the uncertainty, 58 which is essential for power system design as it has uncer-59 tain parameters like RES. In such situations, uncertainty 60 can be excessively risky. Therefore, decision-makers deter-61 mine the parameters of the power system to ensure that 62 the power system does not cross the allowed limits due to 63 uncertainty. Various techniques have been used to model 64 uncertainty, such as possibilistic, Z-number, interval analysis, 65 robust optimization, and information gap decision theory 66 [2]. The probabilistic approach has been used to model the 67 uncertainty effectively [3]. Stochastic programming is the 68 main tool used in designing the parameters and finding their 69 probability and optimal solutions. To deal with the uncer-70 tain load values, electricity market price, and daily distance 71 traveled by the electrical vehicles, Monte Carlo simulations 72 response can be changed as per the requirement. Future smart 126 grids and MGs will have communication and IoT sources 127 for efficient coordination. The DR can also coordinate using 128 the available sources in normal and emergency events [17], 129 [18], [19], [20], [21]. In case of power fluctuations, the 130 requirements of power ramp-up and ramp-down are a bit 131 challenging. Nevertheless, the DR can provide a better and 132 faster ancillary service for a stable economic operation [22]. 133 If flexible demand response and uncertainty of RES are 134 considered together then a stable integration of community 135 energy users to the main power system can be developed. 136 A strong community-integrated energy system considering 137 electric vehicle charging stations using sequence operation 138 theory is developed by [23]. To test the balanced coordina-139 tion between the community-integrated energy system and 140 electric vehicle charging stations and the effective role of 141 flexible demand response and RES, a real-time case study in 142 North China has been considered. Stackelberg game-based 143 DR models have been a great source of benefits for provid-144 ing power system stability to both consumers and the main 145 grid [24], [25], [26]. From [8], [9], [10], [11], [12], [13] 146 to [27], [28], [29], it has been observed that the research 147 interest was on the robust solution and lack of focus on the 148 opportunistic solution. Here, the sympathetic impact of IGDT 149 (SI-IGDT) has been exploited to boost the opportunistic solu-150 tion that would maintain system stability from minimum to 151 maximum RES available. It means that maximum energy 152 is harvested from RES whether it is greater or lower than 153 the forecasted energy. Although DR has been modeled in 154 [24] and [25] to fill the gap between power generation and 155 demand, there is still space to improve the consumer behavior 156 to the main grid. In this work, consumer behavior analysis 157 and control are designed by a novel factor using SDR. In this 158 model, power is exchanged between the prosumers by con-159 sidering not only their technical and economic benefits but 160 also the selection priority which causes the power system loss 161 reduction.

163
The main contributions of this paper are summarized as 164 follows: 165 1) To utilize the maximum RES power, uncertainty is 166 modeled using the SI-IGDT which has made possible 167 the integration of RES whether it is greater or less than 168 the forecasted value. The rest of the paper is organized as follows: the sym- The discrepancy between known and unknown data is inter-198 preted as uncertainty, which is modeled by the IGDT. This  Here, the slope-bound model has been adopted. Related 213 function M (α, m) is given in (1), Here m (t) and m(t) are the real and forecasted values of the 216 uncertain parameters respectively while α and ϕ(t) denote  Table 1  Before detailing the IGDT model used in this study, it is 227 beneficial to briefly review the uncertainty model used in [27] 228 and [28]. Here, an assumption was made that actual uncertain and the minimum available RES in [27] and [28] respectively. 233 In addition to the same assumption made in [27] for a robust 234 solution, another assumption was made in [29], that unknown 235 values of RES would be greater than forecasted values to find 236 the opportunistic solution. In both cases, the operating cost 237 of the smart grid and MG was the objective function. So, the 238 maximum possible cost with the minimum RES power in the 239 robust case, and the minimum cost with the maximum possi-240 ble RES power in the opportunistic case were determined. All 241 the above cases were more focused on the robust solution with 242 the pre-assumptions, which availed the least power of PV and 243 WT. However, the goal of this study is to utilize the maximum 244 possible available RES power with minimum possible cost 245 without any pre-assumptions which is more close to the real 246 uncertain behavior of RES.

247
In general, the two main functions of IGDT are; 248 1) The RF is related to the risk-averse method, and 249 2) The OF is related to the risk-seeker method.

250
A deep study of [7] shows that RF shows immunity to 251 failure while OF shows immunity to possible success. With 252 uncertainty limits α 1 and α 2 , general form of RF and OF are 253 given in (3) and (4) respectively, where x is the decision variable, W r and W o are the reward 257 values for RF and OF respectively with W t_r and W t_o as the 258 threshold values. RF tends to gain the maximum permissible 259 cost (minimum reward) with a wide range of uncertainty 260 resulting in improved immunity to failure. While OF has the 261 immunity to possible success but within a minimum possible 262 range of uncertainty. The immunity expected response is 263 shown in FIGURE 1.

264
The left side of FIGURE 1 shows a tendency of the robust 265 function, which seeks maximum uncertainty with low reward 266 but it is immune to failure. Thus, it is considered a risky  (5) and (6).
where (5) deals with the situation when the actual unknown 284 RES profile value is greater than the forecasted value and (6) 285 is applied when the forecasted RES profile value is greater 286 than the actual value. It is found that the data is found 287 more uncertain in the robust case, that's why it is better to 288 deal with the uncertainty margin for RF and OF separately.

289
Overall, the real RES profile data is estimated without any 290 assumption. It is important to note that both α 2 and α 1 are 291 minimized which ultimately tends to achieve the maximum 292 target reward. If the condition in (7) is fulfilled, then both 293 immunities will sympathetically support each other, From (7) it is clear that if the rate of change of opportunistic 296 function value concerning robust target reward is positive 297 then it means both functions are sympathetic otherwise antag-298 onistic. Now we can conclude that a new function named here 299 as the sympathetic impact function (SIF) can be developed as 300 in (9): The SIF combines the features of RF and OF from (3) and 304 (4) in (9) by using (5), (6), and (8). The unique feature of 305 SIF is that it tends to minimize uncertainty and maximize the 306 target reward.

308
Demand response has a strong relationship with RES and 309 smart grids [30], [31]. Balancing the load and power genera-310 tion, specifically at peak hours of the main grid, is especially 311 challenging. This issue can be resolved either by managing 312 the power generation sources or the loads. The first solution is 313 relatively difficult as it is complex and costly due to the power 314 ramp-up and ramp-down operations of the power generation 315 sources. The second solution balances the power by control-316 ling loads of consumers as per the required power manage-317 ment. Despite the difficulty of this task, emerging algorithm 318 development, advancement in communication technology, 319 and advanced metering infrastructure have made it possible 320 to develop an SDR [32].

321
There are two types of DR programs: incentive-based DR 322 and price-based DR. For the price-based DR, the consumer 323 manages the load to get the minimum price available at a 324 specific time slot. Despite this, the price-based DR consumer 325 does not get any benefit from the utility except the reduced 326 cost. In contrast, for the incentive-based DR, the load of 327 consumers is controlled either by the utility or the consumer 328 itself under any DR type. The consumer gets the incentives 329 either in the form of a reduction of energy units or cash 330 payment [33]. Consequently, more consumers are encouraged 331 to participate in incentive-based DR. Thus, consumers can 332 play the role of a VP as well. As shown in FIGURE 2, 333 SDR coordinates between the SDO and prosumers. The SDO 334 interprets the real-time prices and incentives of the main grid 335 and subsequently communicates them to the prosumers. It is assumed here that the consumer either behaves as a VP 338 or RP. Let k denote the number of VPs and n denote RPs. 339 Generation of the RP either consists of PV or WT or both. 340 The RP is further divided into two types RP seller (RPS) and 341 RP buyer (RPB). 342 VOLUME 10, 2022 Consumers are differentiated by using the following 343 generation-to-demand ratio GD n (10), where subscript s and b shows seller and buyer index number 346 respectively. While G n and D n are power generation and 347 demand at the consumer node respectively.

348
The behavior of the RPS can be modeled using the UF the UF is given by (11),

354
where σ n > 0 is a prosumer preference parameter, θ n is a 355 predetermined constant, and t is the time interval in hours.

356
The UF of RPB and RPS is given by (12) and (14) respec- otherwise the RPB will be shifted to the grid, as shown in (16). 373 The UF of the VP is defined using R t k , as given in (17) where in (16) ρ t d,b is the power bought from the main grid 378 (subscript 'd' is used because of SDO), in (17) D t k is the 379 power reduced by the VP ω k is the dissatisfaction cost, which 380 shows how much the VP has violated the agreement with the 381 main grid through the SDO, in (18) D base k is the base-load of 382 VP, L R,k is load reduction limit. In (17) k is defined as the 383 dissatisfaction factor of the agreed load reduction.

384
The dissatisfaction cost is given in (19), where σ k denotes the type of prosumer and θ k is the load 387 reduction behavior.

389
The UF of SDO includes the UF of RPS, RPB, VP, generation 390 cost, and the cost of the reserve power. It is given by (20), In (20) 0.03 is 3% benefits of seller paid to the main grid 399 through SDO, R g is the cost, P g is the power generation of the 400 main grid, rg is the reserve power generation factor, P rg is 401 the reserve power and R rg is the generation cost for the reserve 402 power. Here rg has the same value as that of k . This means 403 that the dissatisfaction with agreed demand reduction leads 404 to the generation of the reserve power. The total incentives 405 offered and paid to the VPs must be less than the maximum 406 allowed budget of the main grid, as shown in (22  The existence is ensured through an algorithm.

421
Definition and Rules: The ultimate goal of this game is to 422 find an optimal beneficial solution for the leader (SDO) and 423 the followers (VP, RPS, and RPB). Each game is played under 424 some specific rules which are listed below [24].

425
Each player in the game adheres to the following rules, 426 1) The strategy set of each player is nonempty, convex, 427 and compact.
428 2) Each player has a unique optimal best-response strat-  3) The SDO adopts a unique optimal strategy by identify-

441
By calculating the first derivative of (24) w.r.t. D t k , we get 442 as,

444
By equating the derivative to zero in (25), the maximum 445 value of D t k is D t k given in (26),

447
The second derivative of (24) has a negative value 448 (− k θ k ); this means that the objective function is concave. the UF of the RPB can be written as,

456
where ρ e,b is the power purchased either from the RPS or the 457 main grid. By using the values from the UF of the RPB, (27) 458 becomes, Now taking the first derivative, (28) becomes, To find the maximum power purchased ρ e,b , we equate the 464 derivative to zero and solve by (30), The second derivative of (28) is negative (−θ b ) and there-467 fore concave, which shows maximization function.

468
Proof 3: The objective function of the RPS maximizes 469 the revenue obtained from selling the power to the RPB. 470 This means that power will be sold in equal proportion to its 471 demand. The UF of the RPS is given in (31), Here, S t s is the total power demand from RPS, and it is 475 assumed to be the nominal case, S t s = ρ t s . By taking the 476 derivative of (31) w.r.t ρ t s , we get The second derivative of (31) is also negative (−θ s ) and 483 concave.

484
Proof 4: After finding the maximum values of D t k , ρ e,b , 485 and ρ t s as D t k , ρ e,b , and ρ t s , respectively, the maximum possi-486 ble value of the main grid energy price R d,b can be found from 487 (21) by using the aforementioned values. Before we derive the 488 expression for R d,b , it is important to note the following, (20% is assumed 494 as the incentive from the main grid at peak hours). 495 Hence, the UF of the SDO from (20) using the values of D t k , 496 ρ e,b , and ρ t s , and considering all the points mentioned above 497 is given as, ing the derivative to zero, as shown in (35) and (36), In (36) STF is termed as the SDR tuning factor for the cost of 516 power from the main grid through SDO which is given as, The unique novel factor STF derived in (37) is the best source 521 to observe the behavior of VP, RPS, and RPB to the main grid.  The brief execution procedure has been given below;  12), (14), (16) and (21)) and maximum possible 577 output values ((26), (30), (33) and (1)) of Stackelberg 578 players are found.

580
For better planning and design of any power system, the 581 objectives must be clearly defined and all sensitive constraints 582 of the system must be considered. The objective of this study 583 is divided into three parts:   So here (39) can be redefined by putting the x and the 627 multi-objective target is given in (40) and (41), Here one thing is noted the minimized values of uncertain 632 profiles of RES will come from algorithm 1. As a result of the 633 (40), maximum power can be penetrated by factor A which 634 VOLUME 10, 2022 would ultimately reduce the operational cost of the main grid.
Here A is named as the amplifying factor of the RES power 636 to penetrate.

637
The total net power P t net should satisfy the power reserve 638 required for a reliable main grid.
where P t g , G t b , S t s , P t g0 , and P t rg are the power generated by   (15) and (47) respectively, 664 which depends on their comfort and allowed budget.  Before analyzing the impact of the proposed methodology, 702 it is essential to show some aspects in the base which will be 703 considered as reference. The buses where RES are connected 704 are also considered the local MGs. Voltage situation at these 705 buses, energy generation and demand, and energy loss at 706 each bus are shown in FIGURE 4, 5, and 6 respectively. 707 In FIGURE 4, it is observed that at buses 7-8 and 33-35 there 708 is a voltage drop below the -5% threshold. The reason for 709 voltage drop is due to energy supply from main grid sources 710 only at bus 26 and 33 and more energy demand than the 711 generation. It is also worth noting that the generation cost 712 of the main grid is 3264887 KRW (Korean Currency). Cost 713 function coefficients are taken from [40]. From FIGURE 6 it 714 is clear that more energy loss is observed on buses 1-9 due 715 to power flow from buses 26 and 33. The gross energy loss 716 during 24 hours is 78 kWh which can accumulate to a huge 717 amount if it is not reduced.

719
The impact of the proposed methodology is analyzed in 720 three parts: analysis of SI-IGDT, the role of the SDO to 721   The opportunistic region limit is 10% more than the fore-           for D t k , ρ s,b and ρ d,b at each bus concerning the STF is shown 815 in FIGURE 14.

816
It is clear from FIGURE 14 that most of the energy at 817 buyer buses is purchased from the main grid but there is 818 also maximum penetrated power by RES which is sold from 819 RPS to RPB. The optimal value of energy-reduced at relevant 820 buses of VP is shown which is based on the incentives from 821 the main grid. Energy reduction at VP buses 1, 3, 7, and 33 is 822  5. Effects of θ k , θ s and θ b at optimal power and utility functions of vp, rps, rpb and sdo (main grid).     Similarly, a decrease in values for θ k , θ s , and θ b lowers 845 the R t d,b and u(SDO), whereas the opposite effect is observed 846 when RPS and its UF are considered.

847
The variation of the STF values that control R t d,b for 848 various θ values is shown in FIGURE 16. The variation of 849 STF has an inverse effect on R t d,b and u(SDO) as given in 850 (36), which can be easily deduced by analyzing FIGURE 16 851 and Table 5 simultaneously. Conclusively, it is observed that 852 at SE energy generation or consumption, energy price and 853 UF values for SDO, VP, RPS, and RPB in Table 5 are the 854 best possible values. Either energy reduced by VP or energy 855 trading between local consumers i.e between RPS and RPB, 856 both ways are effective for the economic operation of the 857 main grid which can be realized by comparing base case grid 858 operational cost with any one of the above cases.

859
To summarize the effect of prosumers behavior on the STF 860 factor that affects the main grid energy price which ultimately 861 affects the participation of VP, RPS, and RPB in the SDR. 862 This is the solid source that helps to achieve the Stackelberg 863 equilibrium for SDR. Participation of VP, RPS, and RPB 864 for the change of θ k , θ s , and θ b ±10% has been drawn in 865 FIGURES 17 and 18.     presented in [24], [25], [26], [27], [28], and [29], which 902 provides a smart control of consumer behaviors. The proposed SI-IGDT based model effectively integrated 904 with the Stackelberg game is an additional advantage 905 over [24], [25], [26], [27], [28], [29]. A brief compari-906 son is given in TABLE 6.

907
It can be observed from TABLE 6 that the proposed 908 research has the advantage of a novel application of SI-IGDT 909 over the articles which have applied IGDT. Most of the 910 game lack RES penetration focus, reserve power, reduction 912 of power loss and any novel STF canbe used to design an 913 autonomous control of consumer loads.

915
In conclusion, our study shows that the SI-IGDT model can