Department of Power Engineering Jadavpur University, Salt Lake Campus Kolkata- 700098

1. Department of Power EngineeringJadavpur University, Salt Lake CampusKolkata- 700098

2. Deregulated Reactive Power Compensation; Minimising Loss, Saving the Environment Niladri ChakrabortyDepartment of Power Engineering, Jadavpur University, Salt Lake Campus, Kolkata- 700098

3. List of Publications: Journal • Biswas (Raha) S, Manadal K. K., Chakraborty N, “Hybrid SMES based Reactive Power Dispatch by Cuckoo Search Algorithm”, Accepted in IEEE Industry Application Magazine, 2017. • Biswas (Raha) S, Manadal K. K., Chakraborty N, “Pareto efficient double auction power transactions for economic reactive power dispatch”, Applied Energy , 2016, 168: 610-627. • Biswas (Raha) S, Mandal K.K., Chakraborty N, “Constriction factor based particle swarm optimization for analyzing tuned reactive power dispatch”, Frontiers in Energy (Springer), 2013, 7(2): 174-181. • Biswas (Raha) S, Chakraborty N, Mandal K.K., “Differential Evolution Technique with Random Localization for Tuned Reactive Power Dispatch Problem”, Electric Power Components and Systems, Taylor & Francis Group, LLC, 2013, 41: 500–518. • Biswas (Raha) S, Mandal K.K., Chakraborty N”, “Modified Differential Evolution based Multi-Objective Congestion Management in Deregulatory Power Environment”, International Journal of Electrical, Electronics and Computer Engineering, 2012, 1(2): 93-97. • Biswas (Raha) S, Chakraborty N, “Tuned reactive power dispatch through modified differential evolution technique”, Frontiers in Energy (Springer), 2012, 6(2): 138-147.

4. List of Publications : Conference • Biswas (Raha) S, Mandal K. K., Chakraborty N, “Hybrid SMES based Reactive Power Dispatch by Cuckoo Search Algorithm”, International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES) July 2016, IEEE, Delhi. • Biswas (Raha) S, Mandal K. K., Chakraborty N, “Modified differential evolution based reactive power dispatch problem involving multilateral power transactions in deregulated power scenario”, Power, Communication and Information Technology Conference (PCITC) Oct, 2015, IEEE, Bhubaneswar. • Biswas (Raha) S, Mandal K. K., Chakraborty N, “Impact of modified differential evolution strategy on reactive power dispatch problem”, India Conference (INDICON), 2014 Annual IEEE.DOI:10.1109/INDICON.2014.7030534. Publication Year: 2014, Page(s): 1 – 5. • Biswas (Raha) S, Som T., Mandal K. K., Chakraborty N, “Cuckoo Search Algorithm based Optimal Reactive Power Dispatch”, Control, Instrumentation, Energy and Communication (CIEC), 2014 International IEEE Conference, DOI: 10.1109/CIEC.2014.6959121.Publication Year: 2014 , Page(s): 412 – 416. • Biswas (Raha) S, Mandal K.K., Chakraborty N, “Parametric Variation based Simulated Annealing for Reactive Power Dispatch” In proceedings of Sustainable energy & intelligent System (SEISCON 2013), Decembar, 2013, IET, Chennai. • Biswas (Raha) S, Mandal K.K., Chakraborty N, “Simulated Annealing Based Real Power Loss Minimization Aspect for a Large Power Network”, Swarm, Evolutionary, and Memetic Computing Lecture Notes in Computer Science, 2013, Volume 8297, 345-35. • Biswas (Raha) S, Mandal K.K., Chakraborty N, “Modified Differential Evolution based Congestion Management in Deregulatory Power environment”, Michael Faraday IET India Summit-2012, (MFIIS-12) 25th Nov, 2012 , Kolkata. • Biswas (Raha) S, Chakraborty N, “Reactive Power Generation Minimization Aspect in Deregulatory Power Scenerio Using Particle Swarm Optimization Technique”, In proceedings of International Conference on Energy, Automation and Signal (ICEAS 2011), Dec, 2011, IEEE, Bhubaneswar. • Raha S, Som T, Chakraborty N, Constriction Factor Based Particle Swarm Optimization Applied to Reactive Power Dispatch in Transmission System, In proceedings of Sustainable energy & intelligent System (SEISCON 2011), July, 2011, 2: 335-339, IET, Chennai. • Raha S, Som T, Chakraborty N., Exploration of Simulated Annealing Technique in Reactive Power Dispatch Domain, In proceedings of National conference on Recent Developments in Electrical Engineering, NCRDEE (2011), 2011, 92-97, Jalpaiguri, WB.

5. Contribution of the Work • The major contributions of the work are as: • This work is focused to solve the restructured RPD problem characterised by BPTs and MPTs. • The dynamic voltage limit crossover is solved here by integrating one of the promising technology namely SMES and combination of capacitor-SMES as hybrid advanced var compensators. • The real power loss is minimised • The economics of the combined capacitor-SMES based var compensation is determined. • This is added to the fundamental global welfare which showed improvement. • In this context, bidding of the market participants are planned such a way that Pareto efficient transactions are achieved. This will further help to provide maximum economic benefit to the system under consideration. • This work is experimented considering medium and larger IEEE standard bus systems. Meanwhile, a 12-hour variable power transactions in an interconnected network is also considered to derive the importance of Pareto efficient power transactions in a competitive power market. Moreover, a variable day ahead inter-regional grid of Indian utility of 62-bus systems are also considered to solve the proposed problem with few complexities likely the power mismatch during the power transactions and respective spot pricing. • The optimal sitting and sizing of the hybrid var compensations are obtained using DERL and CSA techniques by settling their optimal parameters suitably. • Therefore, the contribution of the work indicates a positive step towards the economic and promising solutions in the deregulated power scenario while solving the RPD problem by suitable meta-heuristics.

6. Novelty of the Work • Determination of Pareto efficient global welfare during the bilateral and multilateral power transactions incorporating economics of the var compensators. • It helped minimising the Power Loss and thereby reduced the Environmental Degradation

7. Points at a glance • Reactive power compensations • Reactive power dispatch (RPD) • RPD considering deregulated power scenarios • Dynamic voltage limit crossover • Economics of the var compensations • Pareto efficient global welfare analysis • Optimal allocations of the advance hybrid var compensations • Choice of different Meta-heuristics methods • Simulation studies • Simulation results • Conclusion • Acknowledgement • References

8. Reactive Power Compensations and Reactive Power Dispatch (RPD) • The reactive power compensations or var compensations are mostly required to improve the power factor and voltage profile of the power network. It helps to reduce real power losses. • The minimisations of real power losses with voltage stability i.e., the reactive power dispatch (RPD) issues can be solved by var compensations. • The var compensations are initiated by controlling the (i) generator bus voltages (ii) transformer tap-settings and other sources of reactive power such as (iii) capacitor banks while satisfying a number of equality and inequality constraints. • Besides the capacitive var compensators, few advanced dynamic var compensating devices are (iv) synchronous condensers, (v) flexible AC transmission devices (FACTs), (vi) energy storage systems and some of their hybrid forms. • This provides better system voltage control, resulting in an improved voltage profile, system security, power transfer capability and overall system operation.

9. Reactive Power Optimisation (RPO)

10. Mathematical Modelling of the Reactive Power Dispatch • Mathematical Modelling of the Reactive Power Dispatch; • It is tuned into the following expression as; • Additionally, the voltage security of the network is measured by cumulating the load bus-voltage deviation (Vdev). It is expressed as;

11. Different Constraints for RPD • Equality Constraint for RPD: • Inequality Constraint for RPD: • Generation Constraints: • Transformer Constraints: • Security Constraints: • Shunt Var Constraints: • SMES Var Constraints:

12. RPD in Deregulated Power Scenarios • The deregulated power scenario improves the efficiency and quality of service at the cheapest rate compared to monopoly power system. • Now, Power transactions are one of the very important aspects of deregulated power markets which are handled by several mechanisms. • Amongst them Bilateral/Multilateral Trading are quite popular. In the Bilateral/Multilateral Trading, the transactions take place between multi-seller/multi-buyer systems, individual buyers and sellers under a self-bargaining or private communication in the surveillance of ISO in an open access model. • In this market model, both the buyers and sellers are well connected through energy auction phenomena. • Now, due to the rapid Power transactions, the problem of dynamic voltage limit crossover becomes significant. • This also generate increasing line current flow with higher power losses. • Therefore, the RPD analysis involving power transactions needs an extensive care in a deregulated environment. • Economics, global welfare, power mismatch • Soft computing techniques

13. RPD Problem with Bilateral Power Transactions • Equality Constraints • Inequality Constraints • Generation Constraints: • Transformer Constraints: • Security Constraints: • Var constraints: Mathematically RPD involving BPTs:

14. RPD Problem with Multilateral Power Transactions • Equality Constraints Mathematically RPD involving MPTs:

15. Inequality Constraints for RPD with MPTs • Generation Cconstraints: • Transformer Constraints: • Security Constraints: • Capacitor Var Constraints: • TCSC Var Constraints: • SMES Var Constraint:

16. Dynamic Voltage Limit Crossover • The Dynamic voltage Limit Crossover handling: • Var compensations by singular compensators as capacitor, synchronous condensers, TCSC and SMES • Combinations of the capacitors with synchronous condensers and SMES respectively Causes of Dynamic Voltage Limit Crossover: Rapid Power Transactions without sufficient varcompensators such as 12-h variable power transactions, Day ahead power trading etc. When these factors are more than 1, Dynamic voltage Limit Crossover is indicated Representations of Dynamic Voltage Limit Crossover: The dynamic voltage limit crossover is expressed by two factors namely the Current Enhancement Factor (CEFij) and Power Loss Enhancement Factors (PLEFij).

17. Economics of the Var Compensations • Economics of the var compensators such as capacitors, SC, TCSC, SMES and some of their hybrid applications are represented here as:

18. Global Welfare Analysis Improved Global Welfare including the economics of the var compensators: For capacitors: For synchronous condensers (SC): For TCSC : For SMES: For capacitors+SC: For capacitors+SMES: • Optimal double auction transactions : • The fundamental global welfare (GW): • The global welfare is inherently dependent on the market clearing in terms of market equilibrium point (MEP), market clearing price (MCP) and the market clearing volume (MCV). • Pareto efficiency • Spot Pricing & balancing Costs • The fundamental global welfare (GW): • The Global Welfare are improved more while incorporating the economics of the var Compensation as reduced merchandising surplus

19. Factors to influence the Global Welfare Off Peak and Peak Hour Operations Power Mismatch In real market, neither party can reliably satisfy its contractual obligations with perfect accuracy due to major reasons. These introduce gaps between load and generation in the real time deregulated power scenario. This gap is termed as power mismatch or power imbalances which are managed in terms of spot market. The spot market provides a mechanism for balancing load and generation. Besides the technical considerations such as balance between the load and generations, the spot market must operate in an economically efficient manner while influencing the global welfare. • Off-peak hours for electrical networks referred to lower, discounted electricity price based durations. • The residential and industrial loads requirements are found less like the night and /or weekends. • Hourwise these are varied in between 8h-12h depending upon location and the nature of load. • Now the peak hours of electrical networks are the time periods when the load demand is significantly higher than the average demand. • Loss minimizations with dynamic voltage limit crossover issues for any operations likely 12-h variable power transactions are majorly dependent on the off-peak and peak hour operations of the considered grid.

20. Choice of the Appropriate Soft-Computing Techniques for Var Compensations • The first attempt was taken to solve RPD by the Simulated Annealing (SA). • Although the proposed method obtained the global optimum results, it is limited by few constraints such as no population space. • Probabilities of generating new solutions are quite less for SA. • Secondly, the Particle Swarm Optimization (PSO) as Swarm Intelligence has been frequently applied to solve the fundamental RPD problem. • Premature convergence problem. • This issue is handled to some extent by incorporating constriction factor however further modifications are required to achieve desired results for solving the restructured RPD problem. • In this regards, one of the Evolutionary Computation technique namely Differential Evolution (DE) was considered to solve the proposed problem. • The slow convergence problem at global optima [231]. • To overcome the drawbacks of the fundamental DE, Kaelo et.al., proposed two modifications namely differential evolution for localisation around the best vectors (DELB) and differential evolution with random localization (DERL). • DERL showed Fast global convergence with higher population. • DERL consumes higher computational time. • To overcome this problem, one optimisations technique based on Swarm Intelligence but being advanced meta-heuristics namely Cuckoo Search Algorithm (CSA) has been observed to derive desired results with less computational time for a fixed parameters.

21. Simulated Annealing Technique • First Proposed: In 1953 by Metropolis • First Approach to OPF: Kirkpatrick, Gelatt and Vecchi proposed a new solution criterion named Simulated Annealing Technique in 1983 • Origin: The annealing process of liquids to freeze or metals and glass to crystallize • Advantages: • It can escape from local minima. • SA has a very simple coding and easy annealing logic formation though to schedule cooling criteria is pretty hard.

22. Simulated Annealing Algorithm Start A B Initialize one set of solution via random number generation, Initial Temperature, Final Temperature yes Is NOF better? No Determine objective function with initialized solution Generate a random number in the 0-1 range Is Metropolis criteria Satisfy? No Define cooling schedule B Yes Determine another new set of solution and corresponding objective function with the new set of solution A Accept the new Solution Is Final Temperature reached? Difference between the new set of objective function (NOF) with initial objective function(IOF) is calculated and it is termed as change in energy level. No End Yes

23. Constriction factor based Particle Swarm Optimization (Cf-PSO) Genesis of PSO • Swarm Intelligence (SI) • SI relates the social behavior of organisms living in colonies. Origin of PSO • Inspiration from bird flocking and fish schooling James Kennedy and R. C. Eberhart initiated this approach in 1995 Constriction factor: Eberhart and Shi first proposed the term. Importance: • This value helped to control velocity dynamism with respect to fast change in position. • Therefore a steady and stable convergence was obtained.

24. Particle Swarm Optimization A Start B Initialize position and velocity with certain population, Local Best and Global Best Position No Is NOF better? Yes Determine objective function with initialized position and velocity, corresponding Local Best and then Global best value is stored Accept the new Solution and Local Best value and Global Best value is calculated Iteration is stared B Is Final Iteration reached? No The velocity and the position will be updated . A Yes With the updated velocity and position new objective transfer function (NOF) is calculated corresponding Local Best value and Global Best value is calculated . End

25. Differential Evolution for localisation around the best vectors (DELB) Algorithm Start Initialize parameters Mutation Crossover Localization around the best vector, i.e. Tuned Crossover Selection End

26. Differential Evolution with Random Localization (DERL) • Disadvantages of DELB method: Computational time required more. • The proposed modified DE technique i.e., differential evolution with random localization (DERL) method introduces tournament best vector selection step after the initialization step of fundamental DE with variable scaling factor which helps to explore the search space in an efficient manner. • The DERL technique comprises of five steps as: • Initialization • Tournament best value selection • Mutation • Crossover • Selection

27. DERL implemented RPD problem • Step 1: Initializationstep generate the target vector (x0) using the uniform probability distribution function. The target vectors are x0= [VG, t, QC, QSMES] • Step 2: In the step, tournament best vector (xtb) is generated amongst the entire population pool by evaluating the fitness function. • Step 3: With the tournament best vector, mutant vector (vij) is formulated as the summation of the base vector (xtb) and weighted difference of the two randomly chosen vectors from the entire population pool. • The mutant vector is given as: where fm is selected randomly and r2, r3 are the unequal randomly chosen numbers. Contd…

28. DERL implemented RPD problem • Step 4: In the crossover step new offspring or trial vector is generated either from the target vector or mutant vector depending upon the crossover factor (CR). • Trial Vector (yij) is shown as: • Step 5: In the selection stage, efficient offspring among the target vector and the trial vector are chosen depending upon their fitness value. The offspring which provides better solution is considered as fitness vector for the next generation. • Thus, DERL based operating cycle will be continued until the maximum generation (Genmax) number has obtained.

29. Cuckoo Search Algorithm • Being inspired by the obligate brood parasitism of some cuckoo species, Yang and Deb proposed cuckoo search algorithm in 2009. • The highlighting feature of the algorithm is its simplicity in coding and parameter setting. • Here, Lévy flights which is a random walk by its heavy step length, is incorporated to search the population space. • Working Steps of CSA: • Parameter Initialisation • Generation of Cuckoo • Replacement • Generation of new nest • Termination • Now, the CSA implemented RPD problem is elaborated suitably by a flowchart.

30. Steps of CSA implemented RPD • Step 1- Parameter Initialization: In this step of CSA algorithm number of host nests (n) as population of cuckoo nests, iteration counter (itermax), probability of discarding cuckoo’s egg by the host bird as are initialized using probability density function. The vectors of the proposed problem are presented as: where d is the dimension of the vector. With this, fitness function i.e., PLOSS is solved. The nest corresponding to best fitness value is termed as Gbest. • Step 2 - Generation of Cuckoo: In the second step new sets of vector as cuckoo are generated by Lévyflight.

31. Steps of CSA implemented RPD Contd.. • The new vectors are obtained by few equations as presented by (29). • where α>0, rand, rand1, rand2 are normally distributed stochastic variable. Moreover, is the distribution factor having a value of and is the distribution function. With this new sets of solution, PLOSS is again solved. • Step 3 - Replacement: Here, the new solution and old solution based fitness functions are comparatively analyzed. The better solution ( ) is accepted for the next iteration.

32. Steps of CSA implemented RPD Contd.. • Step 4 - Generation of New Nest: Now, abundant of worse nests are required to consider here since cuckoo birds are considered here. Based on the probability factor (pa), new solution ( ) is developed as Here, K is the revised coefficient set and can be found by Moreover, is obtained utilising the following equ • where, and are the random perturbations vector from the revised population space. With the revised vectors, the fitness function (power loss) is re-calculated.

33. Steps of CSA implemented RPD Contd.. • Step 5- Termination: Until the stopping criterion is met, the CSA based optimization process will be continued to receive the optimum solution satisfied by upper and lower constraint limit. In this work the terminating condition is set as reaching to the maximum iteration number.

34. Cuckoo Search Algorithm A A

35. Simulation Studies • Case Study 1: Initially, fundamental RPD problem including the voltage security and reactive power generation minimisation issues are solvedby controlling generator bus voltages, transformer tap settings and shunt capacitor placement using different meta-heuristics. To obtain improved response, the different advanced var compensating devices such as FACTs, SMES and hybrid applications with capacitors are integrated. • Case Study 2: RPD withthe bilateral power transactions are occurring frequently. Dynamic voltage limit crossover occurs. The increasing voltage drop enhances the line current as well as power losses leading to network congestion. Therefore, capacitors and few advanced varcompensators likely synchronous condensers (SC), SMES and some of their combinations with capacitors are incorporated to handle the situations. Moreover, economics of the var compensations and its impact on Pareto efficient global welfare is determined. Planned bidding considering double auction power transactions are applied. • Case Study 3: Similar with case 2, the restructured RPD considering multilateral power transactions with power mismatch is solved as case 3. Further, the dynamic voltage stability analysis, spot pricing based global welfare including the economics of the advanced varcompensations are considered. As var compensators capacitors, TCSCs, SMES and some of their combinations with capacitors.

36. Simulation Result & Discussion • Programming Platform- MATLAB 7.1 • Test Systems 1- IEEE 14 • Test Systems 2- IEEE 30 • Test Systems 3-IEEE 57 • Test Systems 4-IEEE 118 • Test Systems 5- Real time Indian scenario with 62 bus systems. • Optimisation Methods: SA Cf-PSO DELB DERL CSA

37. Result Analysis for Case Study-1

38. Result Analysis for Case Study-2 • First Case: Economic Reactive Power Dispatch and Dynamic Voltage Limit Crossover Analysis: • In this work, the RPD issue with different case studies was considered involving bilateral power transaction (BPT) by Cuckoo Search Algorithm (CSA) based optimisations. Initially, the proposed problem was optimised by controlling Vg and t with unconstrained security constraints. • The proposed problem was revisited by different var compensators such as shunt capacitors, synchronous condensers (QSC), SMES (QSMES) and some of their combinations with other controlled variables as Vg and t with constrained security constraints one by one. • Here, IEEE 118-bus system was considered as test system 4 where 546 MW of power was traded by six participants of the bilateral power transactions. • The optimal parameters for the proposed CSA technique was chosen as host nests (n) = 25, maximum number of iteration=150 and pa=0.25 considering 100 runs.

39. Case Study 2:-First Case; Part 1: Loss Minimisations • CSA based RPD was initially solved by optimizing Vg and t without considering any var compensating devices as case 1. • Case 2: 12 Capacitor as var compensator • Case 3: 3 Synchronous Condenser as var compensator • Case 4: 7 Capacitor - 2 Synchronous Condenser as hybrid var compensator • Case 5: 10 SMES as var compensator • Case 6: 7 Capacitor- 5 SMES as hybrid var compensator • It showed that during the 150 iterations, there were several local optimum points till the 90th iteration where the PLOSS might converge. But the presence of Lévy flight due to its heavy step length distribution prevented the local convergence by exploring the search space extensively. This further helped PLOSS to converge at the global minima. Figure 1.The power loss optimization curves for the case 1- case 6 Table 1. Six cases based PLOSS and % PLOSS during the bilateral power transaction

40. Case Study 2:- First Case; Part 1: Dynamic Voltage Limit Crossover Analysis contd.. Table 2. Bus voltage profile (V) of the distinguished buses during the bilateral Transaction • The security constraints of the network was found to fluctuate near the boundary value for case 1. • Even in the three buses ((j_enhancedth) namely 9th, 30th and 37th, the voltages were observed to violate the boundary value of 0.95p.u. to 1.10 p.u which therefore influenced the other associated buses (jth) with limit crossover. • After var compensations, the specified lines comprising of V30 and V26 were found here very close to each other particularly for case 4-6. • Dynamic voltage limit crossover issue majorly in terms of enhanced line current flow and power losses for the eleven lines are found to solve.

41. Case Study 2:-First Case; Part 1: Dynamic Voltage Limit Crossover Analysis • In this direction, the factors CEFij and PLEFij were plotted in Figure 2 and Figure 3 respectively to indicate that out of eleven lines, eight lines based CEFij and PLEFij were found between the 1.08 to 1.52 and 1.18 to 2.32 respectively. • Amongst all the voltage deviated lines, the 30th-26th line showed highest dynamic voltage limit crossover issues as CEFij and PLEFij as 1.52 and 2.32 respectively due to the higher voltage deviation of the 30th bus. Figure 2. Congestion projection in terms of CEFij for the case 1- case 6 Table 3 Dynamic voltage stability for different var compensators Figure 3. Congestion projection in terms of PLEFijfor thecase 1- case 6

42. Case Study 2:-First Case; Part 2 Economics of var-compensation: Table 4. Economics of the different var -compensating devices The HICSCwas obtained 9 times higher than the HICCapacitor, although the case 3 based incentive returns had found 1.34 times better compared to the case 2. The incentive returns for case 4 was obtained almost 2.088 times more than the case 2 TheNMBSMES+Capacitor was found 3.464, 3.143, 1.876 and 1.825 times more than the case 2, case 3, case 4, and case 5 respectively Case 6 based investment cost (HICCapacitor+SMES) of the capacitor-SMES combinations was determined. This cost is certainly 7.60 times more than the HICCapacitor and 1.19, 1.30, 1.80 times less compared to HICSC, HICCapacitor+SC, HICSMES respectively. HICCapacitor+SCwas found 10 times more than the HICCapacitor however the NMBCapacitor+SCwas obtained 1.67 times better compared to the case 2 based operations.

43. Case Study 2:-First Case; Part 3 • Global welfare analysis of the bilateral power transactions: • The matching point of the curves as shown in Figure 4, provided MCP as 3100 $/ MW h and respective MCV as 600 MW. • For case 1, the net profit of the suppliers, the net surplus of the consumers and the fundamental global welfare of the system were obtained as 822285 $/ h, 620110 $/ h and 1442395 $/h respectively. • Now, the contribution of var compensation which was referred to as reduced congestion rent were cumulated to the fundamental global welfare. This further helped to improve fundamental global welfare. • Hence the proposed bilateral transaction could not be termed as the Pareto efficient transaction • Introduced the dead weight losses of 5400 $/ h. • This indicated economically profitable situation of the power market. Figure 4. Matching of supplier and customer aggregated curve Table 6 Net profit, surplus of the suppliers and consumers Table 5 Final bids for different market participants

44. Case Study 2:-First Case; Part 3 contd.. Here, 2nd and 3rd supplier and 3rd consumer were deriving 20 % each and 29 % of the total global welfare respectively due to their planned bidding. Table 7 Individual profit, surplus of the suppliers and consumers Figure 5. Percent of welfare sharing by the suppliers and consumers of the multilateral power transactions

45. Case Study 2:-Second Case • Pareto Efficient Double Auction Bilateral Power Transactions for Economic Reactive Power Dispatch: • In this work, the economic RPD issue in an inter-regional deregulated power scenario with 12-h variable bilateral power transactions considering the IEEE 57-bus systems was solved by DERL optimisation method. • The optimal parameters of the DERL method was found as Np=30, , Cr= 0.8, Genmax=100 after 100 trial runs. Here, the participant buses of the 12-h variable transactions were optimally chosen such a way that the total power losses are minimum. • Further, the amounts of power by each participant were deceided by planned biding to achieve higher economic benefit. Here, the 8th and 9th buses were considered as the power producers while 12th and 8th buses were found as power consumers. • In this trading, it was assumed to have zero power mismatches. Figure 6. Variable bilateral power transaction schedule

46. Case Study 2:-Second Case; Part 1: Loss Minimizations • From the Table 8 and Figure 7 it could be stated that the PLOSS were increasing with the increase in transacted amount of power and minimised according to the decreasing power transactions. • Since, the 12-h variable traded power were following a non-linearity, the variations of PLOSS was maintaining a non-linear asymmetry during the 12-h of variable power transactions. • A comprehensive explanation of such PLOSS characteristics could be generated by comparing 3rd and 12th, 4th and 11th, 5th and 10th, 7th and 9th hour based data (PLOSS) in Table 8 as well as Figure 7. Figure 7. Power loss variation for 12-h variable bilateral transactions Table 8. Power loss (PLOSS) involving 12-h variable double auction bilateral power transaction

47. Case Study 2:-Second Case; Part 1: Dynamic Voltage Limit Crossover Analysis contd.. • Dynamic voltage limit crossover was found for case 1 when there were no varcompensators. • The voltage profile lies in between 0.95 pu - 1.1199 pu. This caused increasing voltage drops which further increased the line current flow followed by huge power losses. • Three buses likely 25th, 30th and 31st were found to be disturbed at almost every hour of power trading. • The hourly average critical voltage was obtained 1.11895 p.u. • This situation was initially handled by incorporating shunt capacitors as varcompensators. • The voltage profile was obtained within 0.95 -1.10 p.u. with reduced losses as described earlier. • Here, the case 2 based bus voltages which generated maximum voltage limit violations in case 1, were found to be 0.9624-1.0956 p.u. • This case 3 on combined varcompensators as capacitor-SMES was further considered. • This provided the voltage profile 0.975-1.095 p.u. • The most deviated buses were found 0.9907 p.u. to 1.0836 p.u. Table 9. Dynamic voltage profile (p.u.) for 12-h variable double auction bilateral power transaction

48. Case Study 2:-Second Case; Part 2 Economics due to Var Compensation: Table 10. Capacitive var compensation based economic analysis Table 11. Capacitor-SMES based var compensation economic analysis • Case 3 based var compensation provided better (minimum 1.5 times more) economic response over case 2. • Out of twelve transactions, the 2nd and 7th hour transactions based monetary benefit ratio were found nearly 2.5. • Amongst them the 7th hour transaction showed the ratio as 2.49 which is maximum • Further it was found that 1st, 4th, 6th, 8th and 11th hour based benefit ratio were nearly 2 which also demonstrated the improved performance. Figure 8. Economic analysis in terms of net monetary benefit ratio between NMBCapacitor+SMES to NMBCapacitor

49. Case Study 2:- Second Case; Part 3 Table 12. Final Bids of the market participants for 12-h variable bilateral power transactions for different cases • Pareto efficient transactions based on bidding: • When the ∆price were reducing, the market equilibrium point (MEP) was moving towards the Pareto efficiency of the power market. • Here, the first four hours and 11th to 12th hourdemonstrated a large value of the ∆price. • The 5th-10th hour except the 8th hour has been generated a small ∆price compared to the other hours. • The hours where the ∆price is very small, are mostly found as the Pareto efficient transactions. • Finally, it has been observed that out of the 12-h variable transactions, three transactions (6th, 7th and 9th hour) satisfied the Pareto efficient criteria. i.e., had reconciled exactly at the MEP which indicated to have the Pareto efficiency at the specified hours. Table 13. Hour wise market clearing representation Figure 9. 12-h variable bilateral power transaction w.r.t MCV

50. Case Study 2:-Second Case; Part 3 contd.. Market clearing at 1st hour Market clearing at 2nd hour Market clearing at 3rd hour Market clearing at 4th hour Market clearing at 5th hour Market clearing at 8th hour Market clearing at 6th hour Market clearing at 7th hour Market clearing at 11th hour Market clearing at 9th hour Market clearing at 10th hour Market clearing at 12th hour