## Description

### Introduction

Congestion management is necessary to tackle load demand in the power system. In our work, we have done this by using PeSOA (penguin search optimization algorithm) optimization for IEEE 30 bus system. The IEEE 30 bus system consists of 6 generators buses, 24 load buses, and 41 transmission lines. The real load of the system is 283.4MW and reactive load is 126.2MVAR. The load bus voltages are maintained between 0.9 and 1.1 p.u. Price bids are submitted by Generating Companies (Gencos) for test system according to which rescheduling of generators occur and the specification of the generators of the bus system are given in Table 1.

Gen No | Min P | Max P | Min Q | Max Q | P^{c} | C^{u} | C^{d} | Max MVA | Bus no |

1 | 0 | 360.2 | -30 | 100 | 0 | 22 | 18 | 250 | 1 |

2 | 20 | 140 | -30 | 100 | 140 | 21 | 19 | 100 | 2 |

3 | 15 | 100 | -30 | 100 | 40 | 42 | 38 | 80 | 5 |

4 | 10 | 100 | -30 | 100 | 40 | 43 | 37 | 60 | 8 |

5 | 10 | 100 | -30 | 100 | 24 | 43 | 35 | 50 | 11 |

6 | 12 | 100 | -30 | 100 | 24 | 41 | 39 | 60 | 13 |

### Add Congestion in Network

To add congestion in the network we intentionally added Outage of the line 4-6 and increase of load at bus 8 to 23 by 50%. It helps us to demonstrate the congestion management scheme in the system. After adding congestion newton raphson load flow analysis is done and power flow in branches is shown in table 5.2 for both cases i.e. with congestion and compensated congestion (discussed ahead) along with the maximum limits of power flow in each line. If any line violates this limit then congestion is considered in that line. We have considered the particle swarm optimization (PSO) for comparison with PeSOA since PeSOA is developed over PSO platform. Table 2 shows the congestion managed line flows for both optimization cases.

From Bus | To Bus | Congested Line Flow | Congestion managed line flow by PSO | Congestion managed line flow by PeSOA | Limit of line flow |

1 | 2 | 216.081362873671 | 14.0998872357903 | 43.1251184635087 | 130 |

1 | 3 | 109.077197041038 | -11.1337740266368 | 7.26421458132521 | 130 |

2 | 4 | 53.2348933397253 | -16.9664714160804 | -5.61665075317485 | 65 |

3 | 4 | 101.800755740037 | -13.7072469327290 | 4.77826121244994 | 130 |

2 | 5 | 91.8686679637457 | 53.1605219987248 | 58.5398422400552 | 130 |

2 | 6 | 81.2878597219604 | -3.94938874631174 | 8.13297634034099 | 65 |

4 | 6 | 119.290127893008 | 53.8427516982375 | 57.9652250595165 | 90 |

5 | 7 | -6.14287015731922 | -42.2881477067936 | -37.1653122046352 | 70 |

6 | 7 | 29.2347524592928 | 67.2026095814695 | 61.6772996595665 | 130 |

6 | 8 | 43.1017428686323 | 26.3351975621824 | 39.9431150833226 | 32 |

6 | 9 | 38.7320023061221 | -44.4404166891601 | -49.1619207024350 | 65 |

6 | 10 | 22.0104270586151 | -23.3265321157728 | -16.4052826587808 | 32 |

9 | 11 | 1.38777878078145e-14 | -10.5124127822219 | -59.5336418647750 | 65 |

9 | 10 | 38.7320023061220 | -33.9280039069457 | 10.3717211623418 | 65 |

4 | 12 | 65.0005353366148 | -74.4600479429099 | -47.1653052640778 | 65 |

12 | 13 | 2.42861286636753e-14 | -72.9371937837922 | -49.6722203825242 | 65 |

12 | 14 | 11.4852554010754 | 11.3238052366744 | 13.0755391852549 | 32 |

12 | 15 | 25.7057777317269 | 32.2646708077852 | 32.5025738282765 | 32 |

12 | 16 | 11.0095022038124 | 18.1979794405344 | 15.4162141131796 | 16 |

14 | 15 | 2.02852758293690 | 4.98359303540007 | 3.58692915932430 | 16 |

16 | 17 | 5.64083589146195 | 14.4209065425481 | 9.96420049743881 | 16 |

15 | 18 | 9.42946573229076 | 10.9798706561239 | 11.1593848070714 | 16 |

18 | 19 | 4.53331279054969 | 7.66039982864500 | 6.23453593856443 | 16 |

19 | 20 | -9.73026595797842 | -1.87534840020770 | -8.03904748922263 | 16 |

10 | 20 | 13.2318330379178 | 4.11872638287960 | 11.4942208087037 | 32 |

10 | 17 | 7.91110569482721 | -5.23881438450684 | 3.62458303936382 | 32 |

10 | 21 | 25.4368956120822 | 15.5078759568119 | 27.7769751217543 | 32 |

10 | 22 | 5.46259501991034 | 12.8674369510809 | 12.9791360787767 | 32 |

21 | 23 | -1.07652892890491 | -2.12598352813885 | 1.23335093866640 | 32 |

15 | 23 | 5.55792955454041 | 17.4017168613355 | 11.9721217817741 | 32 |

22 | 24 | 5.43229403185675 | 12.7563417770619 | 12.8667100481899 | 16 |

23 | 24 | -0.357731460180524 | 11.7935684816078 | 8.27270304570332 | 16 |

24 | 25 | -3.67804323821013 | 15.4964522838742 | 12.1744529735436 | 16 |

25 | 26 | 3.54621773645282 | 3.54582147782035 | 3.54531208502573 | 16 |

25 | 27 | -7.26706872934651 | 11.4806092529309 | 8.34144587611262 | 16 |

28 | 27 | 20.6168206989131 | 2.01348541513320 | 5.06136613635792 | 16 |

27 | 29 | 6.19422335630399 | 6.19398243168133 | 6.19239665058304 | 65 |

27 | 30 | 7.09746262965867 | 7.09715514397189 | 7.09513120320249 | 16 |

29 | 30 | 3.70502427797168 | 3.70495049032661 | 3.70446488546962 | 16 |

8 | 28 | -2.14282673247694 | -3.81172144200995 | -5.28511213610207 | 26 |

6 | 28 | 22.8574029633774 | 5.85150819870413 | 10.3884430003831 | 32 |

In this case, a line such as 1-2, 2-6, 4-6, 6-8, 4-12 and 28-27 get overloaded as a consequence of outage of line 4-6. The flow limits in those lines are violating. Net power violation is found to be 187.37 MW as given in table 3. For a secure system, the power flow in the transmission line should not exceed their permissible limit. Hence suitable corrective action should be carried out to alleviate the above said overloads.

Table 3: Simulated Case

Type of Contingency | CongestedÂ Lines | Line Power (MW) | % Overload | Total Power Violation (%) |

Outage of line 4-6 | 1-2 | 216.081362873671 | 66.22 | 187.37 |

2-6 | 81.2878597219604 | 25.06 | ||

4-6 | 119.290127893008 | 32.54 | ||

6-8 | 43.1017428686323 | 34.69 | ||

4-12 | 65.0005353366148 | 8.2359e-04 | ||

28-27 | 20.6168206989131 | 28.86 |

### Sensitivity Analysis for Congested Bus Detection

To take out the potential buses sensitivity analysis is done and we have picked up the top 4 highest sensitive buses on which renewable energy source will be inserted to provide extra power to mitigate congestion. These are 2,6,27 and 25. On these buses, a renewable energy source will be added to get more active power in the system. To know more about sensitivity analysis, we recommend reading our article

Optimal Placement of Distribution Generators in IEEE 14 Bus System

### Distribution Generators Insertion

Here in this work, only active power insertion in the system is considered, so renewable energy source like a solar cell, wind plant which generates active power can be introduced in our system to avoid congestion. PeSOA optimization is used to decide the optimal size of the renewable energy source placed on the potential buses. The objective function is a combination of the total cost incurred in congestion management and penalty function based on the distance of a solution from the feasible region, so it should be minimized.

#### Objective Function

The objective function for power congestion management to get the desired minimum rescheduled cost is

objf=F+Pwhere F=fitness function to regulate the power congestion management cost, and

P = a penalty function based on distance of a solution from the feasible region

The cost of placing the DG on the buses is defined as

FÂ = âˆ‘g

_{â‚¬Ng}(C^{u}_{g}Ã—âˆ†P^{u}Gg +C^{d}gÃ—âˆ†P^{d}Gg)where

F=total cost incurred for congestion management in ($/hr)

âˆ†P

^{u}GgÂ = active power increment of generator g due to congestion management (MW)âˆ†P

^{d}Gg _=Â active power decrement of generator g due to congestion management (MW)C

^{u}_{g}Â =Â Â price bids submitted by generator g to increase its pool power for congestion management ($/MWhr)C

^{d}gÂ = price bids submitted by generator g to decrease its pool power for congestion management ($/MWhr)

This cost of congestion management is constrained by many equality and inequality constraints

##### Equality Constraints

P

_{Gi}â€“P_{Di}= V_{i}âˆ‘N_{j}^{i}Vj (G_{ij}cosÎ¸_{ij}â€“ B_{ij}sinÎ¸_{ij})Q

_{Gi}â€“Q_{Di}= V_{i}âˆ‘N_{j}^{i}Vj (G_{ij}sinsÎ¸_{ij}â€“ B_{ij}cosÎ¸_{ij})P

_{Gg}Â = P^{C}_{Gg }+ âˆ†P^{u}_{Gg}– âˆ†P^{d}_{GgÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â }P

_{DJ}= P^{C}_{DJÂ Â Â Â Â Â Â Â }

NB = no. of buses

P

_{Gi}= generated real power at bus i (MW)P

_{Di}Â = real load power at bus i (MW)Q

_{Gi}= generated reactive power at bus i (MVar)Q

_{Di}= reactive load power at bus i (MVar)V

_{i}= voltage at bus i (Volt)G

_{ij }= conductance of line between i & j (mho)B

_{ij}= suseptance of line between i & j (siemens)Î¸

_{ij }= admittance angle of line between buses i and j (radian)k = number of participating generator

P

_{Gg}= final real power generation of generator g (MW)P

^{C}= active power produced by generator g as determined by the market clearing price (MW)_{Gg}P

_{DJ}= final real power consumption at load bus j (MW)P

^{C}_{DJÂ }= active power consumed by load bus j as determined by the market clearing price (MW)

The equality constraints represent the power flow equation. The constraints maintain the generated power at a bus satisfying both the load and the loss successfully for both real and reactive power.

##### Inequality Constraints

P

^{min}_{Gg}â‰¤ P_{Gg}â‰¤ P^{max}_{Gg}g â‚¬ NgÂ Â Â Â Â Â Â Â

P

^{min}_{Gg}Â = minimum real power limit of generator (MW)P

^{max}_{Gg}Â = maximum real power limit of generator (MW)P

_{Gg}Â = final real power generation of generator (MW)

The generated real power of the generator is within the upper and lower limit of the generator

Q

^{min}_{Gg}â‰¤ Q_{Gg}â‰¤ Q^{max}_{Gg}g â‚¬ NgÂ ÂQ

^{min}_{Gg}Â = minimum reactive power limit of generator (MVar)Q

^{max}_{Gg}Â Â = maximum reactive power limit of generator (MVar)Q

_{Gg}=final reactive power generation of generator (MVar)

The generated reactive power of the generator is within the upper and lower limit of the generator

Pg â€“ Pâ‰¤Â^{min}_{g }= âˆ†P^{min}_{g}Ââˆ†PgÂ Ââ‰¤Ââˆ†P^{max}_{g}Â = P^{max}_{g}â€“PgÂ Â Â

The upper and lower bound of real power adjustment

Â V

_{l}^{min}â‰¤ V_{l }â‰¤Â Â V_{l}^{max}Â Â Â Â l â‚¬ N_{lÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â }V

_{l}^{min}= minimum voltage of load bus (Volt)V

_{l}^{max}Â = maximum voltage of load bus (Volt)V

_{lÂ }= voltage of load bus (Volt)N

_{l}Â = no. of load bus

This is a security constraint and provides the upper and lower voltage bound of load buses.

Â Pij â‰¤ P

_{ij}^{maxÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â }Pij = real power flow in line i-j (MW)

P

_{ij}^{maxÂ }= maximum power flow limit of line i-j (MW)

The line loading should not exceed the maximum limit.

The penalty factor *PÂ *is also formulated as:

P = pf1 âˆ‘

^{Nl}_{i=1 max }(0_{, }Pl) + pf2 âˆ‘^{NB}_{j=1 }max (0, Pv) + pf3max (0, Ps)

Pf_{1}, Pf_{2}, Pf_{3} are user-defined and P_{l}, P_{v}, P_{s} can be checked here.

#### Conclusion

The objective of this project is to minimize or alleviate power congestion of the network by the rescheduling of the active power of generators at minimum cost satisfying the operational constraints. The method proposed here using PeSOA optimization has been implemented on IEEE 30 bus system. The congestion is knowingly introduced by increasing the outage in line 2-3 for the test purpose and has been successfully managed with minimum cost and maintaining system constraints. Results of PeSOA are compared with PSO optimized results and unoptimized results. An improvement 47.38% from unoptimized results and approx 12% form PSO in total line losses are observed by PeSOA algorithm. The total change in the active power of generators is also less than PSO case and cost is also reduced.

So in a compact sense, in the deregulated market scenario this technique is acceptable both technically and economically.

Note: The performance of PeSOA might not improve than PSO in every trial. However, the optimized results are better than unoptimized.

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