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 46 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  1.38777878078145e14  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  2.42861286636753e14  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 12, 26, 46, 68, 412 and 2827 get overloaded as a consequence of outage of line 46. 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 46  12  216.081362873671  66.22  187.37 
26  81.2878597219604  25.06  
46  119.290127893008  32.54  
68  43.1017428686323  34.69  
412  65.0005353366148  8.2359e04  
2827  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+P
where 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}_{Gg} = active power produced by generator g as determined by the market clearing price (MW)
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 Â
Q^{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€“ P^{min}_{g }= âˆ†P^{min}_{g}Â â‰¤Â âˆ†PgÂ Â â‰¤Â âˆ†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 ij (MW)
P_{ij}^{maxÂ }= maximum power flow limit of line ij (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 userdefined 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 23 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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