Power Congestion Management in IEEE30 Bus System

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	Pc	Cu	Cd	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	Congested  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+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

F  = ∑g_€Ng (C^u_g×∆P^uGg +C^dg×∆P^dGg)

where

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

∆P^uGg  = active power increment of generator g due to congestion management (MW)

∆P^dGg _=  active power decrement of generator g due to congestion management (MW)

C^u_g  =   price bids submitted by generator g to increase its pool power for congestion management ($/MWhr)

C^dg  = 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

1. P_Gi –P_Di = V_i ∑N_jⁱ Vj (G_ijcosθ_ij – B_ijsinθ_ij)

2. Q_Gi –Q_Di = V_i ∑N_jⁱ Vj (G_ijsinsθ_ij – B_ijcosθ_ij)

3. P_Gg  = P^C_Gg + ∆P^u_Gg – ∆P^d_{Gg                  Â} 

4. P_DJ = P^C_{DJ             Â} 
   

NB = no. of buses

P_Gi = generated real power at bus i (MW)

P_Di  = 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)

θ_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_DJ  = 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 ≤ P_Gg ≤ P^max_Gg g € Ng              

P^min_Gg  = minimum real power limit of generator (MW)

P^max_Gg  = maximum real power limit of generator (MW)

P_Gg  = 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 ≤ Q_Gg ≤ Q^max_Gg g € Ng   

Q^min_Gg  = minimum reactive power limit of generator (MVar)

Q^max_Gg   = 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 – P^min_g = ∆P^min_g  ≤  ∆Pg   ≤  ∆P^max_g  = P^max_g –Pg     

The upper and lower bound of real power adjustment

 V_l^min ≤ V_l ≤   V_l^max     l € N_{l                                                                                                     Â} 

V_l^min = minimum voltage of load bus (Volt)

V_l^max  = maximum voltage of load bus (Volt)

V_l  = voltage of load bus (Volt)

N_l  = no. of load bus

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

 Pij ≤ P_ij^{max                                                                                                                                                              Â} 

Pij = real power flow in line i-j (MW)

P_ij^max  = maximum power flow limit of line i-j (MW)

The line loading should not exceed the maximum limit.

The penalty factor P is also formulated as:

P = pf1 ∑^Nl _{i=1 max} (0_, Pl) + pf2 ∑^NB_j=1 max (0, Pv) + pf3max (0, Ps)

Pf₁, Pf₂, Pf₃ 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.