5 Market Based TransmissionExpansionPlanning 58 Table 5.4- Characteristics of loads of IEEE 30 bus test system Bus No. Min (MW) PDF of Load (MW) Bid ($/MWhr) Unavailability 3 0 N~(160, 12) 15 0.05 5 0 N~(85, 7.5) 14 0.05 7 0 N~(50, 5) 15 0.05 8 0 N~(25, 2) 17 0.05 10 0 N~(190, 15) 20 0.05 12 0 N~(50, 4) 18 0.05 13 0 N~(20, 2) 19 0.05 14 0 N~(50, 4.5) 17 0.05 15 0 N~(50, 5) 16 0.05 16 0 N~(9, 0.5) 20 0.05 8 0 N~(35, 2) 21 0.05 19 0 N~(17, 0.5) 23 0.05 20 0 N~(60, 4.5) 17 0.05 21 0 N~(34, 2.5) 19 0.05 23 0 N~(85, 7.5) 22 0.05 24 0 N~(9, 0.6) 25 0.05 25 0 N~(9, 0.2) 25 0.05 27 0 N~(27, 2) 23 0.05 29 0 N~(35, 2.5) 24 0.05 continued till reach a zero congestion cost network, we will also have a flat price profile. Vice versa, if standard deviation of mean of LMP (or weighted standard deviation of mean of LMP) is used as planning criterion and it is tried to reduce standard deviation of mean of LMP by expansion planning, other criteria will reduce and after achieving a flat price profile we will also have zero congestion cost (see (4.2)). Planning criteria propose different paths (expansion plans) to achieve flat price profile or zero congestion cost. To determine the impacts of reduction of one criterion on the other criteria, and to determine which criterion leads to zero congestion cost and flat price profile at minimum cost or at minimum number of expansion plans, transmission expansion planning is performed eight times (stages) under different criteria. For each criterion, after determining the minimax regret plan, it is added to the network and the approach is repeated. At the first stage of planning between each two buses which have average LMP difference greater than SV=$5/MWhr a new line is suggested as transmission candidate. As new lines are added to the network, price profile becomes flatter. Therefore, number of candidates for the next planning stages decreases. In the stages that suggested candidates do not improve the selected criterion or in the stages that only a few candidates are suggested, SV is decreased to have reasonable number of candidates. To determine the effects of non-random uncertainties on the performance of market based criteria expansion planning is performed under two different assumptions: There is not any nonrandom uncertainty, and there is non-random uncertainty.
5 Market Based TransmissionExpansionPlanning 59 5.3.1 Case 1: There Is Not Any Non-random Uncertainty In this case there is only one scenario, the scenario which is shown in tables 5.3 and 5.4. Therefore, the minimax regret plan and the optimal plan are the same. Transmission planning is performed under the following market based criteria: a) b) c) σ : Standard deviation of mean of LMP (SML) µ lmp σ : Standard deviation of mean of LMP weighted with mean of µ , w= Pg lmp generation power (WG) σ : Standard deviation of mean of LMP weighted with mean of load (WD) µ , w= Pd lmp d) σ : Standard deviation of mean of LMP weighted with mean of µ , w= P + Pd e) f) lmp g sum of generation power and load (WGD) k µ : Average congestion cost (ACC) tcc k µ : Average load payment (ALP) tlp Table 5.5 shows the result of planning under SML criterion. In this table rows 1-4 show SV, number of suggested candidates (NC), optimal plan (OP), and capacity of optimal plan (COP) at different stages of planning. Rows 5-10 show the values of different market based criteria in different stages of planning if SML is used as planning criterion. Consider the first stage of planning (column 3 of table 5.5). At first stage of planning SV is $5/MWhr and 88 candidates are suggested for transmission expansion. If SML is used as planning criterion line 22-29 is the optimal expansion plan. Capacity of this line must be 60 MW in order to ensure the probability of violating its limit is less than one percent. If line 22-29 is added to the network, standard deviation of mean of LMP reduces from $2.6351/MWhr to $2.0798/MWhr and average congestion cost reduces from $2240.8/hr to $2023.6/hr. At fourth stage of planning with SV = $5/MWhr only 8 candidates are suggested. In order to avoid from losing the optimal plan, SV reduces to $4/MWhr. Tables 5.6-5.10 shows the results of planning under other market based criteria. In tables 5.5-5.10 smaller SV indicates flatter price profile since SV is reduced when enough candidates are not suggested for transmission expansion. At a constant SV, smaller number of candidates indicates flatter price profile since number of candidates is equal to number of pairs of buses which have LMP difference greater than SV. Figure 5.4 shows how SML changes in different stages of planning when SML, WG, WD,