As the time for delivery approaches, if the utility did not make forward subscription tenders with the buyers, customers will be driven more by the spot market. Due to the penetration of distributed generation in the spot market, spot price could be different from that in forward transaction. Trans- active Energy business model permit utilities to purchase power from these distributed generators and later sell them to customers at spot price. By purchasing power these distributed generators, utilities can meet their load demand which they fail to make tenders in forward position. Fur- thermore, utilities benefits from transport cost savings as most of these distributed generators are in location proximity to buyers. In this section, an algorithm for spot transaction optimization is proposed which calculates minimum power to be purchased from distributed generation to meet the load demand in spot market. Load in forward transaction and expected load in spot market was calculated in the previous section. The algorithm to optimize the spot market transactions and to calculate power purchased from distributed generators to maximize the utility profit and to minimize load shedding is proposed here.
3.2.1 Minimum power purchase calculations from DG
In previous section, load in forward transaction and spot market was calculated for every hour of the day. Here, the main objectives of the optimization is to purchase minimum power from the distributed generator so as to meet maximum spot market load, along with minimizing total cost of production and satisfying all system constraints. Once again an AC optimal power flow with standard Newton Raphson technique is used for optimization. The mathematics behind the proposed algorithm to optimize spot market transaction is presented below.
Minimize: (i)J = nG P i=1 Ci(PU G(i)) +Ci(QU G(i)) ×IU G(i) +S(i) + N P i=1 Ci PDG(i) ×IDG(i) (3.6) (ii)G= N X i=1 (PDG(i)) (3.7)
subject to: nG X i=1 PU G(i)×IU G(i) + N X i=1 PDG(i)×IDG(i) =PL PU Gmin(i)≤PU G(i)≤PU Gmax(i) Vmin(i)≤V(i)≤Vmax(i) ∀Fk≤Fkmax nIL ∀ nL X k=1 Fk≤PILmax where,
J = Objective function to minimize the total cost of generation
G= Objective function to minimize the total power purchased from distributed generators
PLS = Total load shedding in MW
nG = Total number of generators
N = Total number of buses
Ci(PU G(i)) = Average marginal cost ($/MW) of utility generator i
Ci(QU G(i)) = Average marginal cost for reactive power ($/MVar) of utility generator i
Ci(PDG(i)) = Average marginal cost for power ($/MVar) of distributed generator i
IU G(i) = Commitment state of Utility’s Generator unit i
IDG(i) = Commitment state of Ditributed Generator uniti
S(i) = Start-up cost of generatori
PU G(i) = MW Output of utility generatori
QU G(i) = MVar Output of utility generator i
PDG(i) = MW Output of distributed generatori
PL(i) = Total Load demand at busiincluding loss in transmission
Vmax(i) = Maximum voltage limit at busi Vmin(i) = Minimum voltage limit at busi Fk= Power flow through the transmission linek
Fkmax(p, q) = Maximum power flow limit through the transmission line k IL= Interface limit
nIL = Number of interface limits
The objective of the optimization have three main objectives, namely minimization of total cost of generation including the cost of production from utility generators and distributed generators, minimization of power purchase from distributed generators to maximize utility profit, and mini- mization of load shedding in real time. Optimization has been performed to minimize load shedding by purchase of power from distributed generators. In order to maximize utility profit, the MW power purchased from DG (PDG) should be minimum and just enough to prevent load shedding.
An algorithm is proposed to find a solution for these three broad objectives by running one main optimization program for each hour of the day with spot market load calculated from forward transaction calculations. The output of these calculations are optimal power flow solution and a map showing optimal location and amount of power to be purchased from DG. Equation 3.9 shows that load in real time is the sum of load in Forward transaction and Spot transaction.
PLSP(t) =PL(t)−PLF M(t) (3.9)
where,
PLF M(t) = Load in Forward Market at hour t PL(t) = System load expected at hour t
PLSP(t) = Load in Spot Market t
load shedding.
DG Power purchased by utility =
N
X
i=1
PDG(i)×IDG(i) (3.10)
Flow chart given by Figure 3.2 depicts the algorithm used for optimization in spot market for each operational period. Unlike the optimization for forward transaction, the program follows path for spot market where purchase of power from DG is permitted. Once the program adds the DG parameters into the case file, it enables the constraint to minimize purchase from DG. Interface mapping and limits are turned on next to restrict the flow through interfaces to a predefined value. The case file along with new objective functions are then passed to optimization block where it uses Newton Raphson technique to solve the minimization function. If there exist a solution without DG, the LP converges without including DG and satisfying all constraints. If the LP do not converge, recommitment of generating units are performed and LP process repeats with different set of units committed until LP converges. If the LP becomes exhausted due to availability of utility generation resource not sufficient to satisfy load demand, it recommits with available set of distributed generation at each bus. The objective to minimize the power from DG is addressed in the OPF block. If the LP gets exhausted even after including DG, load shedding is needed. The loadshedding function shed the load to its least possible value so that when OPF restarts, LP converges to a result. This process is repeated for next load hours until optimal power flow and generator dispatch for each load is found out. Once forward and spot transactions are over the OPF results are then passed to the next section where price of power at each hour is determined.