DEPARTMENT OF ENGINEERING SCIENCE
ENGSCI 391: Computing Assignment Part II – 2015 (10 marks)
Figure 1 shows a simple network representation of the New Zealand electricity transmission
grid. This is an approximation of the full grid which has about 250 nodes
at which electricity is priced in the wholesale electricity market1.
Figure 1: New Zealand transmission grid model.
You must formulate and solve a model of the linear program that dispatches power
from generators at nodes of the grid in Figure 1 to consumers in this grid. The basic
form of this model is as follows.
Here fk is the power flow in MW in line k in the direction shown, and xg is the power
generated in MW by generator g. Generator g has capacity Gg MW. The flow in
each line k can be positive or negative but must lie between Kk and Kk. The net
1You can find a map of the full New Zealand grid here.
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flow into each node is "
fk where I (n) indexes arcs with heads
at node n and O (n) indexes arcs with tails at node n. The first set of constraints
holds at each node and says that the production of electricity at each node and the
net flow in must add up to the demand dn for electric power in node n. Note that
L (n) indexes the generators at node n. The objective is the total hourly cost of
generating power at the prices φg ($/MWh) offered by each generator.
代做ENGSCI 391作业、代写Matlab语言作业、Matlab编程设计作业调试
This exercise will use the data in Tables 1 and 2 (all data are in MW or $/MWh).
These very approximately represent the system data in a typical hour in June 2008
assuming full HVDC capacity2
.
Generator Node Capacity Offer Price
Table 1: Generator locations, capacities (MW), and offer prices ($/MWh).
Node Demand
Table 2: Demand at the nodes and the line capacities (MW).
2Actually most of the line capacities are guesses as they represent maximum transfers between
regions rather than the capacities of actual lines.
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1. Write some Matlab code that will build a constraint matrix for this problem.
The code should take as input vectors for φ, G, K and d, and produce matrices/vectors
A, c, and b, so that SD is in standard computational form, as
below:
The code should be able to recover the original optimal variables from the
solution to SDCF. The code should build A in blocks. So adding upper bound
constraints on variables can be done by adding a block of rows to a matrix
using:
newA=[oldA,zeros(m,n);eye(n,n),eye(n,n)];
2. Using the data in Tables 1 and 2 solve SD using your code assuming all Kk
and Gg are infinite (i.e. ignore these constraints). Check that the solution
makes sense and explain in one sentence why it is the solution you obtain.
3. Using the data in Tables 1 and 2 solve SD using your code assuming all Kk are
infinite (i.e. ignore these constraints). Check that the solution makes sense
and explain in one sentence why it is the solution you obtain.
4. Include the real Kk values and solve the problem. Present the optimal solution
in a table that shows:
(a) the generation of each generator;
(b) the flow in each transmission line;
(c) the total cost of generation;
(d) the energy price at each node (how much extra one extra MWh at node
n would cost).
5. The flows in the transmission lines must meet some loop flow constraints dictated
by Kirchhoff’s laws for DC load flow. These are as follows:
fHN + fNW = fHNP + fNPW,
fDB + fBC = 0.4 × fDC.
Add these to your model and re-solve it. Display:
(a) the generation of each generator;
(b) the flow in each transmission line;
(c) the total cost of generation;
(d) the energy price at each node.
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6. Keep the constraints added in question 5. It is known that up to 10% of power
flowing on the (HVDC) line between B and W (in either direction) is lost as
heat in transmission. In fact each MW in the first 500 MW loses 5% of the
power sent in transmission, and each MW of power flow above this loses 15%
of what is sent. (This means that if 600MW is sent then 40MW is lost so
only 560MW arrives at the other end.) Carefully reformulate the constraints
involving this line to model these losses and solve the problem again using
your code. Display:
(a) the generation of each generator;
(b) the flow in each transmission line;
(c) the total cost of generation;
(d) the energy price at each node.
What to hand in:
Hand in a listing of the Matlab code that builds the problem, and the answers to
questions 1 through 6.
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