Incorporating Grid Expansion Calculation Algorithms in the TIMES ...

Incorporating Grid Expansion Calculation Algorithms in the TIMES model, for improved Operation under wide-scale RES Penetration IEW 2013, June Paris

G. Giannakidis, K. Tigas, C. Vournas, P. Georgilakis, A. Lehtilla, A. Kanudia, D. Dimitroulas, J. Mantzaris, N. Sakellaridis, P. Siakkis, J. Morbee presentation by Kostas Tigas

Backround

Present methodology was implemented in the context of : SERVICE CONTRACT with JRC Peten FOR THE INTEGRATION OF TIMES-BASED ENERGY SYSTEM MODELING WITH ELECTRICITY GRID MODELING 2012/S 21-033025 Slide 2

The TIMES model

TIMES model is not able to consider in detail the various non-linear aspects of a power system It includes a rather elementary approach for dispatching, transmission and non dispatchable RES generation As a result, the optimal technology mix computed by TIMES may not be optimal when considering the geographically specific transmission grid investments resulting from that technology mix

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Methodology Issues Load forecast, generation expansion and route preference are of significant importance in transmission expansion planning To find solutions within a reasonable amount of calculations the analysis can include : a simple linear flow estimation of the transmission network (e.g. DC load flow)

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Methodology Issues

To obtain an accurate least cost solution for RES penetration it is necessary to develop geographical databases with RES potential which will be connected to the TIMES model describing areas with classes of the same RES technology with different costs

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Methodology Issues

TIMES model solution will then prioritize different classes of RES investments according to their real cost which would incorporate • balancing units and storage units costs • grid expansion and connection costs • utilization factors of RES in specific areas

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Methodology Issues

to include the expansion cost of the transmission grid into TIMES we incorporate a linear (DC) power flow algorithm and resolve a rather aggregated form of the transmission grid (equivalent grid) simulated in a regional TIMES transmission grid expansion may be a consequence either of : • connecting areas with significant potential for electricity generation such as RES, coal, etc. • or areas with significant increase of generation and/or demand

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DC Power Flow simulation in regional TIMES

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Methodology Issues

distinction between :  shallow connections  deep connections Shallow connections are generally related to connections of wider areas with significant RES potential or other resources (coal, lignite, etc.) to power transmission grid Deep connections refer to internal grid infrastructure which is related to secure and reliable transmission of electric power

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Shallow Connection

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Deep Connection reinforcement

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Methodology Issues

The equivalent grid TIMES model cannot incorporate several thousands circuits for a detailed simulation of the transmission grid It is necessary to develop an equivalent grid that would incorporate only a few hundreds circuits and the appropriate simulation that will allow the identification of potential reinforcements due to a wide scale penetration of Renewables

Slide 12

DC Power Flow equations into TIMES The general form of the DC power flow equations incorporated into TIMES are as follows: For every bus (node) i:

or

𝑮𝑮𝒊𝒊 − 𝑳𝑳𝒊𝒊 = 𝑷𝑷𝒊𝒊 i=1,N 𝑴𝑴𝒊𝒊

𝑮𝑮𝒊𝒊 − 𝑳𝑳𝒊𝒊 = � 𝑷𝑷𝒊𝒊,𝒋𝒋

and

(1.1)

(1.2)

𝒋𝒋=𝟏𝟏

𝑴𝑴𝒊𝒊

𝑴𝑴𝒊𝒊

𝒋𝒋=𝟏𝟏

𝒋𝒋=𝟏𝟏

𝑷𝑷𝒊𝒊 = � 𝑷𝑷𝒊𝒊,𝒋𝒋 = � 𝑩𝑩𝒊𝒊,𝒋𝒋 ∙ (𝜹𝜹𝒊𝒊 − 𝜹𝜹𝒋𝒋 )

(1.3)

where : N: the total number of nodes Mi : the number of nodes connected with bus (node) i, Gi : active power injected into node i by generators Li : active power consumed in node i by loads Pi : net power injected(generation-load) into node i Pij : branch flow between nodes i and j Bij : susceptance of the branch connecting nodes i and j δi: voltage phase angles of node i with respect to a reference angle in TIMES formulation all parallel branches between nodes i and j are represented as one equivalent corridor ij. Slide 13

DC Power Flow equations into TIMES Rewriting the nodal active power balance equations, in matrix notation, we have: [𝑩𝑩𝒇𝒇 ] ∙ 𝜹𝜹 = 𝑷𝑷

(1.4)

𝑩𝑩 ∙ 𝑩𝑩−𝟏𝟏 𝒇𝒇 ∙ 𝑷𝑷 =𝑷𝑷𝒇𝒇 ⇒ 𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 ∙ 𝑷𝑷 = 𝑷𝑷𝒇𝒇

(1.6)

𝑷𝑷𝒊𝒊,𝒋𝒋 = 𝒍𝒍𝒊𝒊,𝒋𝒋 ∙ (𝑩𝑩𝒊𝒊,𝒋𝒋 /𝒍𝒍𝒊𝒊,𝒋𝒋 ) ∙ �𝜹𝜹𝒊𝒊 − 𝜹𝜹𝒋𝒋 �

(1.7)

[Bf] being the flow admittance matrix and δ the nodal voltage angle vector. In addition, the branch power flow equation is: (1.5) 𝑩𝑩 ∙ 𝜹𝜹 = 𝑷𝑷𝒇𝒇 where 𝑃𝑃𝑓𝑓 = 𝑃𝑃𝑖𝑖,𝑗𝑗

solving for δ we have :

for branch i,j :

where : li,j : the length of the line i,j (𝐵𝐵𝑖𝑖,𝑗𝑗 /𝑙𝑙𝑖𝑖,𝑗𝑗 ) : susceptance per km

Note that Bi,j in TIMES is the equivalent susceptance of all the parallel circuits between nodes i and j. Slide 14

DC Power Flow equations into TIMES Due to power transfer limits of the lines we have: 𝑷𝑷𝒊𝒊,𝒋𝒋 − 𝜺𝜺𝒊𝒊,𝒋𝒋 𝑷𝑷𝒎𝒎𝒎𝒎𝒎𝒎 ≤ 𝟎𝟎 𝒊𝒊,𝒋𝒋

(1.8)

𝑚𝑚𝑚𝑚𝑚𝑚 where 𝑃𝑃𝑖𝑖,𝑗𝑗 is the (constant) limit of the line and ε is the loading factor of corridor ij and 𝜀𝜀𝑖𝑖,𝑗𝑗 the available loading factor of corridor ij.

Power transfer limits include thermal, voltage drop and stability limits. For DC power flow studies these limits are usually approximated as functions of line length and surge impedance loading using. In case transmission expansion is required, i.e. 𝑚𝑚𝑚𝑚𝑚𝑚 if 𝑃𝑃𝑖𝑖,𝑗𝑗 − 𝜀𝜀𝑖𝑖,𝑗𝑗 ∙ 𝑃𝑃𝑖𝑖,𝑗𝑗 ≥0,

𝑚𝑚𝑚𝑚𝑚𝑚 then an additional circuit with ∆𝑃𝑃𝑖𝑖,𝑗𝑗 is introduced, giving:

𝑷𝑷𝒊𝒊,𝒋𝒋 ≤ 𝜺𝜺𝒊𝒊,𝒋𝒋 ∙ (𝑷𝑷𝒎𝒎𝒎𝒎𝒎𝒎 + ∆𝑷𝑷𝒎𝒎𝒎𝒎𝒎𝒎 ) 𝒊𝒊,𝒋𝒋 𝒊𝒊,𝒋𝒋

(1.9)

𝒊𝒊𝒊𝒊𝒊𝒊 𝑲𝑲𝒊𝒊,𝒋𝒋 = 𝑲𝑲𝒊𝒊,𝒋𝒋 ∙ ∆𝑷𝑷𝒎𝒎𝒎𝒎𝒎𝒎 𝒊𝒊,𝒋𝒋

(1.10)

where 𝜀𝜀𝑖𝑖,𝑗𝑗 is the available loading factor of the corridor ij. The additional connection cost for investing in a new line between nodes i,j is :

where : 𝐾𝐾𝑖𝑖,𝑗𝑗 is the linear unitary cost for the additional circuit used in line i,j in Euro/kW.km and 𝑖𝑖𝑖𝑖𝑖𝑖 𝐾𝐾𝑖𝑖,𝑗𝑗 is the cost for constructing a new circuit in the ij corridor lij : length of line i,j

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Allocation of additional generation and loads

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Allocation of additional generation and loads

In the context of the TIMES resolution one has to determine the set of necessary equations for calculating the injections of the additional generation and loads in each time slice of TIMES

During the relevant procedure , we distribute generation and load of every region to nodes, based on linear equations and we formulate power flow scenarios

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Overall Algorithm and Iterations Step 1 Solving DC Power Flow Equations We incorporate and execute DC power flow into TIMES for the same B matrix in all time periods and using the calculated (by TIMES) injections on the nodes of the grid. In addition, initial values for ε are used.

The flow vector 𝑃𝑃

[𝐵𝐵𝑓𝑓 ] ∙ 𝛿𝛿 = 𝑃𝑃

(a)

𝑠𝑠 𝑠𝑠 𝑃𝑃𝑛𝑛,𝑟𝑟 = 𝐺𝐺𝑛𝑛,𝑟𝑟 − 𝐿𝐿𝑠𝑠𝑛𝑛,𝑟𝑟

(b)

is calculated using the generation and load allocation equations (b), (c) and (d) :

Where [b] is applied for every region

s G ns,r = ∑ g n ,u EGtimes ,r ,u

(c)

∀u

where gn,u is a constant obtained from statistics and s Lsn ,r = ∑ f n ,l E times ,r ,l ∀l

where fn,l is also a constant obtained from statistics.

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(d)

Overall Algorithm and Iterations Step 2 Initialization of ε ij Let us suppose that we have the ij right-of-way, which is composed of n ij circuits, as Figure 1.5 shows. Then, the maximum capacity of the ij right-of-way is:

Pijmax = ∑ Pkmax

(e)

nij

where Pkmax is the capacity of the k - th circuit of the ij right-of-way. i

j . . . .

. . . .

2 1

Figure 1.5 : The ij right-of-way, which is composed of n ij circuits. Slide 19

Overall Algorithm and Iterations If n ij > 1 , the initial (topological) value of ε ij is computed as follows:         min  ∑ Pkmax  min  ∑ Pkmax       nij −1 ⇒ε = nij −1 ε ij = ij max max Pij ∑ Pk nij

   max  where min  ∑ Pk  is the minimum of   nij −1  right-of-way (corridor).

∑P

nij −1

max k

each time removing one of the n ij circuits of the ij

Consequently the expression for initializing ε ij in TIMES is as follows:       min  ∑ Pkmax      nij −1  ε ij =  max Pk  ∑ nij  0.9  

Slide 20

, if nij > 1 , if nij = 1

(f)

Overall Algorithm and Iterations

Step 3 Formulation of a NEPLAN model based on TIMES results This step includes the incorporation of the loads and injections calculated in TIMES into the NEPLAN model. In addition an algorithm is developed for the discretization of the transmission system investments calculated in TIMES into realistic transmission lines in NEPLAN. It has to be noted that TIMES calculates new Pijmax values in overloaded lines which represent the necessary change in capacity based on a linear transmission capacity cost function.

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Overall Algorithm and Iterations

Step 4 N-1 security analysis performed in NEPLAN After formulating the new grid in the previous step we execute the NEPLAN model and perform N-1 security analysis. Then we calculate in NEPLAN the new [B] matrix for the forthcoming time periods When the network is Ν - 1 insecure, we implement the algorithm described before

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Overall Algorithm and Iterations

Step 5 Performing a new iteration in TIMES We incorporate the new [B] matrix into TIMES for the different time slices together with coefficients εij and . Based on this input we are executing the next iteration from Step 1.

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Overall Algorithm and Iterations

Step 6 Convergence Criterion The iterative procedure will continue until there will be no need for additional transmission lines investments.

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Overall Algorithm and Iterations

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Mixed Integer Programming The methodology was applied in a simplified electricity network comprised of sixteen nodes with twenty two interconnecting lines The expansion of the system in a time period from 2010 to 2050 was modelled into TIMES together the grid load flow algorithm, using two alternative formulations : a) continuous investments option for the grid lines (no-Mixed Integer Programming) and b) b) discrete investment options for the grid lines (with MIP), in order to examine the effect of the two approaches on the result the MIP approach leads to a gradual increase of the grid lines capacities

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Conclusions

The present methodology is providing a significant improvement for the calculations related to the energy technology investment costs where the additional costs related to grid expansion are calculated these costs can be important decision parameters in the case of a wide scale penetration of Renewable Technologies it is obvious that energy policy scenarios results are significantly improved through the present work

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Next Steps

Improving the methodology for formulating the equivalent grid is necessary Combining the present algorithm with calculations regarding storage and load balancing capacity requirements

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