A Study of Transmission Congestion Effects on Nodal Power Prices

Using an Agent-Based Electricity Market Simulator

Marko Delimar, Slavko Krajcar University of Zagreb

Faculty of Electrical Engineering and Computing

Department of Power Systems

Unska 3, 10000 Zagreb, Croatia

ivan.rajsl@fer.hr

Abstract. This paper presents a small

electricity market study based on an agent-based power network simulator in deregulated conditions.

A simple six node network is modelled in EMCAS to observe effects of transmission line

outages and transmission congestion problems. The effects of price variations due to line outages are presented and discussed. Possible economic

indexes for power system planning are also discussed.

Keywords. Power system modelling, Power market simulator, Congestion management.

1. Introduction

Agent-based modelling and simulation (ABMS) represents a rather new approach to modelling systems that comprises interacting autonomous agents [7].

The fundamental feature of an agent is the capability of making independent decisions. Agents are diverse, heterogeneous and dynamic

in their attributes and behavioural rules. These

rules vary in their complexity, amount of

decisions,

including models of other agents and the extent

of memory of past events the agent retains and

uses in its decisions.

ABMS has strong roots in the fields of multi-agent systems (MAS) and robotics from the field of AI. But ABMS is not only tied to designing

roots are in modelling human social and organizational behaviour and individual decision-making. With this, there comes the need to represent social interaction, collaboration,

group behaviour, and the emergence of higher order social structure.

Agent-based modelling is so becoming widespread. There are several reasons for that. Traditional modelling tools are no longer as applicable as they once were due to the complexity of simulated phenomena. An example application area is the deregulation of the electric power industry. Some systems have always been too complex to adequately model

(stock market,

supply chains, spread of epidemics and many

others). An agent-based approach in modelling

such systems modelling each subject

separately, instead of a system as a whole can

yield satisfactory results.

Complex interactions and interdependencies

among participants in deregulated, decentralized

electricity markets are much like those studied in

the game theory [4]. However, the strategies

used by many power market participants are

often too complex to be conveniently modelled

by standard game theory techniques. In

particular, the ability of market participants to

repeatedly pursue market probing and rapidly

adapt strategies adds additional complexity.

Computational social science involving ABMS

offers appealing extensions to the traditional

game theory. Good examples of application of

ABMS in power system can be found in [3],[6]

and [8]

Argonne National Laboratory developed the Electricity Market Complex Adaptive System (EMCAS) software to meet the growing need for advanced modelling approaches that simulate how electricity markets may evolve over time and how participants in these markets may react to the changing physical, economic, financial, and regulatory environments in which they operate.

773Proceedings of the ITI 2008 30th Int. Conf. on Information Technology Interfaces, June 23-26, 2008, Cavtat, Croatia

Unlike conventional electric systems analysis

tools, the EMCAS model does not postulate a

single decision maker with a single objective for

the entire system. Rather, the agents are allowed

to establish their own objectives and apply their

own decision rules. The complex adaptive

systems modelling approach simulates the agents

that learn from their previous experiences and

change their behaviour when future opportunities

arise. That is, as the simulation progresses, the

agents can adapt their strategies on the basis of

the success or failure of previous efforts. Genetic

algorithms are used to provide a learning

capability for certain agents. With its agent-

based approach, EMCAS is specifically designed

to analyze multi-agent markets and allow testing

of regulatory structures before they are applied to

real systems [1][2].

All market participants work on several levels

(physical, several business levels, regulator).

Decisions are made based on various time spans,

from one hour to few years and the agent makes

the set of decisions that can be changed and

improved during a certain time period [10].

Description of another ABMS tool

implementation in power system is described in

[9].

Using EMCAS simulation tool, a congestion in transmission network and its effects on market prices and physical power flow through the network can be analysed.

2. Modelling a simple power system in

EMCAS

To simplify the analysis and allow a simple comparison, an existing 6-node network will be used. It is based on a test network described in Wood and Wollenberg (1996). Transmission network, generator and load data are exactly the same [5].

This relatively simple network model makes it easier to follow and understand both physical and economic features of the power system. The basic network elements are the nodes and transmission lines that carry the power between the connecting nodes. Each node can represent generation, load, both or none.

This six node model contains three consumer nodes and three generation nodes. Nodes are connected into a uniform system by a total of eleven transmission lines. Nodes are enumerated 1-6, and transmission lines 1-11 (Figure 1).

constant load of 70 MW connected (there are no

load variations).

have a generation of 200, 150, 180 MW

respectively. Generators are represented by small

black filled circles next to the corresponding

nodes. Assumed nominal power flow direction is

set from a lower enumerated node towards a

higher enumerated node. If power flows, e.g.

from node 3 to node 6, it will be positive and if it

flows, e.g. from node 5 to node 4 it will be

negative.

When an outage of a transmission lines

occurs, power flow changes throughout the

system. In such a case power flow in some lines

can reach physical capacity constraints, thus

creating the transmission line congestions.

2

1

3

4

5

6

1

2

3

4

5

6

7

8

9

10

11

Figure 1. Network overview

EMCAS is used to observe effects of a single transmission line outage and, consequently, possible transmission congestion issues. Such contingencies may cause price changes in various nodes throughout the network. Power flow, a physical response of the system to such a contingency, is redistributed after a line outage. A secondary response is an economical one a nodal price change. Electricity market responds to the new conditions generators adjust their production to extract maximum profit in this new situation. Contingency analysis (N-1) is one of the basic analysis for power system operation and planning. Standard security indexes such as voltage range and line loads are taken into account in the network planning. Additional indexes could take into account not only congestion but also economic parameters. Line outages influence on nodal electricity prices could be one such index

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(economic N-1). Optimal economic system state is that where no line outage effects on nodal prices. This state will be introduced using 6-node model.

3. Results

3.1. Case 0 No outages (default network)

In t network, nodal prices are uniform throughout the system.

Generators 2 and 3 are producing energy, with generator 1 being idle. This is a consequence of different technical characteristics of the generators. Power flow in the whole network is optimized, with no congestion on any of the transmission lines.

Each node has the same real time local marginal price (LMP).

Figure 2. Power Flow and generation Case 0

Table I. Power Flow Case 0

Line

ID

Nominal

Capacity

[MW]

Actual

Power

Flow

[MW]

Line

ID

Nominal

Capacity

[MW]

Actual

Power

Flow

[MW]

1 40 17,48 7 90 21,43

2 60 11,33 8 70 29,51

3 40 6,15 9 80 66.17

4 40 9,33 10 20 1,05

5 60 57,62 11 40 17,59

6 30 17,80

Table II. Generation Case 0

Generator Installed capacity

[MW] Actual generation [MW]

1 200,00 0,00

2 150,00 105,00

3 180,00 105,00

Table III. Real Time Nodal Price, LMP Case 0

Node ID 1 2 3 4 5 6

Real Time

LMP

[$/MWh]

13,85 13,85 13,85 13,85 13,85 13,85

3.2. Case 1 Line 1 outage

Transmission line 1 is intentionally switched off (line 1 outage).

Generator 1 is producing 18 MW while generator 3 is producing 18 MW less than in default network. Generator 2 production remains unchanged. Line 5 is congested unable to carry any more power (marked in table 4). Congestion in line 5 the main supply line for node 4 has for a consequence a raise in node 4 LMP, in a bigger percentage than in other nodes.

Congestion

Figure 3. Power Flow and generation Case 1

Figure 4. Real time LMPs Case 1

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Table IV. Power Flow Case 1

Line

ID

Nominal

Capacity

[MW]

Actual

Power

Flow

[MW]

Line

ID

Nominal

Capacity

[MW]

Actual

Power

Flow

[MW]

1 40 0,00 7 90 26,52

2 60 10,52 8 70 26,00

3 40 7,71 9 80 58,56

4 40 2,21 10 20 0,52

5 60 60,00 11 40 15,08

6 30 20,69

Table V. Generation Case 1

Generator Installed capacity

[MW] Actual generation [MW]

1 200,00 18,23

2 150,00 105,00

3 180,00 86,77

Table VI. Real Time Nodal Price, LMP Case 1

Node ID 1 2 3 4 5 6

Real Time

LMP

[$/MWh]

14,43 13,63 13,85 14,73 13,99 13,89

It's obvious that transmission line 1 outage affects on real time nodal prices. Most of these prices are higher, however the price in node 2 is even lower than in default network.

3.3. Case 2 to 11

All other cases are simulated in the same manner. Case 1 refers to the transmission line 1 outage while all other lines are in operation. Case 2 to 11 refer to the transmission lines 2 to 11 outages respectively while all other lines are in operation.

Table VII. Power Flow [MW] Case 1-11

Line ID 1 2 3 4 5 6

Case 1 0,00 10,52 7,71 2,21 60,00 20,69

Case 2 25,44 0,00 23,63 27,69 60,00 6,67

Case 3 14,10 14,10 0,00 8,11 56,38 19,44

Case 4 16,30 11,68 4,62 0,00 55,95 15,48

Case 5 33,95 50,00 6,67 5,42 0,00 29,30

Case 6 16,57 13,43 13,53 1,45 60,00 0,00

Case 7 19,17 10,83 8,33 7,74 60,00 21,11

Case 8 17,86 12,14 10,95 12,75 60,00 22,85

Case 9 18,03 11,97 10,60 37,91 60,00 22,62

Case 10 17,51 11,60 5,86 9,53 58,34 17,53

Case 11 18,24 11,76 10,19 10,32 60,00 22,35

Line ID 7 8 9 10 11

Case 1 26,52 26,00 58,56 0,52 15,08

Case 2 5,38 34,32 80,00 10,00 15,38

Case 3 23,19 30,22 66,67 0,48 19,86

Case 4 17,28 32,47 72,53 2,38 19,81

Case 5 36,33 28,60 59,10 20,00 25,43

Case 6 29,88 29,75 63,39 3,43 23,28

Case 7 0,00 31,80 77,92 0,83 7,92

Case 8 24,06 0,00 80,00 2,14 34,06

Case 9 42,26 62,56 0,00 1,97 27,74

Case 10 21,13 29,39 66,08 0,00 17,22

Case 11 14,73 35,71 55,27 1,76 0,00

Table VIII. Real Time Nodal Price, LMP [$/MWh] Case 1-11

Node ID 1 2 3 4 5 6

Case 1 14,43 13,63 13,85 14,73 13,99 13,89

Case 2 14,43 13,35 14,59 28,03 16,06 15,47

Case 3 13,85 13,85 13,85 13,85 13,85 13,85

Case 4 13,85 13,85 13,85 13,85 13,85 13,85

Case 5 14,43 14,00 13,85 15,32 13,76 13,83

Case 6 14,43 13,36 13,85 15,69 14,15 13,93

Case 7 14,31 13,35 13,85 15,44 14,05 13,98

Case 8 14,43 14,09 13,85 14,82 14,37 14,35

Case 9 14,43 13,61 13,85 15,48 14,10 13,99

Case 10 13,85 13,85 13,85 13,85 13,85 13,85

Case 11 14,43 13,65 13,85 15,35 14,24 13,78

Table IX. Generation [MW] Case 1-11

Generator 1 2 3

Case 1 18,23 105,00 86,77

Case 2 49,07 18,92 142,01

Case 3 0,00 105,00 105,00

Case 4 0,00 105,00 105,00

Case 5 22,71 105,00 82,29

Case 6 10,40 105,00 94,60

Case 7 0,00 92,54 117,46

Case 8 5,23 112,02 92,75

Case 9 4,53 105,00 100,47

Case 10 0,00 105,00 105,00

Case 11 3,71 105,00 101,29

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0,00

5,00

10,00

15,00

20,00

25,00

30,00

Node 1 Node 2 Node 3 Node 4 Node 5 Node 6

Default network

Case 2

Figure 5. Default and Case 2 real time LMP comparison [$/MWh]

13

13,5

14

14,5

15

15,5

16

16,5

17

17,5

Default Network average LMP

Average nodal real time LMP

Figure 6. Default and Case 1 to 11 average real time LMP comparison [$/MWh]

3.4. Optimal economic system state

Desirable system state is a state in which single line outages do not affect any nodal prices.

Considering 6 - node model this state could be accomplished by building new lines, parallel to existing ones, or by increasing exiting lines capacities. The analysis has shown that, to achieve the optimal economic system state the following line capacities should be increased:

Table X. Line Capacity Increase

Line ID From [MW] To [MW]

1 40,00 44,74

4 40,00 40,32

5 60,00 67,39

9 80,00 87,10

10 20,00 23,98

New line limits were obtained from N-1 analysis.

4. Discussion

Without congestion in the network, prices are set as shown in the aggregate generation curve (Fig.7). The load in the network of 210 MW requires only generator 2 and 3 to operate, setting the energy price at 13,85 $/MWh. It is important to note that only in regular operating conditions no contingencies, no congestion, prices are expected to change in correlation with the aggregate generation curve.

Price

[$/MWh]

12

13

14

15

16

Generation/Load [MW]

1000 200 300 400 500

Generator 2

Generator 3

Generator 1

Load = 210 MW

13,85

Figure 7. Aggregate Generation curve

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Results show that in three cases (3, 4 and 10) ,

while of course affecting power flow in the network. It is an expected response of the system since these lines are not significantly loaded in a normal (default) case.

In other cases, line outages have an impact on power flow, generator behaviour, and finally, nodal prices. As it can be seen from Fig. 6, the outage on line 2 has the biggest impact on nodal prices (average real time LMP). In this case price on node 4 has changed significantly. It rises to an amount that is more than a double amount of the normal price. This phenomena is dashed black in table VIII. Node 4 has the greatest price volatility as shown in Fig. 5.

The price volatility regarding the line outages could be reduced by increasing line capacities or building new lines which represents a very high investment cost and is therefore often not easily economically justifiable. However, such

reasoning can be taken into account in power

system planning. After taking into account

physical constraints, economic aspects should as

well be considered.

5. Conclusion

Contingencies in the network that cause congestion on some lines lead to normally unexpected nodal price levels. Without complex calculating systems it would be difficult to gain comprehensive insight of the system behaviour and price fluctuations. As presented in this paper, bottle necks in the power network that cause congestions resulting in significant price spikes can be identified with agent based electricity market simulators, such as EMCAS. Although the considered simple power network is fictive, it can give some basic guidance for some more complex, real examples in existing power networks. It shows that market simulators may be used as decision making tools when planning expansions of the system, mainly transmission network, especially in conjunction with a reliability analysis tool.

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[3]

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Based Syst. , (2006), doi:10.1016 /j.knosys.2006.06.004

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