A Comparative Study of Electricity Price Variations with Wind Energy Penetration

Avinash D. M. Tech. student, Electrical Engineering Department

National Institute of Technology, Kurukshetra Haryana, India

avinash.6474@yahoo.co.in

Shelly Vadhera Assoc. Prof., Electrical Engineering Department

National Institute of Technology, Kurukshetra Haryana, India

shelly_vadhera@rediffmail.com

Abstract—This paper aims to compare the effect of wind energy penetration on electricity prices by considering different levels of installed wind capacities. The market clearing problem is formulated as a two stage stochastic optimization problem, where the first stage represents the clearing of the market with scheduled wind production and the second stage models the balancing market operations with different possible wind energy scenarios. A comparison is made between the size of the system and the price variations by taking three different test systems.

Keywords—Locational marginal prices (LMPs), stochastic programming, wind energy.

I. INTRODUCTION The amount of wind generation is rapidly increasing in all

the electric energy systems, according to GWEC report [1] the total installed wind energy all over the world could reach 2000 GW by 2030. This makes all electricity markets to consider the wind energy in market clearing operations. Electricity markets for short term energy transactions usually comprises of two trading stages such as day-ahead stage and balancing stage. In day ahead stage the market determines the production level of each generating company and the price for each hour in the upcoming 24 hour period where as the balancing market operations are carried at the actual time of load dispatch, to settle the unscheduled load variations or the other uncertainties.

Hence the market clearing problem can be formulated as a two stage stochastic programming problem where the first stage represents the day ahead market operation and the second stage represents the balancing market operation [2]. The increased penetration of wind energy introduces uncertainty into the system, which can be modeled using probabilistic methods [3]. The technique of stochastic programming is initially applied to unit commitment considering outages of generation in [4] and further extended in [5] to determine the spinning and non spinning reserves in a power system with wind producers. As the wind uncertainty increases the system operator has to make sure that the sufficient reserve is present in the system to cope up with the variations, reserve margin planning is discussed in [6] including the hydro systems, in [7] the problem is considered by adding generator outages, wind and load forecasts. The impact of correlation between the two wind farms on

locational marginal prices (LMPs) is discussed in [8]. In this paper the market clearing algorithm is based on single auction mechanism where only generating companies submits bids to the market and dc power flow is used in the optimization problem. In the balancing stage several wind energy scenarios are considered, which are different from the scheduled one in the day ahead market, to find the effect of uncertainties on system LMPs. In this the prices are derived as the dual variables of the power balance constraints of a linear programming problem [2], which is a simple and robust method.

This paper is organized as follows. Section II gives a brief introduction to the stochastic programming, section III describes the modeling of the method used to clear the electricity market, section IV presents the results for IEEE 14 bus, 24 bus and 30 bus systems and section V concludes the paper.

II. STOCHASTIC PROGRAMMING

A. Motivation Power system operation always consists of some level of

uncertainty in the form of load variation, faults and some other unexpected outages. With the inclusion of the wind power in the system the level of uncertainty is further increased, this uncertain data is represented as a possible set of scenarios with some weights and used as an input data to the optimization problem. This represents the stochastic programming technique.

B. Modelling The expression for two stage linear stochastic

programming is given by equations (1) to (3)

Minimize ( ){ }sQFxcz T += (1)

Subject to BAx = (2)

Xx ∈ (3)

Where

( )sQ is given by equations (4) to (6)

Minimize )()( sysq T (4)

Subject to ( ) ( ) ( ) ( )shsysWxsT =+ (5)

( ) SsYsy ∈∀∈ , (6) where x and )(sy are the first and second stage decision variables, AshsWsTBsqc ),(),(),(,),(, are the known vectors and matrices which are in appropriate size, s represents the scenario index and S represents the set of all possible scenarios.

III. METHODOLOGY The method described by equations (1) to (6) is applied to

clear the electricity market comprising of two stage operation. The algorithm of the proposed method is as follows

A. Algorithm • All the participating generators submit bids to the

market operator for day ahead stage, which is cleared as the first stage variable, in this method load is assumed to be constant for a single period time for which it is considered

• The bidding for reserve is included as the simultaneous trading [9] and the scheduled wind energy is considered in the day ahead market.

• The formulation consist of several scenarios of wind energy deviations, which may occur at the actual time of energy delivery, with certain probabilities

• Thus the solution consists of marginal clearing price at day ahead stage and also the price for each scenario

B. Formulation Minimize

( )⎥⎦

⎤⎢⎣

⎡ −∏+++ ∑∑∑∈∈∈ Kk

Dks

Dk

Uks

Uk

Sss

Dk

RDk

Uk

RUk

Kkkk rCrCRCRCPC

⎥⎦

⎤⎢⎣

⎡∏+ ∑∑∈∈ Ll

shedls

LOLl

Sss LV (7)

Subject to

( ) 000 =−−−+ ∑∑∑∑Φ∈Φ∈Φ∈Φ∈

mnm

nml

nq

shq

kk

Mn

Ln

Qn

Kn

bLWP δδ (8)

: nn ∀,λ

( ) ( )∑∑∑Φ∈Φ∈Φ∈

−−++−Qn

Ln

Kn q

spillqs

shqqs

l

shedls

k

Dks

Uks WWWLrr (9)

( ) snb nsmsmnsnm

nmMn

∀∀=+−−+ ∑Φ∈

,,:000 λδδδδ

kPP kk ∀≤ ,max (10)

skrrP Dks

Uksk ∀∀≥−+ ,,0 (11)

skPrrP kD

ksUksk ∀∀≤−+ ,,max (12)

( ) ( ) ,,,max00 Λ∈∀≤− mnCb nmmnnm δδ (13)

( ) ( ) smnCb nmmsnsnm ∀Λ∈∀≤− ,,,maxδδ (14)

kRR uk

Uk ∀≤≤ ,0 max (15)

kRR dk

Dk ∀≤≤ ,0 max (16)

skRr Uk

Uks ∀∀≤ ,, (17)

skRr Dk

Dks ∀∀≤ ,, (18)

slLL lshedls ∀∀≤ ,, (19)

sqWW qsspill

qs ∀∀≤ ,, (20)

kPP kk ∀≥ ,min (21)

skrr Dks

Uks ∀∀≥ ,,0, (22)

sqWqW spillqs

shq ∀∀≥∀≥ ,,0;,0 (23)

slLshedls ∀∀≥ ,,0 (24) 0nδ free nsn δ;∀ free sn ∀∀ , (25)

where (7) represents the expected cost of power system operation which is to be minimized, K is the set of generating units, kC , D

kUk

RDk

RUk CCCC ,,, are the production cost,

upward/downward reserve costs, increasing/decreasing costs of producer k at balancing stage respectively.

Dks

Uks

Dk

Ukk rrRRP ,,,, represents the power generation, reserve

up/reserve down, and the increased/decreased generation at balancing stage of a unit k, where s represents the considered scenario. sΠ is the probability of scenario s where LOL

lV is the value of lost load at a load point given by the set L ,

shedlsL is the amount of load shed in a scenario s . Equations

(8) and (9) are the power balance constraints at day ahead and balancing stages respectively, where mn, both represent the index of nodes in the system and q is used to represent the index of wind farms. The dual variables associated with these equations are nλ , nsλ which give the marginal prices in day

ahead and balancing market stages. The notation αnΦ is used

as the set which relates between the set α and the set of nodes ( n ) for e.g. K

nΦ is the set of generators connected to the

node n . qssh

q WW , are the scheduled wind energy and the

actual wind energy generated during the scenario s , spillqsW is

the wind energy that is spilled because of line flow constraints, nsnnmb δδ ,, 0 represents the susceptance in per unit value, phase angle of the buses at day ahead stage and also at balancing stage in each scenario respectively. Equations (13)

and (14) are the line flow constraints where maxnmC is line flow

limit between the nodes n and m . QLK ,, represent the set of generators, loads and wind farms present in the system and set Λ gives the information about interconnected lines.

C. Assumptions • It is assumed that the cost of wind energy generation is

zero and hence it is not considered in the optimization problem

• The fuel cost of the generators is considered as a piece wise linear curve to perform the optimization as a linear programming problem

• The forecasted load is assumed to be constant for the time of operation

IV. RESULTS The method described in section III was implemented on

the General Algebraic Modeling System (GAMS). The problem was formulated as a linear programming problem and solved using CPLEX 12.1.0 under GAMS.

A. 14 Bus System The IEEE 14 bus test system is considered from [10] and

the wind farm is connected at node 14 as in [11]. The total demand of the system is 259 MW and the system consists of 2 generators, 20 lines, 3 synchronous condensers and 11 load points. The scenarios for wind energy can be obtained from past historical data, in this paper the data given in [12] is used to obtain the probabilities of scenarios. The cost data for the generators (including 24 and 30 bus systems) is taken from [13], initially, in the day ahead market stage the system is cleared by taking some scheduled wind energy and then in the actual time of energy delivery, two scenarios of wind energy deviations are considered which are indicated by low and high wind energy scenarios. It is to be noted that in Tables I to VI case I represents low wind energy scenario and case II represents high wind energy scenario. This process is tested for two cases of different installed wind farm capacities of 12.3% and 26.3% of total system demand as in [2], prices for 12.3% penetration of wind energy are given in Table I

TABLE I. MARGINAL PRICES IN DAY AHEAD AND BALANCING STAGES FOR 12.3% OF WIND ENERGY PENETRATION IN 14 BUS SYSTEM

Node Day ahead market cleared price

($/MWh)

Case I price

($/MWh)

Case II price

($/MWh)

1 10.89 10.89 10.89

2 10.89 10.89 10.89

7 10.89 10.89 10.89

9 10.89 10.89 10.89

12 10.89 10.89 10.89

14 10.89 10.89 10.89

Since the installed wind capacity is of low value (31.86 MW) with comparison to the system demand, the price variation in the above case is zero in all scenarios. Table II gives the data for a wind energy penetration level of 26.3% (68.12 MW). In this the cost at node 14 is decreased because of additional increase in the wind energy but in case II operation, the energy from wind farm is high enough to create congestion in the system (due to line flow constraints) hence at node 14 the cost is almost zero and at node 12 it is reaching a high value. In Fig. 1 the variations of price from 12.3% to 26.3% wind energy penetration in the case of high wind scenario is shown.

TABLE II. MARGINAL PRICES IN DAY AHEAD AND BALANCING STAGES FOR 26.3% OF WIND ENERGY PENETRATION IN 14 BUS SYSTEM

Node Day ahead market cleared price

($/MWh)

Case I price

($/MWh)

Case II price

($/MWh) 1 10.89 10.89 10.89

2 10.88 10.89 10.84

7 10.49 10.89 08.92

9 10.32 10.89 08.03

12 11.90 10.89 15.94

14 08.71 10.89 0

Fig. 1. Price variations in high wind scenario from 12.3% to 26.3% wind energy penetration in IEEE 14 bus system

B. 24 Bus System This system is taken from the single area version of the

IEEE Reliability Test System, 1996 [14] which consists of 2850 MW as the system demand supplied by 12 generators through 34 lines. The wind farms are connected at nodes 7 and 8 as in [2]. Table III gives the prices of this system for a wind energy penetration of 12.3% (350.55 MW), thus the total capacity of wind farms is around 350 MW having 140 wind turbines rated at 2.5 MW each [2].

TABLE III. MARGINAL PRICES IN DAY AHEAD AND BALANCING STAGES FOR 12.3% OF WIND ENERGY PENETRATION IN 24 BUS SYSTEM

Node Day ahead market cleared price

($/MWh)

Case I price

($/MWh)

Case II price

($/MWh)

1 20.70 26.11 13.32

5 20.70 26.11 13.32

Node Day ahead market cleared price

($/MWh)

Case I price

($/MWh)

Case II price

($/MWh) 7 20.70 26.11 13.32

8 20.70 26.11 13.32

9 20.70 26.11 13.32

15 20.70 26.11 13.32

24 20.70 26.11 13.32

For this case there is no congestion in the network and hence the price level is same across all nodes, as the wind energy increased from low scenario (case I) to high scenario (case II) the cost of the system is decreased from 26.11 $/MWh to 13.32 $/MWh. The price details for a wind energy penetration level of 26.3% are given in Table IV. In this case because of the increased wind energy penetration (750 MW) and because of the line flow constraints, congestion is created in the system and hence the price variations which are as shown below.

TABLE IV. MARGINAL PRICES IN DAY AHEAD AND BALANCING STAGES FOR 26.3% OF WIND ENERGY PENETRATION IN 24 BUS SYSTEM

Node Day ahead market cleared price

($/MWh)

Case I price

($/MWh)

Case II price

($/MWh) 1 13.32 20.93 11.09

5 13.44 20.93 11.73

7 11.10 20.93 0

8 11.10 20.93 0

9 12.93 20.93 09.17

15 13.20 20.93 10.52

24 13.17 20.93 10.36

Fig. 2. Price variations in high wind scenario from 12.3% to 26.3% wind energy penetration in IEEE 24 bus system

In Fig. 2 the variations of price from 12.3% to 26.3% wind energy penetration in the case of high wind scenario is shown.

C. 30 Bus System This system is taken from [10], according to [15] the wind

farm is connected at node 7. This system has a total demand of 283.4 MW which is distributed through 21 load points and supplied by 6 generating units. Tables V and VI give the price

details of system considering two levels of wind energy penetration.

TABLE V. MARGINAL PRICES IN DAY AHEAD AND BALANCING STAGES FOR 12.3% OF WIND ENERGY PENETRATION IN 30 BUS SYSTEM

Node Day ahead market cleared price

($/MWh)

Case I price

($/MWh)

Case II price

($/MWh) 1 13.32 23.11 12.52

5 13.32 23.11 12.52

7 13.32 23.11 12.52

11 13.32 23.11 12.52

14 13.32 23.11 12.52

27 13.32 23.11 12.52

TABLE VI. MARGINAL PRICES IN DAY AHEAD AND BALANCING STAGES FOR 26.3% OF WIND ENERGY PENETRATION IN 30 BUS SYSTEM

Node Day ahead market cleared price

($/MWh)

Case I price

($/MWh)

Case II price

($/MWh) 1 12.52 17.21 12.52

5 13.32 18.54 12.52

7 13.26 18.45 12.52

11 13.21 18.37 12.52

14 13.19 18.34 12.52

27 13.22 18.38 12.52

Fig. 3. Price variations in low wind scenario from 12.3% to 26.3% wind energy penetration in IEEE 30 bus system

In the second case of the above system, initially congestion is created between the nodes 1 and 2 hence in day ahead and case I operations, there is a variation of prices among the nodes but in case II operation, congestion is removed because of extra energy flow from wind farm and thus the price variations are removed. In this system due to congestion, low wind scenario prices shown predominant variations from 12.3% to 26.3% wind energy penetration as shown in Fig. 3.

V. CONCLUSIONS This paper gives a comparison of prices for different

systems considering the different scenarios of wind energy penetration. Here it is seen that the increased penetration of wind energy decreases the system cost but increases the price

variation among the nodes. Future work can be extended to add all the start up and shut down costs of the generators in the objective function and also a 24 hour load pattern can be considered in place of a constant load.

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