Value of VAR support in a competitive environment

14th PSCC, Sevilla, 24-28 June 2002

Session 40, Paper 5, Page 1

VALUE OF VAR SUPPORT IN A COMPETITIVE ENVIRONMENT Danny Pudjianto, Goran Strbac UMIST

S Ahmed, Keith Bell National Grid

Peter Turner Powergen

United Kingdom Abstract – This paper presents a method for allocation and evaluation of reactive power (VAr) support contracts necessary to maintain system security and quality of supply. The method also quantifies the value of VAr support from individual generators or a portfolio of generators. Such information may be useful both to generating companies in preparing VAr tenders and to the market operator in assessing the value of VAr support tenders. For this purpose a novel sensitivity analysis based security constrained OPF (SA-SCOPF) is described that caries out the evaluation of VAr support offered from various generators across several demand levels taking into account a number of contingent systems. Case studies are presented to demonstrate the performance of the developed solution scheme of the SA-SCOPF on the England and Wales 1092 bus network.

Keywords: reactive power market, value of reactive support, system security, optimal power flow 1. INTRODUCTION The function of transmission in a power system is centred on the fundamental requirements of providing efficient transport of electrical energy from large generators to demand centres, while maintaining required standards of security and quality of supply. Among other requirements, these standards specify the permitted voltage fluctuations under both normal and contingent conditions. In order to efficiently maintain the required level of voltage regulation, an adequate management of reactive power is essential. There will be a need for a margin of reactive reserve to be held on a number of generators and other dynamic reactive compensation plant. These reactive reserves are maintained primarily to provide additional reactive power in the event of outages. For instance, with the loss of a transmission circuit, the network configuration changes resulting in an increase in system impedance, which in turn increases reactive demand. This increase is supplied from reactive reserves. System operation must therefore, ensure that sufficient reactive reserve is held for all credible contingencies. Due to localised requirement of reactive support, these reserves must be appropriately distributed across the network. Since privatisation of the electricity supply industry in England and Wales, a ‘Grid Code’ has applied specifying, among other things, a minimum requirement for generators’ reactive power capabilities [1]. In order to enable generators to offer and be rewarded for enhanced reactive power services, since early 1998,

twice a year the National Grid Company (NGC), owner and operator of the England and Wales transmission system, has sought ‘reactive market’ tenders from generators. In this market, generators can offer bids composed of capacity and utilisation elements [2]. The capacity bid takes the form of the total amount of MVAr offered with a price per MVAr, while the utilisation bid specifies the MVArh price curve. Bilateral contracts are awarded for successful tenders and payments are made for both capability and utilisation of reactive power based on the accepted bids. Generators that do not submit bids are nevertheless required by the Grid Code to provide reactive power but receive a default payment based on a predefined value of per unit reactive energy. The process for selection of bids takes into account the location of generators, various network configurations and the costs of competitive options. Generating companies that provide VAr support and the network operator responsible for buying it are interested in understanding the value of the services offered. Such understanding requires the availability of network data, demand and generation profile data and reports on past activity in the market. This information is provided by National Grid in England and Wales in the annual ‘SYS’ (Seven Year Statement) and on the internet [3,4]. This paper describes a new sensitivity analysis based security constrained optimal power flow (SA-SCOPF) developed to calculate the optimal amount of VAr support that needs to be committed while fully exploiting the available control capabilities of the system. The optimal portfolio of reactive contracts to be accepted should be adequate to maintain system security and quality of supply across a number of loading conditions while taking credible contingencies into account. The SA-SCOPF adopts two optimisation stages to solve the problem. The first stage is called the ‘decision making’ sub-problem and the second stage is the ‘decision evaluation’ sub-problem. A similar problem has been tackled in [5] by using a Benders decomposition technique. However, the standard Benders scheme suffers from a poor convergence rate when the number of control variables to be optimised is very large [6-8]. Case studies are presented based on the published England and Wales 1092 bus system [3] to demonstrate the validity of the developed SA-SCOPF.

14th PSCC, Sevilla, 24-28 June 2002

Session 40, Paper 5, Page 2

The rest of the paper is organised as follows: a description and formulation of the problem is addressed in the next section. The decomposition strategy and solution algorithm are discussed in section 3 followed by a description of the decision evaluation sub-problem in section 4. In section 5, the decision making subproblem is discussed. Case Studies performed are presented in section 6. Finally, concluding remarks are in section 7. 2. PROBLEM FORMULATION The minimum overall annual cost associated with VAr support contracts, new VAr investment and expected VAr utilisation, is determined through solving a multi-level security constrained Optimal Power Flow Problem, formulated as follows (the variables typed in bold are vectors): T e T e T p T p min Ψ = Cc Qc + Cr Q r + Cc Qc + Cr Q r +

Q , k ,k , x

NL

∑ Subject to

l =1

( 1) (CTc τlQ0cl + CTr τlQ0rl )

Pl − Pd,l − P(x lj , k lj , k l ) = 0

( 2)

j j j Q g, l − Q d,l − Q( x l , k l , k l ) = 0

( 3)

k min ≤ k lj ≤ k max

( 4)

k min ≤ k l ≤ k max

( 5)

j j x min ≤ x lj ≤ x max S(x lj , k lj , k l ) ≤ S max j e − Q er − Q pr ≤ Q g, l ≤ Qc

( 6) ( 7) + Q cp

( 8)

0 ≤ Q ec ≤ Q cE

( 9)

0 ≤ Q er ≤ Q Er

( 10)

Q cp ≥ 0 , Q pr ≥ 0 j = 0, NS l =1, NP

( 11)

In the above model, the abbreviations used have the following meanings: c : Reactive generation r : Reactive absorption g : Generator d : Load (demand) l : Load level (demand period) e : Existing sources p : Potential sources E : Existing maximum j : Label of an operating state NS : Total number of contingent states (intact system: j=0) NP : Total number of load levels : Objective function ψ

Q P x

: Reactive power injection : Active power injection : State variables(voltage V and phase angles θ) j

kl kl

: Control variables adjusted in corrective mode in system state j at load level l : Control variables adjusted in preventive mode

at load level l : Number of hours reactive energy is utilised in intact network In objective function (1), C c , C r , C c , C r , C c , C r , τl

denote the offered annual capacity prices for existing reactive power generation/absorption (£/MVAr.year), the annual capacity investment prices for potential (new) reactive power generation /absorption (£/MVAr.year), and the offered prices for utilisation of reactive energy generation/absorption within the offered capacity (£/MVArh), respectively. The primary objective is to allocate VARs among the existing generators ( Q ec , Q er ), and, where necessary, to install additional ones ( Q cp , Q pr ). Costs of VAr reinforcement are given as the annuitised capital costs. In the above model, the dispatch of active power is assumed to be specified for each load level. Therefore, active power related costs do not appear in the objective function (1). Equations (2) and (3) represent the nodal active and reactive power balance equations in each of the system states. Equation (4) enforces the limits on the corrective j

control variables k l . These include the taps of OLTC (On load tap changing) transformers, shunts, phase shifters and SVC output that can be optimally dispatched in corrective mode. Equation (5) imposes the limits on the control variables k l that can be operated in

preventive mode only. Hence there is no opportunity to adjust these controls after an outage occurs. Generators’ set voltages are considered fixed at pre-specified values. The pre-fault adjustment of reactive power supplied by generators is achieved through changing generator transformer taps. The limits on the state variables are enforced by Equation (6). Equation (7) ensures that the thermal limits j of branches are not violated. Q g,l in Equation (8) j j and Q r,l represent the summation of Q c,l . Potential

reactive supports and SVCs are modelled as generators. 3. SOLUTION ALGORITHM In this paper the two-stage decomposition scheme shown in Figure 1 is proposed and implemented to solve the above optimisation problem. At the Master ‘decision making’ level, a portfolio of reactive support contracts is purchased and the settings of preventive controls are made.

14th PSCC, Sevilla, 24-28 June 2002

Session 40, Paper 5, Page 3

The feasibility of the proposed VAr support portfolio is evaluated at the Slave ‘decision evaluation’ level (second stage). For each contingent state at each load condition (demand level), this assessment is carried out using an advanced non-linear programming based optimal power flow (OPF) [9,10].

Reactive Power commitment and demand specific preventive control settings

Load Level #1

Load Level NP

Adding constraints

Decision Evaluation: State 0

Selection of severely violated constraints

Decision Evaluation: State NS

Decision Evaluation: State 0

Selection of severely violated constraints

Decision Evaluation: State NS

Figure 1: Two stage solution algorithm of Multi-level SASCOPF

In contrast to a conventional sensitivity analysis based decomposition, the developed algorithm directly enforces the satisfaction of the constraints in the decision evaluation sub-problem (discussed further in section 4). For each individual system state studied, the sensitivities of violated voltages, flows and reactive power injections at voltage controlled buses are calculated with respect to reactive power injections at non-controlled buses including preventive controls. After selecting the most severely violated constraints from the decision evaluation problem, from each load level, a new set of constraints is formed and fed back to the Master problem. A new solution is then found which improves the portfolio of VAr support contracts purchased and re-adjusts reactive controls accordingly. The Master-Slave interaction process continues until there are no more changes to the contract portfolio purchased (and/or new VAr resources installed)such that the system security requirements are satisfied.

4. DECISION EVALUATION SUB-PROBLEM The decision evaluation sub-problem represents a feasibility assessment of the proposed VAr support

contracts, given through a reactive capacity layout ( Q ec , Q er , Q cp , Q pr ), including proposed settings of j

preventive controls ( k l ).

The decision evaluation sub-problem is an OPF problem that minimises the cost of VAr enforcement required to satisfy all voltage and thermal constraints while optimising the corrective control devices at each state and load level separately. This single state OPF problem can be formulated as follows: Objective: Tˆe Tˆe Tˆp Tˆp min Ψ = Cc Q c + C r Q r + Cc Q c + Cr Q r + Q ,k , k , x ( 12) T T Cc τ lQ c,l + C r τ lQ r,l Subject to: Pl − Pd,l − P(x lj , k lj , k l ) = 0

( 13)

j j j Q g, l − Q d,l − Q( x l , k l , k l ) = 0

( 14)

k min ≤ k lj ≤ k max

( 15)

k l = k 0l

( 16)

j j x min ≤ x lj ≤ x max

( 17)

ˆ e −Q ˆ p ≤ Q j ≤ Qe + Qp + Q ˆ e +Q ˆp − Q er − Q pr − Q c c c c r r g,l ( 18) S(x lj , k lj , k l ) ≤ S max ˆ e ≤ QE - Qe 0≤Q c c c e E ˆ 0 ≤ Q r ≤ Q r - Q er ˆ p ≥0 ;Q ˆ p ≥0 Q c r

( 19) ( 20) ( 21) ( 22)

ˆ e ,Q ˆ e ,Q ˆ p ,and Q ˆ p represent additional capacity Q c r c r of reactive generation and absorption from existing and potential (fictitious) sources respectively, necessary to enforce the feasibility of the system. As the number of hours τ 0 spent in the intact network is much higher than τ j≠0 in the contingent condition, for simplicity it is considered τ j≠0 =0. It is important to note that for each demand level 0

preventive controls ( k l ) are optimised by the decision making sub-problem, and are hence kept constant at the decision evaluation level. On the other hand, corrective controls can be optimised for each system state specifically. If the current VAr support proposal is not adequate i.e. there are voltage constraint violations, the decision evaluation sub-problem will enforce the satisfaction of violated constraints through installing minimum cost fictitious VArs, according to Equation (12). This optimisation problem is solved through an advanced non-linear primal dual interior point method developed on the basis of work published in [9,10].

14th PSCC, Sevilla, 24-28 June 2002

5.

Session 40, Paper 5, Page 4

DECISION MAKING SUB PROBLEM

Proposals for VARs support contracts, VAr reinforcement requirements and preventive control settings are created at the Master level (Figure 1). This optimisation problem takes the following form: Objective T e T e T p T p min Ψ = C c Q c + C r Q r + Cc Q c + Cr Q r + Q,k ,k ,x

NL

∑ (C Tc τ l Q 0cl + C Tr τ l Q 0rl ) l =1

Subject to 1. Nodal violated voltage constraints for non voltage controlled buses: ( u = (Q gj l , k l ) ( 23)

(

)

∂Vlj ( 24) u − u ( 0) ≤ Vmax ∂u 2. Reactive power constraints for voltage controlled buses : Vmin ≤ Vlj(0) +

− Q er, l − Q pr ≤ Q gj(0) l + ∂ Q g,j l

(u − u ) ≤ Q (0)

∂u 3. MVA constraints :

S lj( 0) +

(

e c, l

)

∂S lj u − u ( 0) ≤ S max ∂u

( 25) + Q cp

( 26)

Bounds: 0 ≤ Q ec,l ≤ Q ec

( 27)

0 ≤ Q er,l ≤ Q er

( 28)

0 ≤ Q ec ≤ Q cE

( 29)

0 ≤ Q er ≤ Q Er Q cp ≥ 0 , Q pr ≥ 0

( 30) ( 31)

u represent the vectors of control variables to be optimised and comprises of vectors of reactive (j injections at non-voltage control buses ( Q g,l ) and positions of preventive controls. Constraints (24) are formed for each load level from the states with the most severely violated voltages. Vlj

represent the vectors of voltages at voltage controlled buses and violated load bus voltages, with superscript j and subscript l referring to the severely violated system j

state and load level .

∂Vl

refer to the vectors of ∂u sensitivity coefficients of the bus voltage magnitudes at demand level l in the j-th system state to the control

variables ( u ). The allowable voltage fluctuation is defined by Vmin and Vmax . It is important to note that constraints in Equation (24) are built only for the voltage-optimised buses. Additional voltage constraints are also built for each bus representing a high-voltage side of the generator transformers (such transformers are operated in preventive mode), and each bus at which a shunt compensation plant is connected. This strategy is adopted to limit the abrupt changes in the corresponding preventive controls during the optimisation process. On the other hand, if the controls are operated in a corrective mode, these constraints are not required as the control positions will be determined in the decision evaluation sub-problem, for each state individually. Constraints in Equation (25) are formed for the voltage-controlled buses for each load level. Vectors of j

reactive power outputs ( Q gl ) at voltage controlled buses (superscript j refers to the state with most severely violated voltage constraint, while subscript l corresponds to the particular load level). Vectors

j ∂Q gl

∂u refer to the sensitivity coefficients of the reactive power output with respect to the control variables. Note that constraints in Equation (25) are the linear approximations of the constraints in Equation (8). Constraints in Equation (26) are formed for the most severely violated MVA flow constraints. If the violation occurs in several system states with a similar degree, then all those states may have to be included in the formulation to mitigate convergence difficulty. After selecting the states with the most severely violated voltages and MVA constraints from each individual load level, the constraints in Equations (24)(26) are formed. These constraints are brought back to the decision making sub-problem, Equations (23)-(31). The decision making sub-problem improves the decision to satisfy all constraints. The improved decisions ( Q ec , Q er , Q cp , Q pr and k l ) are then fed to

the decision evaluation sub-problem which performs the feasibility checks. It is important to remember that Equations (24-26) are valid only for small changes in the control variables due to the non-linear nature of the power system equations. Thus, changes in the reactive injections are limited up to 10 MVAr and tap-changers up to 0.01 p.u. A smaller range may be required when the system is highly loaded which tends to increase system nonlinearity. However, if only small changes are permitted, the convergence process may require too many iterations. In order to speed up the process, the changes in the control variables are not limited at the beginning of the process. 6. CASE STUDIES On the basis of the SA-SCOPF, analysis of the value of reactive support and competitiveness of individual

14th PSCC, Sevilla, 24-28 June 2002

Session 40, Paper 5, Page 5

Table 1: Available control devices and operation modes Item Transformer Phase shifter Shunt

Total 870 13 272

Fix 119 0 144

Preventive 320 13 128

Corrective 431 0 0

In order to assess the value of VAr support of the selected group of generators (located across the system as indicated in Figure 2) their bid prices (for reactive capacity) were varied together relative to the price of all other generators in the system. That is, the selected group of generators always had the same capacity price as each other, given as a certain ratio – the ‘price ratio index’ – relative to the prices of the other generators. The price ratios used were 0.5, 0.75, 1.0, 1.25, 1.5 and 2.0. All generators were shown as having the same utilisation price per MVArh.

Station 2 Station 1

Station 3

Station 4 Station 5 Figure 2: Location of the generators in selected group

The case study results are shown in figure 3. From Figure 3 it can be observed that the total system reactive requirements were not considerably affected by the variation of price offered by the selected group of generators. Total requirement varied from 9519 MVAr to 9620 MVAr. All these reactive supports were provided by the existing reactive resources and no additional investment was required to maintain system security requirements.

12000 MVAr required

generators can be carried out. In this paper it is proposed that the value of reactive power support of each particular generator can be quantified by the reactive power support purchased from that generator when all system generators offer the same price for the service. Studying the sensitivity of the capacity sold to the system by a generator or a group of generators (or revenue received for reactive capacity provided) with respect to changes in prices relative to other generators, can provide useful indication about the competitiveness of the individual generator or the portfolio in the reactive market. The developed SA-SCOPF has been applied to the national transmission network of England and Wales [3] to allocate VAr support contracts and quantify the competitiveness of a selected group of generators. The system consists of 1092 buses, 1670 branches and 320 generators including SVCs. Table 1 gives the summary of control devices present in the system and their operation mode. Five loading conditions were considered (simultaneously) to capture annual variations in demand. Voltage limit is 0.95 – 1.1 p.u. for both intact contingent system conditions. For this study critical 18 contingencies were selected in the south-west region of the network

10000 8000 6000 4000 2000 0 0

0.5

1 1.5 Price ratio

Total Qcap required

2

2.5

Qcap commited from A

Figure 3: Reactive capacity requirement

The reactive capacity committed from the selected group of generators varied with the changes in price ratio index. If the selected group of generators offered a price that was 50% lower than the rest of the system generators (price ration index of 0.5), the total capacity purchased by the system was almost 2000MVAr. However, for a price ratio index of 2, the total reactive support provided by these generators dropped to only 54MVAr. From these case studies, it may be concluded that the amount of reactive support purchased from this group of selected generators will be very price sensitive and that the group has no market power in the reactive power market. The individual reactive power support required to be provided by each of the generators in this group is shown in Figure 4. Figure 4 gives individual performances of each of the generators within the group in the context of their contribution to the reactive market in the case study, i.e. under the particular active power despatch, control modes, prices and contingencies studied. Generators at Station 4, for example, were not very competitive, and their reactive capacity would not be required if their relative price were slightly above the average. In contrast, the value of VAr support from Station 3 was higher. Even when its bid price increased, with a price ratio index of 1.25, the reactive capacity allocated to this plant did not change significantly. But when the price ratio index was increased further, the allocation fell from 300 MVAr to 136 MVAr (Pr = 1.5) and 0 MVAr at Pr = 2. It is interesting to observe the performance of Station 1. This Station was required to

14th PSCC, Sevilla, 24-28 June 2002

Session 40, Paper 5, Page 6

provide some reactive support even when the price ratio index reached 2.

500 400 300 200 0.75

MVAr requirement

600

8. ACKNOWLEDGEMENTS The authors gratefully acknowledge the support from EPSRC (GR/L/37489) and the valuable input from National Grid Company and Power Gen.

c Pri

100

eR

1.25

o ati

9. REFERENCES

0

2

5

4

3

1

2

[1] The National Grid Company plc, The Grid Code. See http://www.nationalgrid.com/uk/indinfo/grid_code/index.html

Station Figure 4: Individual reactive capacity committed

20

1500

15

1000

10 500

5 0

0

Revenue (p.u.)

Following this analysis it is also possible to determine the market share (in terms of both capacity sold and revenue received) for the group of selected generators, which is shown in Figure 5.

Market share (%)

number of demand levels taking into account some credible contingencies. A system operator may used this kind of tool to optimally select the portfolio of required reactive contracts. On the other hand, generating companies can use this tool to estimate the value of their VAR support services and to prepare their VAr tenders. Case studies performed show that the developed SASCOPF is applicable to large scale power systems.

0.5 0.75 1 1.25 1.5 2 Price ratio Market Share

Revenue

Figure 5: market share and revenue for reactive power capacity provided by company A

Market share for the group varied with the price ratio. It varied from 1% (Pr=2) to 14.6% (Pr=0.75). Clearly, such an analysis would be useful both for generators when formulating tenders for the provision of reactive support and for the market operator when assessing tenders. 7. CONCLUSIONS In this paper, a novel sensitivity analysis based security constrained OPF developed to select an optimal portfolio of reactive power support contracts and to quantify the value of reactive support provided by individual generators has been described. This tool can optimise the reactive support of system demand across a

[2] IEE Colloquium on “Economic provision of reactive power for system voltage control”, London, October, 1996 [3] The National Grid Company plc, Seven Year Statement, http://www.nationalgrid.com/uk/library/index.html [4] The National Grid Company plc, Tenders, agreements and market reports. See http://www.nationalgrid.com/uk/ indinfo/balancing/mn_tenders.html [5] S. Ahmed, G. Strbac, A method for simulation and analysis of Reactive Power market, IEEE Trans. Power Systems, Vol.15, No.3, August 2000, pp.1047-1052. [6] S Ahmed et al, Method for green field security constrained allocation of reactive support, IEE Proceedings on Gen.,Trans. and Distribution, Vol. 146, No.1, January 1999, pp 65-71. [7] G. Strbac et al, Co-ordination of investment decisions and controls in reactive power planning, Paper 342-05, CIGRE symposium on Open access, Tours, France, 8-12 June 1997. [8] W.M. Lebow. A hierarchical approach to reactive volt ampere (VAR) optimisation in the system planning, IEEE Trans. on Power Systems, 1985, PAS-104,(8), pp. 20512057 [9] J..Kubokawa et al, An Interior Point nonlinear programming for Optimal Power Flow with a novel data structure, IEEE Trans. on Power Systems, Vol.13, No.3, August 1998, pp. 870-877. [10]V.H. Quintana et. al, Interior Point methods and their applications to Power Systems: A classification of publications and Software codes, IEEE Trans. on Power Systems, Vol.15, No.1, February 2000, pp. 170-176.