Reactive Power

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Reactive Power as an Ancillary Service Kankar Bhattacharya and Jin Zhong

Abstract—This paper addresses the problem of reactive power procurement by an independent system operator (ISO) in deregulated electricity markets. A reactive bid structure is proposed in the context of a reactive power market. Based on the reactive power price offers and technical constraints involved in reactive power planning, a two-tier approach is developed to determine the most beneficial reactive power contracts for the ISO. The reactive capability of a generator and therefore the opportunity costs in providing reactive power is also included in the model. Uncertainty in reactive demand and in reactive bids of participating parties is incorporated through Monte Carlo simulations and the expected reactive power procurement plan for the ISO is hence determined. The CIGRÉ 32-bus network, approximately representing the Swedish system, is used for the studies. Index Terms—Ancillary services, deregulation, independent system operator (ISO), Monte Carlo simulation, reactive power.

I. INTRODUCTION

I

N A DEREGULATED power system, the basic responsibility of the Independent System Operator (ISO) is to maintain system reliability and security by providing for ancillary services such as reactive power support, spinning reserves, energy balancing and frequency regulation. Sufficient reactive power support need to be provided in the system in order to maintain the power flow limits on transmission lines and voltage limits at bus bars. Also, since it is not desirable to transport reactive power over the network, it should be procured at different locations in the system depending upon perceived demand conditions, mix of the load and availability of reactive support devices. Such devices however, have different characteristics for example, generators are fast acting reactive support devices with high operating and opportunity costs, while capacitors are slow devices with lower installation and operating costs. Many of the deregulated markets are yet to establish a mechanism for financial compensation for reactive power ancillary services e.g., the Nordic countries. On the other hand, some markets do have schemes for payment for reactive support services. In UK, the National Grid Company, which carries out the functions of the ISO, invites tenders for reactive support services. The generators can bid for reactive power support through bids composed of capacity components (price per MVAr and quantity on offer) and an utilization component (MVAr-h price curve). The selected bidders get into annual bilateral contracts

Manuscript received September 11, 2000. This work was supported by the Sydkraft Research Foundation, Sweden, for the research project on ancillary ervices pricing. The authors are with the Department of Electric Power Engineering Chalmers University of Technology S-41296 Gothenburg, Sweden. Publisher Item Identifier S 0885-8950(01)03795-6.

with NGC and are paid for both the capability and utilization components [1]. In the New York system, the ISO (NYISO) is responsible for procuring reactive power support service, and the service is provided at embedded cost-based prices. Generating resources, which operate within their capability limits, are directed by the ISO to produce or absorb reactive power to maintain voltages within limits [3]. Further, the NYISO also provides for compensation to generators in case of revenue lost due to increased reactive power generation requests. If the ISO dispatches or directs a generator to reduce its real power output the generator receives a Lost Opportunity Cost (LOC) for the amount of revenue it loses from the lost generation and energy sell. The Australian electricity market and its ISO (NEMCO) also recognizes reactive power as an ancillary service and financial compensation is provided to generators and synchronous compensators for their service provisions [4]. All reactive support providers are eligible for the availability payment componentfor their preparedness to provide the service when called for. Synchronous compensators also receive the enabling payment component- paid when their service is activated by the ISO for use. On the other hand a generator receives the compensation payment component- which is based on its opportunity cost and paid when it has been constrained from operating according to its market decisions. For example if a generator has to provide reactive power where it has to reduce its real power generation in order to operate within the unit’s field and armature winding heating limits, the generator will be compensated for its lost real power generation. This payment component is similar to the LOC payment made in NYISO. These developments in the deregulated electricity markets indicate the trend toward treating reactive power as ancillary services and creating financial compensation schemes for reactive power providers. In the same context therefore, it is also important that the ISO identifies its reactive power requirements and device appropriate criteria for selecting the reactive power provider. For example, procurement of reactive power involves payments to be made by the ISO. Thus the ISO could seek those providers which minimize its total payments. Although this is a seemingly fair enough objective, this criterion could result in increased reactive flows on the network and hence increased energy losses in the system or even require curtailment of contracted trades. Increased energy loss will require the ISO to procure loss compensation services thus involving additional payments, which is undesirable. Complexities also arise when the ISO procures reactive power from independent generators, which are business entities. If the ISO requires such a generator to increase its reactive power, depending upon the operating point, it might have to reduce its real

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Fig. 2.

Generator’s expectation of financial compensation.

will hence incur revenue loss (RL), which needs to be compensated net of its cost savings from reduced generation, expressed as follows:

Fig. 1. Synchronous generator capability curve.

power generation in order to adhere to the field current limits in the rotor. With this backing down of generation, the generator will not be able to fulfill the contracted trades. In this paper we attempt to determine an appropriate scheme applicable to the ISO for procurement of reactive support from independent providers. II. GENERATOR REACTIVE POWER CAPABILITY The power output of a generator is usually limited to a value within the MVA rating by the capability of its prime mover. When real power and terminal voltage is fixed, its armature and field winding heating limits restrict the reactive power generation from the generator. The armature heating limit is a circle , centered on the origin , and with radius given by, (1) The field heating limit is also a circle, centered at , radius and given by (2) (Fig. 1) [5] (2) is the voltage at the generator terminal bus, is the steadyis the excitation voltage and is state armature current, the synchronous reactance. and are real and reactive power generation from the machine, respectively. The machine rating in MVA, is the point of intersection of the two circles (“ ” in Fig. 1). The corresponding real power generation is denoted by . When the limit on reactive power is imposed by the generator’s field heating limit (2) while, when the armature heating limit (1) imposes restricts the generators reactive power output. There is also an under-excitation limit, , to restrict the unit operation in under-excited mode due to localized heating in the end region of the armature. ( ) on the limiting Consider the operating point curve defined by (2). If more reactive power is required from the , the operating point requires shifting back along unit, say ), where . This signifies the curve to point ( that the unit has to reduce its real power generation to adhere to field heating limits when higher reactive power is demanded. It

(3)

RL

is the generation cost where, is the real power price, and as a function of production. If the operating point lies inside the limiting curve, say at ) then the unit can increase its reactive generation ( up to without incurring any additional cost, revfrom enue loss or real power generation shift. III. REACTIVE BID STRUCTURE In many deregulated markets, the ISO has a limited access to information on generators and hence may not be able to determine a generator’s revenue loss, which requires information on real power price (sometimes bilaterally fixed) and generator cost function. An appropriate option in such markets is to call for reactive bids from generators. We discussed regions on the reactive power coordinate in the previous section, which are now explicitly defined here to formulate the generator’s expectation of payment function. From a knowledge of generators expectation of payment, the ISO can call for reactive bids from all parties. : Reactive power Region-I: output in this range is used by the generator to meet its own requirements such as in boiler feed pump motors, circulating water system pump motors, ID fan and FD fan motors, step-up transformers, etc. The generator is not entitled to receive any payment for reactive power generation in this range. : This region denotes Region-II: without the reactive power that a generator provides over rescheduling its real power output. Though there is no increased cost due to the additional reactive output, the generator expects a payment for making available its service. This payment is made at a constant rate on a per MVAr basis, and analogous to the capacity charge. : This region denotes Region-III: the reactive power which a generator supplies, at the expense of reducing its real power output. The generator stands to lose revenue from loss of power sell. The payment that the generator expects from the ISO for this reactive support service will be proportional to the amount of reactive support it provides and at a rate determined by its revenue loses as given by (3). A typical expectation of financial compensation function can accordingly be shown as in Fig. 2. As seen from Fig. 2, the

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financial compensation and vis-á-vis the reactive bids called for, by the ISO, will require being in two parts, a constant term and one proportional to reactive power. This can be expressed mathematically as follows:

Subject to the Following Constraints: Load Flow Equations: (6) (7)

gen

(4)

is the bid-price from an independent generator , is is the the fixed component of bid price in $/MVAr and variable price proportional to reactive support provided in $/MVAr/MVAr. It is to be noted that unlike the usual two-part tariff structures, the above bid structure is different since the variable component payment is applicable only after complete utilization of reactive capacity from the constant price bid component.

Contracted real power generation at bus , p.u. Actual real power transaction between load at bus and generators, gen Reactive power support at bus , p.u Reactive power demand at bus , p.u Element of network and admittance matrix, p.u Angle associated with , radians Bus Voltage Limits: (8)

IV. REACTIVE POWER PROCUREMENT

Limit on Bilateral Transactions:

With a reactive bid structure established, the ISO requires a proper criterion to determine the best offers and hence formulate its reactive power procurement plan. Unlike real power markets where bids are selected in ascending order of prices, reactive power markets need to incorporate the location aspects also. For example, a low priced reactive bid at a bus remotely located, is not an attractive option for the ISO. Such a reactive support may prove to be detrimental for the system while also increasing transmission losses. Therefore the ISO needs to consider both the technical aspects involved in reactive support allocation as well as the bid price offers from parties and arrive at an optimal contract, best suited to the system. A two step approach proposed and presented below to address this problem: Step-I: The ISO determines the marginal benefit of each reactive bid with regard to system losses. The ISO shall seek to minimize losses lest, it would require to procure higher loss compensation services (also involving payments). Step-II: With the marginal benefit of each reactive bid known to the ISO, it seeks to maximize a societal advantage function (SAF) formulated by incorporating the price bid offers at this stage. A. Marginal Benefit from a Reactive Support Service The marginal benefit to the system from one unit of reactive support at a bus from a reactive bid can be determined from the duals of the system constraints applied to appropriate OPF models representing the grid. Consider the following modified OPF: Minimize: System transmission losses given by, (5) is the conductance of line bus voltage, p.u. voltage angle, radians.

, p.u.

(9) is the contracted real power transactions by a load at . bus with a generator The bilateral transactions are modeled using the method discussed in [6]. Reactive Power Capability Limit of Generators: (10a) (10b) Equation (10a) is applicable when the field heating limit acts as ) and (10b) when the armature the upper limit (i.e., for ). heating limit is applicable (i.e., for Lower Limits on Reactive Power Generation: As mentioned , is fixed a priori in Section II, the under-excitation limit, and hence the lower limit of reactive power generation is governed by the constraint, (11) 1) Duals Associated with Reactive Power Constraints: For the modified OPF described by equations (5)–(11), we use three sets of lagrange multipliers associated with the three reactive power constraints (7), (10), (11) to derive important conclusions. a) : Dual of Reactive Balance Constraint: This parameter is obtained from the dual of the reactive power balance (7) and denotes the sensitivity of the system loss parameter to reactive demand changes at a bus. is in units of MW/MVAr denoting the change in MW loss per MVAr change in reactive demand. is multiplied with a cost (in $/MW) denoting the valuation of reduced loss, parameter to obtain the marginal benefit. Thus the marginal benefit to the ISO from a change in reactive demand at a bus is given by, MB

in /MVAr

(12)

BHATTACHARYA AND ZHONG: REACTIVE POWER AS AN ANCILLARY SERVICE

b) : Dual of Generator Reactive Capability Constraint: When the generator is operating at its reactive capability limits, it is of interest to know how the system will benefit if it chooses to increase its reactive generation beyond this point. The dual of the constraint (10a) and (10b) obtained while minimizing system loss provides important information on these lines. indicates by how much the system loss will Thus, change for a unit change in generator reactive power capability. indicates that the reactive power generation is below that specified by the field/armature current limits (i.e., if , ). If , it indicates that the system losses will reduce if reactive generation at the bus is increased ), which is only possible by reducing real (i.e., , it indicates that the system losses power generation. If will increase if reactive generation is increased It is then not desirable to provide additional reactive power by reducing real power generation. The marginal benefit to the ISO from a generator supplying reactive power at its field/armature winding heating limit is given by, MB

/MVAr

/MVAr

Reactive Power Generation Limits: In Section IV-A we considered that the upper limit on reactive power is constrained by the field or armature heating limits. Now we consider that the generator is willing to reduce its real power output from to (refer Fig. 1) in order to provide higher reactive power (for a price). The constraint (16) states that the maximum reactive for an operating point, support available from a generator is (16) Reactive Power Generation Limits: According to the three regions on the reactive power domain, discussed in Section III, the reactive power output from a generator can be classified , or , to represent rein any of the three components: gions I, II or III, respectively. The governing algebraic relations between them can be written as follows (17)

(18) (19)

(13)

c) : Dual of Reactive Power Constraint on Lower Limit: This parameter is the dual associated with reactive constraint (11) applicable to reactive lower limits. Therefore, MB

297

(14)

, and are binary variables for the discrete selection of a reactive component from any of the three regions. According to (19) only one of the binary variables can be selected. This automatically restricts that can be in only one of the bidding areas shown in Fig. 2.

B. Societal Advantage Function of the ISO Marginal benefit (MB) for reactive support at each bus, and for each reactive power provider, is bid parameters and now available to the ISO. Then, we can define the composite advantage function for the ISO as follows: SAF

(15) and represent regions II and III mentioned in Section III, respectively. SAF in (15) represents the ISOs viewpoint, seeking contribution to system performance (in terms of loss reduction) from reactive power providers with lowest possible cost. C. SAF Maximization: Reactive Power Procurement Once the ISOs composite advantage function is constructed as in (15), the optimal reactive power procurement plan can be obtained from a second level model constructed using the information now available. Maximize: Societal Advantage Function given by (15). Subject to the Following Constraints: Load Flow Equations: [Equations (6) and (7)] Bus Voltage Limits: [Equation (8)] Limit on Bilateral Transaction: [Equation (9)]

V. RESULTS AND DISCUSSIONS The Swedish 32-bus test system [7] (Fig. 3) is used in this work to evaluate the optimal reactive power procurement plan for the ISO. The system consists of four major areas: • North—with basically hydro generation and some load. • Central—with a large amount of load and rather large thermal power generation. • Southwest—with a few thermal units and some load. • External—connected to the North. It has a mix of generation and load. A. Step-I: Obtain MB from Reactive Support at a Bus The marginal benefit from reactive power support at a bus is obtained by solving the modified OPF discussed in Section IV-A. The model is a nonlinear programming problem and is solved using the high-level programming platform GAMS and nonlinear programming solver MINOS-5 [8]. , and associated with each generator’s reactive power constraint, and discussed earlier in Section IV-A-1, is listed in Table I. The corresponding marginal benefits are determined /MW. from , and and (12)–(14), assuming The optimum reactive support, , which evolves from the model solution, is also shown. Either the field or armature winding heating limit, according to the operating condition, while the lower limit is specifies the upper limit fixed apriori. Accordingly, either or assume a nonzero value if touches the upper or lower limit, respectively. The

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TABLE II REACTIVE POWER PROCUREMENT PLAN AFTER FINAL OPTIMIZATION

B. Step-II: Final Optimization

Fig. 3. CIGRÉ-32 bus test system network configuration. TABLE I MARGINAL VALUES AND OPTIMAL REACTIVE POWER SCHEME

The second stage of optimization therefore seeks to find a compromise between the technically best and a financially safe solution for the ISO. Marginal benefits and offered bid prices are used in the final optimization that seeks to maximize the SAF (15). This problem (stated in Section IV-C) is a mixedinteger nonlinear programming problem and is solved using the GAMS/DICOPT solver. GAMS/MINOS5 and GAMS/XA are invoked by DICOPT as the nonlinear programming and integer programming solvers, respectively. The optimal reactive power procurement plan obtained after the second step is listed in Table II. Note that now the reac(at buses 4071, tive power plan at certain buses exceeds 4062, 1012 and 1022). These generators will require reducing their real power output to provide the additional reactive power, and will be compensated as per the bid price. When falls in region-III (ref. Section III), we desegregate in two compoand . denotes how much it provides within the nents, shows how much it provides above its reactive limits, and reactive limits (by reducing real output). The solution yields a positive and fairly high societal advantage for ISO. As expected, the system bears a higher transmission loss from this reactive power procurement plan since this plan is financially safe for the ISO. C. Uncertainty in Reactive Demand and Bid Price: Monte Carlo Simulation

Lagrange multipliers are zero if lies between the range of and . Therefore, the reactive power support plan which evolves in Table I adheres to the field/armature heating limits. The ISO achieves a minimum transmission loss with the above reactive power procurement plan. However, if the associated bid price of respective reactive power support is accounted for, we see that the ISO ends up with a very high and negative societal advantage value from the above plan. This is not desirable from the ISO’s viewpoint in deregulated markets.

The solution obtained in Section V-B assumes a particular load condition and a given set of reactive bid prices. Understandably, the solution obtained is a biased solution depending on the nature of input information. Monte Carlo simulation is used to model the uncertainty associated with the demand and bid prices. If the distribution form of uncertain parameters is known, the expected behavior of the system can be studied by averaging the outcomes of different simulation cases. Among the advantages of Monte Carlo simulation is its conceptual simplicity i.e., each simulation exercise (or sampling) can be viewed as a possible state of system operation. The reactive demand and bid prices have been assigned a range of variation, a normal distribution for the former and an uniform distribution for the later. Simulations are carried out over the range of uncertainties and the expected outcome is evaluated by averaging over the entire simulation samples.

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TABLE III OPTIMAL SOLUTION WITH UNCERTAINTY IN REACTIVE DEMAND

Fig. 4.

Expected reactive power on bus 4072 with uncertain reactive demand.

1) Uncertainty in Reactive Power Demand, : A normal distribution is considered for simulating the reactive demand uncertainty. Bid prices are held at their nominal values during this case. The optimal solution is obtained for each Monte Carlo simulation sample using the two-step approach discussed in Section IV and shown in Sections V-A and V-B. The expected reactive power procurement plan is given in Table III while Fig. 4 shows the solution convergence to the expected value with increasing sample size of Monte Carlo simulation. The reactive power procurement at bus “4072” converges to 0.49 p.u.MVAr in a Monte Carlo simulation with 200 samples. The expectations in Table III are somewhat different from the single simulation solution shown in Table II. The expected system loss is less and the expected societal advantage is more than the single simulation case. This indicates that the single simulation case was a typically high reactive demand case simulated. Over a range of reactive demand, the solution converges around the expectation values, shown in Table III. and : The 2) Uncertainty in Bid Price Parameters, is assumed to be uniformly distributed uncertainty in and over a range. The expected optimal solution is given in Table IV and Fig. 5 shows the solution convergence to the expected value with increasing sample size of Monte Carlo simulation. Reactive power procurement at bus “4072” converges to 0.29 p.u.MVAr with a sample size of 400. The expectations in Table IV are somewhat different from the single sample solution of Table II. However, the solution is quite close to the Monte Carlo simulation solution in Table III with

TABLE IV OPTIMAL SOLUTION WITH UNCERTAINTY IN BID PRICE

Fig. 5.

Expected reactive power on bus 4072 with uncertain bid prices.

reactive demand uncertainty. The large sample size with Monte Carlo simulations smoothens the otherwise biased single input and introduces a fairness in the solution. VI. CONCLUSION Procurement of various ancillary services is a complex issue for the independent system operator in deregulated electricity markets. Among various factors that need to be considered, are the benefit to the system from a particular service-in terms of system security, economics and reliability, and the cost of the service in terms of payments to be made to the service providers. In this paper we discuss the procurement of reactive power support. The benefit from reactive support at a bus is determined using the dual of the reactive power constraints. It is seen that the ISO tends to procure reactive power support from those providers, which provide the best societal advantage, i.e., have high marginal benefit from the service with price bids within acceptable ranges. Understandably, as the bid prices reduce, the reactive power selection plan changes. Similarly, the marginal benefit function also has a role in deciding the reactive power procurement plan. REFERENCES [1] The National Grid Company, plc., “NGC Reactive Market Report,”, Nov. 1999. [2] S. Ahmed and G. Strbac, “A method for simulation and analysis of reactive power market,” in Proceedings of Power Industry Computer Applications Conference 1999, 1999, pp. 337–341. [3] New York Independent System Operator, NYISO Ancillary Services Manual, 1999.

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[4] National Electricity Market Management Company (Australia), “National electricity market ancillary services,”, Nov. 1999. [5] A. E. Fitzgerald, C. Kingsley, and S. D. Umans, Electric Machinery, Fifth ed: McGraw-Hill Book Company, 1992. [6] J. Zhong and K. Bhattacharya, “Optimum Var support procurement for maintenance of contracted transactions,” Proc. Intl. Conf. on Electric Utility Deregulation, Restructuring and Power Technologies, 2000. [7] K. Walve, “Nordic 32A—A Cigré test system for simulation of transient stability and long term dynamics,” Svenska Kraftnat, Sweden, 1993. [8] GAMS Release 2.50, “A user’s guide,” GAMS Development Corporation, 1999.

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Kankar Bhattacharya received the Ph.D.degree from I.I.T. New Delhi in 1993. During 1993–1998, he was in the faculty of IGIDR, Bombay. Since 1998, he is with Chalmers University of Technology, Sweden. His interests are in power system dynamics, economic operations and deregulation issues.

Jin Zhong received the B.Sc. degree (Eng) from Tsinghua University, China in 1995 and the M.Sc. degree (Eng) from Electric Power Research Institute, China in 1998, where she continued as a Researcher till 1999. Currently, she is a Ph.D. student in Chalmers University of Technology.