reactive power dispatch in the operation programming ...

REACTIVE POWER DISPATCH IN THE OPERATION PROGRAMMING OF LARGE HYDROTHERMAL POWER SYSTEMS VICTOR M. DOÑA ALEJANDRO HOESE Instituto de Energía Eléctrica (IEE) National University of San Juan Avda. Libertador San Martín 1109 (O) – (5400) San Juan, Argentina. Tel: ++54 (264) 4226444 - Fax ++54 (264) 4210299 - www.iee.unsj.edu.ar - [email protected] ARGENTINA

ABSTRACT Reactive power dispatch is required to maintain an appropriate voltage level throughout the power system. The lack of an accurate dispatch scheduling of reactive power may result in non-scheduled or forced starts of generating units. Thus, nodal spot prices are incremented with negative effects over the economic operation of the power system. This paper presents a proposal to dispatch generating units associated to reactive power and voltage control needs. This is done within the calculation of the economic dispatch during the operation programming of the power system. The main methodological aspects are shown together with the results obtained in a real network.

KEYWORDS: Operation programming - Reactive power dispatch- Voltage control - Low meshed networks

1. INTRODUCTION During operation programming stages, where dispatch of thermal and hydraulic generating units are defined, the electric network of the considered power system plays an important roll among a great number of other constraints involved. The importance and incidence of introducing the network in this calculation depends generally on the topological structure and characteristics of the considered power system. Power systems with networks that are enough redundant (high transmission reserve) and highly meshed do not present limitations in the normal operation. Therefore, the economic operation of the power system can be found successfully without modeling the electric network. The economic dispatch is then solved in "unique bus". Nevertheless, some power systems have an exten-

sive and weakly meshed network configuration with a low transmission reserve. Furthermore, there exist certain limitations, which impose severe network operation constraints. These types of systems are common in geographical extensive countries, which is the case of most latinamerican countries. In this situation, economic dispatch should be achieved including the transmission network constraints. Otherwise, the scheduled dispatch in unique bus would not be feasible of being operated. There are mainly two problems that would arise if the electric network is not considered: • •

Transmission congestion (normally extensive links due to stability constraints). Low voltage levels in certain buses, areas or electrical regions (need of reactive power).

The lack of an accurate dispatch scheduling of reactive power may result in non-scheduled or forced starts of generating units. Thus, nodal spot prices are incremented with negative effects over the economic operation of the power system.

2. AIM OF THE WORK Traditionally, a simplified electric network model has been considered for the operation programming. It has been done with the aim of controlling the first aspect before mentioned, i.e. transmission congestion. The introduction of an original and novel methodology to solve the second aspect, related with the fulfillment of level voltage constraints and reactive power needs, is put forward in this work. The model has been developed to be embedded into a complex software to solve the optimal operation programming of multi-nodal and multireservoirs hydrothermal systems, which has allowed to achieve important results and conclusions.

The aim of the presented methodology is summarized as:

3.2 Reactive power and voltage control

“It should be responsible, during the optimization process of the operation programming, of - detecting those buses or electric areas having reactive power deficit, - quantifying their magnitude and - proposing the start of generating units to avoid these reactive power deficits."

In the problem associated to reactive power, following tasks should be done: • To solve locally (by electrical regional networks) the voltage control problem. It should be done in coordination with the use of available compensation of reactive power in transmission and distribution. • To supply the reactive power requirement as near as possible to loads. • To maintain a reactive power reserve, i.e. to maintain rotating units and compensation equipment below their technical limits.

3. PROBLEM ANALYSIS Under certain conditions, the constraints that would be controlled with the incorporation of the transmission network are mainly related to: 1) a problem associated to active power (transmission constraints) and , 2) a problem associated to reactive power (voltage constraints).

3.1 Decoupling of the problem Following characteristics appear in high and very high voltage power systems (132 kV to 750 kV), where the relation R/X is less than 1/4 per unit. • • •

Strong sensitivity among active power flows and nodal voltage angles. Strong sensitivity among reactive power flows and nodal voltage magnitudes. Weak cross sensitivity.

Therefore there exist following properties: • • •

small cooper losses in lines and transformers, small iron losses in transformers, small angles differences ∆θ among adjacent buses.

The last property is related to stability studies that impose active power transmission constraints. For static stability conditions it is known that this angle difference has the value of ∆θ = (20......30)° . For transient stability constraints ∆θ is even smaller. Because of the before mentioned characteristics, there exists a decoupled behavior between active and reactive power models. Therefore, transmission congestion can be considered into the active power model while voltage constraints can be considered into the reactive power model.

The fulfillment of these objectives has following advantages: • Reduction of reactive power flow through the network. • Minimization of active and reactive losses. • Reduction of voltage falls and improvement of the bus voltage levels. • Operation of generators with high power factors. • Availability of reactive power reserve for contingencies. This also implies a benefit in the operation costs of the electric system. The availability of greater reserve margin of reactive power is linked to the improvement in the operation security. Thus, damages due to possible voltage collapses could be avoided.

4. MODELING The actual network can be modeled in detail or through a simplified equivalent containing the main components of the network (for example the main transmission system). In this case, regional networks are modeled as equivalents in some buses of the simplified network. The reactive power information is summarized at these regional buses. The simplification of one regional network is shown in Figure 1. regional network linked to bus i Qcar k Ui / θ i

Ui /θ i

Qi

Qi

G Sgi = Pgi + j Qgi

Qper ind Qper cap

FIGURE 1 -

j j

Sdi = Pdi + j Qdi

Regional network Si modeled in bus i.

The simplified equivalent model of the network is quite exact if: • All active and reactive power loads (included the simplified regional networks) are transferred to buses of the equivalent network. • All compensation equipment of reactive power (both fixed and variable) is transferred to buses of the equivalent network. • All active and reactive power losses of simplified regional networks are transferred to buses of the equivalent network. These values are calculated with referential values of voltage and current.

STAGE III (Active power re-dispatch): The optimal dispatch considering the information of the previous stages and all operation constraints of generating units is determined.

5. DEVELOPED METHODOLOGY

The DESTER module is the core of STAGE I and STAGE III. This module calculates the economic dispatch of thermal units having into account transmission network constraints, spinning reserve, min. operation times and out-of-service times, ramping, etc., for a given hydraulic dispatch within the iterative process of the hydrothermal dispatch optimization. Details of this model can be analyzed at the complementary reference [4].

The calculation of reactive power deficit and the dispatch proposal is done through an integrated and fast methodology embedded into the optimal operation programming. Decoupling hypothesis of active and reactive power models allow treating network constraints separately. In order to fulfill these constraints the proposed methodology is inserted in a hierarchical three-stage decoupled problem. STAGE I (Active power pre-dispatch): The methodology includes an economic dispatch model of thermal units considering transmission constraints. A DC power flow is solved in this model obtaining, among other results, the phase angles per bus. At this stage, the dispatch methodology is unable to see reactive power deficits per bus that may occur due to voltage problems. STAGE II (Reactive power dispatch): Reactive power deficits are calculated and starts of generating units are proposed to reduce voltage level problems. The model uses the calculated values of phase angles and -as additional information- external reference files of seasonal nodal voltages and currents. The location and magnitude of reactive power deficits are detected at this stage. It is done by comparing needs vs. availability of reactive power at each bus of the network. The availability of reactive power is calculated using the capability curves of dispatched generators and compensation equipment related to each bus. A given percentage of reactive power reserve in generators and variable compensators (synchronic compensators and static var systems SVC) is also considered. Reactive power deficits could be avoided by proposing starts of local generating units in the deficit area. A heuristic process tends to mitigate the reactive power deficit per bus until all values remain bellow pre-established tolerances. In order to do this, starting thermal units and redispatching of hydoelectric units is considered.

Although this methodology leads to higher operation costs, the security of this dispatch is guaranteed. In the long run it will lead to lower operation costs, because forced starting of non economic units due to voltage problems are minimized.

5.1 Component blocks

STAGE II is done by means of the MODREA module, that integrates following calculation blocks: • Block INYREA: Calculation of reactive power injection. • Block DEMREA: Calculation of reactive power demand. • Block COMREA: Calculation of reactive power compensation. • Block GENREA: Calculation of reactive power generation. • Block DEFREA: Calculation of reactive power deficit. • Block DESREA: Reactive power dispatch. These blocks are linked each other to analyze all network busses. A summarized global structure of the developed methodology is presented follows in Figure 2.

5.2 Methodological description The function of DESTER module (STAGE I and III) and of each block of MODREA module (STAGE II) is briefly described hereinafter. •

DESTER Module

During the operation programming, decisions of hydraulic dispatch interact with decisions of the thermal dispatch in order to fulfill the optimum criteria within a

complex hydrothermal coordination. Reference [5] describes the short-term optimization process. Within this complex coordination the DESTER module calculates the economic dispatch of thermal units considering transmission congestion management. iteration k

A model of non-linear optimization is stated: a linear function of operation costs is used as objective function, generating powers and phase angles as control variables, and generation and transmission capacity limits as constraints. The non-linear problem including network power losses is solved iteratively using CPLEX [4]. A DC power flow is internally solved and the resulting phase angles θ are used as input data for STAGE II.

HYDROTHERMAL DISPATCH

• Hydraulic dispatch

Load

This block allows determining Qi injections of reactive power for each bus using θ angles, admittance nodal matrix and buses voltage magnitudes U. The last are taken from external referential values pre-calculated for typical load states.

DESTER Module

Network

Tita angles

STAGE II

Capability curves

In this step the following reactive power balance is used: Qi = Qgi − Qdi = U i2 ⋅ Bii + (1) + ∑U i ⋅U k [Gik ⋅ sen(θi − θk ) − Bik ⋅ cos(θi − θk )] k∈nv

INYREA Block Referencial voltages and currents

where nv is the number of links with the node i,, Gik and Bik are elements of the admittance nodal matrix.

DEMREA Block

• COMREA Block

Seasonal calculations of the complete network

GENREA Block

Yes network bus i+1

Block INYREA

STAGE I

Qgi < Qgi max dispatched units ?

No

DEFREA Block

Block DEMREA

Reactive load powers Qdi are calculated in this block for each bus i of the network. As it is shown in Figure 1, a regional network Si can be taken as equivalent in bus i. In order to calculate the Qd reactive load it is taken into account: - the actual reactive load of bus i, - the actual reactive load of the buses of the subsystem Si and - an additional reactive load corresponding to the estimated 'reactive power losses’ (for the k iteration) of inductive and capacitive power in all Si subsystem components.

DESREA Block

For the Π circuit modeling, the 'reactive power losses’ in a component ik are: STAGE III DESTER Module

HYDROTHERMAL DISPATCH iteration k+1

FIGURE 2 - Structure of the general methodology

B B 2 Q perik ≅ I ik ⋅ X ik − U i2 ⋅ ik − U k2 ⋅ ik 2 2

(2)

where currents and voltages values are taken from precalculated referential information. •

Block COMREA

This block calculates the maximum available capacity Qci of the compensation equipment per bus i. Fixed (shunt banks) and variable (synchronic compensators and SVCs) compensation equipment available in the Si subsystem

are included. In order to have reactive power reserve in the variable equipment to face possible contingencies during the operation, convenient reserve margins per equipment can be set. •

Simplifications and hypothesis done in the present methodological proposal can be considered enough for the treatment of the reactive power in this phase of the optimal operation programming.

Block GENREA:

6. RESULTS This block calculates the minimum necessary reactive power generation Qgi and the maximum effectively available reactive power generation of the proposed dispatch Qmax at each bus i. Qgi is calculated having into account gi injection, demand and compensation of reactive power is found having into account the cafor each bus i. Qgmax i pability curves and a reserve factor for each dispatched unit. •

Block DEFREA:

This block calculates the reactive power deficit for each bus i as:

Q def i = Q gi - Q max gi •

(3)

Block DESREA:

Finally, this block takes decisions to modify the previously programmed dispatch in order to avoid reactive power deficits. Thus, a heuristic is implemented, which tries to reduce such deficits per bus bellow a given tolerance. These steps are: 1. Reduce the local deficit of a bus i, using partially reactive power reserve in buses with negative deficit and directly linked to the bus i. 2. If power deficit persists, reduce it by a redistribution of the hydraulic power dispatched. That is to say, the starting of more hydraulic units at a same power plant (if available) satisfying the same active power previously dispatched. First, power plants linked directly to the given bus i are analyzed, and then those directly linked to neighboring buses. 3. If power deficit still persists, reduce it through the starting of thermal generating units. The start requires the combination among this subset of machines, which would cover the most possible lacking reactive power deficit at the least operation cost (calculated at minimum operation power). First those units linked directly with the given bus i are started, then those directly linked to neighboring buses. 4. If even then power deficit persists, a signal is sent to the thermal unit dispatch in order to decide about the feasibility of the current hydrothermal dispatch. Forcing of thermal units at technical minimum due to reactive power requirements are considered in a next call to the DESTER module (STAGE III).

The developed methodology has been applied to the Central-North electric power system of Peru (SICN). This system is conformed by an extensive and weakly meshed network in 220 kV, 138 kV and 60 kV. It has 172 buses and 103 thermal and hydraulic units. The program calculates an equivalent reduced network of 43 nodes and 71 lines and transformers starting from the actual complete network. This simplified network maintains the complete structure in 220 kV and some sections of 138 kV and 60 kV. Some regional networks were reduced in their linking bus with the main system. The methodology was validated through various sensitivity analyses that allow verifying the impact in the reduction of reactive power deficits: • • • • •

Sensitivity to referential nodal voltages. Sensitivity to dispatch of generating units. Sensitivity to available reactive power reserve from neighboring buses. Sensitivity to redistribution of active power dispatches in hydraulic power plants. Sensitivity to preventive maintenance of reactive power compensation.

The following verifications have been also done: • • • •

Verification of effective reduction of total power reactive power deficit per bus. Verification of effective reduction of active transmission power losses. Verification of effective increase of maximum reactive power capacity dispatched. Verification of resulting bus voltages.

The analysis has been done on several runs carried out with the short-term (1-week horizon) and medium-term (3-years horizon) hydrothermal optimization models. Some results are shown for a shor-term optimization case having 7 days in 102 periods of time (48-24-6-6-66-6). It is observed in Figure 3 the reduction of total reactive power deficit (all buses) for the second day. Series 1 shows the initial reactive power deficit per hour detected after pre-dispatch of STAGE I. Series 2 corresponds to the deficit situation after running MODREA at STAGE II. It is observed that, in some periods, reactive power deficit is reduced to zero while in others it still

Voltage level improvement

persists. Further improvements cannot be done without varying the hydraulic dispatch. V Difference (%)

Figure 4 shows comparatively the profile of initial and final bus voltages obtained for the 43 buses of the equivalent network (period Nº 8). In this case MODREA obtains an improvement of max. 5.3% in voltage level, as it is observed in Figure 5. Power losses are reduced in 2.71% (from158.98 MW to 154.67 MW for this period).

6 5 4 3 2 1 0 -1

Bus

7. CONCLUSIONS FIGURE 5 – Improvement of the voltage profile This paper presents a methodology to deal with the aspects linked to reactive power and voltage control requirements during the optimization of hydrothermal operation programming. In weakly meshed networks the methodology produces savings in operation costs in comparison with situations of forced non-programmed dispatches. Reactive Power Deficit Variation [MVAr]

The developed methodology shows a good integration to the whole optimization process. It presents good reliability in the solution and reduced calculation time. No convergence difficulties have been observed. The reduced calculation time allows MODREA to be embedded into the core of the economic dispatch and transmission congestion management process for operation programming.

500

Applications of this methodology were done to the actual Peruvian power system in both short-term and mediumterm models. Dispatches for different periods with and without MODREA were analyzed. The results obtained validate a good performance of the developed methodology. It can be observed the start of thermal units in areas with high reactive power deficit. An improvement in the final voltage profile is achieved as well as a reduction in the transmission active power losses.

450

Qdef [MVAr]

400 350 300 250 200 150 100 50 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Series 1

Series 2

Period

FIGURE 3 – Reduction of the reactive deficit.

V-withoutMODREA

V-with MODREA

8. REFERENCES [1] V. Doña, “Zur Frage der optimalen zeitabhängigen

[2]

1.1

[3]

V (pu)

1

0.9

[4] 0.8

[5]

0.7

Bus

FIGURE 4 – Voltages profile with and without the model

Nutzung des (n-1)-Kriteriums in schwachvermaschten Verbundsystemen“, Ph.D Thesis, National University of San Juan, Argentina, February 1996. E. Handschin, “Elektrische Energieübertragungssysteme”, Hüthig Verlag, Heidelberg, Germany, 1987. V. Doña, “MODREA: A methodology to dispatch generating units in order to maintain the nodal voltages levels”, Internal reports. IEE, National University of San Juan, Argentina, May 1998, March 1999, May 2000. A. Hoese, V. Doña. “Spot pricing and transmission congestion management in large hydrothermal power systems”. EuroPES, Greece, July 2001. T. J. Strada, O. Mut “Short-term operation programming of complex hydrothermal power systems. TULUM Model”. IX Cigré Latinamerican Regional Meeting (ERLAC), Foz do Iguazú, Brazil, May 2001.