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MODULE IV
ECONOMIC OPERATION OF POWER SYSTEM
INTRODUCTION
One of the earliest applications of on-line centralized control was to provide a central facility, to operate economically, several generating plants supplying the loads of the system. Modern integrated systems have different types of generating plants, such as coal fired thermal plants, hydel plants, nuclear plants, oil and natural gas units etc. The capital investment, operation and maintenance costs are different for different types of plants.
The operation economics can again be subdivided into two parts.
i) Problem of economic dispatch, which deals with determining the power output of each plant to meet the specified load, such that the overall fuel cost is minimized.
ii) Problem of optimal power flow, which deals with minimum – loss delivery, where in the power flow, is optimized to minimize losses in the system. In this chapter we consider the problem of economic dispatch.
During operation of the plant, a generator may be in one of the following states:
i) Base supply without regulation: the output is a constant.
ii) Base supply with regulation: output power is regulated based on system load.
iii) Automatic non-economic regulation: output level changes around a base setting as area control error changes.
iv) Automatic economic regulation: output level is adjusted, with the area load and area control error, while tracking an economic setting.
Regardless of the units operating state, it has a contribution to the economic operation, even though its output is changed for different reasons. The factors influencing the cost of generation are the generator efficiency, fuel cost and transmission losses. The most efficient generator may not give minimum cost, since it may be located in a place where fuel cost is high. Further, if the plant is located far from the load centers, transmission losses may be high and running the plant may become uneconomical. The economic dispatch problem basically determines the generation of different plants to minimize total operating cost. Modern generating plants like nuclear plants, geo-thermal plants etc, may require capital investment of millions of rupees. The economic dispatch is however determined in terms of fuel cost per unit power generated and does not include capital investment, maintenance, depreciation, start-up and shut down costs etc.
PERFORMANCE CURVES
INPUT-OUTPUT CURVE
This is the fundamental curve for a thermal plant and is a plot of the input in British thermal units (Btu) per hour versus the power output of the plant in MW as shown in Fig.4.
Fig.4.1: Input output curve
HEAT RATE CURVE
The heat rate is the ratio of fuel input in Btu to energy output in KWh. It is the slope of the input
- output curve at any point. The reciprocal of heat – rate is called fuel – efficiency. The heat rate curve is a plot of heat rate versus output in MW. A typical plot is shown in Fig.
Incremental cost curve
The incremental cost is the product of incremental fuel rate and fuel cost (Rs / Btu or $/Btu). The curve in shown in Fig.4.4. The unit of the incremental fuel cost is Rs / MWh or $ /MWh.
Fig. 4.4: Incremental Cost curve
In general, the fuel cost Fi for a plant, is approximated as a quadratic function of the
generated output PGi.
Fi aibiPGiciPGi^2 Rs/h
The incremental fuel cost is given by
dPGii^ bi ciP^ Gi
dF (^) 2 Rs/MWh
The incremental fuel cost is a measure of how costly it will be produce an increment of power. The incremental production cost, is made up of incremental fuel cost plus the incremental cost of labour, water, maintenance etc. which can be taken to be some percentage of the incremental fuel cost, instead of resorting to a rigorous mathematical model. The cost curve can be approximated by a linear curve. While there is negligible operating cost for a hydel plant, there is a limitation on the power output possible. In any plant, all units normally operate between P (^) Gmin, the
minimum loading limit, below which it is technically infeasible to operate a unit and P (^) Gmax, which is the maximum output limit.
ECONOMIC GENERATION SCHEDULING NEGLECTING LOSSES AND GENERATOR LIMITS
In an early attempt at economic operation it was decided to supply power from the most efficient plant at light load conditions. As the load increased, the power was supplied by this most efficient plant till the point of maximum efficiency of this plant was reached. With further increase in load, the next most efficient plant would supply power till its maximum efficiency is reached. In this way the power would be supplied by the most efficient to the least efficient plant to reach the peak demand. Unfortunately however, this method failed to minimize the total cost of electricity generation. We must therefore search for alternative method which takes into account the total cost generation of all the units of a plant that is supplying a load.
The simplest case of economic dispatch is the case when transmission losses are neglected. The model does not consider the system configuration or line impedances. Since losses are neglected, the total generation is equal to the total demand P (^) D.
Consider a system with n (^) g number of generating plants supplying the total demand PD. If F (^) i is the cost of plant i in Rs/h, the mathematical formulation of the problem of economic scheduling can be stated as follows:
Minimize
n g T (^) i i
F F
1
Such that
n g i Gi^ D
P P
1
Where FT = total cost PGi= generation of plant i PD = total demand This is a constrained optimization problem, which can be solved by Lagrange’s Method.
LAGRANGE METHOD FOR SOLUTION OF ECONOMIC SCHEDULE
The above equation is called the co-ordination equation. Simply stated, for economic generation scheduling to meet a particular load demand, when transmission losses are neglected and generation limits are not imposed, all plants must operate at equal incremental production costs, subject to the constraint that the total generation be equal to the demand.
ECONOMIC SCHEDULE INCLUDING LIMITS ON GENERATOR (NEGLECTING LOSSES)
The power output of any generator has a maximum value dependent on the rating of the generator. It also has a minimum limit set by stable boiler operation. The economic dispatch problem now is to schedule generation to minimize cost, subject to the equality constraint.
n g i Gi^ D
P P
1
and the inequality constraint
PGi(min) ≤ P (^) Gi ≤ PGi(max) i = 1, 2, ……… n (^) g
The procedure followed is same as before i.e. the plants are operated with equal incremental fuel costs, till their limits are not violated. As soon as a plant reaches the limit (maximum or minimum) its output is fixed at that point and is maintained a constant. The other plants are operated at equal incremental costs.
ECONOMIC DISPATCH INCLUDING TRANSMISSION LOSSES
When transmission distances are large, the transmission losses are a significant part of the generation and have to be considered in the generation schedule for economic operation. The mathematical formulation is now stated as
Minimize
n g T (^) i i
F F
1
Such that (^) L
n i Gi^ D
P P P
g
^
1 Where P (^) L is the total loss
The Lagrange function is now written as
1^ L
n T D i Gi
L F P P P
g
The minimum point is obtained when
(^1 )^0
Gi
L Gi
T Gi P
P
P
F
P
L i =1,2,........... n (^) g
^
ng D (^) i Gi L
L P P P
1 0 (same as the constraint)
Since Gi
i Gi
T dP
dF P
F
Gi
L Gi
i dP
dP dP
dF
Gi
Gi L
i dP
dP dP
dF 1
^1
The term
Gi
L dP 1 dP
(^1) is called the penalty factor of plant i , Li. The coordination equations including
losses are given by
dPGii^ L^ i dF i =1,2, ............, n (^) g
The minimum operation cost is obtained when the product of the incremental fuel cost and the penalty factor of all units is the same, when losses are considered.
A rigorous general expression for the loss P (^) L is given by
PL m n PGmBmnP Gn
Fig.4.5: Schematic diagram of automatic load dispatching components
Data Input: The computer receives a lot of data from the telemetering system and from the paper tape. Telemetering data comes to the computer either as analog signals representing line power flows, plant outputs or as signal bits indicating switch or isolator positions. Paper tape stores all the basic data required e.g. the system parameters, load predictions, security constraints, etc.
Console: It is the component through which the operator can converse with the computer. He can obtain certain information required for some action to be taken under emergency condition or he can put data into it if needed. The console has the facilities of security checking and load flows for the network calculations.
Machine Controller: The computer sends information regarding the optimal generation to the machine controller at regular intervals which in turn implements them. Control on each machine is applied by a closed loop system which uses a measure of actual power generated and which operates through a conventional speeder motor. These are referred to as controller power loops. In the power frequency loop an error signal proportional to the difference between the derived and actual frequency and power is developed. A summed error signal is formed from these two components and is converted in the motor controller to a train of pulses that are applied to a speed governor reference setting motor called the speeder motor. The duration and amplitude of these pulses are fixed but the pulse rate is made proportional to the summed error signal. The pulses are applied as raise or lower command to the speeder motor in accordance with the error signal and thus the output of the generator is increased or decreased accordingly.
HYDROTHERMAL SCHEDULING LONG AND SHORT TERMS-
Long-Range Hydro-Scheduling:
The long-range hydro-scheduling problem involves the long-range forecasting of water availability and the scheduling of reservoir water releases (i.e., “drawdown”) for an interval of time that depends on the reservoir capacities. Typical long-range scheduling goes anywhere from 1 week to 1 yr or several years. For hydro schemes with a capacity of impounding water over several seasons, the long-range problem involves meteorological and statistical analyses.
Short-Range Hydro-Scheduling
Short-range hydro-scheduling (1 day to 1 wk) involves the hour-by-hour scheduling of all generation on a system to achieve minimum production cost for the given time period. In such a scheduling problem, the load, hydraulic inflows, and unit availabilities are assumed known. A set of starting conditions (e.g., reservoir levels) is given, and the optimal hourly schedule that minimizes a desired objective, while meeting hydraulic steam, and electric system constraints, is sought. Hydrothermal systems where the hydroelectric system is by far the largest component may be scheduled by economically scheduling the system to produce the minimum cost for the thermal system. The schedules are usually developed to minimize thermal generation production costs, recognizing all the diverse hydraulic constraints that may exist.
Fig. 4.6: Hydro Scheduling
The hydroplant can supply the load by itself for a limited time. That is, for any time period j,
So steam plant should be run at constant incremental cost for the entire period it is on. Let this optimum value of steam-generated power be Ps*, which is the same for all time intervals the steam unit is on.
The total cost over the interval is
Ns s j
N T s j s j j s s F F P n FP n F P T 1 1
( *^ ) ( *) ( *)
T (^) s is the total run time for the steam plant
The total cost FT ( a bPs *^ cPs *^2 ) Ts
Also
N s s j
N sj j j s j s s Pn Pn PT E 1 1
So (^) * s (^) P s
T E
( * *^2 )( * )
T s s P s F a bP cP E
Minimizing FT , we get Ps * ac
So the unit should be operated at its maximum efficiency point (Ps*) long enough to supply the energy needed, E. Optimal hydrothermal schedule is as shown below:
Fig.4.7: Optimal Hydrothermal Scheduling
FACTS
The large interconnected transmission networks are susceptible to faults caused by lightning discharges and decrease in insulation clearances. The power flow in a transmission line is determined by Kirchhoff’s laws for specified power injections (both active and reactive) at various nodes. While the loads in a power system vary by the time of the day in general, they are also subject to variations caused by the weather (ambient temperature) and other unpredictable factors. The generation pattern in a deregulated environment also tends to be variable (and hence less predictable). The factors mentioned in the above paragraph point to the problems faced in maintaining economic and secure operation of large interconnected systems. The probles are eased if sufficient margins (in power transformer) can be maintained. The required safe operating margin can be substantially reduced by the introduction of fast dynamic control over reactive and active power by high power electronic controllers. This can make the AC transmission network flexible to adapt to the changing conditions caused by contingencies and load variations. Flexible AC Transmission System (FACTS) is used as Alternating current transmission systems incorporating power electronic-based and other static controllers to enhance controllability and increase power transfer capability. The FACTS controller is used as a power electronic based system and other static equipment that provide control of one or more AC transmission system parameters like voltage, current, power, impedance etc. Benefits of utilizing FACTS devices : The benefits of utilizing FACTS devices in electrical transmission systems can be summarized as follows:
- Better utilization of existing transmission system assets.
- Increased transmission system reliability and availability.
- Increased dynamic and transient grid stability and reduction of loop flows.
- Increased quality of supply for sensitive industries. FACTs controllers: Structures & Characteristics of following FACTs Controllers The FACTS controllers can be classified as—
- Shunt connected controllers
- Series connected controllers
- Combined series-series controllers
- Combined shunt-series controller
capacitive reactance. Even through a TCSC in the normal operating range in mainly capacitive, but it can also be used in an inductive mode. The power flow over a transmission line can be increased by controlled series compensation with minimum risk of sub-synchronous resonance (SSR).TCSC is a second generation FACTS controller, which controls the impedance of the line in which it is connected by varying the firing angle of the thyristors. A TCSC module comprises a series fixed capacitor that is connected in parallel to a thyristor controlled reactor (TCR). A TCR includes a pair of anti-parallel thyristors that are connected in series with an inductor. In a TCSC, a Metal Oxide Varistor (MOV) along with a bypass breaker is connected in parallel to the fixed capacitor for overvoltage protection. A complete compensation system may be made up of several of these modules. TCSC controllers use thyristor-controlled reactor (TCR) in parallel with capacitor segments of series capacitor bank. The combination of TCR and capacitor allow the capacitive reactance to be smoothly controlled over a wide range and switched upon command to a condition where the bi- directional thyristor pairs conduct continuously and insert an inductive reactance into the line. TCSC is an effective and economical means of solving problems of transient stability, dynamic stability, steady state stability and voltage stability in long transmission lines. A TCSC is a series controlled capacitive reactance that can provide continuous control of power on the ac line over a wide range.
Fig.4.9: Thyristor Controlled Series Capacitor
Static Synchronous Series Compensator (SSSC)
A SSSC is a static synchronous generator operated without an external electric energy source as a series compensator whose output voltage is in quadrature with, and controllable
independently of the line current for the purpose of increasing or decreasing the overall reactive voltage drop across the line and thereby controlling the transmitted electric power. The SSSC may include transiently rated energy source or energy absorbing device to enhance the dynamic behaviour of the power system by additional temporary real power compensation, to increase or decrease momentarily, the overall real voltage drop across the line.
A SSSC incorporates a solid state voltage source inverter that injects an almost sinusoidal voltage of variable magnitude in series with a transmission line. The SSSC has the same structure as that of a STATCOM except that the coupling transformer of an SSSC is connected in series with the transmission line. The injected voltage is mainly in quadrature with the line current. A small part of injected voltage, which is in phase with the line current, provides the losses in the inverter. Most of injected voltage, which is in quadrature with the line current, emulates a series inductance or a series capacitance thereby altering the transmission line series reactance. This reactance, which can be altered by varying the magnitude of injected voltage, favourably influences the electric power flow in the transmission line.
Fig.4.10: Static Synchronous Series Compensator
SSSC is a solid-state synchronous voltage source employing an appropriate DC to AC inverter with gate turn- off thyristor. It is similar to the STATCOM, as it is based on a DC capacitor fed VSI that generates a three - phase voltage, which is then injected in a
Fig.4.11: Static Synchronous Compensator By controlling the magnitude of the STATCOM voltage the reactive power exchange between the STATCOM and the transmission line and hence the amount of shunt compensation can be controlled. In STATCOM, the resonance phenomenon has been removed. So STATCOM is having more superior performance as compared to SVC.
Unified Power Flow Controller (UPFC) The UPFC, by means of angularly unconstrained series voltage injection, is able to control, concurrently or selectively, the transmission line voltage, impedance, and angle or, alternatively, the real and reactive power flow in the line. The UPFC may also provide independently controllable shunt reactive compensation. The UPFC is the most versatile and powerful FACTS device. UPFC is also known as the most comprehensive multivariable flexible ac transmission system (FACTS) controller. Simultaneous control of multiple power system variables with UPFC poses enormous difficulties. In addition, the complexity of the UPFC control increases due to the fact that the controlled and the variables interact with each other. The Unified Power Flow Controller (UPFC) is used to control the power flow in the transmission systems by controlling the impedance, voltage magnitude and phase angle. This controller offers advantages in terms of static and dynamic operation of the power system. The basic structure of the UPFC consists of two voltage source inverter (VSI); where one converter is connected in parallel to the transmission line while the other is in series with the transmission line. The UPFC consists of
two voltage source converters; series and shunt converter, which are connected to each other with a common dc link. Series converter or Static Synchronous Series Compensator (SSSC) is used to add controlled voltage magnitude and phase angle in series with the line, while shunt converter or Static Synchronous Compensator (STATCOM) is used to provide reactive power to the ac system, beside that, it will provide the dc power required for both inverter. Each of the branch consists of a transformer and power electronic converter. These two voltage source converters share a common dc capacitor. The energy storing capacity of this dc capacitor is generally small. Therefore, active power drawn by the shunt converter should be equal to the active power generated by the series converter. The reactive power in the shunt or series converter can be chosen independently, giving greater flexibility to the power flow control. The coupling transformer is used to connect the device to the system.
Fig.4.11: Unified Power Flow Controller
