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ISSN 0005-1144 ATKAFF 51(1), 3–18(2010)
Krešimir Vrdoljak, Nedjeljko Peri´ , Ivan Petrovi´ c c
Applying Optimal Sliding Mode Based Load-Frequency Control in Power Systems with Controllable Hydro Power Plants
UDK 621.311.07 681.537 IFAC 5.5.4
Original scientiﬁc paper
In this paper an optimal load-frequency controller for a nonlinear power system is proposed. The mathematical model of the power system consists of one area with several power plants, a few concentrated loads and a transmission ne

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Krešimir Vrdoljak, Nedjeljko Peri´ c, Ivan Petrovi´ c
Applying Optimal Sliding Mode Based Load-Frequency Controlin Power Systems with Controllable Hydro Power Plants
UDKIFAC621.311.07681.5375.5.4
Original scientiﬁc paper
In this paper an optimal load-frequency controller for a nonlinear power system is proposed. The mathema-tical model of the power system consists of one area with several power plants, a few concentrated loads and atransmission network, along with simpliﬁed models of the neighbouring areas. Firstly, a substitute linear modelis derived, with its parameters being identiﬁed from the responses of the nonlinear model. That model is used forload-frequency control (LFC) algorithm synthesis, which is based on discrete-time sliding mode control. Due toa non-minimum phase behaviour of hydro power plants, full-state feedback sliding mode controller must be used.Therefore, an estimation method based on fast output sampling is proposed for estimating the unmeasured systemstates and disturbances. Finally, the controller parameters are optimized using a genetic algorithm. Simulationresults show that the proposed control algorithm with the proposed estimation technique can be used for LFC in anonlinear power system.
Key words:
Fast output sampling, Genetic algorithm, Identiﬁcation, Load-frequency control, Power systemmodel, Sliding mode control
Primjena optimalnog kliznog režima upravljanja u sekundarnoj regulaciji frekvencije i djelatne snagerazmjene regulacijskim hidroelektranama.
U radu se predlaže optimalna regulacija frekvencije i djelatne snagerazmjene za nelinearni elektroenergetski sustav. Unutar matematiˇckog modela sustava jedno se regulacijsko po-druˇcje sastoji od nekoliko elektrana, manjeg broja koncentriranih trošila i prijenosne mreže. Ostala su regulacijskapodruˇcja u modelu modelirana pojednostavljeno, nadomjesnim linearnim modelom sustava ˇciji su parametri do-biveni identiﬁkacijom iz odziva nelinearnog sustava. Taj je linearni model zatim primijenjen u sintezi algo-ritma sekundarne regulacije koji je zasnovan na kliznom režimu upravljanja. Zbog neminimalno-faznog vladanjahidroelektrana primijenjena je struktura regulatora zasnovana na svim varijablama stanja sustava. Estimacija nem- jerljivih stanja i poreme´caja zasnovana je na metodi brzog uzorkovanja izlaznih signala sustava. Optimizacijaparametara regulatora provedena je korištenjem genetiˇckog algoritma. Simulacijski rezultati pokazuju kako je pred-loženi upravljaˇcki algoritam, uz predloženu metodu estimacije, mogu´ce koristiti za sekundarnu regulaciju frekven-cije i djelatne snage razmjene u nelinearnom elektroenergetskom sustavu.
Klju ˇcne rije ˇci:
brzo uzorkovanje izlaznog signala, genetiˇcki algoritam, identiﬁkacija, sekundarna regulacijafrekvencije i djelatne snage razmjene, model elektroenergetskog sustava, klizni režim upravljanja
1 INTRODUCTION
Power systems are complex, nonlinear systems that usu-ally consist of several interconnected subsystems or con-trolareas(CAs). CAs areinterconnectedbytie-lines. Mostof European countries are members of the European Net-work of Transmission System Operators for Electricity (ENTSO-E) interconnection [1].Deviation of system’s frequency from its nominal valueis a measure of imbalance between generated and con-sumed power. When there is more/less generated thanconsumed active power in a system its frequency in-creases/decreases. For power system’s safe operation it isnecessary to keep an equilibrium of consumed and genera-ted active power.The consumption of electrical energy in a power sys-tem constantly changes. Because the electrical energy can-not be stored in sufﬁcient amounts, the task of the powersystem is to continuously track the amount of consumedpower by changing generation of its power plants. That isroughly carried out by day-ahead consumption predictionand most of the power plants in a CA follow their day-ahead hourly schedule. Since the prediction is not perfect,difference of the actual consumption of active power fromitspredictedvaluemustbecompensatedbyload-frequency
ISSN 0005-1144ATKAFF 51(1), 3–18(2010)AUTOMATIKA 51(2010) 1, 3–18
3
Applying Optimal Sliding Mode Based Load-Frequency Control in Power Systems K. Vrdoljak, N. Peri´c, I. Petrovi´c
control (LFC). LFC within a CA is in charge of keepingarea’s frequency at reference value and active power ex-changes with all neighbor areas at contracted values. Thatis obtained by changing reference powers of generators en-gaged in LFC in a CA. For LFC studies it is usually as-sumed that each CA consists of a coherent group of gener-ators and that the frequency is unique within each CA. OneLFC controller is usually responsible only for its CA.Before applying any new LFC algorithm to real powersystem, its behavior must be thoroughly tested through si-mulations. An example power system is usually modeledas an interconnection of a few CAs. Models for LFC algo-rithms testing purposes are generally linear and they haveallpowerplantsengagedinLFCwithinaCAreplacedwith just one substitute power plant [2–5]. That power plant canbe of thermal type [6–9] or hydro type [10–13].Since linearized models are valid only in the vicinityof the operating point, they trustworthily represent realpower system dynamics only for close-to-nominal systemoperation. Changing of power system’s operating point iscaused by current amount and characteristic of power con-sumption, characteristics of all power plants within a CAand current number of power plants engaged in LFC ina CA. Additionally, linear models have constant parame-ters, while parameters of real power systems constantlyvary in time, due to their dependency on the operatingcondition. However, these commonly used models mayhave nonlinearities within turbines and their governors,but generator dynamics and nonlinearities in tie-lines areusually neglected. Although simpliﬁed and linear powersystem models are mostly used for testing new LFC al-gorithms, they may not be sufﬁcient to demonstrate algo-rithm’s adequacy and preparedness for proper functioningin real power system.As opposed, in this paper a detailed nonlinear powersystem model is used for LFC algorithm testing. In themodel one CA is modeled in detail, while other CAs withinthe interconnection are modeled with several simpliﬁca-tions. Besides, many different nonlinearities are present inthe model.Nowadays, proportional-integral (PI) algorithms withconstant parameters are mostly used in real power sys-tems [14–17]. The reasons to replace them with someadvanced control algorithm are the following: 1) systemswith PI control have long settling time and relatively largeovershoots in frequency’s transient responses [18]; 2) PIcontrol algorithm provides required behavior only in thevicinity of the nominal operating point for which it is de-signed; 3) future power systems will rely on large amountsof distributed generation with large percentage of renew-able energy based sources and that will further increasesystem uncertainties [19]; 4) the shortening of time peri-ods in which each level of frequency regulation must beﬁnished is also expected in the future [20].Therefore, throughout the recent decades many diffe-rent LFC algorithms were studied [21,22] and they showedvery good results on linearized power system models.Those algorithms are based on various methods, such asrobust control theory [14, 23], fuzzy logic [12, 24], neu-ral networks [25, 26], model predictive control [27, 28],optimal control [29,30], adaptive control [31,32], slidingmode control (SMC) [33,34] and others. Despite their ad-vantages, new and innovative LFC algorithms have hardlymanaged to replace classical and proven PI algorithm withconstant parameters, which is still prevailing in real powersystems.What is the reason for the prevalent usage of PI al-gorithm in real power systems despite the developmentof many advanced control techniques for LFC purpose?Could it be that simpliﬁed and linearized models used inthe studies of advanced methods are not adequate, andgood results obtained on simulations do not replicate inreal power systems? In this paper we’ll try to ﬁnd out if that’s true by testing the behavior of an advanced LFC al-gorithm (whose behavior is already proven on linear powersystem model [35]) on a nonlinear power system model.The nonlinear model used in this paper is created usingMATLAB’s SimPowerSystems Toolbox [36]. Althoughthe detailed nonlinear model is used here for testing the al-gorithm, its synthesis is based on the substitute linearizedmodel, as it is common in control applications. The sub-stitute linear model parameters are obtained by analyzingresponse signals recorded from the nonlinear model [37].An advanced controller based on discrete-time SMCfrom [35] is tested in this paper. When compared to PIcontroller, this controller shows improvement of system’sbehavior regarding: better disturbance rejection, maintain-ing required control quality in the wider operating range,simultaneous shortening of frequency’s transient responsesand avoidance of the overshoots and also robustness to un-certainties present in the system.In SMC, system closed-loop behavior is determined bya sub-manifold in the state space, which is called a slidingsurface. The goal of the sliding mode control is to drivethe system trajectory to reach the sliding surface and thento stay on it. When the trajectory is on the surface, systeminvariance to particular uncertainties and parameter vari-ations is guaranteed. The trajectory’s convergence fromany point in state space towards the surface can be ensuredwith an appropriate choice of a reaching law [38]. Theideal sliding along the sliding surface can only be achievedwhen continuous-time SMC with very high switching fre-quency of the control signal is used. Since in real powersystem LFC control signal is sent to power plants in dis-crete time, a discrete-time sliding mode controller is used4
AUTOMATIKA 51(2010) 1, 3–18
Applying Optimal Sliding Mode Based Load-Frequency Control in Power Systems K. Vrdoljak, N. Peri´c, I. Petrovi´c
here. In discrete-time SMC system the trajectory couldonly be kept inside a small band around the sliding sur-face. Optimal parameters of the sliding surface and of thereaching law are obtained by an optimization procedure,which is conducted using genetic algorithm (GA).If only thermal power plants are used for LFC in a CAthen stable sliding mode controller can be designed usingonly measured output signals. But in some power sys-tem there are either both, hydro and thermal power plants,or only hydro power plants that are engaged in LFC (e.g.Croatian power system [39]). Sliding mode based on fullstate feedback must be used in those systems because non-minimum phase behavior is present within a hydro powerplant. Therefore, from system’s measured output and state,all unmeasured system state must be estimated. State esti-mation method used here is based on fast output sampling(FOS) [40]. That method is appropriate for estimations inLFC due to the availability of multiple measurements of output signals in each sampling period of the controller.FOS estimation method is also used for the estimation of external disturbance, what additionally improves overallsystem behavior.The brief outline of the paper is as follows. Section 2presents nonlinear power system model and Section 3 de-scribes an identiﬁcation procedure which results in its sub-stitute linear model. Section 4 describes state and distur-bance estimation technique for the substitute model. Sec-tion 5 presents discrete-time SMC algorithm, while in Sec-tion 6 that algorithm is applied for LFC. Finally, Section7 contains simulation results obtained on nonlinear powersystem model.
2 NONLINEAR POWER SYSTEM MODEL
An interconnection of four CAs, as shown in Fig. 1,is used to test the proposed LFC controller. CA1 is mod-eled in high detail, with many nonlinearities present, whileall other CAs are partly simpliﬁed. The model is built us-ing SimPowerSystem, which is one of MATLAB’s tool-boxes. A nonlinear model of CA1 is shown in Fig. 2. CA1consists of seven power plants, which are hydro power
Control Area 3(thermal)Control Area 4(thermal)Control Area 1(hydrothermal)Control Area 2(hydro)
Fig. 1. Four control areas interconnection
plants (HPPs) or thermal power plants (TPPs). Three hy-dro power plants (HPPs 1, 2 and 3) are engaged in LFC.All loads within the CA are modeled as three concentratedinstances (Loads 1, 2 and 3). Breakers are used to switchparts of loads on or off, or to switch off thermal powerplant TPP 2. These switchings are done at different timeinstances. Transmission lines connecting plants and loads,as well as CAs of the interconnection, are modeled as
Π
sections of various lengths. Buses are used to measure ac-tive powers on important power lines. They measure pro-duction of each HPP engaged in LFC and total interchangewith neighbor CAs. In each of neighbor CAs total powergeneration is represented with a single power plant. Thepower plants in CA3 and CA4 are thermal power plants,while the power plant in CA2 is of hydro type. All valuesin the model are expressed in per units of their base values,which is common in LFC studies. Although, wherever it isneeded, those values are converted into real SI values.There are several inputs to LFC block in Fig. 2: 1)reference value of system’s frequency (50 Hz or 1 p.u.),2) measured value of system’s frequency from TPP 1, 3)reference value of total tie line active power, 4) measuredvalue of total tie line active power, and 5) total generatedpower from all HPPs engaged in LFC. Based on those va-lues, LFC block computes a change in total generation of all power plants engaged in LFC. That generation is thendivided among the power plants engaged in LFC and sentto them as control signals
u
1
,
u
2
and
u
3
.SMC based LFC algorithm has already been designedfor linear power system with hydro power plants engagedin LFC [35]. In order to apply that algorithm to the pro-posed nonlinear model, a linearization of the nonlinearmodel must be done ﬁrstly.
3 SUBSTITUTE LINEAR POWER SYSTEMMODEL
A linear model of a CA represented with single hydropower plant is shown in Fig. 3, while signals and parame-ters of that model are given in Tab. 1. The linear modelfrom Fig. 3 can be described with the following equations:
˙
x
i
(
t
) =
A
i
x
i
(
t
) +
N
CA
j
=1
j
=
i
A
ij
x
j
(
t
) +
B
i
u
i
(
t
) +
F
i
d
i
(
t
)
,y
i
(
t
) =
C
i
x
i
(
t
)
,
(1)where
x
i
∈
4
n
is the system’s state vector,
x
j
∈
4
p
is astate vector of a neighbor system,
u
i
∈
4
m
is the controlsignal vector,
d
i
∈
4
k
is the disturbance vector and
y
∈
4
l
is the output vector. Matrices in (1) have appropriatedimensions:
A
i
∈
4
n
×
n
,
A
ij
∈
4
n
×
p
,
B
i
∈
4
n
×
m
,
F
i
∈
4
n
×
k
and
C
i
∈
4
l
×
n
.
N
CA
is a number of CAs inthe interconnection.
AUTOMATIKA 51(2010) 1, 3–18
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Applying Optimal Sliding Mode Based Load-Frequency Control in Power Systems K. Vrdoljak, N. Peri´c, I. Petrovi´c
==> Tie line
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
||||||||||
|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
||||||||||
Load 1
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
||||||||||
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
||||||||||
Load 2
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
|||||||||||||
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
||||||||||||||
Load 3
C3B2A1Planned_Gen_2Planned_PtiePlanned_Gen_6Planned_Gen_3Planned_Gen_7Planned_Gen_4Planned_Gen_5Planned_Gen_11TPP 2PrefABCTPP 1PrefW11ABCLoad 3BABCLoad 3AABCLoad 2BABCLoad 2AABCLoad 1BABCLoad 1AABCLine 9 (33 km)ABCABCLine 8 (43 km)ABCABCLine 7 (15 km)ABCABCLine 6 (20 km)ABCABCLine 5 (70 km)ABCABCLine 4 (55 km)ABCABCLine 3 (5 km)ABCABCLine 2 (40 km)ABCABCLine 10 (17 km)ABCABCLine 1 (35 km)ABCABCLFCF_measPtie_measF_refPtie_refP_lfcu1u2u3HPP 5PrefABCHPP 4PrefABCHPP 3PrefABCHPP 2PrefABCHPP 1PrefABCBus 4Bus 3Bus 2Bus 1Breaker 5
A BC a b c
Breaker 4ABCabcBreaker 3
ABCabcBreaker 2
ABCabcBreaker 1
ABCabc
Fig. 2. A nonlinear model of CA1
11
1i
sT
+
11
Ri2i
sT sT
++
1
PiPi
K sT
+
2
s
π
1
i
R
--+
i
u
di
P
Δ
i
f
Δ
i
δ
Δ
+-
gi
x
Δ
gi
P
Δ
12
π
Bi
K
++
tiei
P
Δ
( )
N sij i j j 1
K
δ δ
=
Δ −Δ
∑
i
ACE
11 0.5
WiWi
sT sT
−+
ghi
x
Δ
Fig. 3. A linear model of
i
-th CA represented with hydro power plant
6
AUTOMATIKA 51(2010) 1, 3–18

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