Power Flow (Helios)

Helios is the STEPSS AC power-flow engine. It solves the Newton-Raphson power flow in polar coordinates with reactive limit enforcement, transformer tap adjustment and SVC modelling, and it produces the operating point that initialises a RAMSES dynamic simulation.

Helios is available three ways, all reading the same data files:

• the helios command-line executable, bundled with the STEPSS GUI and published on the Helios releases page;
• stepss.helios.HeliosSession from Python, see Power Flow with Helios;
• the C API shared library (libhelios_api), for embedding in other tools.

The power flow uses the following network records documented in Network Modeling: BUS, LINE, SWITCH, TRANSFO, TRFO, NRTP.

The additional records specific to power flow computations are documented below.

Load and Shunt Data

Load and shunt data are specified in an extended version of the BUS record:

BUS NAME VNOM PLOAD QLOAD BSHUNT QSHUNT ;

Field	Description	Unit
NAME	Bus name (max 8 characters)
VNOM	Nominal voltage	kV
PLOAD	Total active power load (positive = consumed)	MW
QLOAD	Total reactive power load (positive = consumed)	Mvar
BSHUNT	Nominal reactive power of constant-susceptance shunt: the reactive power produced under the nominal voltage of the bus (positive = capacitor, negative = reactor)	Mvar
QSHUNT	Reactive power of constant-power shunt (positive = capacitor)	Mvar

If no load is connected to the bus, set PLOAD and QLOAD to zero. If no shunt is connected, set BSHUNT and QSHUNT to zero. QSHUNT is optional: a five-field BUS record is accepted and QSHUNT defaults to zero.

The total reactive power $Q$ produced by both shunt components:

$$Q = \text{BSHUNT} \cdot \left(\frac{V}{V_{nom}}\right)^2 + \text{QSHUNT}$$

Note

The PLOAD, QLOAD, BSHUNT, and QSHUNT fields are ignored by RAMSES.

Generator Data

GENER NAME BUS P Q VIMP SNOM QMIN QMAX BR ;

Field	Description	Unit
NAME	Generator name (max 20 characters)
BUS	Connection bus name
P	Active power produced	MW
Q	Reactive power produced (ignored if VIMP ≠ 0)	Mvar
VIMP	Imposed voltage (0 = PQ bus, nonzero = PV bus)	pu
SNOM	Nominal apparent power	MVA
QMIN	Lower reactive power limit	Mvar
QMAX	Upper reactive power limit	Mvar
BR	Breaker status (0 = open)

For PV buses, if the upper reactive power limit QMAX is exceeded, the bus switches to PQ type with QMAX enforced, and Newton iterations continue. If subsequently the bus voltage rises above VIMP, the bus switches back to PV type. Similarly, if QMIN is exceeded, the bus switches to PQ type with QMIN enforced; it switches back to PV if the voltage subsequently drops below VIMP.

QMIN and QMAX are used only if VIMP is nonzero (PV bus).

An extended variant with active power limits and a participation factor exists:

GENER NAME BUS P Q VIMP SNOM QMIN QMAX PMIN PMAX PART BR ;

Field	Description	Unit
PMIN	Minimum active power the generator can produce	MW
PMAX	Maximum active power the generator can produce	MW
PART	Participation factor used when redistributing an active power imbalance

PMIN/PMAX are not enforced during Newton iterations. They are used to clamp the specified P before the computation (the slack generator is exempted by default; see $PLIM below), and together with PART when generation is redispatched after system modifications or contingencies.

Both variants also accept an additional bus-name field between BUS and P (making 10 or 13 fields in total); that field is accepted and ignored.

Only one generator is allowed per bus.

All generators are memorized, even those which are disconnected. A disconnected generator has zero power output but can be put into service during dynamic simulation.

Note

A generator producing constant active and reactive powers can be modeled as a negative load using the BUS record (negative PLOAD/QLOAD) without a GENER record.

Slack Bus

A slack bus is mandatory for power flow computations: not all buses can be of PV or PQ type, since this would require knowing the active power losses in the network before performing the calculation.

A PV-type generator must be connected to the slack bus. Its voltage magnitude (from the GENER record) is imposed, and the voltage phase angle is set to zero.

SLACK NAME ;

Field	Description
NAME	Bus name (max 8 characters)

There must be exactly one SLACK record in the data.

Only one connected network (island) is solved. If the graph is disconnected, only the sub-network containing the slack bus is treated; equipment on the discarded buses is disabled and the lost active power is reported so that it can be redispatched.

Static Var Compensators (SVC)

Although reference is made to an SVC, the model can be used in general for any component controlling voltage with a droop. The SVC is assumed lossless: the active current injected at the controlled bus is zero.

The SVC is modeled with a controllable susceptance $B$ at a controlled bus $i$, regulating the voltage at a monitored bus $j$:

$$I_{Qi} = G(V_j^o - V_j) V_i \quad \text{(voltage control)}$$ $$I_{Qi} = B_{max} V_i \quad \text{(upper limit)} \quad\quad I_{Qi} = B_{min} V_i \quad \text{(lower limit)}$$

Data Format

SVC NAME CON_BUS MON_BUS V0 Q0 SNOM BMAX BMIN G BR ;

Field	Description	Unit
NAME	SVC name (max 20 characters)
CON_BUS	Controlled bus where the susceptance $B$ is varied (max 8 characters)
MON_BUS	Monitored bus whose voltage is regulated (max 8 characters)
V0	Voltage setpoint $V_j^o$ (0 = constant power mode with $P=0$, $Q=Q0$, no limits tested)	pu
Q0	Reactive power setpoint (ignored if V0 ≠ 0)	Mvar
SNOM	Nominal reactive power	Mvar
BMAX	Maximal nominal reactive power: reactive power produced under $V_i = 1$ pu when $B = B_{max}$	Mvar
BMIN	Minimal nominal reactive power: reactive power produced under $V_i = 1$ pu when $B = B_{min}$	Mvar
G	Gain, in pu on the ($V_B$, SNOM) base, where $V_B$ is the nominal voltage at the controlled bus	pu
BR	Breaker status (0 = open, other = closed)

It is common for BMAX to be positive and BMIN negative, but other combinations are allowed.

For SVCs with nonzero V0, the voltage control equation is solved initially. If the susceptance upper limit BMAX is exceeded, the limit is enforced and Newton iterations continue. The SVC reverts to voltage control when $G(V_j^o - V_j) < B_{max}$. Similarly, if BMIN is exceeded, the lower limit is enforced; the SVC reverts when $G(V_j^o - V_j) > B_{min}$.

Only one SVC is allowed per bus. It is not allowed to connect both a generator and an SVC to the same bus.

All SVCs are memorized, even those which are disconnected. A disconnected SVC can be put into service during dynamic simulation.

Transformer Ratio Adjustment for Voltage Control

The ratio of a designated transformer can be adjusted to bring a controlled voltage inside a deadband $[V_{des} - \epsilon,\; V_{des} + \epsilon]$, where $V_{des}$ is the desired voltage and $\epsilon$ is the tolerance.

The ratio is changed in discrete steps between a minimum and maximum value. During computation, the ratio is changed by one step at a time, after which Newton iterations run until convergence. The process repeats until the controlled voltage falls in the deadband. When multiple transformers are adjusted, some may reach their deadbands before others.

Via TRFO Record

The controlled bus is CONBUS in the TRFO record. This must be one of the two ending buses of the transformer. An empty or blank string enclosed within quotes indicates that the transformer ratio is not to be adjusted; in this case, dummy values must still be provided for the remaining fields.

The ratio corresponding to tap position $p$ ($1 \le p \le \text{NBPOS}$):

$$n = \frac{\text{NFIRST}}{100} + \frac{p-1}{\text{NBPOS}-1} \cdot \frac{\text{NLAST} - \text{NFIRST}}{100}$$

The initial ratio from the N field of the TRFO record is adjusted to the nearest tap position before starting the power flow computation.

Relevant fields in the TRFO record:

Field	Description	Unit
NFIRST	Ratio at first tap position (lower bound)	%
NLAST	Ratio at last tap position (upper bound)	%
NBPOS	Total number of tap positions (including first and last)
TOLV	Voltage tolerance $\epsilon$	pu
VDES	Desired voltage $V_{des}$	pu

Via LTC-V Record

The second way to specify ratio adjustment is through a separate LTC-V record. This is more natural in association with a TRANSFO record.

LTC-V NAME CON_BUS NFIRST NLAST NBPOS TOLV VDES ;

Field	Description	Unit
NAME	Name of the controlled transformer (max 20 characters)
CON_BUS	Controlled bus (max 8 characters)
NFIRST	Ratio at first tap position (lower bound)	%
NLAST	Ratio at last tap position (upper bound)	%
NBPOS	Total number of tap positions (including first and last)
TOLV	Voltage tolerance $\epsilon$	pu
VDES	Desired voltage $V_{des}$	pu

A transformer can be controlled by a single tap changer only. The LTC-V record can also be associated with a TRFO record, provided that no adjustment is specified in the TRFO record itself.

Only this seven-field linear-ratio form is supported; there is no per-tap reactance variant.

Phase-Shifting Transformer Adjustment (PSHIFT-P)

The phase angle of a transformer can be adjusted to bring the active power flow in a monitored branch inside a deadband $[P_{des} - \epsilon,\; P_{des} + \epsilon]$. The adjustment mechanism is similar to the in-phase ratio adjustment described above.

PSHIFT-P CONTRFO MONBRANCH PHAFIRST PHALAST NBPOS SIGN PDES TOLP ;

Field	Description	Unit
CONTRFO	Name of the transformer whose phase angle is adjusted (max 20 characters, defined in a TRFO or TRANSFO record). If the transformer does not exist, the record is ignored with a warning
MONBRANCH	Name of the branch where active power $P$ is monitored (max 20 characters, defined in a LINE, TRFO, or TRANSFO record). $P$ is the active power leaving the first bus of the branch record
PHAFIRST	Phase angle $\phi$ at first tap position (lower bound)	degrees
PHALAST	Phase angle $\phi$ at last tap position (upper bound)	degrees
NBPOS	Number of tap positions
SIGN	Direction indicator: 1 means $\phi$ must increase to increase power flow; -1 means decrease. Any other value causes the program to stop
PDES	Desired active power flow	MW
TOLP	Tolerance $\epsilon$	MW

The phase angle $\phi$ at tap position $p$ ($1 \le p \le \text{NBPOS}$) is:

$$\phi = \text{PHAFIRST} + \frac{p-1}{\text{NBPOS}-1}(\text{PHALAST} - \text{PHAFIRST})$$

The initial phase angle from the PHI field of the TRANSFO record is adjusted to the nearest tap position before starting the power flow computation.

A sensitivity analysis determines whether the phase angle should be increased or decreased. If this analysis indicates a direction opposite to SIGN, a warning is issued and SIGN is ignored. On output, SIGN is set to the value from the sensitivity analysis.

Only one PSHIFT-P record per transformer is allowed. The PSHIFT-P record is intended for use with a TRANSFO record, but can also be used with a TRFO record (in which case the angle is initialized to zero).

A transformer cannot be controlled by both an LTC-V and a PSHIFT-P record.

A detailed form with per-tap data (10 + 4k fields) is also accepted.

Records that are not supported

Two records of the historical Fortran engine are rejected with a hard error rather than silently ignored:

• PSHIFT-I (current-controlled phase shifter): never adjusted by the old engine either, so nothing is lost by removing it from the data.
• TURLIM (legacy active power limit record): use the 12/13-field GENER variant above, which carries PMIN, PMAX and PART.

Records that are not part of the power-flow format at all (SYNC_MACH, INJEC, DCTL, and the rest of the dynamic data) are skipped with a warning, so a combined data file can be handed to the power flow unchanged.

Zone and Cut Aggregation

Two optional records group equipment for reporting. They do not affect the solution.

BUSPART ZONE_NAME BUS_NAME PARTP PARTQ ;

Field	Description
ZONE_NAME	Zone name; the zone is created on first use
BUS_NAME	Bus to include in the zone (max 8 characters)
PARTP	Active power participation weight of this bus in the zone
PARTQ	Reactive power participation weight of this bus in the zone

Zones drive the zone-power display and the zone-wide load and generation changes of the modify menu. Buses with unrecognised names are skipped.

BRAPART CUT_NAME BRANCH_NAME BUS_NAME SIGN ;

Field	Description
CUT_NAME	Cut name; the cut is created on first use
BRANCH_NAME	Branch to include in the cut (max 20 characters)
BUS_NAME	One endpoint of the branch, fixing the direction of the flow that is summed
SIGN	+1 or -1, applied to that branch’s contribution

The cut power is the signed sum of the member branch flows, reported per branch and as a total.

Bus Voltages: Initial Values and Results (LFRESV)

On output, the power flow produces a file with the computed bus voltage magnitudes and phase angles. These are stored in LFRESV records. The syntax is:

LFRESV BUS MODV PHASV ;

Field	Description	Unit
BUS	Bus name (max 8 characters)
MODV	Voltage magnitude	pu
PHASV	Voltage phase angle, referenced to slack bus	radians

Note

If LFRESV records are provided as input, they are used as initial voltages for Newton iterations.

Note

Default initialization: PQ buses start at 1 pu magnitude and 0 angle; PV buses start at the generator-specified voltage and 0 angle.

Note

The output LFRESV records can be fed back as input. This results in zero Newton iterations (round-trip property). This is an easy way to verify that system data come with their corresponding voltages.

Note

LFRESV is the output that initializes RAMSES dynamic simulation.

Note

The exported operating-point file (the VT menu command, write_voltrat() in the API) contains one LFRESV record per bus plus one TRANSFO record per in-service LTC transformer, carrying its solved ratio. Hand-maintained operating-point files (e.g. volt_rat_B.dat of the Nordic test system) often use TRFO records instead. The two styles are interchangeable as RAMSES input: RAMSES ignores the LTC fields of a TRFO record (see the record-sharing table below), and dynamic tap-changer behaviour is defined by the DCTL LTC records of the dynamic data.

Interactive Menu Commands

After loading data and solving, Helios presents these commands:

Command	Description
P	Take new control parameters from file
D	Display output values
1	Display outputs on 1-line diagram (SVG)
M	Modify system (change loads, generators, topology)
RI	Reset system to initial configuration
CA	Perform contingency analysis
CL	Check operating limits (voltage bounds, branch overloads)
O	Change output file
DF	Update all records and dump them to a file
VT	Generate a file with voltages and adjustable transformer ratios (LFRESV format)
S	Save operating point and Y matrix to MATLAB file
E	Exit

The VT command produces the LFRESV file needed to initialize RAMSES.

Computation Control Parameters

The power flow uses Newton-Raphson iterations to solve the power flow equations. Convergence is achieved when both the active and reactive power mismatches fall below specified thresholds, all transformer ratio and phase-shift controls are satisfied, and all generators and SVCs are within their reactive limits.

Three convergence indices are used:

• $\epsilon_P$: largest absolute mismatch of the active power equations
• $\epsilon_Q$: largest absolute mismatch of the reactive power equations
• $\epsilon_S$: largest apparent power mismatch, used to trigger limit checks (via $MISQLIM), factorization reuse (via $MISBLOC), and transformer adjustments (via $MISADJ)

The following records control the computation. Each record starts with $ and has a single numeric field; a known $ record with any other field count is a hard error, and an unknown $ key is ignored.

Parameter	Default	Unit	Description
$SBASE	100	MVA	System base power (on which pu values are expressed)
$TOLAC	0.1	MW	Convergence tolerance on active power mismatch ($\epsilon_P$)
$TOLREAC	0.1	Mvar	Convergence tolerance on reactive power mismatch ($\epsilon_Q$)
$NBITMA	20		Maximum number of Newton iterations
$MISQLIM	20	MVA	Apparent power mismatch threshold below which generator/SVC reactive limits are checked and enforced (set to 0 to skip)
$MISBLOC	10	MVA	Apparent power mismatch threshold below which the Jacobian factorization reuses the previous pivot ordering. Jacobian values are recomputed at every iteration regardless
$MISADJ	10	MVA	Apparent power mismatch threshold below which transformer ratios and phase shifts are adjusted (set to 0 to skip)
$DIVDET	0		Set to 1 to activate divergence detection; 0 to skip
$PLIM	1		1 = the slack generator’s PMIN/PMAX are bypassed during initial P clamping; 0 = the slack is clamped like any other generator

Note

Divergence is detected when $\varphi(k) > 1.1\,\varphi(k-1)$, where:

$\varphi(k) = \sum_i \sqrt{(f_i - P_i^o)^2 + (g_i - Q_i^o)^2}$

Under normal convergence, $\varphi$ decreases at each iteration; an increase signals divergence. The test is temporarily suspended following limit adjustments or transformer ratio changes, as these cause increases in $\varphi$ unrelated to divergence.

$PLIM only affects 12/13-field GENER records, the only ones that carry real active power limits.

Exit Status

In non-interactive use (-t command file mode and pipe mode), Helios reports the outcome of the run through its process exit status:

Exit	Meaning
0	Converged, the results are usable
1	Input or usage error: bad command file, unreadable data file, parse failure, unknown command
2	The solve ran but did not converge: maximum iterations, divergence, or a singular Jacobian. Results may still have been written, but they are not a valid power-flow solution

Only 0 means the results can be trusted. Where a command file modifies the system and re-solves, the status reflects the final solve. The interactive TUI always exits 0.

Each non-interactive run also writes one machine-readable line to stderr:

helios: status: CONVERGED (2 iterations)
helios: status: NOT_CONVERGED (max iterations)
helios: status: NOT_CONVERGED (diverged)
helios: status: NOT_CONVERGED (singular)
helios: status: NOT_RUN

NOT_RUN means no solve was requested (for example $NBITMA 0), which exits 0. Scripts should use the exit status and this line rather than parsing stdout.

These values are shared with the Helios C API, where HELIOS_OK is 0 and HELIOS_NOT_CONVERGED is 2 (1 is reserved and never returned by the API). HELIOS_NOT_CONVERGED is 2 from Helios 1.4.1 onward; in 1.3.0 and earlier it was 1. The stepss.helios.HeliosSession wrapper exposes convergence as the boolean pf.converged and the pf.solver_status enum, neither of which is affected by the numbering.

Record Sharing Between Power Flow and RAMSES

The following table summarises which records are used by the power flow and by RAMSES respectively.

Record	Power flow	RAMSES
BUS	All 6 fields (QSHUNT optional)	First 2 fields (NAME, VNOM)
LINE	All fields	All fields
SWITCH	All fields	All fields
NRTP	All fields	All fields
TRANSFO	All fields	All fields
TRFO	All fields	Fields 1 to 9 and 15 only
SHUNT	Ignored	All fields
GENER	All fields	Ignored
SVC	All fields	Ignored
SLACK	Used	Used
LFRESV	Input: initial values; Output: solution	Input: initial values for RAMSES
LTC-V	Used	Ignored
PSHIFT-P	Used	Ignored
BUSPART, BRAPART	Used for reporting	Ignored

Historical Note: PFC

Helios succeeds PFC, the Fortran power-flow calculator written by Dr. Thierry Van Cutsem that was the STEPSS power flow from the beginning. Helios reimplements its Newton-Raphson formulation in C++20, reads the same input files, and matches its solver defaults, so data prepared for PFC runs unchanged. PFC is no longer shipped with STEPSS or with stepss; nothing on this page requires it.

Two numerical points are worth knowing when comparing old results with new ones:

• The two engines use different sparse linear solvers, so the last displayed decimal can differ.
• Helios recomputes the Jacobian values at every iteration, a true Newton method, where PFC froze them below $MISBLOC. Iteration counts can therefore differ slightly.

Next Steps

• Reference Frames & Initialization, Understand how RAMSES initializes from the power flow solution
• Dynamic Data Records, Define synchronous machines, injectors, and controllers