This program is by Karl Schneider and is used here by permission.

This program is supplied without representation or warranty of any kind. Karl Schneider and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

**PROGRAM FUNCTION:** Calculates transfer of complex power between two AC
buses

**DESIGNED FOR:** HP-33S (using ALG mode)

**DIRECTLY PORTABLE TO:** No other models

**SIMILAR PROGRAMS TAILORED FOR:** HP-32S, HP-32SII, and HP-33S (using RPN mode)

**FUNCTIONAL DESCRIPTION:**

This program calculates the total active (real) power "P" and reactive power "Q" injected into either end of an AC line or pair of paralleled AC lines joined by two buses. The AC line(s) may be three-phase or single-phase.

Each AC line is modeled with one set of "balanced-pi" parameters of series resistance, series reactance, and shunt susceptance. The AC bus voltages are defined in terms of rms magnitudes and a phase-angle difference.

The program includes a routine "Z" that will calculate the equivalent parameters of a parallel line-pair, if needed. The user may also run "Z" separately as a stand-alone program.

IMPORTANT: This program was originally written for RPN logic, and adapted so that users can input data in Algebraic (ALG) mode. The routines perform computations in RPN mode, but switch to ALG mode for INPUT and VIEW commands, and at completion. Users who normally operate the HP-33S in RPN mode should consider the RPN-mode version of this program.

**RESOURCES:**

Total storage: 468 bytes Program labels: 4 Stored variables: 10 Flags: 1 (flag 2)

**PROGRAM CODE SUMMARY:**

Label Bytes Checksum DescriptionS 42 93A7 Starts program; prompts for input variables C 135 3B49 Drives calculation of the output variables P 168 8A66 Calculates all injections of real and reactive power Z 123 0FBE Calculates equivalent parameters of line-pair

**INPUT VARIABLES (in order of entry):**

Variable Description Unit of measure NotesV Voltage magnitude at first bus [per unit] (1) W Voltage magnitude at second bus [per unit] (1) D Voltage-angle difference between buses [degrees] (2) R Series resistance of line [per unit] (3) X Series reactance of line [per unit] (3) B Total shunt susceptance of line [per unit] (4) R Series resistance of second line [per unit] (3,5) X Series reactance of second line [per unit] (3,5) B Total shunt susceptance of second line [per unit] (4,5) (1) 1-phase lines: Base voltage is rms nominal line-ground (LG) voltage 3-phase lines: Base voltage is rms nominal line-line (LL) voltage = sqrt(3)*LG (2) Positive-valued angle difference is inputted for voltage at the first busleadingthat of the second bus; negative-valued angle difference is entered for a lagging first-bus voltage. (3) Base impedance for R and X is the squared base voltage divided by power base (100 MVA in line P0028). (4) Base admittance for B is the reciprocal of base impedance. (5) R, X, and B for the second line are to be input only if two lines are modeled.

**OUTPUT VARIABLES (in order of display)**:

Variable Description Unit of measure NotesP, S Real power injected by first bus [MW] (6,7) Q, T Reactive power injected by first bus [MVAr] (6,8) P Real power injected by second bus [MW] (6) Q Reactive power injected by second bus [MVAr] (6) P Real-power consumption (losses) on the line [MW] (6,9) Q Reactive-power consumption on the line [MVAr] (6,9) (6) These units (MW or MVAr) assume a base voltage in kV and base power of 100 MVA. (7) P is re-stored to variable S when second-bus power is calculated. (8) Q is re-stored to variable T when second-bus power is calculated. (9) P and Q losses are also placed in the display as a complex-valued number.

**PROCEDURE:**

- Set Flag 2 if two parallel transmission lines are to be entered
- Start program using "XEQ S"
- Enter input variables V, W, D, R, X, and B
- Enter additional input variables R, X, and B for second line if necessary
- Read total first-bus real power P; press "R/S"
- Read total first-bus reactive power Q; press "R/S"
- Read total second-bus real power P; press "R/S"
- Read total second-bus reactive power Q; press "R/S"
- Read total real-power line losses; scroll down to read total reactive-power line losses

**TIPS:**

- SHORTCUT: When the correct values of all other input variables are already entered, just modify individual variables using "STO" and calculate all results by entering "XEQ C", or calculate only first-bus injections by entering "XEQ P".
- Voltage magnitudes and line parameters may be inputted in physical units, rather than per-unit. To obtain correct results in the desired units, the power base (in line P0028) must be changed to the appropriate value.
- The SOLVE root-finding function can be utilized to iteratively solve for
__one__input variable based upon a single "target" output value, with minor modification to the routine labeled "P" or "C".

S0001 LBL S Enter main program S0002 ALG S0003 DEG S0004 INPUT V First-bus voltage magnitude (V1) S0005 INPUT W Second-bus voltage magnitude (V2) S0006 INPUT D Voltage-angle difference (d) S0007 FS? 2 2-line network? S0008 XEQ Z -- If yes, run parallel-line program S0009 FS? 2 S0010 GTO C S0011 INPUT R -- Else, enter line parameters here S0012 INPUT X S0013 INPUT B S0014 GTO C C0001 LBL C C0002 CF 2 C0003 XEQ P Calculate power from first bus C0004 RCL P C0005 STO S Copy P from first bus C0006 RCL Q C0007 STO T Copy Q from first bus C0008 RCL V Set variables to calculate power from second bus: C0009 x<> W -- Swap V and W C0010 STO V C0011 RCL D -- Change sign of D C0012 +/- C0013 STO D C0014 XEQ P Calculate power from second bus C0015 RCL V Restore original values of V, W, and D C0016 x<> W C0017 STO V C0018 RCL D C0019 +/- C0020 STO D C0021 RPN C0022 RCL T Add complex power at first bus and second bus C0023 RCL S C0024 RCL Q C0025 RCL P C0026 CMPLX+ C0027 STO P Store P losses C0028 x<>y C0029 STO Q Store Q losses C0030 ALG C0031 SF 10 C0032 "LOSSES: P+Qi" [Unquoted text is entered in Equation mode] C0033 PSE C0034 CF 10 C0035 RCL P C0036 + C0037 RCL Q C0038 CMPLX C0039 ENTER Display losses P (real part) and Q (imag part) as complex C0040 RTN P0001 LBL P Begin calculation of power injections P0002 RPN P0003 RCL D Voltage-angle difference (d) P0004 RCL V First-bus voltage magnitude (V1) P0005 RCL W Second-bus voltage magnitude (V2) P0006 * P0007 Th,r->y,x P0008 0 P0009 RCL V P0010 x^{2}P0011 Rdown P0012 Rdown P0013 CMPLX- V_dif = V1^2 - V1*V2*(cos d + j*sin d) P0014 RCL X P0015 +/- P0016 RCL R P0017 CMPLX/ S through line [in pu] = V_dif / (R - j*X) P0018 RCL B P0019 2 P0020 / P0021 RCL V P0022 x^{2}P0023 * P0024 0 P0025 CMPLX- Subtract line-charging Q (= j*B/2 * V1^2) P0026 0 P0027 ENTER P0028 100 Power base = 100 MVA P0029 CMPLX* Multiply P and net Q by power base P0030 STO P P0031 x<>y P0032 STO Q P0033 ALG P0034 VIEW P Show P injected into line(s) P0035 VIEW Q Show Q injected into line(s) P0036 RTN Z0001 LBL Z Z0002 ALG Z0003 INPUT R Enter resistance of first line (R1) Z0004 INPUT X Enter reactance of first line (X1) Z0005 INPUT B Enter susceptance of first line (B1) Z0006 RPN Z0007 RCL X Z0008 RCL R Z0009 CMPLX1/x Z0010 STO S Real part in temporary storage Z0011 x<>y Z0012 STO T Imaginary part in temporary storage Z0013 ALG Z0014 INPUT R Enter resistance of second line (R2) Z0015 INPUT X Enter reactance of second line (X2) Z0016 RPN Z0017 RCL X Z0018 RCL R Z0019 CMPLX1/x Z0020 RCL T Z0021 RCL S Z0022 CMPLX+ Z0023 CMPLX1/x (Req + j*Xeq) = (R1+ j*X1) || (R2 + j*X2) Z0024 STO R Z0025 x<>y Z0026 STO X Z0027 RCL B Z0028 STO S Z0029 ALG Z0030 INPUT B Enter susceptance of second line (B2) Z0031 RCL+ S Z0032 STO B Beq = B1 + B2 Z0033 CLx Z0034 STO S Clear S and T temporary registers Z0035 STO T Z0036 FS? 2 Is "Z" being run from AC transfer program? Z0037 RTN -- If yes, return without displaying results Z0038 VIEW R -- Else, display Req, Xeq, Beq in sequence Z0039 VIEW X Z0040 VIEW B Z0041 RTN

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